diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index 379e70d..a3ec780 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -283,9 +283,10 @@ This is the Charlwood test suite

pdf


-

Rich



+

Rich Integrals



This portion of the CATS suite involves Albert Rich's Integration Suite. -They have been rewritten using Axiom syntax. +They have been rewritten using Axiom syntax.
+See Integration Test Suite Problems

(a+b x)^m (c+d x)^n (part 1) source @@ -293,12 +294,12 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d x)^n (part 2) source pdf
- +
(a+b x)^m (A+B x) (d+e x)^p source pdf
+
(a+b x)^m (c+d)^n (e+f x)^p (part 1) - source pdf
(a+b x)^m (c+d)^n (e+f x)^p (part 2) @@ -358,7 +359,7 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d)^n (e+f x)^p (part 20) source pdf
- +
x^m (a+b x^n)^p (part 1) source pdf
@@ -389,9 +390,11 @@ They have been rewritten using Axiom syntax. x^m (a+b x^n)^p (part 10) source pdf
+
(a+b x^n)^m (c+d x^n)^p source pdf
+
x^m (a+b x^n)^p (c+d x^n)^q (part 1) source pdf
@@ -407,6 +410,183 @@ They have been rewritten using Axiom syntax. x^m (a+b x^n)^p (c+d x^n)^q (part 5) source pdf
+
+ (a+b x^n)^m (c+d x^n)^p (e+f x^n)^q (part 1) + source + pdf
+
+ x^m (a x^q+b x^n)^p (part 1) + source + pdf
+ x^m (a x^q+b x^n)^p (part 2) + source + pdf
+ x^m (a x^q+b x^n)^p (part 1) + source + pdf
+ x^m (a x^q+b x^n)^p (part 2) + source + pdf
+
+ x^m (a+b x+c x^2)^p (part 1) + source + pdf
+ x^m (a+b x+c x^2)^p (part 2) + source + pdf
+
+ (d+e x)^m (a+b x+c x^2)^p (part 1) + source + pdf
+ (d+e x)^m (a+b x+c x^2)^p (part 2) + source + pdf
+ (d+e x)^m (a+b x+c x^2)^p (part 3) + source + pdf
+ (d+e x)^m (a+b x+c x^2)^p (part 4) + source + pdf
+ (d+e x)^m (a+b x+c x^2)^p (part 5) + source + pdf
+ (d+e x)^m (a+b x+c x^2)^p (part 6) + source + pdf
+
+ x^m (d+e x)^n (a+b x+c x^2)^p (part 1) + source + pdf
+ x^m (d+e x)^n (a+b x+c x^2)^p (part 2) + source + pdf
+ x^m (d+e x)^n (a+b x+c x^2)^p (part 3) + source + pdf
+ x^m (d+e x)^n (a+b x+c x^2)^p (part 4) + source + pdf
+ x^m (d+e x)^n (a+b x+c x^2)^p (part 5) + source + pdf
+ +

+

Rich Derivatives



+The Rich Integration test suite provides integrands and their +optimal integrals. These have been verified by Albert Rich using +Mathematica. This test suite shows Axiom's results. +

+ (a+b x)^m (c+d x)^n (part 1) + source + pdf
+ (a+b x)^m (c+d x)^n (part 2) + source + pdf
+
+ (a+b x)^m (A+B x) (d+e x)^p + source + pdf
+
+ (a+b x)^m (c+d)^n (e+f x)^p (part 1) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 2) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 3) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 4) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 5) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 6) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 7) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 8) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 9) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 10) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 11) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 12) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 13) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 14) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 15) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 16) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 17) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 18) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 19) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 20) + source + pdf
+
+ x^m (a+b x^n)^p (part 1) + source + pdf
+ x^m (a+b x^n)^p (part 2) + source + pdf
+ x^m (a+b x^n)^p (part 3) + source + pdf
+ x^m (a+b x^n)^p (part 4) + source + pdf
+ x^m (a+b x^n)^p (part 5) + source + pdf
+ x^m (a+b x^n)^p (part 6) + source + pdf
+
+ (a+b*x^n)^m*(c+d*x^n)^p + source + pdf
+
+ x^m (a+b x^n)^p (c+d x^n)^q (part 1) + source + pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 2) + source + pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 3) + source + pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 4) + source + pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 5) + source + pdf
+


Rich



diff --git a/src/axiom-website/CATS/rich10a.input.pamphlet b/src/axiom-website/CATS/rich10a.input.pamphlet new file mode 100644 index 0000000..8e6ee52 --- /dev/null +++ b/src/axiom-website/CATS/rich10a.input.pamphlet @@ -0,0 +1,41579 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich10a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(d+e x)^m (a+b x+c x^2)^p| +There are: +\begin{itemize} +\item 300 integrals in this file. +\item 300 supplied "optimal results". +\item 369 matching answers. +\item 0 cases where Axiom answer differs from Rubi +\item 113 cases where Axiom supplied 2 results. +\item 1 case that Axiom failed to integrate. +\item 43 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich10a.output +)spool rich10a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1726 +t0:=(d+e*x)^m*(b*x+c*x^2) +--R +--R +--R 2 m +--R (1) (c x + b x)(e x + d) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1726 +r0:=d*(c*d-b*e)*(d+e*x)^(1+m)/(e^3*(1+m))-(2*c*d-b*e)*(d+e*x)^(2+m)/_ + (e^3*(2+m))+c*(d+e*x)^(3+m)/(e^3*(3+m)) +--R +--R +--R (2) +--R 2 m + 3 +--R (c m + 3c m + 2c)(e x + d) +--R + +--R 2 m + 2 +--R ((b e - 2c d)m + (4b e - 8c d)m + 3b e - 6c d)(e x + d) +--R + +--R 2 2 2 2 m + 1 +--R ((- b d e + c d )m + (- 5b d e + 5c d )m - 6b d e + 6c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 +--R (c e m + 3c e m + 2c e )x +--R + +--R 3 2 2 3 2 3 2 +--R ((b e + c d e )m + (4b e + c d e )m + 3b e )x +--R + +--R 2 2 2 2 2 2 3 +--R (b d e m + (3b d e - 2c d e)m)x - b d e m - 3b d e + 2c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 +--R (c e m + 3c e m + 2c e )x +--R + +--R 3 2 2 3 2 3 2 +--R ((b e + c d e )m + (4b e + c d e )m + 3b e )x +--R + +--R 2 2 2 2 2 2 3 +--R (b d e m + (3b d e - 2c d e)m)x - b d e m - 3b d e + 2c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 m + 3 +--R (- c m - 3c m - 2c)(e x + d) +--R + +--R 2 m + 2 +--R ((- b e + 2c d)m + (- 4b e + 8c d)m - 3b e + 6c d)(e x + d) +--R + +--R 2 2 2 2 m + 1 +--R ((b d e - c d )m + (5b d e - 5c d )m + 6b d e - 6c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1726 +t0:=(d+e*x)^4*(b*x+c*x^2) +--R +--R +--R (1) +--R 4 6 4 3 5 3 2 2 4 2 2 3 3 +--R c e x + (b e + 4c d e )x + (4b d e + 6c d e )x + (6b d e + 4c d e)x +--R + +--R 3 4 2 4 +--R (4b d e + c d )x + b d x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1726 +r0:=1/5*d*(c*d-b*e)*(d+e*x)^5/e^3-1/6*(2*c*d-b*e)*(d+e*x)^6/e^3+_ + 1/7*c*(d+e*x)^7/e^3 +--R +--R +--R (2) +--R 1 7 7 1 7 2 6 6 4 6 6 2 5 5 +--R - c e x + (- b e + - c d e )x + (- b d e + - c d e )x +--R 7 6 3 5 5 +--R + +--R 3 2 5 3 4 4 4 3 4 1 4 3 3 1 4 3 2 1 6 +--R (- b d e + c d e )x + (- b d e + - c d e )x + - b d e x - -- b d e +--R 2 3 3 2 30 +--R + +--R 1 7 +--R --- c d +--R 105 +--R / +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 7 + +--S 8 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 1 4 2 3 6 4 3 6 2 2 5 +--R - c e x + (- b e + - c d e )x + (- b d e + - c d e )x +--R 7 6 3 5 5 +--R + +--R 3 2 2 3 4 4 3 1 4 3 1 4 2 +--R (- b d e + c d e)x + (- b d e + - c d )x + - b d x +--R 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1726 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 +--R -- b d e - --- c d +--R 30 105 +--R (4) ------------------- +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 9 + +--S 10 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 10 + +)clear all + +--S 11 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1726 +r0:=1/4*d*(c*d-b*e)*(d+e*x)^4/e^3-1/5*(2*c*d-b*e)*(d+e*x)^5/e^3+_ + 1/6*c*(d+e*x)^6/e^3 +--R +--R +--R (2) +--R 1 6 6 1 6 3 5 5 3 5 3 2 4 4 +--R - c e x + (- b e + - c d e )x + (- b d e + - c d e )x +--R 6 5 5 4 4 +--R + +--R 2 4 1 3 3 3 1 3 3 2 1 5 1 6 +--R (b d e + - c d e )x + - b d e x - -- b d e + -- c d +--R 3 2 20 60 +--R / +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 12 + +--S 13 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 6 1 3 3 2 5 3 2 3 2 4 +--R - c e x + (- b e + - c d e )x + (- b d e + - c d e)x +--R 6 5 5 4 4 +--R + +--R 2 1 3 3 1 3 2 +--R (b d e + - c d )x + - b d x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1726 +m0:=a0-r0 +--R +--R +--R 1 5 1 6 +--R -- b d e - -- c d +--R 20 60 +--R (4) ------------------ +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 15 + +)clear all + +--S 16 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2) +--R +--R +--R 2 4 2 3 2 2 2 +--R (1) c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1726 +r0:=1/2*b*d^2*x^2+1/3*d*(c*d+2*b*e)*x^3+1/4*e*(2*c*d+b*e)*x^4+1/5*c*e^2*x^5 +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (2) - c e x + (- b e + - c d e)x + (- b d e + - c d )x + - b d x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (3) - c e x + (- b e + - c d e)x + (- b d e + - c d )x + - b d x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 1726 +t0:=(d+e*x)*(b*x+c*x^2) +--R +--R +--R 3 2 +--R (1) c e x + (b e + c d)x + b d x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1726 +r0:=1/2*b*d*x^2+1/3*(c*d+b*e)*x^3+1/4*c*e*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - c e x + (- b e + - c d)x + - b d x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 2 +--R (3) - c e x + (- b e + - c d)x + - b d x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1726 +t0:=b*x+c*x^2 +--R +--R +--R 2 +--R (1) c x + b x +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1726 +r0:=1/2*b*x^2+1/3*c*x^3 +--R +--R +--R 1 3 1 2 +--R (2) - c x + - b x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 3 1 2 +--R (3) - c x + - b x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1726 +t0:=(b*x+c*x^2)/(d+e*x) +--R +--R +--R 2 +--R c x + b x +--R (1) ---------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1726 +r0:=-(c*d-b*e)*x/e^2+1/2*c*x^2/e+d*(c*d-b*e)*log(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 +--R (- 2b d e + 2c d )log(e x + d) + c e x + (2b e - 2c d e)x +--R (2) ----------------------------------------------------------- +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (- 2b d e + 2c d )log(e x + d) + c e x + (2b e - 2c d e)x +--R (3) ----------------------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 +--R c x + b x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1726 +r0:=c*x/e^2-d*(c*d-b*e)/(e^3*(d+e*x))-(2*c*d-b*e)*log(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((b e - 2c d e)x + b d e - 2c d )log(e x + d) + c e x + c d e x + b d e +--R + +--R 2 +--R - c d +--R / +--R 4 3 +--R e x + d e +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((b e - 2c d e)x + b d e - 2c d )log(e x + d) + c e x + c d e x + b d e +--R + +--R 2 +--R - c d +--R / +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 +--R c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1726 +r0:=-1/2*d*(c*d-b*e)/(e^3*(d+e*x)^2)+(2*c*d-b*e)/(e^3*(d+e*x))+c*log(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R (2c e x + 4c d e x + 2c d )log(e x + d) + (- 2b e + 4c d e)x - b d e +--R + +--R 2 +--R 3c d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2c e x + 4c d e x + 2c d )log(e x + d) + (- 2b e + 4c d e)x - b d e +--R + +--R 2 +--R 3c d +--R / +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 +--R c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1726 +r0:=-1/3*d*(c*d-b*e)/(e^3*(d+e*x)^3)+1/2*(2*c*d-b*e)/_ + (e^3*(d+e*x)^2)-c/(e^3*(d+e*x)) +--R +--R +--R 2 2 1 2 1 1 2 +--R - c e x + (- - b e - c d e)x - - b d e - - c d +--R 2 6 3 +--R (2) ------------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R e x + 3d e x + 3d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R - 6c e x + (- 3b e - 6c d e)x - b d e - 2c d +--R (3) ----------------------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 +--R c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1726 +r0:=-1/4*d*(c*d-b*e)/(e^3*(d+e*x)^4)+1/3*(2*c*d-b*e)/_ + (e^3*(d+e*x)^3)-1/2*c/(e^3*(d+e*x)^2) +--R +--R +--R 1 2 2 1 2 1 1 1 2 +--R - - c e x + (- - b e - - c d e)x - -- b d e - -- c d +--R 2 3 3 12 12 +--R (2) ------------------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R - 6c e x + (- 4b e - 4c d e)x - b d e - c d +--R (3) ----------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1726 +t0:=(d+e*x)^m*(b*x+c*x^2)^2 +--R +--R +--R 2 4 3 2 2 m +--R (1) (c x + 2b c x + b x )(e x + d) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1726 +r0:=d^2*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^5*(1+m))-2*d*(c*d-b*e)*_ + (2*c*d-b*e)*(d+e*x)^(2+m)/(e^5*(2+m))+(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)*(d+e*x)^(3+m)/(e^5*(3+m))-2*c*(2*c*d-b*e)*_ + (d+e*x)^(4+m)/(e^5*(4+m))+c^2*(d+e*x)^(5+m)/(e^5*(5+m)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 m + 5 +--R (c m + 10c m + 35c m + 50c m + 24c )(e x + d) +--R + +--R 2 4 2 3 2 2 +--R (2b c e - 4c d)m + (22b c e - 44c d)m + (82b c e - 164c d)m +--R + +--R 2 2 +--R (122b c e - 244c d)m + 60b c e - 120c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (b e - 6b c d e + 6c d )m + (12b e - 72b c d e + 72c d )m +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (49b e - 294b c d e + 294c d )m + (78b e - 468b c d e + 468c d )m +--R + +--R 2 2 2 2 +--R 40b e - 240b c d e + 240c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 4 +--R (- 2b d e + 6b c d e - 4c d )m +--R + +--R 2 2 2 2 3 3 +--R (- 26b d e + 78b c d e - 52c d )m +--R + +--R 2 2 2 2 3 2 +--R (- 118b d e + 354b c d e - 236c d )m +--R + +--R 2 2 2 2 3 2 2 2 +--R (- 214b d e + 642b c d e - 428c d )m - 120b d e + 360b c d e +--R + +--R 2 3 +--R - 240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 2 3 2 4 4 2 2 2 3 2 4 3 +--R (b d e - 2b c d e + c d )m + (14b d e - 28b c d e + 14c d )m +--R + +--R 2 2 2 3 2 4 2 +--R (71b d e - 142b c d e + 71c d )m +--R + +--R 2 2 2 3 2 4 2 2 2 3 2 4 +--R (154b d e - 308b c d e + 154c d )m + 120b d e - 240b c d e + 120c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 5 3 2 5 2 2 5 2 5 5 +--R (c e m + 10c e m + 35c e m + 50c e m + 24c e )x +--R + +--R 5 2 4 4 5 2 4 3 +--R (2b c e + c d e )m + (22b c e + 6c d e )m +--R + +--R 5 2 4 2 5 2 4 5 +--R (82b c e + 11c d e )m + (122b c e + 6c d e )m + 60b c e +--R * +--R 4 +--R x +--R + +--R 2 5 4 4 2 5 4 2 2 3 3 +--R (b e + 2b c d e )m + (12b e + 16b c d e - 4c d e )m +--R + +--R 2 5 4 2 2 3 2 +--R (49b e + 34b c d e - 12c d e )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (78b e + 20b c d e - 8c d e )m + 40b e +--R * +--R 3 +--R x +--R + +--R 2 4 4 2 4 2 3 3 +--R b d e m + (10b d e - 6b c d e )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (29b d e - 36b c d e + 12c d e )m +--R + +--R 2 4 2 3 2 3 2 +--R (20b d e - 30b c d e + 12c d e )m +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 2 2 3 3 2 2 +--R - 2b d e m + (- 18b d e + 12b c d e )m +--R + +--R 2 2 3 3 2 2 4 +--R (- 40b d e + 60b c d e - 24c d e)m +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 4 2 3 2 4 2 5 +--R 2b d e m + (18b d e - 12b c d e)m + 40b d e - 60b c d e + 24c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 4 2 5 3 2 5 2 2 5 2 5 5 +--R (c e m + 10c e m + 35c e m + 50c e m + 24c e )x +--R + +--R 5 2 4 4 5 2 4 3 +--R (2b c e + c d e )m + (22b c e + 6c d e )m +--R + +--R 5 2 4 2 5 2 4 5 +--R (82b c e + 11c d e )m + (122b c e + 6c d e )m + 60b c e +--R * +--R 4 +--R x +--R + +--R 2 5 4 4 2 5 4 2 2 3 3 +--R (b e + 2b c d e )m + (12b e + 16b c d e - 4c d e )m +--R + +--R 2 5 4 2 2 3 2 +--R (49b e + 34b c d e - 12c d e )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (78b e + 20b c d e - 8c d e )m + 40b e +--R * +--R 3 +--R x +--R + +--R 2 4 4 2 4 2 3 3 +--R b d e m + (10b d e - 6b c d e )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (29b d e - 36b c d e + 12c d e )m +--R + +--R 2 4 2 3 2 3 2 +--R (20b d e - 30b c d e + 12c d e )m +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 2 2 3 3 2 2 +--R - 2b d e m + (- 18b d e + 12b c d e )m +--R + +--R 2 2 3 3 2 2 4 +--R (- 40b d e + 60b c d e - 24c d e)m +--R * +--R x +--R + +--R 2 3 2 2 2 3 2 4 2 3 2 4 2 5 +--R 2b d e m + (18b d e - 12b c d e)m + 40b d e - 60b c d e + 24c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 4 2 3 2 2 2 2 m + 5 +--R (- c m - 10c m - 35c m - 50c m - 24c )(e x + d) +--R + +--R 2 4 2 3 2 2 +--R (- 2b c e + 4c d)m + (- 22b c e + 44c d)m + (- 82b c e + 164c d)m +--R + +--R 2 2 +--R (- 122b c e + 244c d)m - 60b c e + 120c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (- b e + 6b c d e - 6c d )m + (- 12b e + 72b c d e - 72c d )m +--R + +--R 2 2 2 2 2 +--R (- 49b e + 294b c d e - 294c d )m +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 78b e + 468b c d e - 468c d )m - 40b e + 240b c d e - 240c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 2 2 3 4 2 2 2 2 3 3 +--R (2b d e - 6b c d e + 4c d )m + (26b d e - 78b c d e + 52c d )m +--R + +--R 2 2 2 2 3 2 +--R (118b d e - 354b c d e + 236c d )m +--R + +--R 2 2 2 2 3 2 2 2 2 3 +--R (214b d e - 642b c d e + 428c d )m + 120b d e - 360b c d e + 240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 2 2 3 2 4 4 2 2 2 3 2 4 3 +--R (- b d e + 2b c d e - c d )m + (- 14b d e + 28b c d e - 14c d )m +--R + +--R 2 2 2 3 2 4 2 +--R (- 71b d e + 142b c d e - 71c d )m +--R + +--R 2 2 2 3 2 4 2 2 2 3 +--R (- 154b d e + 308b c d e - 154c d )m - 120b d e + 240b c d e +--R + +--R 2 4 +--R - 120c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1726 +t0:=(d+e*x)^4*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 8 4 2 3 7 2 4 3 2 2 2 6 +--R c e x + (2b c e + 4c d e )x + (b e + 8b c d e + 6c d e )x +--R + +--R 2 3 2 2 2 3 5 2 2 2 3 2 4 4 +--R (4b d e + 12b c d e + 4c d e)x + (6b d e + 8b c d e + c d )x +--R + +--R 2 3 4 3 2 4 2 +--R (4b d e + 2b c d )x + b d x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 1726 +r0:=1/5*d^2*(c*d-b*e)^2*(d+e*x)^5/e^5-1/3*d*(c*d-b*e)*(2*c*d-b*e)*_ + (d+e*x)^6/e^5+1/7*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*(d+e*x)^7/e^5-_ + 1/4*c*(2*c*d-b*e)*(d+e*x)^8/e^5+1/9*c^2*(d+e*x)^9/e^5 +--R +--R +--R (2) +--R 1 2 9 9 1 9 1 2 8 8 1 2 9 8 8 6 2 2 7 7 +--R - c e x + (- b c e + - c d e )x + (- b e + - b c d e + - c d e )x +--R 9 4 2 7 7 7 +--R + +--R 2 2 8 2 7 2 2 3 6 6 +--R (- b d e + 2b c d e + - c d e )x +--R 3 3 +--R + +--R 6 2 2 7 8 3 6 1 2 4 5 5 2 3 6 1 4 5 4 +--R (- b d e + - b c d e + - c d e )x + (b d e + - b c d e )x +--R 5 5 5 2 +--R + +--R 1 2 4 5 3 1 2 7 2 1 8 1 2 9 +--R - b d e x + --- b d e - --- b c d e + --- c d +--R 3 105 140 630 +--R / +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 9 1 4 1 2 3 8 1 2 4 8 3 6 2 2 2 7 +--R - c e x + (- b c e + - c d e )x + (- b e + - b c d e + - c d e )x +--R 9 4 2 7 7 7 +--R + +--R 2 2 3 2 2 2 2 3 6 6 2 2 2 8 3 1 2 4 5 +--R (- b d e + 2b c d e + - c d e)x + (- b d e + - b c d e + - c d )x +--R 3 3 5 5 5 +--R + +--R 2 3 1 4 4 1 2 4 3 +--R (b d e + - b c d )x + - b d x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 63 + +--S 64 of 1726 +m0:=a0-r0 +--R +--R +--R 1 2 7 2 1 8 1 2 9 +--R - --- b d e + --- b c d e - --- c d +--R 105 140 630 +--R (4) ------------------------------------- +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 64 + +--S 65 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 65 + +)clear all + +--S 66 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R Type: Polynomial(Integer) +--E 66 + +--S 67 of 1726 +r0:=1/3*b^2*d^3*x^3+1/4*b*d^2*(2*c*d+3*b*e)*x^4+1/5*d*(c^2*d^2+6*b*c*d*e+_ + 3*b^2*e^2)*x^5+1/6*e*(3*c^2*d^2+6*b*c*d*e+b^2*e^2)*x^6+_ + 1/7*c*e^2*(3*c*d+2*b*e)*x^7+1/8*c^2*e^3*x^8 +--R +--R +--R (2) +--R 1 2 3 8 2 3 3 2 2 7 1 2 3 2 1 2 2 6 +--R - c e x + (- b c e + - c d e )x + (- b e + b c d e + - c d e)x +--R 8 7 7 6 2 +--R + +--R 3 2 2 6 2 1 2 3 5 3 2 2 1 3 4 1 2 3 3 +--R (- b d e + - b c d e + - c d )x + (- b d e + - b c d )x + - b d x +--R 5 5 5 4 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 67 + +--S 68 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 8 2 3 3 2 2 7 1 2 3 2 1 2 2 6 +--R - c e x + (- b c e + - c d e )x + (- b e + b c d e + - c d e)x +--R 8 7 7 6 2 +--R + +--R 3 2 2 6 2 1 2 3 5 3 2 2 1 3 4 1 2 3 3 +--R (- b d e + - b c d e + - c d )x + (- b d e + - b c d )x + - b d x +--R 5 5 5 4 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 69 + +--S 70 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +)clear all + +--S 71 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1726 +r0:=1/3*b^2*d^2*x^3+1/2*b*d*(c*d+b*e)*x^4+1/5*(c^2*d^2+4*b*c*d*e+_ + b^2*e^2)*x^5+1/3*c*e*(c*d+b*e)*x^6+1/7*c^2*e^2*x^7 +--R +--R +--R (2) +--R 1 2 2 7 1 2 1 2 6 1 2 2 4 1 2 2 5 +--R - c e x + (- b c e + - c d e)x + (- b e + - b c d e + - c d )x +--R 7 3 3 5 5 5 +--R + +--R 1 2 1 2 4 1 2 2 3 +--R (- b d e + - b c d )x + - b d x +--R 2 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 72 + +--S 73 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 7 1 2 1 2 6 1 2 2 4 1 2 2 5 +--R - c e x + (- b c e + - c d e)x + (- b e + - b c d e + - c d )x +--R 7 3 3 5 5 5 +--R + +--R 1 2 1 2 4 1 2 2 3 +--R (- b d e + - b c d )x + - b d x +--R 2 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 1726 +t0:=(d+e*x)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1726 +r0:=1/3*b^2*d*x^3+1/4*b*(2*c*d+b*e)*x^4+1/5*c*(c*d+2*b*e)*x^5+1/6*c^2*e*x^6 +--R +--R +--R 1 2 6 2 1 2 5 1 2 1 4 1 2 3 +--R (2) - c e x + (- b c e + - c d)x + (- b e + - b c d)x + - b d x +--R 6 5 5 4 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 2 1 2 5 1 2 1 4 1 2 3 +--R (3) - c e x + (- b c e + - c d)x + (- b e + - b c d)x + - b d x +--R 6 5 5 4 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1726 +t0:=(b*x+c*x^2)^2 +--R +--R +--R 2 4 3 2 2 +--R (1) c x + 2b c x + b x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1726 +r0:=1/3*b^2*x^3+1/2*b*c*x^4+1/5*c^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (2) - c x + - b c x + - b x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (3) - c x + - b c x + - b x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x) +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) --------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 1726 +r0:=-d*(c*d-b*e)^2*x/e^4+1/2*(c*d-b*e)^2*x^2/e^3-1/3*c*(c*d-2*b*e)*_ + x^3/e^2+1/4*c^2*x^4/e+d^2*(c*d-b*e)^2*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 2 2 3 2 4 2 4 4 +--R (12b d e - 24b c d e + 12c d )log(e x + d) + 3c e x +--R + +--R 4 2 3 3 2 4 3 2 2 2 2 +--R (8b c e - 4c d e )x + (6b e - 12b c d e + 6c d e )x +--R + +--R 2 3 2 2 2 3 +--R (- 12b d e + 24b c d e - 12c d e)x +--R / +--R 5 +--R 12e +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 4 2 4 4 +--R (12b d e - 24b c d e + 12c d )log(e x + d) + 3c e x +--R + +--R 4 2 3 3 2 4 3 2 2 2 2 +--R (8b c e - 4c d e )x + (6b e - 12b c d e + 6c d e )x +--R + +--R 2 3 2 2 2 3 +--R (- 12b d e + 24b c d e - 12c d e)x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) --------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 1726 +r0:=(c*d-b*e)*(3*c*d-b*e)*x/e^4-c*(c*d-b*e)*x^2/e^3+1/3*c^2*x^3/e^2-_ + d^2*(c*d-b*e)^2/(e^5*(d+e*x))-2*d*(c*d-b*e)*(2*c*d-b*e)*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R ((- 6b d e + 18b c d e - 12c d e)x - 6b d e + 18b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R c e x + (3b c e - 2c d e )x + (3b e - 9b c d e + 6c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (3b d e - 12b c d e + 9c d e)x - 3b d e + 6b c d e - 3c d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R ((- 6b d e + 18b c d e - 12c d e)x - 6b d e + 18b c d e - 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R c e x + (3b c e - 2c d e )x + (3b e - 9b c d e + 6c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (3b d e - 12b c d e + 9c d e)x - 3b d e + 6b c d e - 3c d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 1726 +r0:=-c*(3*c*d-2*b*e)*x/e^4+1/2*c^2*x^2/e^3-1/2*d^2*(c*d-b*e)^2/_ + (e^5*(d+e*x)^2)+2*d*(c*d-b*e)*(2*c*d-b*e)/(e^5*(d+e*x))+_ + (6*c^2*d^2-6*b*c*d*e+b^2*e^2)*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (2b e - 12b c d e + 12c d e )x + (4b d e - 24b c d e + 24c d e)x +--R + +--R 2 2 2 3 2 4 +--R 2b d e - 12b c d e + 12c d +--R * +--R log(e x + d) +--R + +--R 2 4 4 4 2 3 3 3 2 2 2 2 +--R c e x + (4b c e - 4c d e )x + (8b c d e - 11c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4b d e - 8b c d e + 2c d e)x + 3b d e - 10b c d e + 7c d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (2b e - 12b c d e + 12c d e )x + (4b d e - 24b c d e + 24c d e)x +--R + +--R 2 2 2 3 2 4 +--R 2b d e - 12b c d e + 12c d +--R * +--R log(e x + d) +--R + +--R 2 4 4 4 2 3 3 3 2 2 2 2 +--R c e x + (4b c e - 4c d e )x + (8b c d e - 11c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4b d e - 8b c d e + 2c d e)x + 3b d e - 10b c d e + 7c d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1726 +r0:=c^2*x/e^4-1/3*d^2*(c*d-b*e)^2/(e^5*(d+e*x)^3)+d*(c*d-b*e)*_ + (2*c*d-b*e)/(e^5*(d+e*x)^2)+(-6*c^2*d^2+6*b*c*d*e-b^2*e^2)/_ + (e^5*(d+e*x))-2*c*(2*c*d-b*e)*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 4 2 3 3 3 2 2 2 2 +--R (6b c e - 12c d e )x + (18b c d e - 36c d e )x +--R + +--R 2 2 2 3 3 2 4 +--R (18b c d e - 36c d e)x + 6b c d e - 12c d +--R * +--R log(e x + d) +--R + +--R 2 4 4 2 3 3 2 4 3 2 2 2 2 +--R 3c e x + 9c d e x + (- 3b e + 18b c d e - 9c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 3b d e + 27b c d e - 27c d e)x - b d e + 11b c d e - 13c d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 3 3 2 2 2 2 +--R (6b c e - 12c d e )x + (18b c d e - 36c d e )x +--R + +--R 2 2 2 3 3 2 4 +--R (18b c d e - 36c d e)x + 6b c d e - 12c d +--R * +--R log(e x + d) +--R + +--R 2 4 4 2 3 3 2 4 3 2 2 2 2 +--R 3c e x + 9c d e x + (- 3b e + 18b c d e - 9c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 3b d e + 27b c d e - 27c d e)x - b d e + 11b c d e - 13c d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1726 +r0:=-1/4*d^2*(c*d-b*e)^2/(e^5*(d+e*x)^4)+2/3*d*(c*d-b*e)*(2*c*d-b*e)/_ + (e^5*(d+e*x)^3)+1/2*(-6*c^2*d^2+6*b*c*d*e-b^2*e^2)/_ + (e^5*(d+e*x)^2)+2*c*(2*c*d-b*e)/(e^5*(d+e*x))+c^2*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R (12c e x + 48c d e x + 72c d e x + 48c d e x + 12c d )log(e x + d) +--R + +--R 4 2 3 3 2 4 3 2 2 2 2 +--R (- 24b c e + 48c d e )x + (- 6b e - 36b c d e + 108c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 4b d e - 24b c d e + 88c d e)x - b d e - 6b c d e + 25c d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R (12c e x + 48c d e x + 72c d e x + 48c d e x + 12c d )log(e x + d) +--R + +--R 4 2 3 3 2 4 3 2 2 2 2 +--R (- 24b c e + 48c d e )x + (- 6b e - 36b c d e + 108c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 4b d e - 24b c d e + 88c d e)x - b d e - 6b c d e + 25c d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1726 +t0:=(d+e*x)^m*(b*x+c*x^2)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 m +--R (1) (c x + 3b c x + 3b c x + b x )(e x + d) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1726 +r0:=d^3*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^7*(1+m))-3*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*(d+e*x)^(2+m)/(e^7*(2+m))+3*d*(c*d-b*e)*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(3+m)/(e^7*(3+m))-(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(4+m)/(e^7*(4+m))+_ + 3*c*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(5+m)/(e^7*(5+m))-_ + 3*c^2*(2*c*d-b*e)*(d+e*x)^(6+m)/(e^7*(6+m))+c^3*(d+e*x)^(7+m)/(e^7*(7+m)) +--R +--R +--R (2) +--R 3 6 3 5 3 4 3 3 3 2 3 3 +--R (c m + 21c m + 175c m + 735c m + 1624c m + 1764c m + 720c ) +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R (3b c e - 6c d)m + (66b c e - 132c d)m + (570b c e - 1140c d)m +--R + +--R 2 3 3 2 3 2 +--R (2460b c e - 4920c d)m + (5547b c e - 11094c d)m +--R + +--R 2 3 2 3 +--R (6114b c e - 12228c d)m + 2520b c e - 5040c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 2 3 2 6 +--R (3b c e - 15b c d e + 15c d )m +--R + +--R 2 2 2 3 2 5 +--R (69b c e - 345b c d e + 345c d )m +--R + +--R 2 2 2 3 2 4 +--R (621b c e - 3105b c d e + 3105c d )m +--R + +--R 2 2 2 3 2 3 +--R (2775b c e - 13875b c d e + 13875c d )m +--R + +--R 2 2 2 3 2 2 +--R (6432b c e - 32160b c d e + 32160c d )m +--R + +--R 2 2 2 3 2 2 2 2 +--R (7236b c e - 36180b c d e + 36180c d )m + 3024b c e - 15120b c d e +--R + +--R 3 2 +--R 15120c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (b e - 12b c d e + 30b c d e - 20c d )m +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (24b e - 288b c d e + 720b c d e - 480c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (226b e - 2712b c d e + 6780b c d e - 4520c d )m +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (1056b e - 12672b c d e + 31680b c d e - 21120c d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (2545b e - 30540b c d e + 76350b c d e - 50900c d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (2952b e - 35424b c d e + 88560b c d e - 59040c d )m + 1260b e +--R + +--R 2 2 2 2 3 3 +--R - 15120b c d e + 37800b c d e - 25200c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 4 6 +--R (- 3b d e + 18b c d e - 30b c d e + 15c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 5 +--R (- 75b d e + 450b c d e - 750b c d e + 375c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R (- 741b d e + 4446b c d e - 7410b c d e + 3705c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (- 3657b d e + 21942b c d e - 36570b c d e + 18285c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 2 +--R (- 9336b d e + 56016b c d e - 93360b c d e + 46680c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 11388b d e + 68328b c d e - 113880b c d e + 56940c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R - 5040b d e + 30240b c d e - 50400b c d e + 25200c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 2 4 3 5 6 +--R (3b d e - 12b c d e + 15b c d e - 6c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 5 +--R (78b d e - 312b c d e + 390b c d e - 156c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 4 +--R (810b d e - 3240b c d e + 4050b c d e - 1620c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (4260b d e - 17040b c d e + 21300b c d e - 8520c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 2 +--R (11787b d e - 47148b c d e + 58935b c d e - 23574c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R (15822b d e - 63288b c d e + 79110b c d e - 31644c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R 7560b d e - 30240b c d e + 37800b c d e - 15120c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 3 2 4 2 2 5 3 6 6 +--R (- b d e + 3b c d e - 3b c d e + c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 5 +--R (- 27b d e + 81b c d e - 81b c d e + 27c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 4 +--R (- 295b d e + 885b c d e - 885b c d e + 295c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (- 1665b d e + 4995b c d e - 4995b c d e + 1665c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 2 +--R (- 5104b d e + 15312b c d e - 15312b c d e + 5104c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 +--R (- 8028b d e + 24084b c d e - 24084b c d e + 8028c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 +--R - 5040b d e + 15120b c d e - 15120b c d e + 5040c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 6 3 7 5 3 7 4 3 7 3 3 7 2 3 7 +--R c e m + 21c e m + 175c e m + 735c e m + 1624c e m + 1764c e m +--R + +--R 3 7 +--R 720c e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 6 2 7 3 6 5 +--R (3b c e + c d e )m + (66b c e + 15c d e )m +--R + +--R 2 7 3 6 4 2 7 3 6 3 +--R (570b c e + 85c d e )m + (2460b c e + 225c d e )m +--R + +--R 2 7 3 6 2 2 7 3 6 2 7 +--R (5547b c e + 274c d e )m + (6114b c e + 120c d e )m + 2520b c e +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 6 2 7 2 6 3 2 5 5 +--R (3b c e + 3b c d e )m + (69b c e + 51b c d e - 6c d e )m +--R + +--R 2 7 2 6 3 2 5 4 +--R (621b c e + 315b c d e - 60c d e )m +--R + +--R 2 7 2 6 3 2 5 3 +--R (2775b c e + 885b c d e - 210c d e )m +--R + +--R 2 7 2 6 3 2 5 2 +--R (6432b c e + 1122b c d e - 300c d e )m +--R + +--R 2 7 2 6 3 2 5 2 7 +--R (7236b c e + 504b c d e - 144c d e )m + 3024b c e +--R * +--R 5 +--R x +--R + +--R 3 7 2 6 6 3 7 2 6 2 2 5 5 +--R (b e + 3b c d e )m + (24b e + 57b c d e - 15b c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (226b e + 393b c d e - 195b c d e + 30c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 3 +--R (1056b e + 1203b c d e - 795b c d e + 180c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2545b e + 1620b c d e - 1245b c d e + 330c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 3 7 +--R (2952b e + 756b c d e - 630b c d e + 180c d e )m + 1260b e +--R * +--R 4 +--R x +--R + +--R 3 6 6 3 6 2 2 5 5 +--R b d e m + (21b d e - 12b c d e )m +--R + +--R 3 6 2 2 5 2 3 4 4 +--R (163b d e - 192b c d e + 60b c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (567b d e - 996b c d e + 600b c d e - 120c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 2 +--R (844b d e - 1824b c d e + 1380b c d e - 360c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 +--R (420b d e - 1008b c d e + 840b c d e - 240c d e )m +--R * +--R 3 +--R x +--R + +--R 3 2 5 5 3 2 5 2 3 4 4 +--R - 3b d e m + (- 57b d e + 36b c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 +--R (- 375b d e + 504b c d e - 180b c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (- 951b d e + 1980b c d e - 1440b c d e + 360c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 +--R (- 630b d e + 1512b c d e - 1260b c d e + 360c d e )m +--R * +--R 2 +--R x +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 +--R 6b d e m + (108b d e - 72b c d e )m +--R + +--R 3 3 4 2 4 3 2 5 2 2 +--R (642b d e - 936b c d e + 360b c d e )m +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 +--R (1260b d e - 3024b c d e + 2520b c d e - 720c d e)m +--R * +--R x +--R + +--R 3 4 3 3 3 4 3 2 5 2 2 +--R - 6b d e m + (- 108b d e + 72b c d e )m +--R + +--R 3 4 3 2 5 2 2 6 3 4 3 2 5 2 +--R (- 642b d e + 936b c d e - 360b c d e)m - 1260b d e + 3024b c d e +--R + +--R 2 6 3 7 +--R - 2520b c d e + 720c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 6 3 7 5 3 7 4 3 7 3 3 7 2 +--R c e m + 21c e m + 175c e m + 735c e m + 1624c e m +--R + +--R 3 7 3 7 +--R 1764c e m + 720c e +--R * +--R 7 +--R x +--R + +--R 2 7 3 6 6 2 7 3 6 5 +--R (3b c e + c d e )m + (66b c e + 15c d e )m +--R + +--R 2 7 3 6 4 2 7 3 6 3 +--R (570b c e + 85c d e )m + (2460b c e + 225c d e )m +--R + +--R 2 7 3 6 2 2 7 3 6 2 7 +--R (5547b c e + 274c d e )m + (6114b c e + 120c d e )m + 2520b c e +--R * +--R 6 +--R x +--R + +--R 2 7 2 6 6 2 7 2 6 3 2 5 5 +--R (3b c e + 3b c d e )m + (69b c e + 51b c d e - 6c d e )m +--R + +--R 2 7 2 6 3 2 5 4 +--R (621b c e + 315b c d e - 60c d e )m +--R + +--R 2 7 2 6 3 2 5 3 +--R (2775b c e + 885b c d e - 210c d e )m +--R + +--R 2 7 2 6 3 2 5 2 +--R (6432b c e + 1122b c d e - 300c d e )m +--R + +--R 2 7 2 6 3 2 5 2 7 +--R (7236b c e + 504b c d e - 144c d e )m + 3024b c e +--R * +--R 5 +--R x +--R + +--R 3 7 2 6 6 3 7 2 6 2 2 5 5 +--R (b e + 3b c d e )m + (24b e + 57b c d e - 15b c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (226b e + 393b c d e - 195b c d e + 30c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 3 +--R (1056b e + 1203b c d e - 795b c d e + 180c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2545b e + 1620b c d e - 1245b c d e + 330c d e )m +--R + +--R 3 7 2 6 2 2 5 3 3 4 3 7 +--R (2952b e + 756b c d e - 630b c d e + 180c d e )m + 1260b e +--R * +--R 4 +--R x +--R + +--R 3 6 6 3 6 2 2 5 5 +--R b d e m + (21b d e - 12b c d e )m +--R + +--R 3 6 2 2 5 2 3 4 4 +--R (163b d e - 192b c d e + 60b c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (567b d e - 996b c d e + 600b c d e - 120c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 2 +--R (844b d e - 1824b c d e + 1380b c d e - 360c d e )m +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 +--R (420b d e - 1008b c d e + 840b c d e - 240c d e )m +--R * +--R 3 +--R x +--R + +--R 3 2 5 5 3 2 5 2 3 4 4 +--R - 3b d e m + (- 57b d e + 36b c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 +--R (- 375b d e + 504b c d e - 180b c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (- 951b d e + 1980b c d e - 1440b c d e + 360c d e )m +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 +--R (- 630b d e + 1512b c d e - 1260b c d e + 360c d e )m +--R * +--R 2 +--R x +--R + +--R 3 3 4 4 3 3 4 2 4 3 3 +--R 6b d e m + (108b d e - 72b c d e )m +--R + +--R 3 3 4 2 4 3 2 5 2 2 +--R (642b d e - 936b c d e + 360b c d e )m +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 +--R (1260b d e - 3024b c d e + 2520b c d e - 720c d e)m +--R * +--R x +--R + +--R 3 4 3 3 3 4 3 2 5 2 2 +--R - 6b d e m + (- 108b d e + 72b c d e )m +--R + +--R 3 4 3 2 5 2 2 6 3 4 3 2 5 2 +--R (- 642b d e + 936b c d e - 360b c d e)m - 1260b d e + 3024b c d e +--R + +--R 2 6 3 7 +--R - 2520b c d e + 720c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 6 3 5 3 4 3 3 3 2 3 3 +--R (- c m - 21c m - 175c m - 735c m - 1624c m - 1764c m - 720c ) +--R * +--R m + 7 +--R (e x + d) +--R + +--R 2 3 6 2 3 5 +--R (- 3b c e + 6c d)m + (- 66b c e + 132c d)m +--R + +--R 2 3 4 2 3 3 +--R (- 570b c e + 1140c d)m + (- 2460b c e + 4920c d)m +--R + +--R 2 3 2 2 3 2 +--R (- 5547b c e + 11094c d)m + (- 6114b c e + 12228c d)m - 2520b c e +--R + +--R 3 +--R 5040c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 2 3 2 6 +--R (- 3b c e + 15b c d e - 15c d )m +--R + +--R 2 2 2 3 2 5 +--R (- 69b c e + 345b c d e - 345c d )m +--R + +--R 2 2 2 3 2 4 +--R (- 621b c e + 3105b c d e - 3105c d )m +--R + +--R 2 2 2 3 2 3 +--R (- 2775b c e + 13875b c d e - 13875c d )m +--R + +--R 2 2 2 3 2 2 +--R (- 6432b c e + 32160b c d e - 32160c d )m +--R + +--R 2 2 2 3 2 2 2 +--R (- 7236b c e + 36180b c d e - 36180c d )m - 3024b c e +--R + +--R 2 3 2 +--R 15120b c d e - 15120c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- b e + 12b c d e - 30b c d e + 20c d )m +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 24b e + 288b c d e - 720b c d e + 480c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 226b e + 2712b c d e - 6780b c d e + 4520c d )m +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 1056b e + 12672b c d e - 31680b c d e + 21120c d )m +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 2545b e + 30540b c d e - 76350b c d e + 50900c d )m +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 2952b e + 35424b c d e - 88560b c d e + 59040c d )m - 1260b e +--R + +--R 2 2 2 2 3 3 +--R 15120b c d e - 37800b c d e + 25200c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 3 3 2 2 2 2 3 3 4 6 +--R (3b d e - 18b c d e + 30b c d e - 15c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 5 +--R (75b d e - 450b c d e + 750b c d e - 375c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R (741b d e - 4446b c d e + 7410b c d e - 3705c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (3657b d e - 21942b c d e + 36570b c d e - 18285c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 2 +--R (9336b d e - 56016b c d e + 93360b c d e - 46680c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (11388b d e - 68328b c d e + 113880b c d e - 56940c d )m +--R + +--R 3 3 2 2 2 2 3 3 4 +--R 5040b d e - 30240b c d e + 50400b c d e - 25200c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 3 2 3 2 3 2 2 4 3 5 6 +--R (- 3b d e + 12b c d e - 15b c d e + 6c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 5 +--R (- 78b d e + 312b c d e - 390b c d e + 156c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 4 +--R (- 810b d e + 3240b c d e - 4050b c d e + 1620c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 +--R (- 4260b d e + 17040b c d e - 21300b c d e + 8520c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 2 +--R (- 11787b d e + 47148b c d e - 58935b c d e + 23574c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R (- 15822b d e + 63288b c d e - 79110b c d e + 31644c d )m +--R + +--R 3 2 3 2 3 2 2 4 3 5 +--R - 7560b d e + 30240b c d e - 37800b c d e + 15120c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 3 3 2 4 2 2 5 3 6 6 +--R (b d e - 3b c d e + 3b c d e - c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 5 +--R (27b d e - 81b c d e + 81b c d e - 27c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 4 +--R (295b d e - 885b c d e + 885b c d e - 295c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 +--R (1665b d e - 4995b c d e + 4995b c d e - 1665c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 2 +--R (5104b d e - 15312b c d e + 15312b c d e - 5104c d )m +--R + +--R 3 3 3 2 4 2 2 5 3 6 3 3 3 +--R (8028b d e - 24084b c d e + 24084b c d e - 8028c d )m + 5040b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 15120b c d e + 15120b c d e - 5040c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1726 +t0:=(d+e*x)^4*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 10 2 4 3 3 9 2 4 2 3 3 2 2 8 +--R c e x + (3b c e + 4c d e )x + (3b c e + 12b c d e + 6c d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 7 +--R (b e + 12b c d e + 18b c d e + 4c d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 6 +--R (4b d e + 18b c d e + 12b c d e + c d )x +--R + +--R 3 2 2 2 3 2 4 5 3 3 2 4 4 3 4 3 +--R (6b d e + 12b c d e + 3b c d )x + (4b d e + 3b c d )x + b d x +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 1726 +r0:=1/4*b^3*d^4*x^4+1/5*b^2*d^3*(3*c*d+4*b*e)*x^5+1/2*b*d^2*(c^2*d^2+_ + 4*b*c*d*e+2*b^2*e^2)*x^6+1/7*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*_ + c*d*e^2+4*b^3*e^3)*x^7+1/8*e*(4*c^3*d^3+18*b*c^2*d^2*e+_ + 12*b^2*c*d*e^2+b^3*e^3)*x^8+1/3*c*e^2*(2*c^2*d^2+4*b*c*d*e+_ + b^2*e^2)*x^9+1/10*c^2*e^3*(4*c*d+3*b*e)*x^10+1/11*c^3*e^4*x^11 +--R +--R +--R (2) +--R 1 3 4 11 3 2 4 2 3 3 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 1 2 4 4 2 3 2 3 2 2 9 +--R (- b c e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 1 3 4 3 2 3 9 2 2 2 1 3 3 8 +--R (- b e + - b c d e + - b c d e + - c d e)x +--R 8 2 4 2 +--R + +--R 4 3 3 18 2 2 2 12 2 3 1 3 4 7 +--R (- b d e + -- b c d e + -- b c d e + - c d )x +--R 7 7 7 7 +--R + +--R 3 2 2 2 3 1 2 4 6 4 3 3 3 2 4 5 1 3 4 4 +--R (b d e + 2b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 11 3 2 4 2 3 3 10 +--R -- c e x + (-- b c e + - c d e )x +--R 11 10 5 +--R + +--R 1 2 4 4 2 3 2 3 2 2 9 +--R (- b c e + - b c d e + - c d e )x +--R 3 3 3 +--R + +--R 1 3 4 3 2 3 9 2 2 2 1 3 3 8 +--R (- b e + - b c d e + - b c d e + - c d e)x +--R 8 2 4 2 +--R + +--R 4 3 3 18 2 2 2 12 2 3 1 3 4 7 +--R (- b d e + -- b c d e + -- b c d e + - c d )x +--R 7 7 7 7 +--R + +--R 3 2 2 2 3 1 2 4 6 4 3 3 3 2 4 5 1 3 4 4 +--R (b d e + 2b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 9 2 3 3 2 8 2 3 2 2 3 2 7 +--R c e x + (3b c e + 3c d e )x + (3b c e + 9b c d e + 3c d e)x +--R + +--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 5 +--R (b e + 9b c d e + 9b c d e + c d )x + (3b d e + 9b c d e + 3b c d )x +--R + +--R 3 2 2 3 4 3 3 3 +--R (3b d e + 3b c d )x + b d x +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 1726 +r0:=1/4*b^3*d^3*x^4+3/5*b^2*d^2*(c*d+b*e)*x^5+1/2*b*d*(c^2*d^2+3*b*c*d*e+_ + b^2*e^2)*x^6+1/7*(c*d+b*e)*(c^2*d^2+8*b*c*d*e+b^2*e^2)*x^7+_ + 3/8*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)*x^8+1/3*c^2*e^2*(c*d+b*e)*_ + x^9+1/10*c^3*e^3*x^10 +--R +--R +--R (2) +--R 1 3 3 10 1 2 3 1 3 2 9 3 2 3 9 2 2 3 3 2 8 +--R -- c e x + (- b c e + - c d e )x + (- b c e + - b c d e + - c d e)x +--R 10 3 3 8 8 8 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 7 +--R (- b e + - b c d e + - b c d e + - c d )x +--R 7 7 7 7 +--R + +--R 1 3 2 3 2 2 1 2 3 6 3 3 2 3 2 3 5 1 3 3 4 +--R (- b d e + - b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 2 2 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 10 1 2 3 1 3 2 9 3 2 3 9 2 2 3 3 2 8 +--R -- c e x + (- b c e + - c d e )x + (- b c e + - b c d e + - c d e)x +--R 10 3 3 8 8 8 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 7 +--R (- b e + - b c d e + - b c d e + - c d )x +--R 7 7 7 7 +--R + +--R 1 3 2 3 2 2 1 2 3 6 3 3 2 3 2 3 5 1 3 3 4 +--R (- b d e + - b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 2 2 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 1726 +r0:=1/4*b^3*d^2*x^4+1/5*b^2*d*(3*c*d+2*b*e)*x^5+1/6*b*(3*c^2*d^2+_ + 6*b*c*d*e+b^2*e^2)*x^6+1/7*c*(c^2*d^2+6*b*c*d*e+3*b^2*e^2)*x^7+_ + 1/8*c^2*e*(2*c*d+3*b*e)*x^8+1/9*c^3*e^2*x^9 +--R +--R +--R (2) +--R 1 3 2 9 3 2 2 1 3 8 3 2 2 6 2 1 3 2 7 +--R - c e x + (- b c e + - c d e)x + (- b c e + - b c d e + - c d )x +--R 9 8 4 7 7 7 +--R + +--R 1 3 2 2 1 2 2 6 2 3 3 2 2 5 1 3 2 4 +--R (- b e + b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 6 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 9 3 2 2 1 3 8 3 2 2 6 2 1 3 2 7 +--R - c e x + (- b c e + - c d e)x + (- b c e + - b c d e + - c d )x +--R 9 8 4 7 7 7 +--R + +--R 1 3 2 2 1 2 2 6 2 3 3 2 2 5 1 3 2 4 +--R (- b e + b c d e + - b c d )x + (- b d e + - b c d )x + - b d x +--R 6 2 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 1726 +t0:=(d+e*x)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 1726 +r0:=1/4*b^3*d*x^4+1/5*b^2*(3*c*d+b*e)*x^5+1/2*b*c*(c*d+b*e)*x^6+_ + 1/7*c^2*(c*d+3*b*e)*x^7+1/8*c^3*e*x^8 +--R +--R +--R (2) +--R 1 3 8 3 2 1 3 7 1 2 1 2 6 +--R - c e x + (- b c e + - c d)x + (- b c e + - b c d)x +--R 8 7 7 2 2 +--R + +--R 1 3 3 2 5 1 3 4 +--R (- b e + - b c d)x + - b d x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 3 2 1 3 7 1 2 1 2 6 +--R - c e x + (- b c e + - c d)x + (- b c e + - b c d)x +--R 8 7 7 2 2 +--R + +--R 1 3 3 2 5 1 3 4 +--R (- b e + - b c d)x + - b d x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 1726 +t0:=(b*x+c*x^2)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R (1) c x + 3b c x + 3b c x + b x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1726 +r0:=1/4*b^3*x^4+3/5*b^2*c*x^5+1/2*b*c^2*x^6+1/7*c^3*x^7 +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (2) - c x + - b c x + - b c x + - b x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (3) - c x + - b c x + - b c x + - b x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 1726 +r0:=-d^2*(c*d-b*e)^3*x/e^6+1/2*d*(c*d-b*e)^3*x^2/e^5-_ + 1/3*(c*d-b*e)^3*x^3/e^4+1/4*c*(c^2*d^2-3*b*c*d*e+3*b^2*e^2)*_ + x^4/e^3-1/5*c^2*(c*d-3*b*e)*x^5/e^2+1/6*c^3*x^6/e+_ + d^3*(c*d-b*e)^3*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 3 3 2 4 2 2 5 3 6 3 6 6 +--R (- 60b d e + 180b c d e - 180b c d e + 60c d )log(e x + d) + 10c e x +--R + +--R 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R (36b c e - 12c d e )x + (45b c e - 45b c d e + 15c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (20b e - 60b c d e + 60b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 30b d e + 90b c d e - 90b c d e + 30c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 +--R (60b d e - 180b c d e + 180b c d e - 60c d e)x +--R / +--R 7 +--R 60e +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 2 2 5 3 6 3 6 6 +--R (- 60b d e + 180b c d e - 180b c d e + 60c d )log(e x + d) + 10c e x +--R + +--R 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R (36b c e - 12c d e )x + (45b c e - 45b c d e + 15c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (20b e - 60b c d e + 60b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 30b d e + 90b c d e - 90b c d e + 30c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 +--R (60b d e - 180b c d e + 180b c d e - 60c d e)x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^2 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1726 +r0:=d*(5*c*d-2*b*e)*(c*d-b*e)^2*x/e^6-1/2*(c*d-b*e)^2*(4*c*d-b*e)*_ + x^2/e^5+c*(c*d-b*e)^2*x^3/e^4-1/4*c^2*(2*c*d-3*b*e)*x^4/e^3+_ + 1/5*c^3*x^5/e^2-d^3*(c*d-b*e)^3/(e^7*(d+e*x))-3*d^2*_ + (c*d-b*e)^2*(2*c*d-b*e)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (60b d e - 240b c d e + 300b c d e - 120c d e)x + 60b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 240b c d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R 4c e x + (15b c e - 6c d e )x + (20b c e - 25b c d e + 10c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (10b e - 40b c d e + 50b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 30b d e + 120b c d e - 150b c d e + 60c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 40b d e + 180b c d e - 240b c d e + 100c d e)x + 20b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 60b c d e + 60b c d e - 20c d +--R / +--R 8 7 +--R 20e x + 20d e +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (60b d e - 240b c d e + 300b c d e - 120c d e)x + 60b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 240b c d e + 300b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R 4c e x + (15b c e - 6c d e )x + (20b c e - 25b c d e + 10c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (10b e - 40b c d e + 50b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 30b d e + 120b c d e - 150b c d e + 60c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 40b d e + 180b c d e - 240b c d e + 100c d e)x + 20b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 60b c d e + 60b c d e - 20c d +--R / +--R 8 7 +--R 20e x + 20d e +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1726 +r0:=-(c*d-b*e)*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)*x/e^6+3/2*c*(c*d-b*e)*_ + (2*c*d-b*e)*x^2/e^5-c^2*(c*d-b*e)*x^3/e^4+1/4*c^3*x^4/e^3-_ + 1/2*d^3*(c*d-b*e)^3/(e^7*(d+e*x)^2)+3*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)/(e^7*(d+e*x))+3*d*(c*d-b*e)*(5*c^2*d^2-5*b*c*d*e+_ + b^2*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 12b d e + 72b c d e - 120b c d e + 60c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 24b d e + 144b c d e - 240b c d e + 120c d e)x - 12b d e +--R + +--R 2 4 2 2 5 3 6 +--R 72b c d e - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R c e x + (4b c e - 2c d e )x + (6b c e - 10b c d e + 5c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (4b e - 24b c d e + 40b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (8b d e - 66b c d e + 126b c d e - 68c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 2 4 2 +--R (- 8b d e + 12b c d e + 12b c d e - 16c d e)x - 10b d e + 42b c d e +--R + +--R 2 5 3 6 +--R - 54b c d e + 22c d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 12b d e + 72b c d e - 120b c d e + 60c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 24b d e + 144b c d e - 240b c d e + 120c d e)x - 12b d e +--R + +--R 2 4 2 2 5 3 6 +--R 72b c d e - 120b c d e + 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R c e x + (4b c e - 2c d e )x + (6b c e - 10b c d e + 5c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (4b e - 24b c d e + 40b c d e - 20c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (8b d e - 66b c d e + 126b c d e - 68c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 2 4 2 +--R (- 8b d e + 12b c d e + 12b c d e - 16c d e)x - 10b d e + 42b c d e +--R + +--R 2 5 3 6 +--R - 54b c d e + 22c d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^4 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1726 +r0:=c*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)*x/e^6-1/2*c^2*_ + (4*c*d-3*b*e)*x^2/e^5+1/3*c^3*x^3/e^4-1/3*d^3*(c*d-b*e)^3/_ + (e^7*(d+e*x)^3)+3/2*d^2*(c*d-b*e)^2*(2*c*d-b*e)/(e^7*_ + (d+e*x)^2)-3*d*(c*d-b*e)*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)/_ + (e^7*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2-10*b*c*d*e+b^2*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (6b e - 72b c d e + 180b c d e - 120c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (18b d e - 216b c d e + 540b c d e - 360c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (18b d e - 216b c d e + 540b c d e - 360c d e)x + 6b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 72b c d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R 2c e x + (9b c e - 6c d e )x + (18b c e - 45b c d e + 30c d e )x +--R + +--R 2 5 2 2 4 3 3 3 3 +--R (54b c d e - 189b c d e + 146c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (18b d e - 54b c d e - 27b c d e + 78c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (27b d e - 162b c d e + 243b c d e - 102c d e)x + 11b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 78b c d e + 141b c d e - 74c d +--R / +--R 10 3 9 2 2 8 3 7 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (6b e - 72b c d e + 180b c d e - 120c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (18b d e - 216b c d e + 540b c d e - 360c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (18b d e - 216b c d e + 540b c d e - 360c d e)x + 6b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 72b c d e + 180b c d e - 120c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 6 2 5 3 2 4 4 +--R 2c e x + (9b c e - 6c d e )x + (18b c e - 45b c d e + 30c d e )x +--R + +--R 2 5 2 2 4 3 3 3 3 +--R (54b c d e - 189b c d e + 146c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (18b d e - 54b c d e - 27b c d e + 78c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (27b d e - 162b c d e + 243b c d e - 102c d e)x + 11b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 78b c d e + 141b c d e - 74c d +--R / +--R 10 3 9 2 2 8 3 7 +--R 6e x + 18d e x + 18d e x + 6d e +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^5 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1726 +r0:=-c^2*(5*c*d-3*b*e)*x/e^6+1/2*c^3*x^2/e^5-1/4*d^3*(c*d-b*e)^3/_ + (e^7*(d+e*x)^4)+d^2*(c*d-b*e)^2*(2*c*d-b*e)/(e^7*(d+e*x)^3)-_ + 3/2*d*(c*d-b*e)*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)/(e^7*(d+e*x)^2)+_ + (2*c*d-b*e)*(10*c^2*d^2-10*b*c*d*e+b^2*e^2)/(e^7*(d+e*x))+_ + 3*c*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 2 6 2 5 3 2 4 4 +--R (12b c e - 60b c d e + 60c d e )x +--R + +--R 2 5 2 2 4 3 3 3 3 +--R (48b c d e - 240b c d e + 240c d e )x +--R + +--R 2 2 4 2 3 3 3 4 2 2 +--R (72b c d e - 360b c d e + 360c d e )x +--R + +--R 2 3 3 2 4 2 3 5 2 4 2 2 5 +--R (48b c d e - 240b c d e + 240c d e)x + 12b c d e - 60b c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 5 3 2 4 4 +--R 2c e x + (12b c e - 12c d e )x + (48b c d e - 68c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (- 4b e + 48b c d e - 48b c d e - 32c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 6b d e + 108b c d e - 252b c d e + 132c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 2 4 2 +--R (- 4b d e + 88b c d e - 248b c d e + 168c d e)x - b d e + 25b c d e +--R + +--R 2 5 3 6 +--R - 77b c d e + 57c d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 5 3 2 4 4 +--R (12b c e - 60b c d e + 60c d e )x +--R + +--R 2 5 2 2 4 3 3 3 3 +--R (48b c d e - 240b c d e + 240c d e )x +--R + +--R 2 2 4 2 3 3 3 4 2 2 +--R (72b c d e - 360b c d e + 360c d e )x +--R + +--R 2 3 3 2 4 2 3 5 2 4 2 2 5 +--R (48b c d e - 240b c d e + 240c d e)x + 12b c d e - 60b c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 2 6 3 5 5 2 5 3 2 4 4 +--R 2c e x + (12b c e - 12c d e )x + (48b c d e - 68c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (- 4b e + 48b c d e - 48b c d e - 32c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 6b d e + 108b c d e - 252b c d e + 132c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 2 4 2 +--R (- 4b d e + 88b c d e - 248b c d e + 168c d e)x - b d e + 25b c d e +--R + +--R 2 5 3 6 +--R - 77b c d e + 57c d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1726 +t0:=(d+e*x)^4/(b*x+c*x^2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1726 +r0:=e^2*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)*x/c^3+1/2*e^3*(4*c*d-b*e)*x^2/c^2+_ + 1/3*e^4*x^3/c+d^4*log(x)/b-(c*d-b*e)^4*log(b+c*x)/(b*c^4) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 6b e + 24b c d e - 36b c d e + 24b c d e - 6c d )log(c x + b) +--R + +--R 4 4 3 4 3 2 2 4 3 3 2 +--R 6c d log(x) + 2b c e x + (- 3b c e + 12b c d e )x +--R + +--R 3 4 2 2 3 3 2 2 +--R (6b c e - 24b c d e + 36b c d e )x +--R / +--R 4 +--R 6b c +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 6b e + 24b c d e - 36b c d e + 24b c d e - 6c d )log(c x + b) +--R + +--R 4 4 3 4 3 2 2 4 3 3 2 +--R 6c d log(x) + 2b c e x + (- 3b c e + 12b c d e )x +--R + +--R 3 4 2 2 3 3 2 2 +--R (6b c e - 24b c d e + 36b c d e )x +--R / +--R 4 +--R 6b c +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1726 +r0:=e^2*(3*c*d-b*e)*x/c^2+1/2*e^3*x^2/c+d^3*log(x)/b-(c*d-b*e)^3*_ + log(b+c*x)/(b*c^3) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2b e - 6b c d e + 6b c d e - 2c d )log(c x + b) + 2c d log(x) +--R + +--R 2 3 2 2 3 2 2 +--R b c e x + (- 2b c e + 6b c d e )x +--R / +--R 3 +--R 2b c +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2b e - 6b c d e + 6b c d e - 2c d )log(c x + b) + 2c d log(x) +--R + +--R 2 3 2 2 3 2 2 +--R b c e x + (- 2b c e + 6b c d e )x +--R / +--R 3 +--R 2b c +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1726 +r0:=e^2*x/c+d^2*log(x)/b-(c*d-b*e)^2*log(b+c*x)/(b*c^2) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- b e + 2b c d e - c d )log(c x + b) + c d log(x) + b c e x +--R (2) ------------------------------------------------------------- +--R 2 +--R b c +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- b e + 2b c d e - c d )log(c x + b) + c d log(x) + b c e x +--R (3) ------------------------------------------------------------- +--R 2 +--R b c +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1726 +t0:=(d+e*x)/(b*x+c*x^2) +--R +--R +--R e x + d +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1726 +r0:=d*log(x)/b-(c*d-b*e)*log(b+c*x)/(b*c) +--R +--R +--R (b e - c d)log(c x + b) + c d log(x) +--R (2) ------------------------------------ +--R b c +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (b e - c d)log(c x + b) + c d log(x) +--R (3) ------------------------------------ +--R b c +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1726 +t0:=1/(b*x+c*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1726 +r0:=log(x)/b-log(b+c*x)/b +--R +--R +--R - log(c x + b) + log(x) +--R (2) ----------------------- +--R b +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1726 +a0:=integrate(t0,x) +--R +--R +--R - log(c x + b) + log(x) +--R (3) ----------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 2 +--R c e x + (b e + c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1726 +r0:=log(x)/(b*d)-c*log(b+c*x)/(b*(c*d-b*e))+e*log(d+e*x)/(d*(c*d-b*e)) +--R +--R +--R - b e log(e x + d) + c d log(c x + b) + (b e - c d)log(x) +--R (2) --------------------------------------------------------- +--R 2 2 +--R b d e - b c d +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1726 +a0:=integrate(t0,x) +--R +--R +--R - b e log(e x + d) + c d log(c x + b) + (b e - c d)log(x) +--R (3) --------------------------------------------------------- +--R 2 2 +--R b d e - b c d +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1726 +r0:=-e/(d*(c*d-b*e)*(d+e*x))+log(x)/(b*d^2)-c^2*log(b+c*x)/(b*(c*d-b*e)^2)+_ + e*(2*c*d-b*e)*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((- b e + 2b c d e )x - b d e + 2b c d e)log(e x + d) +--R + +--R 2 2 2 3 +--R (- c d e x - c d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((b e - 2b c d e + c d e)x + b d e - 2b c d e + c d )log(x) + b d e +--R + +--R 2 +--R - b c d e +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R ((- b e + 2b c d e )x - b d e + 2b c d e)log(e x + d) +--R + +--R 2 2 2 3 +--R (- c d e x - c d )log(c x + b) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((b e - 2b c d e + c d e)x + b d e - 2b c d e + c d )log(x) + b d e +--R + +--R 2 +--R - b c d e +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1726 +t0:=1/((d+e*x)^3*(b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1726 +r0:=-1/2*e/(d*(c*d-b*e)*(d+e*x)^2)-e*(2*c*d-b*e)/(d^2*(c*d-b*e)^2*(d+e*x))+_ + log(x)/(b*d^3)-c^3*log(b+c*x)/(b*(c*d-b*e)^3)+e*(3*c^2*d^2-_ + 3*b*c*d*e+b^2*e^2)*log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 +--R (- 2b e + 6b c d e - 6b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4b d e + 12b c d e - 12b c d e )x - 2b d e + 6b c d e - 6b c d e +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2c d e x + 4c d e x + 2c d )log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2b e - 6b c d e + 6b c d e - 2c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4b d e - 12b c d e + 12b c d e - 4c d e)x + 2b d e - 6b c d e +--R + +--R 2 4 3 5 +--R 6b c d e - 2c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2b d e - 6b c d e + 4b c d e )x + 3b d e - 8b c d e + 5b c d e +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 4 2 2 3 2 +--R (- 2b e + 6b c d e - 6b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4b d e + 12b c d e - 12b c d e )x - 2b d e + 6b c d e - 6b c d e +--R * +--R log(e x + d) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2c d e x + 4c d e x + 2c d )log(c x + b) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2b e - 6b c d e + 6b c d e - 2c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4b d e - 12b c d e + 12b c d e - 4c d e)x + 2b d e - 6b c d e +--R + +--R 2 4 3 5 +--R 6b c d e - 2c d +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2b d e - 6b c d e + 4b c d e )x + 3b d e - 8b c d e + 5b c d e +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e)x + 2b d e - 6b c d e +--R + +--R 2 2 7 3 8 +--R 6b c d e - 2b c d +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1726 +t0:=(d+e*x)^5/(b*x+c*x^2)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) -------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1726 +r0:=-d^5/(b^2*x)+e^4*(5*c*d-2*b*e)*x/c^3+1/2*e^5*x^2/c^2-(c*d-b*e)^5/_ + (b^2*c^4*(b+c*x))-d^4*(2*c*d-5*b*e)*log(x)/b^3+(c*d-b*e)^4*_ + (2*c*d+3*b*e)*log(b+c*x)/(b^3*c^4) +--R +--R +--R (2) +--R 5 5 4 2 4 3 3 2 3 5 4 6 5 2 +--R (6b c e - 20b c d e + 20b c d e - 10b c d e + 4c d )x +--R + +--R 6 5 5 4 4 2 2 3 2 4 4 5 5 +--R (6b e - 20b c d e + 20b c d e - 10b c d e + 4b c d )x +--R * +--R log(c x + b) +--R + +--R 5 4 6 5 2 2 4 4 5 5 3 3 5 4 +--R ((10b c d e - 4c d )x + (10b c d e - 4b c d )x)log(x) + b c e x +--R + +--R 4 2 5 3 3 4 3 5 5 4 2 4 2 +--R (- 3b c e + 10b c d e )x + (- 4b c e + 10b c d e )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2b e - 10b c d e + 20b c d e - 20b c d e + 10b c d e - 4b c d )x +--R + +--R 2 4 5 +--R - 2b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 2 4 3 3 2 3 5 4 6 5 2 +--R (6b c e - 20b c d e + 20b c d e - 10b c d e + 4c d )x +--R + +--R 6 5 5 4 4 2 2 3 2 4 4 5 5 +--R (6b e - 20b c d e + 20b c d e - 10b c d e + 4b c d )x +--R * +--R log(c x + b) +--R + +--R 5 4 6 5 2 2 4 4 5 5 3 3 5 4 +--R ((10b c d e - 4c d )x + (10b c d e - 4b c d )x)log(x) + b c e x +--R + +--R 4 2 5 3 3 4 3 5 5 4 2 4 2 +--R (- 3b c e + 10b c d e )x + (- 4b c e + 10b c d e )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2b e - 10b c d e + 20b c d e - 20b c d e + 10b c d e - 4b c d )x +--R + +--R 2 4 5 +--R - 2b c d +--R / +--R 3 5 2 4 4 +--R 2b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1726 +t0:=(d+e*x)^4/(b*x+c*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1726 +r0:=-d^4/(b^2*x)+e^4*x/c^2-(c*d-b*e)^4/(b^2*c^3*(b+c*x))-_ + 2*d^3*(c*d-2*b*e)*log(x)/b^3+2*(c*d-b*e)^3*(c*d+b*e)*log(b+c*x)/(b^3*c^3) +--R +--R +--R (2) +--R 4 4 3 2 3 4 3 5 4 2 +--R (- 2b c e + 4b c d e - 4b c d e + 2c d )x +--R + +--R 5 4 4 3 2 3 3 4 4 +--R (- 2b e + 4b c d e - 4b c d e + 2b c d )x +--R * +--R log(c x + b) +--R + +--R 4 3 5 4 2 2 3 3 4 4 3 2 4 3 +--R ((4b c d e - 2c d )x + (4b c d e - 2b c d )x)log(x) + b c e x +--R + +--R 4 4 2 5 4 4 3 3 2 2 2 2 3 3 4 4 2 3 4 +--R b c e x + (- b e + 4b c d e - 6b c d e + 4b c d e - 2b c d )x - b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 2 3 4 3 5 4 2 +--R (- 2b c e + 4b c d e - 4b c d e + 2c d )x +--R + +--R 5 4 4 3 2 3 3 4 4 +--R (- 2b e + 4b c d e - 4b c d e + 2b c d )x +--R * +--R log(c x + b) +--R + +--R 4 3 5 4 2 2 3 3 4 4 3 2 4 3 +--R ((4b c d e - 2c d )x + (4b c d e - 2b c d )x)log(x) + b c e x +--R + +--R 4 4 2 5 4 4 3 3 2 2 2 2 3 3 4 4 2 3 4 +--R b c e x + (- b e + 4b c d e - 6b c d e + 4b c d e - 2b c d )x - b c d +--R / +--R 3 4 2 4 3 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1726 +r0:=-d^3/(b^2*x)-(c*d-b*e)^3/(b^2*c^2*(b+c*x))-d^2*(2*c*d-3*b*e)*_ + log(x)/b^3+(c*d-b*e)^2*(2*c*d+b*e)*log(b+c*x)/(b^3*c^2) +--R +--R +--R (2) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((b c e - 3b c d e + 2c d )x + (b e - 3b c d e + 2b c d )x) +--R * +--R log(c x + b) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3b c d e - 2c d )x + (3b c d e - 2b c d )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (b e - 3b c d e + 3b c d e - 2b c d )x - b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((b c e - 3b c d e + 2c d )x + (b e - 3b c d e + 2b c d )x) +--R * +--R log(c x + b) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3b c d e - 2c d )x + (3b c d e - 2b c d )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (b e - 3b c d e + 3b c d e - 2b c d )x - b c d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1726 +r0:=-d^2/(b^2*x)-(c*d-b*e)^2/(b^2*c*(b+c*x))-2*d*(c*d-b*e)*log(x)/b^3+_ + 2*d*(c*d-b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- 2b c d e + 2c d )x + (- 2b c d e + 2b c d )x)log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((2b c d e - 2c d )x + (2b c d e - 2b c d )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- b e + 2b c d e - 2b c d )x - b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((- 2b c d e + 2c d )x + (- 2b c d e + 2b c d )x)log(c x + b) +--R + +--R 2 3 2 2 2 2 2 +--R ((2b c d e - 2c d )x + (2b c d e - 2b c d )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- b e + 2b c d e - 2b c d )x - b c d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1726 +t0:=(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1726 +r0:=-d/(b^2*x)+(-c*d+b*e)/(b^2*(b+c*x))-(2*c*d-b*e)*log(x)/b^3+_ + (2*c*d-b*e)*log(b+c*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R ((- b c e + 2c d)x + (- b e + 2b c d)x)log(c x + b) +--R + +--R 2 2 2 2 2 +--R ((b c e - 2c d)x + (b e - 2b c d)x)log(x) + (b e - 2b c d)x - b d +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((- b c e + 2c d)x + (- b e + 2b c d)x)log(c x + b) +--R + +--R 2 2 2 2 2 +--R ((b c e - 2c d)x + (b e - 2b c d)x)log(x) + (b e - 2b c d)x - b d +--R / +--R 3 2 4 +--R b c x + b x +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1726 +t0:=1/(b*x+c*x^2)^2 +--R +--R +--R 1 +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1726 +r0:=(-1)/(b^2*x)-c/(b^2*(b+c*x))-2*c*log(x)/b^3+2*c*log(b+c*x)/b^3 +--R +--R +--R 2 2 2 2 2 +--R (2c x + 2b c x)log(c x + b) + (- 2c x - 2b c x)log(x) - 2b c x - b +--R (2) --------------------------------------------------------------------- +--R 3 2 4 +--R b c x + b x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R (2c x + 2b c x)log(c x + b) + (- 2c x - 2b c x)log(x) - 2b c x - b +--R (3) --------------------------------------------------------------------- +--R 3 2 4 +--R b c x + b x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1726 +r0:=(-1)/(b^2*d*x)-c^2/(b^2*(c*d-b*e)*(b+c*x))-(2*c*d+b*e)*log(x)/_ + (b^3*d^2)+c^2*(2*c*d-3*b*e)*log(b+c*x)/(b^3*(c*d-b*e)^2)+_ + e^3*log(d+e*x)/(d^2*(c*d-b*e)^2) +--R +--R +--R (2) +--R 3 3 2 4 3 +--R (b c e x + b e x)log(e x + d) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((- 3b c d e + 2c d )x + (- 3b c d e + 2b c d )x)log(c x + b) +--R + +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((- b c e + 3b c d e - 2c d )x + (- b e + 3b c d e - 2b c d )x)log(x) +--R + +--R 3 2 2 2 2 3 3 4 2 3 2 2 2 3 +--R (- b c d e + 3b c d e - 2b c d )x - b d e + 2b c d e - b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 4 3 +--R (b c e x + b e x)log(e x + d) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((- 3b c d e + 2c d )x + (- 3b c d e + 2b c d )x)log(c x + b) +--R + +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((- b c e + 3b c d e - 2c d )x + (- b e + 3b c d e - 2b c d )x)log(x) +--R + +--R 3 2 2 2 2 3 3 4 2 3 2 2 2 3 +--R (- b c d e + 3b c d e - 2b c d )x - b d e + 2b c d e - b c d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R (b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1726 +r0:=(-1)/(b^2*d^2*x)-c^3/(b^2*(c*d-b*e)^2*(b+c*x))-e^3/(d^2*_ + (c*d-b*e)^2*(d+e*x))-2*(c*d+b*e)*log(x)/(b^3*d^3)+2*c^3*_ + (c*d-2*b*e)*log(b+c*x)/(b^3*(c*d-b*e)^3)+2*e^3*(2*c*d-b*e)*_ + log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2b c e - 4b c d e )x + (2b e - 2b c d e - 4b c d e )x +--R + +--R 5 4 4 2 3 +--R (2b d e - 4b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4b c d e - 2c d e)x + (4b c d e + 2b c d e - 2c d )x +--R + +--R 2 3 4 4 5 +--R (4b c d e - 2b c d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2b c e + 4b c d e - 4b c d e + 2c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2b e + 2b c d e + 4b c d e - 4b c d e - 2b c d e + 2c d )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2b d e + 4b c d e - 4b c d e + 2b c d )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2b c d e + 4b c d e - 4b c d e + 2b c d e)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2b d e + 3b c d e - 3b c d e + 2b c d )x - b d e + 3b c d e +--R + +--R 3 2 4 2 3 5 +--R - 3b c d e + b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2b c e - 4b c d e )x + (2b e - 2b c d e - 4b c d e )x +--R + +--R 5 4 4 2 3 +--R (2b d e - 4b c d e )x +--R * +--R log(e x + d) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4b c d e - 2c d e)x + (4b c d e + 2b c d e - 2c d )x +--R + +--R 2 3 4 4 5 +--R (4b c d e - 2b c d )x +--R * +--R log(c x + b) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2b c e + 4b c d e - 4b c d e + 2c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2b e + 2b c d e + 4b c d e - 4b c d e - 2b c d e + 2c d )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2b d e + 4b c d e - 4b c d e + 2b c d )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2b c d e + 4b c d e - 4b c d e + 2b c d e)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2b d e + 3b c d e - 3b c d e + 2b c d )x - b d e + 3b c d e +--R + +--R 3 2 4 2 3 5 +--R - 3b c d e + b c d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (b c d e - 3b c d e + 3b c d e - b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (b d e - 2b c d e + 2b c d e - b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (b d e - 3b c d e + 3b c d e - b c d )x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1726 +t0:=(d+e*x)^5/(b*x+c*x^2)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R (1) -------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1726 +r0:=-1/2*d^5/(b^3*x^2)+d^4*(3*c*d-5*b*e)/(b^4*x)+1/2*(c*d-b*e)^5/_ + (b^3*c^3*(b+c*x)^2)+(c*d-b*e)^4*(3*c*d+2*b*e)/(b^4*c^3*(b+c*x))+_ + d^3*(6*c^2*d^2-15*b*c*d*e+10*b^2*e^2)*log(x)/b^5-(c*d-b*e)^3*_ + (6*c^2*d^2+3*b*c*d*e+b^2*e^2)*log(b+c*x)/(b^5*c^3) +--R +--R +--R (2) +--R 5 2 5 2 5 3 2 6 4 7 5 4 +--R (2b c e - 20b c d e + 30b c d e - 12c d )x +--R + +--R 6 5 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 40b c d e + 60b c d e - 24b c d )x +--R + +--R 7 5 4 3 3 2 3 4 4 2 5 5 2 +--R (2b e - 20b c d e + 30b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (20b c d e - 30b c d e + 12c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (40b c d e - 60b c d e + 24b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (20b c d e - 30b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 6 5 5 2 4 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 10b c d e + 20b c d e - 30b c d e + 12b c d )x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (3b e - 5b c d e - 10b c d e + 30b c d e - 45b c d e + 18b c d )x +--R + +--R 4 3 4 3 4 5 4 3 5 +--R (- 10b c d e + 4b c d )x - b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 5 2 5 3 2 6 4 7 5 4 +--R (2b c e - 20b c d e + 30b c d e - 12c d )x +--R + +--R 6 5 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 40b c d e + 60b c d e - 24b c d )x +--R + +--R 7 5 4 3 3 2 3 4 4 2 5 5 2 +--R (2b e - 20b c d e + 30b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (20b c d e - 30b c d e + 12c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (40b c d e - 60b c d e + 24b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (20b c d e - 30b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 6 5 5 2 4 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 10b c d e + 20b c d e - 30b c d e + 12b c d )x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (3b e - 5b c d e - 10b c d e + 30b c d e - 45b c d e + 18b c d )x +--R + +--R 4 3 4 3 4 5 4 3 5 +--R (- 10b c d e + 4b c d )x - b c d +--R / +--R 5 5 4 6 4 3 7 3 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1726 +t0:=(d+e*x)^4/(b*x+c*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1726 +r0:=-1/2*d^4/(b^3*x^2)+d^3*(3*c*d-4*b*e)/(b^4*x)+1/2*(c*d-b*e)^4/_ + (b^3*c^2*(b+c*x)^2)+(c*d-b*e)^3*(3*c*d+b*e)/(b^4*c^2*(b+c*x))+_ + 6*d^2*(c*d-b*e)^2*log(x)/b^5-6*d^2*(c*d-b*e)^2*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 4 2 2 5 3 6 4 4 +--R (- 12b c d e + 24b c d e - 12c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (- 24b c d e + 48b c d e - 24b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (- 12b c d e + 24b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (12b c d e - 24b c d e + 12c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (24b c d e - 48b c d e + 24b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (12b c d e - 24b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 5 4 3 3 2 2 2 4 3 5 4 3 +--R (- 2b c e + 12b c d e - 24b c d e + 12b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- b e - 4b c d e + 18b c d e - 36b c d e + 18b c d )x +--R + +--R 4 2 3 3 3 4 4 2 4 +--R (- 8b c d e + 4b c d )x - b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 5 3 6 4 4 +--R (- 12b c d e + 24b c d e - 12c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (- 24b c d e + 48b c d e - 24b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (- 12b c d e + 24b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (12b c d e - 24b c d e + 12c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (24b c d e - 48b c d e + 24b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (12b c d e - 24b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 5 4 3 3 2 2 2 4 3 5 4 3 +--R (- 2b c e + 12b c d e - 24b c d e + 12b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- b e - 4b c d e + 18b c d e - 36b c d e + 18b c d )x +--R + +--R 4 2 3 3 3 4 4 2 4 +--R (- 8b c d e + 4b c d )x - b c d +--R / +--R 5 4 4 6 3 3 7 2 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1726 +r0:=-1/2*d^3/(b^3*x^2)+3*d^2*(c*d-b*e)/(b^4*x)+1/2*(c*d-b*e)^3/_ + (b^3*c*(b+c*x)^2)+3*d*(c*d-b*e)^2/(b^4*(b+c*x))+3*d*(c*d-b*e)*_ + (2*c*d-b*e)*log(x)/b^5-3*d*(c*d-b*e)*(2*c*d-b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 3 2 4 2 5 3 4 +--R (- 6b c d e + 18b c d e - 12c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12b c d e + 36b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6b c d e + 18b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6b c d e - 18b c d e + 12c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12b c d e - 36b c d e + 24b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6b c d e - 18b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6b c d e - 18b c d e + 12b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- b e + 9b c d e - 27b c d e + 18b c d )x + (- 6b c d e + 4b c d )x +--R + +--R 4 3 +--R - b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 5 3 4 +--R (- 6b c d e + 18b c d e - 12c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12b c d e + 36b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6b c d e + 18b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6b c d e - 18b c d e + 12c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12b c d e - 36b c d e + 24b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6b c d e - 18b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6b c d e - 18b c d e + 12b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- b e + 9b c d e - 27b c d e + 18b c d )x + (- 6b c d e + 4b c d )x +--R + +--R 4 3 +--R - b c d +--R / +--R 5 3 4 6 2 3 7 2 +--R 2b c x + 4b c x + 2b c x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2)^3 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1726 +r0:=-1/2*d^2/(b^3*x^2)+d*(3*c*d-2*b*e)/(b^4*x)+1/2*(c*d-b*e)^2/_ + (b^3*(b+c*x)^2)+(c*d-b*e)*(3*c*d-b*e)/(b^4*(b+c*x))+(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)*log(x)/b^5-(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*_ + log(b+c*x)/b^5 +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 +--R (- 2b c e + 12b c d e - 12c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 4b c e + 24b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 2b e + 12b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R (2b c e - 12b c d e + 12c d )x + (4b c e - 24b c d e + 24b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (2b e - 12b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (2b c e - 12b c d e + 12b c d )x + (3b e - 18b c d e + 18b c d )x +--R + +--R 4 3 2 4 2 +--R (- 4b d e + 4b c d )x - b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 4 +--R (- 2b c e + 12b c d e - 12c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 4b c e + 24b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 2b e + 12b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R (2b c e - 12b c d e + 12c d )x + (4b c e - 24b c d e + 24b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (2b e - 12b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (2b c e - 12b c d e + 12b c d )x + (3b e - 18b c d e + 18b c d )x +--R + +--R 4 3 2 4 2 +--R (- 4b d e + 4b c d )x - b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1726 +t0:=(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1726 +r0:=-1/2*d/(b^3*x^2)+(3*c*d-b*e)/(b^4*x)+1/2*c*(c*d-b*e)/(b^3*(b+c*x)^2)+_ + c*(3*c*d-2*b*e)/(b^4*(b+c*x))+3*c*(2*c*d-b*e)*log(x)/b^5-_ + 3*c*(2*c*d-b*e)*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 3 2 2 2 +--R ((6b c e - 12c d)x + (12b c e - 24b c d)x + (6b c e - 12b c d)x ) +--R * +--R log(c x + b) +--R + +--R 3 4 4 2 2 3 3 +--R (- 6b c e + 12c d)x + (- 12b c e + 24b c d)x +--R + +--R 3 2 2 2 +--R (- 6b c e + 12b c d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 6b c e + 12b c d)x + (- 9b c e + 18b c d)x + (- 2b e + 4b c d)x - b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 2 2 3 3 3 2 2 2 +--R ((6b c e - 12c d)x + (12b c e - 24b c d)x + (6b c e - 12b c d)x ) +--R * +--R log(c x + b) +--R + +--R 3 4 4 2 2 3 3 +--R (- 6b c e + 12c d)x + (- 12b c e + 24b c d)x +--R + +--R 3 2 2 2 +--R (- 6b c e + 12b c d)x +--R * +--R log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 6b c e + 12b c d)x + (- 9b c e + 18b c d)x + (- 2b e + 4b c d)x - b d +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1726 +t0:=1/(b*x+c*x^2)^3 +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1726 +r0:=(-1/2)/(b^3*x^2)+3*c/(b^4*x)+1/2*c^2/(b^3*(b+c*x)^2)+3*c^2/_ + (b^4*(b+c*x))+6*c^2*log(x)/b^5-6*c^2*log(b+c*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 +--R (- 12c x - 24b c x - 12b c x )log(c x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12c x + 24b c x + 12b c x )log(x) + 12b c x + 18b c x + 4b c x - b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 +--R (- 12c x - 24b c x - 12b c x )log(c x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12c x + 24b c x + 12b c x )log(x) + 12b c x + 18b c x + 4b c x - b +--R / +--R 5 2 4 6 3 7 2 +--R 2b c x + 4b c x + 2b x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 3 7 2 3 6 2 2 5 3 2 4 3 3 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1726 +r0:=(-1/2)/(b^3*d*x^2)+(3*c*d+b*e)/(b^4*d^2*x)+1/2*c^3/(b^3*(c*d-b*e)*_ + (b+c*x)^2)+c^3*(3*c*d-4*b*e)/(b^4*(c*d-b*e)^2*(b+c*x))+_ + (6*c^2*d^2+3*b*c*d*e+b^2*e^2)*log(x)/(b^5*d^3)-c^3*(6*c^2*d^2-_ + 15*b*c*d*e+10*b^2*e^2)*log(b+c*x)/(b^5*(c*d-b*e)^3)+e^5*_ + log(d+e*x)/(d^3*(c*d-b*e)^3) +--R +--R +--R (2) +--R 5 2 5 4 6 5 3 7 5 2 +--R (- 2b c e x - 4b c e x - 2b e x )log(e x + d) +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (20b c d e - 30b c d e + 12c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (40b c d e - 60b c d e + 24b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (20b c d e - 30b c d e + 12b c d )x +--R * +--R log(c x + b) +--R + +--R 5 2 5 2 5 3 2 6 4 7 5 4 +--R (2b c e - 20b c d e + 30b c d e - 12c d )x +--R + +--R 6 5 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 40b c d e + 60b c d e - 24b c d )x +--R + +--R 7 5 4 3 3 2 3 4 4 2 5 5 2 +--R (2b e - 20b c d e + 30b c d e - 12b c d )x +--R * +--R log(x) +--R + +--R 5 2 4 3 4 3 2 2 5 4 6 5 3 +--R (2b c d e - 20b c d e + 30b c d e - 12b c d )x +--R + +--R 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (4b c d e - b c d e - 30b c d e + 45b c d e - 18b c d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (2b d e - 2b c d e - 6b c d e + 10b c d e - 4b c d )x - b d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R 3b c d e - 3b c d e + b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 5 4 6 5 3 7 5 2 +--R (- 2b c e x - 4b c e x - 2b e x )log(e x + d) +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (20b c d e - 30b c d e + 12c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (40b c d e - 60b c d e + 24b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (20b c d e - 30b c d e + 12b c d )x +--R * +--R log(c x + b) +--R + +--R 5 2 5 2 5 3 2 6 4 7 5 4 +--R (2b c e - 20b c d e + 30b c d e - 12c d )x +--R + +--R 6 5 3 4 3 2 2 5 4 6 5 3 +--R (4b c e - 40b c d e + 60b c d e - 24b c d )x +--R + +--R 7 5 4 3 3 2 3 4 4 2 5 5 2 +--R (2b e - 20b c d e + 30b c d e - 12b c d )x +--R * +--R log(x) +--R + +--R 5 2 4 3 4 3 2 2 5 4 6 5 3 +--R (2b c d e - 20b c d e + 30b c d e - 12b c d )x +--R + +--R 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (4b c d e - b c d e - 30b c d e + 45b c d e - 18b c d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (2b d e - 2b c d e - 6b c d e + 10b c d e - 4b c d )x - b d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R 3b c d e - 3b c d e + b c d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (2b c d e - 6b c d e + 6b c d e - 2b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (2b d e - 6b c d e + 6b c d e - 2b c d )x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1726 +r0:=(-1/2)/(b^3*d^2*x^2)+(3*c*d+2*b*e)/(b^4*d^3*x)+1/2*c^4/(b^3*_ + (c*d-b*e)^2*(b+c*x)^2)+c^4*(3*c*d-5*b*e)/(b^4*(c*d-b*e)^3*_ + (b+c*x))-e^5/(d^3*(c*d-b*e)^3*(d+e*x))+3*(2*c^2*d^2+2*b*c*d*e+_ + b^2*e^2)*log(x)/(b^5*d^4)-3*c^4*(2*c^2*d^2-6*b*c*d*e+5*b^2*e^2)*_ + log(b+c*x)/(b^5*(c*d-b*e)^4)+3*e^5*(2*c*d-b*e)*log(d+e*x)/_ + (d^4*(c*d-b*e)^4) +--R +--R +--R (2) +--R 6 2 7 5 3 6 5 7 7 6 2 6 5 3 2 5 4 +--R (- 6b c e + 12b c d e )x + (- 12b c e + 18b c d e + 12b c d e )x +--R + +--R 8 7 6 2 2 5 3 8 6 7 2 5 2 +--R (- 6b e + 24b c d e )x + (- 6b d e + 12b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 4 3 7 5 2 8 6 5 +--R (- 30b c d e + 36b c d e - 12c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (- 60b c d e + 42b c d e + 12b c d e - 12c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (- 30b c d e - 24b c d e + 60b c d e - 24b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (- 30b c d e + 36b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 4 3 7 5 2 8 6 5 +--R (6b c e - 12b c d e + 30b c d e - 36b c d e + 12c d e)x +--R + +--R 7 7 6 2 6 5 3 2 5 3 5 4 3 2 6 5 2 +--R 12b c e - 18b c d e - 12b c d e + 60b c d e - 42b c d e +--R + +--R 7 6 8 7 +--R - 12b c d e + 12c d +--R * +--R 4 +--R x +--R + +--R 8 7 6 2 2 5 4 4 4 3 3 5 5 2 2 6 6 +--R 6b e - 24b c d e + 30b c d e + 24b c d e - 60b c d e +--R + +--R 7 7 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 4 4 5 2 3 5 6 2 6 7 2 +--R (6b d e - 12b c d e + 30b c d e - 36b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 2 5 3 5 4 3 2 6 5 2 7 6 4 +--R (6b c d e - 12b c d e + 30b c d e - 36b c d e + 12b c d e)x +--R + +--R 7 6 6 2 2 5 5 3 3 4 4 4 4 3 3 5 5 2 +--R 12b c d e - 21b c d e - 6b c d e + 45b c d e - 24b c d e +--R + +--R 2 6 6 7 7 +--R - 18b c d e + 12b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R 6b d e - 6b c d e - 13b c d e + 12b c d e + 33b c d e +--R + +--R 3 5 6 2 6 7 +--R - 50b c d e + 18b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 5 7 +--R (3b d e - 8b c d e + 2b c d e + 12b c d e - 13b c d e + 4b c d )x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - b d e + 4b c d e - 6b c d e + 4b c d e - b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 7 5 3 6 5 7 7 6 2 6 5 3 2 5 4 +--R (- 6b c e + 12b c d e )x + (- 12b c e + 18b c d e + 12b c d e )x +--R + +--R 8 7 6 2 2 5 3 8 6 7 2 5 2 +--R (- 6b e + 24b c d e )x + (- 6b d e + 12b c d e )x +--R * +--R log(e x + d) +--R + +--R 2 6 4 3 7 5 2 8 6 5 +--R (- 30b c d e + 36b c d e - 12c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (- 60b c d e + 42b c d e + 12b c d e - 12c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (- 30b c d e - 24b c d e + 60b c d e - 24b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (- 30b c d e + 36b c d e - 12b c d )x +--R * +--R log(c x + b) +--R + +--R 6 2 7 5 3 6 2 6 4 3 7 5 2 8 6 5 +--R (6b c e - 12b c d e + 30b c d e - 36b c d e + 12c d e)x +--R + +--R 7 7 6 2 6 5 3 2 5 3 5 4 3 2 6 5 2 +--R 12b c e - 18b c d e - 12b c d e + 60b c d e - 42b c d e +--R + +--R 7 6 8 7 +--R - 12b c d e + 12c d +--R * +--R 4 +--R x +--R + +--R 8 7 6 2 2 5 4 4 4 3 3 5 5 2 2 6 6 +--R 6b e - 24b c d e + 30b c d e + 24b c d e - 60b c d e +--R + +--R 7 7 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 4 4 5 2 3 5 6 2 6 7 2 +--R (6b d e - 12b c d e + 30b c d e - 36b c d e + 12b c d )x +--R * +--R log(x) +--R + +--R 6 2 6 5 3 2 5 3 5 4 3 2 6 5 2 7 6 4 +--R (6b c d e - 12b c d e + 30b c d e - 36b c d e + 12b c d e)x +--R + +--R 7 6 6 2 2 5 5 3 3 4 4 4 4 3 3 5 5 2 +--R 12b c d e - 21b c d e - 6b c d e + 45b c d e - 24b c d e +--R + +--R 2 6 6 7 7 +--R - 18b c d e + 12b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R 6b d e - 6b c d e - 13b c d e + 12b c d e + 33b c d e +--R + +--R 3 5 6 2 6 7 +--R - 50b c d e + 18b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 5 7 +--R (3b d e - 8b c d e + 2b c d e + 12b c d e - 13b c d e + 4b c d )x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - b d e + 4b c d e - 6b c d e + 4b c d e - b c d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (2b c d e - 8b c d e + 12b c d e - 8b c d e + 2b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 5 6 9 4 +--R (4b c d e - 14b c d e + 16b c d e - 4b c d e - 4b c d e + 2b c d )x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 6 5 9 3 +--R (2b d e - 4b c d e - 4b c d e + 16b c d e - 14b c d e + 4b c d )x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2)^(1/2) +--R +--R +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (1) (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1726 +r0:=1/240*e*(132*c^2*d^2-132*b*c*d*e+35*b^2*e^2)*(b*x+c*x^2)^(3/2)/c^3+_ + 1/5*e*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c+1/40*e*(d*(10*c*d-3*b*e)+_ + 7*e*(2*c*d-b*e)*x)*(b*x+c*x^2)^(3/2)/c^2-1/128*b^2*(2*c*d-b*e)*_ + (16*c^2*d^2-16*b*c*d*e+7*b^2*e^2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + c^(9/2)+1/128*b*(2*c*d-b*e)*(16*c^2*d^2-16*b*c*d*e+7*b^2*e^2)*_ + sqrt(b*x+c*x^2)/c^4+1/64*(2*c*d-b*e)*(16*c^2*d^2-16*b*c*d*e+_ + 7*b^2*e^2)*x*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R +-+ +--R 5 3 4 2 3 2 2 2 3 3 x\|c +--R (105b e - 450b c d e + 720b c d e - 480b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 3 4 3 3 4 2 3 +--R 384c e x + (48b c e + 1440c d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 56b c e + 240b c d e + 1920c d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (70b c e - 300b c d e + 480b c d e + 960c d )x - 105b e +--R + +--R 3 2 2 2 2 3 3 +--R 450b c d e - 720b c d e + 480b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 1920c \|c +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 3 4 2 3 2 2 2 3 3 +--R (105b e - 450b c d e + 720b c d e - 480b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 3 4 3 3 4 2 3 +--R 768c e x + (96b c e + 2880c d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 112b c e + 480b c d e + 3840c d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (140b c e - 600b c d e + 960b c d e + 1920c d )x - 210b e +--R + +--R 3 2 2 2 2 3 3 +--R 900b c d e - 1440b c d e + 960b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 3840c \|c +--R , +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R (105b e - 450b c d e + 720b c d e - 480b c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 3 4 3 3 4 2 3 +--R 384c e x + (48b c e + 1440c d e )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- 56b c e + 240b c d e + 1920c d e)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (70b c e - 300b c d e + 480b c d e + 960c d )x - 105b e +--R + +--R 3 2 2 2 2 3 3 +--R 450b c d e - 720b c d e + 480b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 1920c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 288 + +--S 289 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 3 4 2 3 2 2 2 3 3 +--R (7b e - 30b c d e + 48b c d e - 32b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 5 3 4 2 3 2 2 2 3 3 x\|c +--R (- 14b e + 60b c d e - 96b c d e + 64b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 3 4 2 3 2 2 2 3 3 +---+ x\|c +--R (- 7b e + 30b c d e - 48b c d e + 32b c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 5 3 4 2 3 2 2 2 3 3 +-+ \|- c \|c x + b x +--R (7b e - 30b c d e + 48b c d e - 32b c d )\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2)^(1/2) +--R +--R +--R +----------+ +--R 2 2 2 | 2 +--R (1) (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1726 +r0:=5/24*e*(2*c*d-b*e)*(b*x+c*x^2)^(3/2)/c^2+1/4*e*(d+e*x)*_ + (b*x+c*x^2)^(3/2)/c-1/64*b^2*(16*c^2*d^2-16*b*c*d*e+5*b^2*e^2)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(16*c^2*d^2-_ + 16*b*c*d*e+5*b^2*e^2)*sqrt(b*x+c*x^2)/c^3+1/32*(16*c^2*d^2-_ + 16*b*c*d*e+5*b^2*e^2)*x*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 4 2 3 2 2 2 x\|c +--R (- 15b e + 48b c d e - 48b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 3 2 3 2 2 3 2 +--R 48c e x + (8b c e + 128c d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 10b c e + 32b c d e + 96c d )x + 15b e - 48b c d e + 48b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 192c \|c +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 2 3 2 2 2 | 2 +-+ +--R (15b e - 48b c d e + 48b c d )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 3 2 3 2 2 3 2 +--R 96c e x + (16b c e + 256c d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 20b c e + 64b c d e + 192c d )x + 30b e - 96b c d e + 96b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 384c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 4 2 3 2 2 2 \|- c \|c x + b x +--R (- 15b e + 48b c d e - 48b c d )atan(-------------------) +--R c x +--R + +--R 3 2 3 2 2 3 2 +--R 48c e x + (8b c e + 128c d e)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (- 10b c e + 32b c d e + 96c d )x + 15b e - 48b c d e + 48b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 192c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 295 + +--S 296 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 4 2 3 2 2 2 | 2 +-+ +--R (5b e - 16b c d e + 16b c d )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 4 2 3 2 2 2 x\|c +--R (10b e - 32b c d e + 32b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 4 2 3 2 2 2 +---+ x\|c +--R (5b e - 16b c d e + 16b c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 4 2 3 2 2 2 +-+ \|- c \|c x + b x +--R (- 5b e + 16b c d e - 16b c d )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 299 + +)clear all + +--S 300 of 1726 +t0:=(d+e*x)*(b*x+c*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (1) (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1726 +r0:=1/3*e*(b*x+c*x^2)^(3/2)/c-1/8*b^2*(2*c*d-b*e)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(5/2)+1/8*b*(2*c*d-b*e)*sqrt(b*x+c*x^2)/c^2+_ + 1/4*(2*c*d-b*e)*x*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 3 2 x\|c +--R (3b e - 6b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (8c e x + (2b c e + 12c d)x - 3b e + 6b c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 3 2 | 2 +-+ +--R (3b e - 6b c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 2 2 +-+ | 2 +--R (16c e x + (4b c e + 24c d)x - 6b e + 12b c d)\|c \|c x + b x +--R / +--R 2 +-+ +--R 48c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 3 2 \|- c \|c x + b x +--R (3b e - 6b c d)atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 2 2 +---+ | 2 +--R (8c e x + (2b c e + 12c d)x - 3b e + 6b c d)\|- c \|c x + b x +--R / +--R 2 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 302 + +--S 303 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 3 2 | 2 +-+ +--R (b e - 2b c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 2 x\|c +--R (- 2b e + 4b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 3 2 +---+ x\|c +--R (- b e + 2b c d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 3 2 +-+ \|- c \|c x + b x +--R (b e - 2b c d)\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 1726 +t0:=(b*x+c*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (1) \|c x + b x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1726 +r0:=-1/4*b^2*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+_ + 1/4*b*sqrt(b*x+c*x^2)/c+1/2*x*sqrt(b*x+c*x^2) +--R +--R +--R +-+ +----------+ +--R 2 x\|c +-+ | 2 +--R - b atanh(-------------) + (2c x + b)\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ------------------------------------------------------ +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R 2 | 2 +-+ +-+ | 2 +--R b log(- 2c\|c x + b x + (2c x + b)\|c ) + (4c x + 2b)\|c \|c x + b x +--R [------------------------------------------------------------------------, +--R +-+ +--R 8c\|c +--R +----------+ +--R +---+ | 2 +----------+ +--R 2 \|- c \|c x + b x +---+ | 2 +--R - b atan(-------------------) + (2c x + b)\|- c \|c x + b x +--R c x +--R -------------------------------------------------------------] +--R +---+ +--R 4c\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 309 + +--S 310 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 2 | 2 +-+ 2 x\|c +--R b log(- 2c\|c x + b x + (2c x + b)\|c ) + 2b atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) ------------------------------------------------------------------- +--R +-+ +--R 8c\|c +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 2 +---+ x\|c 2 +-+ \|- c \|c x + b x +--R b \|- c atanh(-------------) - b \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R 4c\|- c \|c +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 313 + +)clear all + +--S 314 of 1726 +t0:=(b*x+c*x^2)^(1/2)/(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ------------- +--R e x + d +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1726 +r0:=-(2*c*d-b*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^2*sqrt(c))+_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^2+sqrt(b*x+c*x^2)/e +--R +--R +--R (2) +--R +-+ +--R x\|c +--R (b e - 2c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R - \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-+ | 2 +--R e\|c \|c x + b x +--R / +--R 2 +-+ +--R e \|c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R | 2 +-+ +--R 2\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R +----------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R (b e - 2c d)log(2c\|c x + b x + (2c x + b)\|c ) + 2e\|c \|c x + b x +--R / +--R 2 +-+ +--R 2e \|c +--R , +--R +--R +----------+ +--R | 2 +-+ +--R (b e - 2c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +------------+ | 2 +----------+ +--R +-+ | 2 d\|c x + b x +-+ | 2 +--R 4\|c \|b d e - c d atan(----------------) + 2e\|c \|c x + b x +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 +-+ +--R 2e \|c +--R , +--R +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R +----------+ +--R +---+ | 2 +----------+ +--R \|- c \|c x + b x +---+ | 2 +--R (b e - 2c d)atan(-------------------) + e\|- c \|c x + b x +--R c x +--R / +--R 2 +---+ +--R e \|- c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R (b e - 2c d)atan(-------------------) +--R c x +--R + +--R +----------+ +--R +------------+ | 2 +----------+ +--R +---+ | 2 d\|c x + b x +---+ | 2 +--R 2\|- c \|b d e - c d atan(----------------) + e\|- c \|c x + b x +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 +---+ +--R e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 316 + +--S 317 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-+ +--R 2\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R +----------+ +--R | 2 +-+ +--R (b e - 2c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R x\|c +--R (- 2b e + 4c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R 2\|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 +-+ +--R 2e \|c +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +--R | 2 +-+ +--R (b e - 2c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R x\|c +--R (- 2b e + 4c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R 2\|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R 4\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 +-+ +--R 2e \|c +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1726 +t0:=(b*x+c*x^2)^(1/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1726 +r0:=2*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^2-1/2*(2*c*d-b*e)*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(e^2*sqrt(d)*sqrt(c*d-b*e))-sqrt(b*x+c*x^2)/(e*(d+e*x)) +--R +--R +--R (2) +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R (4e x + 4d)\|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +--R ((- b e + 2c d e)x - b d e + 2c d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R - 2e\|- b e + c d \|d \|c x + b x +--R / +--R 3 2 +-----------+ +-+ +--R (2e x + 2d e )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R (2e x + 2d)\|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 +--R ((b e - 2c d e)x + b d e - 2c d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2e\|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 3 2 | 2 +--R (2e x + 2d e )\|- b d e + c d +--R , +--R +--R +------------+ +----------+ +--R +-+ | 2 +-+ | 2 +--R (e x + d)\|c \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 2 \|b d e - c d \|c x + b x +--R ((- b e + 2c d e)x - b d e + 2c d )atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R - e\|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 3 2 | 2 +--R (e x + d e )\|b d e - c d +--R , +--R +--R 2 2 +--R ((b e - 2c d e)x + b d e - 2c d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R (4e x + 4d)\|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2e\|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 3 2 | 2 +--R (2e x + 2d e )\|- b d e + c d +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 2 \|b d e - c d \|c x + b x +--R ((- b e + 2c d e)x - b d e + 2c d )atan(----------------------------) +--R (b e - c d)x +--R + +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R (2e x + 2d)\|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R - e\|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 3 2 | 2 +--R (e x + d e )\|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 323 + +--S 324 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-----------+ +-+ +-+ +--R 2\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R +-----------+ +-+ +--R (b e - 2c d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +-+ +--R | 2 +-----------+ +-+ +-+ x\|c +--R - 4\|- b d e + c d \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R (b e - 2c d)\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R 2e \|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +----------+ +--R +-----------+ +-+ +-+ | 2 +-+ | 2 +--R 2\|- b e + c d \|c \|d \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R +------------+ +-+ +--R +-----------+ +-+ +-+ | 2 x\|c +--R - 4\|- b e + c d \|c \|d \|b d e - c d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R (b e - 2c d)\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 2b e + 4c d)\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R 2e \|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1726 +t0:=(b*x+c*x^2)^(1/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1726 +r0:=-1/8*b^2*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+1/4*(b*d+_ + (2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^2) +--R +--R +--R (2) +--R 2 2 2 2 2 2 (b e - 2c d)x - b d +--R (- b e x - 2b d e x - b d )atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R ((2b e - 4c d)x - 2b d)\|- b e + c d \|d \|c x + b x +--R / +--R 3 2 2 2 2 2 3 3 4 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e)x + 8b d e - 8c d ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 2 2 +--R (b e x + 2b d e x + b d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R ((2b e - 4c d)x - 2b d)\|- b d e + c d \|c x + b x +--R / +--R 3 2 2 2 2 2 3 3 4 +--R ((8b d e - 8c d e )x + (16b d e - 16c d e)x + 8b d e - 8c d ) +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 2 2 2 2 2 \|b d e - c d \|c x + b x +--R (- b e x - 2b d e x - b d )atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R ((b e - 2c d)x - b d)\|b d e - c d \|c x + b x +--R / +--R 3 2 2 2 2 2 3 3 4 +--R ((4b d e - 4c d e )x + (8b d e - 8c d e)x + 4b d e - 4c d ) +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 330 + +--S 331 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R b \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R b \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (8b d e - 8c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R b \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R - 2b \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (8b d e - 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 334 + +)clear all + +--S 335 of 1726 +t0:=(b*x+c*x^2)^(1/2)/(d+e*x)^4 +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1726 +r0:=-1/3*e*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^3)-1/16*b^2*_ + (2*c*d-b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 1/8*(2*c*d-b*e)*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^2*_ + (c*d-b*e)^2*(d+e*x)^2) +--R +--R +--R (2) +--R 3 4 2 3 3 3 3 2 2 2 2 +--R (- 3b e + 6b c d e )x + (- 9b d e + 18b c d e )x +--R + +--R 3 2 2 2 3 3 3 2 4 +--R (- 9b d e + 18b c d e)x - 3b d e + 6b c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (6b e - 8b c d e + 8c d e)x + (16b d e - 28b c d e + 24c d )x +--R + +--R 2 2 3 +--R - 6b d e + 12b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 2 3 3 3 3 2 2 2 2 +--R (3b e - 6b c d e )x + (9b d e - 18b c d e )x +--R + +--R 3 2 2 2 3 3 3 2 4 +--R (9b d e - 18b c d e)x + 3b d e - 6b c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (6b e - 8b c d e + 8c d e)x + (16b d e - 28b c d e + 24c d )x +--R + +--R 2 2 3 +--R - 6b d e + 12b c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (48b d e - 96b c d e + 48c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (144b d e - 288b c d e + 144c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (144b d e - 288b c d e + 144c d e)x + 48b d e - 96b c d e + 48c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 3 4 2 3 3 3 3 2 2 2 2 +--R (- 3b e + 6b c d e )x + (- 9b d e + 18b c d e )x +--R + +--R 3 2 2 2 3 3 3 2 4 +--R (- 9b d e + 18b c d e)x - 3b d e + 6b c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (3b e - 4b c d e + 4c d e)x + (8b d e - 14b c d e + 12c d )x +--R + +--R 2 2 3 +--R - 3b d e + 6b c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R / +--R 2 2 5 3 4 2 4 3 3 +--R (24b d e - 48b c d e + 24c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (72b d e - 144b c d e + 72c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 2 7 +--R (72b d e - 144b c d e + 72c d e)x + 24b d e - 48b c d e + 24c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 337 + +--S 338 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R (b e - 2b c d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 | 2 (b e - 2c d)x - b d +--R (b e - 2b c d)\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (16b d e - 32b c d e + 16c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 | 2 (b e - 2c d)x - b d +--R (b e - 2b c d)\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 3 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 2b e + 4b c d)\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (16b d e - 32b c d e + 16c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 341 + +)clear all + +--S 342 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1726 +r0:=1/64*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*x*(b*x+_ + c*x^2)^(3/2)/c^3+1/840*e*(244*c^2*d^2-244*b*c*d*e+63*b^2*_ + e^2)*(b*x+c*x^2)^(5/2)/c^3+1/7*e*(d+e*x)^2*(b*x+c*x^2)^(5/2)/_ + c+1/84*e*(d*(14*c*d-5*b*e)+9*e*(2*c*d-b*e)*x)*(b*x+c*x^2)^(5/2)/_ + c^2+3/1024*b^4*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-3/1024*b^3*(2*c*d-_ + b*e)*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*sqrt(b*x+c*x^2)/c^5+_ + 1/512*b^2*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*x*_ + sqrt(b*x+c*x^2)/c^4+1/128*b*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+_ + 3*b^2*e^2)*x^2*sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R +-+ +--R 7 3 6 2 5 2 2 4 3 3 x\|c +--R (- 315b e + 1470b c d e - 2520b c d e + 1680b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 3 6 5 3 6 2 5 +--R 5120c e x + (6400b c e + 17920c d e )x +--R + +--R 2 4 3 5 2 6 2 4 +--R (128b c e + 23296b c d e + 21504c d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 144b c e + 672b c d e + 29568b c d e + 8960c d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (168b c e - 784b c d e + 1344b c d e + 13440b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 210b c e + 980b c d e - 1680b c d e + 1120b c d )x + 315b e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 1470b c d e + 2520b c d e - 1680b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 35840c \|c +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 3 6 2 5 2 2 4 3 3 +--R (315b e - 1470b c d e + 2520b c d e - 1680b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 3 6 5 3 6 2 5 +--R 10240c e x + (12800b c e + 35840c d e )x +--R + +--R 2 4 3 5 2 6 2 4 +--R (256b c e + 46592b c d e + 43008c d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 288b c e + 1344b c d e + 59136b c d e + 17920c d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (336b c e - 1568b c d e + 2688b c d e + 26880b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 420b c e + 1960b c d e - 3360b c d e + 2240b c d )x + 630b e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 2940b c d e + 5040b c d e - 3360b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 71680c \|c +--R , +--R +--R 7 3 6 2 5 2 2 4 3 3 +--R (- 315b e + 1470b c d e - 2520b c d e + 1680b c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 6 3 6 5 3 6 2 5 +--R 5120c e x + (6400b c e + 17920c d e )x +--R + +--R 2 4 3 5 2 6 2 4 +--R (128b c e + 23296b c d e + 21504c d e)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 144b c e + 672b c d e + 29568b c d e + 8960c d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (168b c e - 784b c d e + 1344b c d e + 13440b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 210b c e + 980b c d e - 1680b c d e + 1120b c d )x + 315b e +--R + +--R 5 2 4 2 2 3 3 3 +--R - 1470b c d e + 2520b c d e - 1680b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 35840c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 344 + +--S 345 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 7 3 6 2 5 2 2 4 3 3 +--R (9b e - 42b c d e + 72b c d e - 48b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 7 3 6 2 5 2 2 4 3 3 x\|c +--R (18b e - 84b c d e + 144b c d e - 96b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 7 3 6 2 5 2 2 4 3 3 +---+ x\|c +--R (9b e - 42b c d e + 72b c d e - 48b c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 7 3 6 2 5 2 2 4 3 3 +-+ \|- c \|c x + b x +--R (- 9b e + 42b c d e - 72b c d e + 48b c d )\|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (1) (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1726 +r0:=1/96*(24*c^2*d^2-24*b*c*d*e+7*b^2*e^2)*x*(b*x+c*x^2)^(3/2)/c^2+_ + 7/60*e*(2*c*d-b*e)*(b*x+c*x^2)^(5/2)/c^2+1/6*e*(d+e*x)*(b*x+_ + c*x^2)^(5/2)/c+1/512*b^4*(24*c^2*d^2-24*b*c*d*e+7*b^2*e^2)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*(24*c^2*d^2-_ + 24*b*c*d*e+7*b^2*e^2)*sqrt(b*x+c*x^2)/c^4+1/768*b^2*(24*c^2*d^2-_ + 24*b*c*d*e+7*b^2*e^2)*x*sqrt(b*x+c*x^2)/c^3+1/192*b*(24*c^2*d^2-_ + 24*b*c*d*e+7*b^2*e^2)*x^2*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 6 2 5 4 2 2 x\|c +--R (105b e - 360b c d e + 360b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 2 5 4 2 5 4 +--R 1280c e x + (1664b c e + 3072c d e)x +--R + +--R 2 3 2 4 5 2 3 +--R (48b c e + 4224b c d e + 1920c d )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 56b c e + 192b c d e + 2880b c d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (70b c e - 240b c d e + 240b c d )x - 105b e + 360b c d e - 360b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 7680c \|c +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 6 2 5 4 2 2 | 2 +-+ +--R (105b e - 360b c d e + 360b c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 2 5 4 2 5 4 +--R 2560c e x + (3328b c e + 6144c d e)x +--R + +--R 2 3 2 4 5 2 3 +--R (96b c e + 8448b c d e + 3840c d )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 112b c e + 384b c d e + 5760b c d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 +--R (140b c e - 480b c d e + 480b c d )x - 210b e + 720b c d e +--R + +--R 3 2 2 +--R - 720b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 15360c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 6 2 5 4 2 2 \|- c \|c x + b x +--R (105b e - 360b c d e + 360b c d )atan(-------------------) +--R c x +--R + +--R 5 2 5 4 2 5 4 +--R 1280c e x + (1664b c e + 3072c d e)x +--R + +--R 2 3 2 4 5 2 3 +--R (48b c e + 4224b c d e + 1920c d )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 56b c e + 192b c d e + 2880b c d )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 +--R (70b c e - 240b c d e + 240b c d )x - 105b e + 360b c d e +--R + +--R 3 2 2 +--R - 360b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 7680c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 351 + +--S 352 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 6 2 5 4 2 2 | 2 +-+ +--R (7b e - 24b c d e + 24b c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 6 2 5 4 2 2 x\|c +--R (- 14b e + 48b c d e - 48b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 6 2 5 4 2 2 +---+ x\|c +--R (- 7b e + 24b c d e - 24b c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 6 2 5 4 2 2 +-+ \|- c \|c x + b x +--R (7b e - 24b c d e + 24b c d )\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1726 +t0:=(d+e*x)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 | 2 +--R (1) (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1726 +r0:=1/8*(2*c*d-b*e)*x*(b*x+c*x^2)^(3/2)/c+1/5*e*(b*x+c*x^2)^(5/2)/c+_ + 3/128*b^4*(2*c*d-b*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-_ + 3/128*b^3*(2*c*d-b*e)*sqrt(b*x+c*x^2)/c^3+1/64*b^2*(2*c*d-b*e)*_ + x*sqrt(b*x+c*x^2)/c^2+1/16*b*(2*c*d-b*e)*x^2*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 5 4 x\|c +--R (- 15b e + 30b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 3 4 3 2 2 3 2 +--R 128c e x + (176b c e + 160c d)x + (8b c e + 240b c d)x +--R + +--R 3 2 2 4 3 +--R (- 10b c e + 20b c d)x + 15b e - 30b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 640c \|c +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 5 4 | 2 +-+ +--R (15b e - 30b c d)log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 4 3 4 3 2 2 3 2 +--R 256c e x + (352b c e + 320c d)x + (16b c e + 480b c d)x +--R + +--R 3 2 2 4 3 +--R (- 20b c e + 40b c d)x + 30b e - 60b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 1280c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 5 4 \|- c \|c x + b x +--R (- 15b e + 30b c d)atan(-------------------) +--R c x +--R + +--R 4 4 3 4 3 2 2 3 2 +--R 128c e x + (176b c e + 160c d)x + (8b c e + 240b c d)x +--R + +--R 3 2 2 4 3 +--R (- 10b c e + 20b c d)x + 15b e - 30b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 640c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 358 + +--S 359 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 5 4 | 2 +-+ +--R (3b e - 6b c d)log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 5 4 x\|c +--R (6b e - 12b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 256c \|c +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 4 +---+ x\|c +--R (3b e - 6b c d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 5 4 +-+ \|- c \|c x + b x +--R (- 3b e + 6b c d)\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 128c \|- c \|c +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 1726 +t0:=(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (1) (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1726 +r0:=1/4*x*(b*x+c*x^2)^(3/2)+3/64*b^4*atanh(x*sqrt(c)/sqrt(b*x+_ + c*x^2))/c^(5/2)-3/64*b^3*sqrt(b*x+c*x^2)/c^2+1/32*b^2*x*_ + sqrt(b*x+c*x^2)/c+1/8*b*x^2*sqrt(b*x+c*x^2) +--R +--R +--R (2) +--R +-+ +----------+ +--R 4 x\|c 3 3 2 2 2 3 +-+ | 2 +--R 3b atanh(-------------) + (16c x + 24b c x + 2b c x - 3b )\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R ----------------------------------------------------------------------------- +--R 2 +-+ +--R 64c \|c +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 | 2 +-+ +--R 3b log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 3 3 2 2 2 3 +-+ | 2 +--R (32c x + 48b c x + 4b c x - 6b )\|c \|c x + b x +--R / +--R 2 +-+ +--R 128c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 4 \|- c \|c x + b x +--R 3b atan(-------------------) +--R c x +--R + +--R +----------+ +--R 3 3 2 2 2 3 +---+ | 2 +--R (16c x + 24b c x + 2b c x - 3b )\|- c \|c x + b x +--R / +--R 2 +---+ +--R 64c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 365 + +--S 366 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 4 | 2 +-+ 4 x\|c +--R 3b log(2c\|c x + b x + (2c x + b)\|c ) - 6b atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) ------------------------------------------------------------------ +--R 2 +-+ +--R 128c \|c +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 4 +---+ x\|c 4 +-+ \|- c \|c x + b x +--R - 3b \|- c atanh(-------------) + 3b \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ------------------------------------------------------------------ +--R 2 +---+ +-+ +--R 64c \|- c \|c +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ------------------------- +--R e x + d +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1726 +r0:=1/3*(b*x+c*x^2)^(3/2)/e-1/8*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e-_ + b^2*e^2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^4)+d^(3/2)*_ + (c*d-b*e)^(3/2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^4+1/8*(8*c^2*d^2-10*b*c*d*e+_ + b^2*e^2-2*c*e*(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(c*e^3) +--R +--R +--R (2) +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (- 3b e - 18b c d e + 72b c d e - 48c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (24b c d e - 24c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +-+ +--R (8c e x + (14b c e - 12c d e )x + 3b e - 30b c d e + 24c d e)\|c +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 24c e \|c +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 3 +--R (3b e + 18b c d e - 72b c d e + 48c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +--------------+ +--R 2 2 | 2 +-+ +--R (48b c d e - 48c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (16c e x + (28b c e - 24c d e )x + 6b e - 60b c d e + 48c d e) +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 48c e \|c +--R , +--R +--R 3 3 2 2 2 2 3 3 +--R (3b e + 18b c d e - 72b c d e + 48c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R +------------+ | 2 +--R 2 2 +-+ | 2 d\|c x + b x +--R (- 96b c d e + 96c d )\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (16c e x + (28b c e - 24c d e )x + 6b e - 60b c d e + 48c d e) +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 48c e \|c +--R , +--R +--R +--------------+ +--R 2 2 | 2 +---+ +--R (24b c d e - 24c d )\|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R +----------+ +--R +---+ | 2 +--R 3 3 2 2 2 2 3 3 \|- c \|c x + b x +--R (- 3b e - 18b c d e + 72b c d e - 48c d )atan(-------------------) +--R c x +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (8c e x + (14b c e - 12c d e )x + 3b e - 30b c d e + 24c d e) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 24c e \|- c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 3 3 2 2 2 2 3 3 \|- c \|c x + b x +--R (- 3b e - 18b c d e + 72b c d e - 48c d )atan(-------------------) +--R c x +--R + +--R +----------+ +--R +------------+ | 2 +--R 2 2 +---+ | 2 d\|c x + b x +--R (- 48b c d e + 48c d )\|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (8c e x + (14b c e - 12c d e )x + 3b e - 30b c d e + 24c d e) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 24c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 372 + +--S 373 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (b e + 6b c d e - 24b c d e + 16c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +--------------+ +--R 2 2 | 2 +-+ +--R (16b c d e - 16c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (2b e + 12b c d e - 48b c d e + 32c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (- 16b c d e + 16c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 4 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (b e + 6b c d e - 24b c d e + 16c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (2b e + 12b c d e - 48b c d e + 32c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R (- 16b c d e + 16c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R 2 2 +-+ | 2 d\|c x + b x +--R (- 32b c d e + 32c d )\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 4 +-+ +--R 16c e \|c +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 376 + +)clear all + +--S 377 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1726 +r0:=-(b*x+c*x^2)^(3/2)/(e*(d+e*x))+3/4*(8*c^2*d^2-8*b*c*d*e+b^2*e^2)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^4*sqrt(c))-3/2*(2*c*d-b*e)*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^4-3/4*(4*c*d-3*b*e-_ + 2*c*e*x)*sqrt(b*x+c*x^2)/e^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 24b c d e + 24c d e)x + 3b d e - 24b c d e + 24c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +-+ +--R ((- 6b e + 12c d e)x - 6b d e + 12c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 3 2 3 2 2 2 +-+ | 2 +--R (2c e x + (5b e - 6c d e )x + 9b d e - 12c d e)\|c \|c x + b x +--R / +--R 5 4 +-+ +--R (4e x + 4d e )\|c +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 | 2 +-+ +--R ((12b e - 24c d e)x + 12b d e - 24c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 24b c d e + 24c d e)x + 3b d e - 24b c d e + 24c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 3 2 3 2 2 2 +-+ | 2 +--R (4c e x + (10b e - 12c d e )x + 18b d e - 24c d e)\|c \|c x + b x +--R / +--R 5 4 +-+ +--R (8e x + 8d e )\|c +--R , +--R +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 24b c d e + 24c d e)x + 3b d e - 24b c d e + 24c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +--R 2 2 +-+ | 2 +--R ((24b e - 48c d e)x + 24b d e - 48c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 3 2 3 2 2 2 +-+ | 2 +--R (4c e x + (10b e - 12c d e )x + 18b d e - 24c d e)\|c \|c x + b x +--R / +--R 5 4 +-+ +--R (8e x + 8d e )\|c +--R , +--R +--R +--------------+ +--R 2 2 | 2 +---+ +--R ((6b e - 12c d e)x + 6b d e - 12c d )\|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 24b c d e + 24c d e)x + 3b d e - 24b c d e + 24c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +----------+ +--R 3 2 3 2 2 2 +---+ | 2 +--R (2c e x + (5b e - 6c d e )x + 9b d e - 12c d e)\|- c \|c x + b x +--R / +--R 5 4 +---+ +--R (4e x + 4d e )\|- c +--R , +--R +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 24b c d e + 24c d e)x + 3b d e - 24b c d e + 24c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +------------+ +--R 2 2 +---+ | 2 +--R ((12b e - 24c d e)x + 12b d e - 24c d )\|- c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R +----------+ +--R 3 2 3 2 2 2 +---+ | 2 +--R (2c e x + (5b e - 6c d e )x + 9b d e - 12c d e)\|- c \|c x + b x +--R / +--R 5 4 +---+ +--R (4e x + 4d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 379 + +--S 380 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-+ +--R (12b e - 24c d)\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R +----------+ +--R 2 2 2 2 | 2 +-+ +--R (3b e - 24b c d e + 24c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 2 2 2 x\|c +--R (- 6b e + 48b c d e - 48c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (12b e - 24c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 4 +-+ +--R 8e \|c +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------+ +--R 2 2 2 2 | 2 +-+ +--R (3b e - 24b c d e + 24c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 2 2 2 x\|c +--R (- 6b e + 48b c d e - 48c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +-----------+ +-+ +-+ +--R (12b e - 24c d)\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R (24b e - 48c d)\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 4 +-+ +--R 8e \|c +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1726 +r0:=-1/2*(b*x+c*x^2)^(3/2)/(e*(d+e*x)^2)-3*(2*c*d-b*e)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))*sqrt(c)/e^4+3/8*(8*c^2*d^2-8*b*c*d*e+b^2*e^2)*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+_ + c*x^2)))/(e^4*sqrt(d)*sqrt(c*d-b*e))+3/4*(4*c*d-b*e+2*c*e*x)*_ + sqrt(b*x+c*x^2)/(e^3*(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 3 +--R ((24b e - 48c d e )x + (48b d e - 96c d e)x + 24b d e - 48c d ) +--R * +--R +-+ +--R +-----------+ +-+ +-+ x\|c +--R \|- b e + c d \|c \|d atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 4 3 2 2 2 2 +--R (- 3b e + 24b c d e - 24c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 6b d e + 48b c d e - 48c d e)x - 3b d e + 24b c d e - 24c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 2 2 +-----------+ +--R (8c e x + (- 10b e + 36c d e )x - 6b d e + 24c d e)\|- b e + c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|d \|c x + b x +--R / +--R 6 2 5 2 4 +-----------+ +-+ +--R (8e x + 16d e x + 8d e )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 2 3 +--R ((12b e - 24c d e )x + (24b d e - 48c d e)x + 12b d e - 24c d ) +--R * +--R +--------------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R \|- b d e + c d \|c log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 4 3 2 2 2 2 +--R (3b e - 24b c d e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (6b d e - 48b c d e + 48c d e)x + 3b d e - 24b c d e + 24c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 3 2 2 2 +--R (8c e x + (- 10b e + 36c d e )x - 6b d e + 24c d e) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 6 2 5 2 4 | 2 +--R (8e x + 16d e x + 8d e )\|- b d e + c d +--R , +--R +--R 3 2 2 2 2 2 3 +-+ +--R ((6b e - 12c d e )x + (12b d e - 24c d e)x + 6b d e - 12c d )\|c +--R * +--R +------------+ +----------+ +--R | 2 +-+ | 2 +--R \|b d e - c d log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 4 3 2 2 2 2 +--R (- 3b e + 24b c d e - 24c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 6b d e + 48b c d e - 48c d e)x - 3b d e + 24b c d e - 24c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +--R 3 2 3 2 2 2 | 2 +--R (4c e x + (- 5b e + 18c d e )x - 3b d e + 12c d e)\|b d e - c d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R +------------+ +--R 6 2 5 2 4 | 2 +--R (4e x + 8d e x + 4d e )\|b d e - c d +--R , +--R +--R 2 4 3 2 2 2 2 +--R (3b e - 24b c d e + 24c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (6b d e - 48b c d e + 48c d e)x + 3b d e - 24b c d e + 24c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 2 2 2 2 3 +--R ((24b e - 48c d e )x + (48b d e - 96c d e)x + 24b d e - 48c d ) +--R * +--R +----------+ +--R +--------------+ | 2 +--R | 2 +---+ \|c x + b x +--R \|- b d e + c d \|- c atan(-------------) +--R +---+ +--R x\|- c +--R + +--R 3 2 3 2 2 2 +--R (8c e x + (- 10b e + 36c d e )x - 6b d e + 24c d e) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 6 2 5 2 4 | 2 +--R (8e x + 16d e x + 8d e )\|- b d e + c d +--R , +--R +--R 2 4 3 2 2 2 2 +--R (- 3b e + 24b c d e - 24c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 6b d e + 48b c d e - 48c d e)x - 3b d e + 24b c d e - 24c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 2 2 2 2 3 +--R ((12b e - 24c d e )x + (24b d e - 48c d e)x + 12b d e - 24c d ) +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 \|c x + b x +--R \|- c \|b d e - c d atan(-------------) +--R +---+ +--R x\|- c +--R + +--R +------------+ +--R 3 2 3 2 2 2 | 2 +--R (4c e x + (- 5b e + 18c d e )x - 3b d e + 12c d e)\|b d e - c d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R +------------+ +--R 6 2 5 2 4 | 2 +--R (4e x + 8d e x + 4d e )\|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 386 + +--S 387 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R | 2 +-----------+ +-+ +-+ +--R (12b e - 24c d)\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R 2 2 2 2 +-----------+ +-+ +--R (3b e - 24b c d e + 24c d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 +-----------+ +-+ +-+ +--R (- 24b e + 48c d)\|- b d e + c d \|- b e + c d \|c \|d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +--------------+ +--R 2 2 2 2 | 2 +--R (3b e - 24b c d e + 24c d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 4 | 2 +-----------+ +-+ +--R 8e \|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R +-----------+ +-+ +-+ | 2 +--R (12b e - 24c d)\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +----------+ +--R +-+ | 2 +--R log(2\|c \|c x + b x + 2c x + b) +--R + +--R +------------+ +--R +-----------+ +-+ +-+ | 2 +--R (- 24b e + 48c d)\|- b e + c d \|c \|d \|b d e - c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +------------+ +--R 2 2 2 2 | 2 +--R (3b e - 24b c d e + 24c d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +--R (- 6b e + 48b c d e - 48c d )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 4 +-----------+ +-+ | 2 +--R 8e \|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1726 +t0:=(d+e*x)^3*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1726 +r0:=1/768*b*(2*c*d-b*e)*(32*c^2*d^2-32*b*c*d*e+11*b^2*e^2)*x^2*_ + (b*x+c*x^2)^(3/2)/c^3+1/384*(2*c*d-b*e)*(32*c^2*d^2-32*b*c*d*e+_ + 11*b^2*e^2)*x*(b*x+c*x^2)^(5/2)/c^3+1/2016*e*(388*c^2*d^2-_ + 388*b*c*d*e+99*b^2*e^2)*(b*x+c*x^2)^(7/2)/c^3+1/9*e*(d+e*x)^2*_ + (b*x+c*x^2)^(7/2)/c+1/144*e*(d*(18*c*d-7*b*e)+11*e*(2*c*d-b*e)*x)*_ + (b*x+c*x^2)^(7/2)/c^2-5/32768*b^6*(2*c*d-b*e)*(32*c^2*d^2-_ + 32*b*c*d*e+11*b^2*e^2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+_ + 5/32768*b^5*(2*c*d-b*e)*(32*c^2*d^2-32*b*c*d*e+11*b^2*e^2)*_ + sqrt(b*x+c*x^2)/c^6-5/49152*b^4*(2*c*d-b*e)*(32*c^2*d^2-32*b*c*d*e+_ + 11*b^2*e^2)*x*sqrt(b*x+c*x^2)/c^5+1/12288*b^3*(2*c*d-b*e)*(32*c^2*d^2-_ + 32*b*c*d*e+11*b^2*e^2)*x^2*sqrt(b*x+c*x^2)/c^4+_ + 1/2048*b^2*(2*c*d-b*e)*(32*c^2*d^2-32*b*c*d*e+11*b^2*e^2)*x^3*_ + sqrt(b*x+c*x^2)/c^3 +--R +--R +--R (2) +--R 9 3 8 2 7 2 2 6 3 3 +--R (3465b e - 17010b c d e + 30240b c d e - 20160b c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 8 3 8 7 3 8 2 7 +--R 229376c e x + (530432b c e + 774144c d e )x +--R + +--R 2 6 3 7 2 8 2 6 +--R (316416b c e + 1824768b c d e + 884736c d e)x +--R + +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (1280b c e + 1119744b c d e + 2138112b c d e + 344064c d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (- 1408b c e + 6912b c d e + 1363968b c d e + 860160b c d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 3 +--R (1584b c e - 7776b c d e + 13824b c d e + 580608b c d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 2 +--R (- 1848b c e + 9072b c d e - 16128b c d e + 10752b c d )x +--R + +--R 7 3 6 2 2 5 3 2 4 4 3 8 3 +--R (2310b c e - 11340b c d e + 20160b c d e - 13440b c d )x - 3465b e +--R + +--R 7 2 6 2 2 5 3 3 +--R 17010b c d e - 30240b c d e + 20160b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 2064384c \|c +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 3 8 2 7 2 2 6 3 3 +--R (3465b e - 17010b c d e + 30240b c d e - 20160b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 8 3 8 7 3 8 2 7 +--R 458752c e x + (1060864b c e + 1548288c d e )x +--R + +--R 2 6 3 7 2 8 2 6 +--R (632832b c e + 3649536b c d e + 1769472c d e)x +--R + +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (2560b c e + 2239488b c d e + 4276224b c d e + 688128c d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (- 2816b c e + 13824b c d e + 2727936b c d e + 1720320b c d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 3 +--R (3168b c e - 15552b c d e + 27648b c d e + 1161216b c d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 2 +--R (- 3696b c e + 18144b c d e - 32256b c d e + 21504b c d )x +--R + +--R 7 3 6 2 2 5 3 2 4 4 3 +--R (4620b c e - 22680b c d e + 40320b c d e - 26880b c d )x +--R + +--R 8 3 7 2 6 2 2 5 3 3 +--R - 6930b e + 34020b c d e - 60480b c d e + 40320b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 6 +-+ +--R 4128768c \|c +--R , +--R +--R 9 3 8 2 7 2 2 6 3 3 +--R (3465b e - 17010b c d e + 30240b c d e - 20160b c d ) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 8 3 8 7 3 8 2 7 +--R 229376c e x + (530432b c e + 774144c d e )x +--R + +--R 2 6 3 7 2 8 2 6 +--R (316416b c e + 1824768b c d e + 884736c d e)x +--R + +--R 3 5 3 2 6 2 7 2 8 3 5 +--R (1280b c e + 1119744b c d e + 2138112b c d e + 344064c d )x +--R + +--R 4 4 3 3 5 2 2 6 2 7 3 4 +--R (- 1408b c e + 6912b c d e + 1363968b c d e + 860160b c d )x +--R + +--R 5 3 3 4 4 2 3 5 2 2 6 3 3 +--R (1584b c e - 7776b c d e + 13824b c d e + 580608b c d )x +--R + +--R 6 2 3 5 3 2 4 4 2 3 5 3 2 +--R (- 1848b c e + 9072b c d e - 16128b c d e + 10752b c d )x +--R + +--R 7 3 6 2 2 5 3 2 4 4 3 +--R (2310b c e - 11340b c d e + 20160b c d e - 13440b c d )x +--R + +--R 8 3 7 2 6 2 2 5 3 3 +--R - 3465b e + 17010b c d e - 30240b c d e + 20160b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 6 +---+ +--R 2064384c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 393 + +--S 394 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 9 3 8 2 7 2 2 6 3 3 +--R (55b e - 270b c d e + 480b c d e - 320b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 9 3 8 2 7 2 2 6 3 3 x\|c +--R (- 110b e + 540b c d e - 960b c d e + 640b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 6 +-+ +--R 65536c \|c +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 9 3 8 2 7 2 2 6 3 3 +---+ +--R (- 55b e + 270b c d e - 480b c d e + 320b c d )\|- c +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 9 3 8 2 7 2 2 6 3 3 +-+ +--R (55b e - 270b c d e + 480b c d e - 320b c d )\|c +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R / +--R 6 +---+ +-+ +--R 32768c \|- c \|c +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 1726 +t0:=(d+e*x)^2*(b*x+c*x^2)^(5/2) +--R +--R +--R (1) +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1726 +r0:=1/384*b*(32*c^2*d^2-32*b*c*d*e+9*b^2*e^2)*x^2*(b*x+c*x^2)^(3/2)/c^2+_ + 1/192*(32*c^2*d^2-32*b*c*d*e+9*b^2*e^2)*x*(b*x+c*x^2)^(5/2)/c^2+_ + 9/112*e*(2*c*d-b*e)*(b*x+c*x^2)^(7/2)/c^2+1/8*e*(d+e*x)*_ + (b*x+c*x^2)^(7/2)/c-5/16384*b^6*(32*c^2*d^2-32*b*c*d*e+9*b^2*e^2)*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(32*c^2*d^2-_ + 32*b*c*d*e+9*b^2*e^2)*sqrt(b*x+c*x^2)/c^5-5/24576*b^4*(32*c^2*d^2-_ + 32*b*c*d*e+9*b^2*e^2)*x*sqrt(b*x+c*x^2)/c^4+1/6144*b^3*(32*c^2*d^2-_ + 32*b*c*d*e+9*b^2*e^2)*x^2*sqrt(b*x+c*x^2)/c^3+1/1024*b^2*(32*c^2*d^2-_ + 32*b*c*d*e+9*b^2*e^2)*x^3*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 8 2 7 6 2 2 x\|c +--R (- 945b e + 3360b c d e - 3360b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 7 2 7 6 2 7 6 +--R 43008c e x + (101376b c e + 98304c d e)x +--R + +--R 2 5 2 6 7 2 5 +--R (62208b c e + 237568b c d e + 57344c d )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (384b c e + 151552b c d e + 143360b c d )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 432b c e + 1536b c d e + 96768b c d )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (504b c e - 1792b c d e + 1792b c d )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 630b c e + 2240b c d e - 2240b c d )x + 945b e - 3360b c d e +--R + +--R 5 2 2 +--R 3360b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 344064c \|c +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 2 7 6 2 2 +--R (945b e - 3360b c d e + 3360b c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 7 2 7 6 2 7 6 +--R 86016c e x + (202752b c e + 196608c d e)x +--R + +--R 2 5 2 6 7 2 5 +--R (124416b c e + 475136b c d e + 114688c d )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (768b c e + 303104b c d e + 286720b c d )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 864b c e + 3072b c d e + 193536b c d )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (1008b c e - 3584b c d e + 3584b c d )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 1260b c e + 4480b c d e - 4480b c d )x + 1890b e - 6720b c d e +--R + +--R 5 2 2 +--R 6720b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 5 +-+ +--R 688128c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 8 2 7 6 2 2 \|- c \|c x + b x +--R (- 945b e + 3360b c d e - 3360b c d )atan(-------------------) +--R c x +--R + +--R 7 2 7 6 2 7 6 +--R 43008c e x + (101376b c e + 98304c d e)x +--R + +--R 2 5 2 6 7 2 5 +--R (62208b c e + 237568b c d e + 57344c d )x +--R + +--R 3 4 2 2 5 6 2 4 +--R (384b c e + 151552b c d e + 143360b c d )x +--R + +--R 4 3 2 3 4 2 5 2 3 +--R (- 432b c e + 1536b c d e + 96768b c d )x +--R + +--R 5 2 2 4 3 3 4 2 2 +--R (504b c e - 1792b c d e + 1792b c d )x +--R + +--R 6 2 5 2 4 3 2 7 2 6 +--R (- 630b c e + 2240b c d e - 2240b c d )x + 945b e - 3360b c d e +--R + +--R 5 2 2 +--R 3360b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 5 +---+ +--R 344064c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 400 + +--S 401 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 8 2 7 6 2 2 | 2 +-+ +--R (45b e - 160b c d e + 160b c d )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 8 2 7 6 2 2 x\|c +--R (90b e - 320b c d e + 320b c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 5 +-+ +--R 32768c \|c +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 8 2 7 6 2 2 +---+ x\|c +--R (45b e - 160b c d e + 160b c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 8 2 7 6 2 2 +-+ \|- c \|c x + b x +--R (- 45b e + 160b c d e - 160b c d )\|c atan(-------------------) +--R c x +--R / +--R 5 +---+ +-+ +--R 16384c \|- c \|c +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 404 + +)clear all + +--S 405 of 1726 +t0:=(d+e*x)*(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (1) (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1726 +r0:=1/24*b*(2*c*d-b*e)*x^2*(b*x+c*x^2)^(3/2)/c+1/12*(2*c*d-b*e)*x*_ + (b*x+c*x^2)^(5/2)/c+1/7*e*(b*x+c*x^2)^(7/2)/c-5/1024*b^6*(2*c*d-_ + b*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+5/1024*b^5*(2*c*d-_ + b*e)*sqrt(b*x+c*x^2)/c^4-5/1536*b^4*(2*c*d-b*e)*x*sqrt(b*x+c*x^2)/_ + c^3+1/384*b^3*(2*c*d-b*e)*x^2*sqrt(b*x+c*x^2)/c^2+1/64*b^2*_ + (2*c*d-b*e)*x^3*sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 7 6 x\|c +--R (105b e - 210b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 3072c e x + (7424b c e + 3584c d)x + (4736b c e + 8960b c d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 +--R (48b c e + 6048b c d)x + (- 56b c e + 112b c d)x +--R + +--R 5 4 2 6 5 +--R (70b c e - 140b c d)x - 105b e + 210b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 21504c \|c +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 7 6 | 2 +-+ +--R (105b e - 210b c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 6144c e x + (14848b c e + 7168c d)x + (9472b c e + 17920b c d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 +--R (96b c e + 12096b c d)x + (- 112b c e + 224b c d)x +--R + +--R 5 4 2 6 5 +--R (140b c e - 280b c d)x - 210b e + 420b c d +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 4 +-+ +--R 43008c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 7 6 \|- c \|c x + b x +--R (105b e - 210b c d)atan(-------------------) +--R c x +--R + +--R 6 6 5 6 5 2 4 5 4 +--R 3072c e x + (7424b c e + 3584c d)x + (4736b c e + 8960b c d)x +--R + +--R 3 3 2 4 3 4 2 3 3 2 +--R (48b c e + 6048b c d)x + (- 56b c e + 112b c d)x +--R + +--R 5 4 2 6 5 +--R (70b c e - 140b c d)x - 105b e + 210b c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 4 +---+ +--R 21504c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 407 + +--S 408 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 7 6 | 2 +-+ +--R (5b e - 10b c d)log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 7 6 x\|c +--R (- 10b e + 20b c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 4 +-+ +--R 2048c \|c +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 7 6 +---+ x\|c +--R (- 5b e + 10b c d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 7 6 +-+ \|- c \|c x + b x +--R (5b e - 10b c d)\|c atan(-------------------) +--R c x +--R / +--R 4 +---+ +-+ +--R 1024c \|- c \|c +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 411 + +)clear all + +--S 412 of 1726 +t0:=(b*x+c*x^2)^(5/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (1) (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1726 +r0:=1/12*b*x^2*(b*x+c*x^2)^(3/2)+1/6*x*(b*x+c*x^2)^(5/2)-5/512*b^6*_ + atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+5/512*b^5*sqrt(b*x+_ + c*x^2)/c^3-5/768*b^4*x*sqrt(b*x+c*x^2)/c^2+1/192*b^3*x^2*_ + sqrt(b*x+c*x^2)/c+1/32*b^2*x^3*sqrt(b*x+c*x^2) +--R +--R +--R (2) +--R +-+ +--R 6 x\|c +--R - 15b atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (256c x + 640b c x + 432b c x + 8b c x - 10b c x + 15b )\|c +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 1536c \|c +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 6 | 2 +-+ +--R 15b log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (512c x + 1280b c x + 864b c x + 16b c x - 20b c x + 30b )\|c +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 3072c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 6 \|- c \|c x + b x +--R - 15b atan(-------------------) +--R c x +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +---+ +--R (256c x + 640b c x + 432b c x + 8b c x - 10b c x + 15b )\|- c +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +---+ +--R 1536c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 414 + +--S 415 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 6 | 2 +-+ 6 x\|c +--R 5b log(- 2c\|c x + b x + (2c x + b)\|c ) + 10b atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) --------------------------------------------------------------------- +--R 3 +-+ +--R 1024c \|c +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 6 +---+ x\|c 6 +-+ \|- c \|c x + b x +--R 5b \|- c atanh(-------------) - 5b \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ---------------------------------------------------------------- +--R 3 +---+ +-+ +--R 512c \|- c \|c +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R e x + d +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1726 +r0:=1/48*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2-6*c*e*(2*c*d-b*e)*x)*_ + (b*x+c*x^2)^(3/2)/(c*e^3)+1/5*(b*x+c*x^2)^(5/2)/e-1/128*_ + (2*c*d-b*e)*(128*c^4*d^4-256*b*c^3*d^3*e+112*b^2*c^2*d^2*e^2+_ + 16*b^3*c*d*e^3+3*b^4*e^4)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(5/2)*e^6)+d^(5/2)*(c*d-b*e)^(5/2)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^6+_ + 1/128*(128*c^4*d^4-288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-_ + 10*b^3*c*d*e^3-3*b^4*e^4-2*c*e*(2*c*d-b*e)*(16*c^2*d^2-_ + 16*b*c*d*e-3*b^2*e^2)*x)*sqrt(b*x+c*x^2)/(c^2*e^5) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 45b e + 150b c d e + 1200b c d e - 7200b c d e + 9600b c d e +--R + +--R 5 5 +--R - 3840c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 3 3 4 4 +-----------+ +-+ +-+ +--R (- 1920b c d e + 3840b c d e - 1920c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 5 4 3 5 4 4 3 +--R 384c e x + (1008b c e - 480c d e )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (744b c e - 1360b c d e + 640c d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 4 5 +--R (30b c e - 1180b c d e + 2080b c d e - 960c d e )x - 45b e +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 150b c d e + 2640b c d e - 4320b c d e + 1920c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 6 +-+ +--R 1920c e \|c +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------------+ +--R 2 2 2 2 3 3 4 4 | 2 +-+ +--R (3840b c d e - 7680b c d e + 3840c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 45b e + 150b c d e + 1200b c d e - 7200b c d e + 9600b c d e +--R + +--R 5 5 +--R - 3840c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 5 4 3 5 4 4 3 +--R 768c e x + (2016b c e - 960c d e )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (1488b c e - 2720b c d e + 1280c d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 4 5 +--R (60b c e - 2360b c d e + 4160b c d e - 1920c d e )x - 90b e +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 300b c d e + 5280b c d e - 8640b c d e + 3840c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 6 +-+ +--R 3840c e \|c +--R , +--R +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 45b e + 150b c d e + 1200b c d e - 7200b c d e + 9600b c d e +--R + +--R 5 5 +--R - 3840c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +------------+ +--R 2 2 2 2 3 3 4 4 +-+ | 2 +--R (7680b c d e - 15360b c d e + 7680c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 5 4 3 5 4 4 3 +--R 768c e x + (2016b c e - 960c d e )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (1488b c e - 2720b c d e + 1280c d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 4 5 +--R (60b c e - 2360b c d e + 4160b c d e - 1920c d e )x - 90b e +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 300b c d e + 5280b c d e - 8640b c d e + 3840c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 2 6 +-+ +--R 3840c e \|c +--R , +--R +--R +--------------+ +--R 2 2 2 2 3 3 4 4 | 2 +---+ +--R (1920b c d e - 3840b c d e + 1920c d )\|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 45b e + 150b c d e + 1200b c d e - 7200b c d e + 9600b c d e +--R + +--R 5 5 +--R - 3840c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 4 5 4 3 5 4 4 3 +--R 384c e x + (1008b c e - 480c d e )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (744b c e - 1360b c d e + 640c d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 4 5 +--R (30b c e - 1180b c d e + 2080b c d e - 960c d e )x - 45b e +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 150b c d e + 2640b c d e - 4320b c d e + 1920c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 6 +---+ +--R 1920c e \|- c +--R , +--R +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 45b e + 150b c d e + 1200b c d e - 7200b c d e + 9600b c d e +--R + +--R 5 5 +--R - 3840c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R +------------+ +--R 2 2 2 2 3 3 4 4 +---+ | 2 +--R (3840b c d e - 7680b c d e + 3840c d )\|- c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 4 5 4 3 5 4 4 3 +--R 384c e x + (1008b c e - 480c d e )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (744b c e - 1360b c d e + 640c d e )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 4 5 +--R (30b c e - 1180b c d e + 2080b c d e - 960c d e )x - 45b e +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 150b c d e + 2640b c d e - 4320b c d e + 1920c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 2 6 +---+ +--R 1920c e \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 421 + +--S 422 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 3 3 4 4 | 2 +-+ +--R (256b c d e - 512b c d e + 256c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3b e + 10b c d e + 80b c d e - 480b c d e + 640b c d e - 256c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6b e - 20b c d e - 160b c d e + 960b c d e - 1280b c d e +--R + +--R 5 5 +--R 512c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 3 3 4 4 +-----------+ +-+ +-+ +--R (256b c d e - 512b c d e + 256c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 2 6 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3b e + 10b c d e + 80b c d e - 480b c d e + 640b c d e - 256c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6b e - 20b c d e - 160b c d e + 960b c d e - 1280b c d e +--R + +--R 5 5 +--R 512c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 3 3 4 4 +-----------+ +-+ +-+ +--R (256b c d e - 512b c d e + 256c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +--R 2 2 2 2 3 3 4 4 +-+ | 2 +--R (512b c d e - 1024b c d e + 512c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 2 6 +-+ +--R 256c e \|c +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^2 +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1726 +r0:=-5/24*(8*c*d-7*b*e-6*c*e*x)*(b*x+c*x^2)^(3/2)/e^3-(b*x+c*x^2)^(5/2)/_ + (e*(d+e*x))+5/64*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-_ + 16*b^3*c*d*e^3-b^4*e^4)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + (c^(3/2)*e^6)-5/2*d^(3/2)*(c*d-b*e)^(3/2)*(2*c*d-b*e)*_ + atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/e^6-5/64*(64*c^3*d^3-112*b*c^2*d^2*e+_ + 48*b^2*c*d*e^2-b^3*e^3-2*c*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)*x)*_ + sqrt(b*x+c*x^2)/(c*e^5) +--R +--R +--R (2) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 15b e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 15b d e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 2 2 3 3 2 2 2 2 3 +--R (480b c d e - 1440b c d e + 960c d e)x + 480b c d e - 1440b c d e +--R + +--R 3 4 +--R 960c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 4 2 5 3 4 3 +--R 48c e x + (136b c e - 80c d e )x +--R + +--R 2 5 2 4 3 2 3 2 +--R (118b c e - 280b c d e + 160c d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 4 +--R (15b e - 410b c d e + 880b c d e - 480c d e )x + 15b d e +--R + +--R 2 2 3 2 3 2 3 4 +--R - 720b c d e + 1680b c d e - 960c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 7 6 +-+ +--R (192c e x + 192c d e )\|c +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (15b e + 240b c d e - 2160b c d e + 3840b c d e - 1920c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 15b d e + 240b c d e - 2160b c d e + 3840b c d e - 1920c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 3 3 2 2 2 +--R (960b c d e - 2880b c d e + 1920c d e)x + 960b c d e +--R + +--R 2 3 3 4 +--R - 2880b c d e + 1920c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 3 5 4 2 5 3 4 3 +--R 96c e x + (272b c e - 160c d e )x +--R + +--R 2 5 2 4 3 2 3 2 +--R (236b c e - 560b c d e + 320c d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 4 +--R (30b e - 820b c d e + 1760b c d e - 960c d e )x + 30b d e +--R + +--R 2 2 3 2 3 2 3 4 +--R - 1440b c d e + 3360b c d e - 1920c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 7 6 +-+ +--R (384c e x + 384c d e )\|c +--R , +--R +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (15b e + 240b c d e - 2160b c d e + 3840b c d e - 1920c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R 15b d e + 240b c d e - 2160b c d e + 3840b c d e - 1920c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 2 2 3 3 2 2 2 +--R (- 1920b c d e + 5760b c d e - 3840c d e)x - 1920b c d e +--R + +--R 2 3 3 4 +--R 5760b c d e - 3840c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 5 4 2 5 3 4 3 +--R 96c e x + (272b c e - 160c d e )x +--R + +--R 2 5 2 4 3 2 3 2 +--R (236b c e - 560b c d e + 320c d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 4 +--R (30b e - 820b c d e + 1760b c d e - 960c d e )x + 30b d e +--R + +--R 2 2 3 2 3 2 3 4 +--R - 1440b c d e + 3360b c d e - 1920c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 7 6 +-+ +--R (384c e x + 384c d e )\|c +--R , +--R +--R 2 3 2 2 2 3 3 2 2 2 +--R (480b c d e - 1440b c d e + 960c d e)x + 480b c d e +--R + +--R 2 3 3 4 +--R - 1440b c d e + 960c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 15b e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 15b d e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 3 5 4 2 5 3 4 3 +--R 48c e x + (136b c e - 80c d e )x +--R + +--R 2 5 2 4 3 2 3 2 +--R (118b c e - 280b c d e + 160c d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 4 +--R (15b e - 410b c d e + 880b c d e - 480c d e )x + 15b d e +--R + +--R 2 2 3 2 3 2 3 4 +--R - 720b c d e + 1680b c d e - 960c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 7 6 +---+ +--R (192c e x + 192c d e )\|- c +--R , +--R +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 15b e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R - 15b d e - 240b c d e + 2160b c d e - 3840b c d e + 1920c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 3 2 2 2 3 3 2 2 2 +--R (- 960b c d e + 2880b c d e - 1920c d e)x - 960b c d e +--R + +--R 2 3 3 4 +--R 2880b c d e - 1920c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 3 5 4 2 5 3 4 3 +--R 48c e x + (136b c e - 80c d e )x +--R + +--R 2 5 2 4 3 2 3 2 +--R (118b c e - 280b c d e + 160c d e )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 4 +--R (15b e - 410b c d e + 880b c d e - 480c d e )x + 15b d e +--R + +--R 2 2 3 2 3 2 3 4 +--R - 720b c d e + 1680b c d e - 960c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 7 6 +---+ +--R (192c e x + 192c d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 428 + +--S 429 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (5b e + 80b c d e - 720b c d e + 1280b c d e - 640c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +--------------+ +--R 2 2 2 2 3 3 | 2 +-+ +--R (320b c d e - 960b c d e + 640c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R - 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(---------------------------------------------------------) +--R e x + d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (10b e + 160b c d e - 1440b c d e + 2560b c d e - 1280c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 3 3 +-----------+ +-+ +-+ +--R (- 320b c d e + 960b c d e - 640c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 6 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (5b e + 80b c d e - 720b c d e + 1280b c d e - 640c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (10b e + 160b c d e - 1440b c d e + 2560b c d e - 1280c d ) +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 3 3 +-----------+ +-+ +-+ +--R (- 320b c d e + 960b c d e - 640c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +--R 2 2 2 2 3 3 +-+ | 2 +--R (- 640b c d e + 1920b c d e - 1280c d )\|c \|b d e - c d +--R * +--R +----------+ +--R | 2 +--R d\|c x + b x +--R atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 6 +-+ +--R 128c e \|c +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^3 +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1726 +r0:=5/12*(8*c*d-3*b*e+2*c*e*x)*(b*x+c*x^2)^(3/2)/(e^3*(d+e*x))-_ + 1/2*(b*x+c*x^2)^(5/2)/(e*(d+e*x)^2)-5/8*(2*c*d-b*e)*(16*c^2*d^2-_ + 16*b*c*d*e+b^2*e^2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^6*_ + sqrt(c))+5/8*(4*c*d-3*b*e)*(4*c*d-b*e)*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*_ + sqrt(c*d-b*e)/e^6+5/8*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2-_ + 4*c*e*(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/e^5 +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 270b c d e + 720b c d e - 480c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 540b c d e + 1440b c d e - 960c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 270b c d e + 720b c d e - 480c d +--R * +--R +-+ +--R x\|c +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 4 3 2 2 2 2 +--R (- 45b e + 240b c d e - 240c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (- 90b d e + 480b c d e - 480c d e)x - 45b d e + 240b c d e +--R + +--R 2 4 +--R - 240c d +--R * +--R +-----------+ +-+ +-+ (b e - 2c d)x - b d +--R \|- b e + c d \|c \|d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 5 4 5 2 4 3 +--R 8c e x + (26b c e - 20c d e )x +--R + +--R 2 5 4 2 2 3 2 +--R (33b e - 110b c d e + 80c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 3 2 +--R (120b d e - 460b c d e + 360c d e )x + 75b d e - 300b c d e +--R + +--R 2 4 +--R 240c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 8 2 7 2 6 +-+ +--R (24e x + 48d e x + 24d e )\|c +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 3 2 2 2 2 +--R (90b e - 480b c d e + 480c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (180b d e - 960b c d e + 960c d e)x + 90b d e - 480b c d e +--R + +--R 2 4 +--R 480c d +--R * +--R +--------------+ +--R | 2 +-+ +--R \|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 270b c d e + 720b c d e - 480c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 540b c d e + 1440b c d e - 960c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 270b c d e + 720b c d e - 480c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 5 4 5 2 4 3 +--R 16c e x + (52b c e - 40c d e )x +--R + +--R 2 5 4 2 2 3 2 +--R (66b e - 220b c d e + 160c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 3 2 +--R (240b d e - 920b c d e + 720c d e )x + 150b d e - 600b c d e +--R + +--R 2 4 +--R 480c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 8 2 7 2 6 +-+ +--R (48e x + 96d e x + 48d e )\|c +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 270b c d e + 720b c d e - 480c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 540b c d e + 1440b c d e - 960c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 270b c d e + 720b c d e - 480c d +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 4 3 2 2 2 2 +--R (180b e - 960b c d e + 960c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (360b d e - 1920b c d e + 1920c d e)x + 180b d e - 960b c d e +--R + +--R 2 4 +--R 960c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +-+ | 2 d\|c x + b x +--R \|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 5 4 5 2 4 3 +--R 16c e x + (52b c e - 40c d e )x +--R + +--R 2 5 4 2 2 3 2 +--R (66b e - 220b c d e + 160c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 3 2 +--R (240b d e - 920b c d e + 720c d e )x + 150b d e - 600b c d e +--R + +--R 2 4 +--R 480c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 8 2 7 2 6 +-+ +--R (48e x + 96d e x + 48d e )\|c +--R , +--R +--R 2 4 3 2 2 2 2 +--R (45b e - 240b c d e + 240c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (90b d e - 480b c d e + 480c d e)x + 45b d e - 240b c d e +--R + +--R 2 4 +--R 240c d +--R * +--R +--------------+ +--R | 2 +---+ +--R \|- b d e + c d \|- c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 270b c d e + 720b c d e - 480c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 540b c d e + 1440b c d e - 960c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 270b c d e + 720b c d e - 480c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 5 4 5 2 4 3 +--R 8c e x + (26b c e - 20c d e )x +--R + +--R 2 5 4 2 2 3 2 +--R (33b e - 110b c d e + 80c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 3 2 +--R (120b d e - 460b c d e + 360c d e )x + 75b d e - 300b c d e +--R + +--R 2 4 +--R 240c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 8 2 7 2 6 +---+ +--R (24e x + 48d e x + 24d e )\|- c +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 270b c d e + 720b c d e - 480c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 540b c d e + 1440b c d e - 960c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 270b c d e + 720b c d e - 480c d +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R atan(-------------------) +--R c x +--R + +--R 2 4 3 2 2 2 2 +--R (90b e - 480b c d e + 480c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (180b d e - 960b c d e + 960c d e)x + 90b d e - 480b c d e +--R + +--R 2 4 +--R 480c d +--R * +--R +----------+ +--R +------------+ | 2 +--R +---+ | 2 d\|c x + b x +--R \|- c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R + +--R 2 5 4 5 2 4 3 +--R 8c e x + (26b c e - 20c d e )x +--R + +--R 2 5 4 2 2 3 2 +--R (33b e - 110b c d e + 80c d e )x +--R + +--R 2 4 2 3 2 3 2 2 2 3 3 2 +--R (120b d e - 460b c d e + 360c d e )x + 75b d e - 300b c d e +--R + +--R 2 4 +--R 240c d e +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 8 2 7 2 6 +---+ +--R (24e x + 48d e x + 24d e )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 435 + +--S 436 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 2 2 | 2 +-+ +--R (30b e - 160b c d e + 160c d )\|- b d e + c d \|c +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2\|- b d e + c d \|c x + b x + (- b e + 2c d)x + b d +--R log(-------------------------------------------------------) +--R e x + d +--R + +--R 3 3 2 2 2 2 3 3 +--R (5b e - 90b c d e + 240b c d e - 160c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (- 10b e + 180b c d e - 480b c d e + 320c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (30b e - 160b c d e + 160c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R 6 +-+ +--R 16e \|c +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (5b e - 90b c d e + 240b c d e - 160c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (- 10b e + 180b c d e - 480b c d e + 320c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (30b e - 160b c d e + 160c d )\|- b e + c d \|c \|d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +------------+ | 2 +--R 2 2 2 2 +-+ | 2 d\|c x + b x +--R (60b e - 320b c d e + 320c d )\|c \|b d e - c d atan(----------------) +--R +------------+ +--R | 2 +--R x\|b d e - c d +--R / +--R 6 +-+ +--R 16e \|c +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 439 + +)clear all + +--S 440 of 1726 +t0:=sqrt(2*x+x^2)/(1+x) +--R +--R +--R +-------+ +--R | 2 +--R \|x + 2x +--R (1) ---------- +--R x + 1 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1726 +r0:=-atan(sqrt(2*x+x^2))+sqrt(2*x+x^2) +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R (2) - atan(\|x + 2x ) + \|x + 2x +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +--R | 2 | 2 | 2 +--R (- 4\|x + 2x + 4x + 4)atan(\|x + 2x - x - 1) + (- 2x - 1)\|x + 2x +--R + +--R 2 +--R 2x + 3x - 1 +--R / +--R +-------+ +--R | 2 +--R 2\|x + 2x - 2x - 2 +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 1726 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R 2atan(\|x + 2x ) - 4atan(\|x + 2x - x - 1) + 1 +--R (4) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 1726 +t0:=(2*x-x^2)^(3/2)/(2-2*x) +--R +--R +--R +---------+ +--R 2 | 2 +--R (x - 2x)\|- x + 2x +--R (1) --------------------- +--R 2x - 2 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1726 +r0:=-1/6*(2*x-x^2)^(3/2)+1/2*atanh(sqrt(2*x-x^2))-1/2*sqrt(2*x-x^2) +--R +--R +--R +---------+ +---------+ +--R | 2 2 | 2 +--R 3atanh(\|- x + 2x ) + (x - 2x - 3)\|- x + 2x +--R (2) ------------------------------------------------ +--R 6 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x 2 | 2 +--R 3log(----------------) - 3log(----------------) + (x - 2x - 3)\|- x + 2x +--R x x +--R --------------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 1726 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - atanh(\|- x + 2x ) +--R x x +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 449 + +)clear all + +--S 450 of 1726 +t0:=(2*x-x^2)^(1/2)/(2-2*x) +--R +--R +--R +---------+ +--R | 2 +--R \|- x + 2x +--R (1) - ------------ +--R 2x - 2 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1726 +r0:=1/2*atanh(sqrt(2*x-x^2))-1/2*sqrt(2*x-x^2) +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R atanh(\|- x + 2x ) - \|- x + 2x +--R (2) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1726 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - \|- x + 2x +--R x x +--R (3) ------------------------------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 1726 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - atanh(\|- x + 2x ) +--R x x +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1726 +t0:=1/((2-2*x)*(2*x-x^2)^(1/2)) +--R +--R +--R 1 +--R (1) - -------------------- +--R +---------+ +--R | 2 +--R (2x - 2)\|- x + 2x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1726 +r0:=1/2*atanh(sqrt(2*x-x^2)) +--R +--R +--R +---------+ +--R | 2 +--R atanh(\|- x + 2x ) +--R (2) ------------------- +--R 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1726 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- x + 2x + x \|- x + 2x - x +--R log(----------------) - log(----------------) +--R x x +--R (3) --------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 1726 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - atanh(\|- x + 2x ) +--R x x +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 1726 +t0:=1/((2-2*x)*(2*x-x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +---------+ +--R 3 2 | 2 +--R (2x - 6x + 4x)\|- x + 2x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1726 +r0:=1/2*atanh(sqrt(2*x-x^2))+(-1/2)/sqrt(2*x-x^2) +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- x + 2x atanh(\|- x + 2x ) - 1 +--R (2) ----------------------------------- +--R +---------+ +--R | 2 +--R 2\|- x + 2x +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R +---------+ | 2 +---------+ | 2 +--R | 2 \|- x + 2x + x | 2 \|- x + 2x - x +--R \|- x + 2x log(----------------) - \|- x + 2x log(----------------) - 1 +--R x x +--R ------------------------------------------------------------------------- +--R +---------+ +--R | 2 +--R 2\|- x + 2x +--R Type: Union(Expression(Integer),...) +--E 462 + +--S 463 of 1726 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - atanh(\|- x + 2x ) +--R x x +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 464 + +)clear all + +--S 465 of 1726 +t0:=1/((2-2*x)*(2*x-x^2)^(5/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R +---------+ +--R 5 4 3 2 | 2 +--R (2x - 10x + 16x - 8x )\|- x + 2x +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1726 +r0:=(-1/6)/(2*x-x^2)^(3/2)+1/2*atanh(sqrt(2*x-x^2))+(-1/2)/sqrt(2*x-x^2) +--R +--R +--R +---------+ +---------+ +--R 2 | 2 | 2 2 +--R (3x - 6x)\|- x + 2x atanh(\|- x + 2x ) - 3x + 6x + 1 +--R (2) -------------------------------------------------------- +--R +---------+ +--R 2 | 2 +--R (6x - 12x)\|- x + 2x +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|- x + 2x + x +--R (3x - 6x)\|- x + 2x log(----------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|- x + 2x - x 2 +--R (- 3x + 6x)\|- x + 2x log(----------------) - 3x + 6x + 1 +--R x +--R / +--R +---------+ +--R 2 | 2 +--R (6x - 12x)\|- x + 2x +--R Type: Union(Expression(Integer),...) +--E 467 + +--S 468 of 1726 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +---------+ +--R \|- x + 2x + x \|- x + 2x - x | 2 +--R log(----------------) - log(----------------) - atanh(\|- x + 2x ) +--R x x +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 469 + +)clear all + +--S 470 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2)^(1/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1726 +r0:=1/8*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+5*b^2*e^2)*atanh(x*sqrt(c)/_ + sqrt(b*x+c*x^2))/c^(7/2)+1/24*e*(52*c^2*d^2-52*b*c*d*e+15*b^2*e^2)*_ + sqrt(b*x+c*x^2)/c^3+1/3*e*(d+e*x)^2*sqrt(b*x+c*x^2)/c+_ + 1/12*e*(d*(6*c*d-b*e)+5*e*(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/c^2 +--R +--R +--R (2) +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (- 15b e + 54b c d e - 72b c d e + 48c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (8c e x + (- 10b c e + 36c d e )x + 15b e - 54b c d e + 72c d e) +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 24c \|c +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 3 +--R (15b e - 54b c d e + 72b c d e - 48c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 3 2 2 2 3 2 +--R 16c e x + (- 20b c e + 72c d e )x + 30b e - 108b c d e +--R + +--R 2 2 +--R 144c d e +--R * +--R +----------+ +--R +-+ | 2 +--R \|c \|c x + b x +--R / +--R 3 +-+ +--R 48c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 3 3 2 2 2 2 3 3 \|- c \|c x + b x +--R (- 15b e + 54b c d e - 72b c d e + 48c d )atan(-------------------) +--R c x +--R + +--R 2 3 2 3 2 2 2 3 2 2 2 +--R (8c e x + (- 10b c e + 36c d e )x + 15b e - 54b c d e + 72c d e) +--R * +--R +----------+ +--R +---+ | 2 +--R \|- c \|c x + b x +--R / +--R 3 +---+ +--R 24c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 472 + +--S 473 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (5b e - 18b c d e + 24b c d e - 16c d ) +--R * +--R +----------+ +--R | 2 +-+ +--R log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 3 2 2 2 2 3 3 x\|c +--R (10b e - 36b c d e + 48b c d e - 32c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 3 +-+ +--R 16c \|c +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 3 3 2 2 2 2 3 3 +---+ x\|c +--R (5b e - 18b c d e + 24b c d e - 16c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 3 3 2 2 2 2 3 3 +-+ \|- c \|c x + b x +--R (- 5b e + 18b c d e - 24b c d e + 16c d )\|c atan(-------------------) +--R c x +--R / +--R 3 +---+ +-+ +--R 8c \|- c \|c +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 476 + +)clear all + +--S 477 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2)^(1/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------ +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1726 +r0:=1/4*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/_ + c^(5/2)+3/4*e*(2*c*d-b*e)*sqrt(b*x+c*x^2)/c^2+1/2*e*(d+e*x)*_ + sqrt(b*x+c*x^2)/c +--R +--R +--R (2) +--R +-+ +--R 2 2 2 2 x\|c +--R (3b e - 8b c d e + 8c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (2c e x - 3b e + 8c d e)\|c \|c x + b x +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 2 2 2 | 2 +-+ +--R (3b e - 8b c d e + 8c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +----------+ +--R 2 2 +-+ | 2 +--R (4c e x - 6b e + 16c d e)\|c \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R , +--R +--R +----------+ +--R +---+ | 2 +--R 2 2 2 2 \|- c \|c x + b x +--R (3b e - 8b c d e + 8c d )atan(-------------------) +--R c x +--R + +--R +----------+ +--R 2 2 +---+ | 2 +--R (2c e x - 3b e + 8c d e)\|- c \|c x + b x +--R / +--R 2 +---+ +--R 4c \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 479 + +--S 480 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 2 2 2 2 | 2 +-+ +--R (3b e - 8b c d e + 8c d )log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 2 2 2 2 x\|c +--R (- 6b e + 16b c d e - 16c d )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 8c \|c +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 2 2 2 2 +---+ x\|c +--R (- 3b e + 8b c d e - 8c d )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 2 2 2 2 +-+ \|- c \|c x + b x +--R (3b e - 8b c d e + 8c d )\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1726 +t0:=(d+e*x)/(b*x+c*x^2)^(1/2) +--R +--R +--R e x + d +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1726 +r0:=(2*c*d-b*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+e*sqrt(b*x+c*x^2)/c +--R +--R +--R +-+ +----------+ +--R x\|c +-+ | 2 +--R (- b e + 2c d)atanh(-------------) + e\|c \|c x + b x +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) ------------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +-+ +-+ | 2 +--R (b e - 2c d)log(- 2c\|c x + b x + (2c x + b)\|c ) + 2e\|c \|c x + b x +--R [-------------------------------------------------------------------------, +--R +-+ +--R 2c\|c +--R +----------+ +--R +---+ | 2 +----------+ +--R \|- c \|c x + b x +---+ | 2 +--R (- b e + 2c d)atan(-------------------) + e\|- c \|c x + b x +--R c x +--R --------------------------------------------------------------] +--R +---+ +--R c\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 486 + +--S 487 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R | 2 +-+ +--R (b e - 2c d)log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R x\|c +--R (2b e - 4c d)atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R +---+ x\|c +--R (b e - 2c d)\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R +-+ \|- c \|c x + b x +--R (- b e + 2c d)\|c atan(-------------------) +--R c x +--R / +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1726 +t0:=1/(b*x+c*x^2)^(1/2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1726 +r0:=2*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/sqrt(c) +--R +--R +--R +-+ +--R x\|c +--R 2atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (2) --------------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1726 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R +---+ | 2 +--R +----------+ \|- c \|c x + b x +--R | 2 +-+ 2atan(-------------------) +--R log(2c\|c x + b x + (2c x + b)\|c ) c x +--R (3) [-------------------------------------,--------------------------] +--R +-+ +---+ +--R \|c \|- c +--R Type: Union(List(Expression(Integer)),...) +--E 493 + +--S 494 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R | 2 +-+ x\|c +--R log(2c\|c x + b x + (2c x + b)\|c ) - 2atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) ------------------------------------------------------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R +---+ x\|c +-+ \|- c \|c x + b x +--R - 2\|- c atanh(-------------) + 2\|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)^(1/2)) +--R +--R +--R 1 +--R (1) ---------------------- +--R +----------+ +--R | 2 +--R (e x + d)\|c x + b x +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1726 +r0:=atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(sqrt(d)*sqrt(c*d-b*e)) +--R +--R +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R (2) - --------------------------------------- +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R / +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R 2atan(----------------------------) +--R (b e - c d)x +--R - -----------------------------------] +--R +------------+ +--R | 2 +--R \|b d e - c d +--R Type: Union(List(Expression(Integer)),...) +--E 500 + +--S 501 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R | 2 +-----------+ +-+ +--R \|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R - 2\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)^(1/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (e x + 2d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1726 +r0:=1/2*(2*c*d-b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-e*sqrt(b*x+c*x^2)/_ + (d*(c*d-b*e)*(d+e*x)) +--R +--R +--R (2) +--R 2 2 +--R ((- b e + 2c d e)x - b d e + 2c d ) +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2e\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 2 3 +-----------+ +-+ +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((b e - 2c d e)x + b d e - 2c d ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R | 2 | 2 +--R 2e\|- b d e + c d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 | 2 +--R ((2b d e - 2c d e)x + 2b d e - 2c d )\|- b d e + c d +--R , +--R +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 2 \|b d e - c d \|c x + b x +--R ((- b e + 2c d e)x - b d e + 2c d )atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R e\|b d e - c d \|c x + b x +--R / +--R +------------+ +--R 2 2 2 3 | 2 +--R ((b d e - c d e)x + b d e - c d )\|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 507 + +--S 508 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R (b e - 2c d)\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R | 2 (b e - 2c d)x - b d +--R (b e - 2c d)\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (2b d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R | 2 (b e - 2c d)x - b d +--R (b e - 2c d)\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 2b e + 4c d)\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (2b d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 511 + +)clear all + +--S 512 of 1726 +t0:=1/((d+e*x)^3*(b*x+c*x^2)^(1/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 | 2 +--R (e x + 3d e x + 3d e x + d )\|c x + b x +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1726 +r0:=1/8*(8*c^2*d^2-8*b*c*d*e+3*b^2*e^2)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/_ + (sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))-_ + 1/2*e*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^2)-3/4*e*(2*c*d-b*e)*_ + sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 2 2 2 2 +--R (- 3b e + 8b c d e - 8c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 6b d e + 16b c d e - 16c d e)x - 3b d e + 8b c d e - 8c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +----------+ +--R 3 2 2 2 +-----------+ +-+ | 2 +--R ((6b e - 12c d e )x + 10b d e - 16c d e)\|- b e + c d \|d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (8b d e - 16b c d e + 8c d e )x + (16b d e - 32b c d e + 16c d e)x +--R + +--R 2 4 2 5 2 6 +--R 8b d e - 16b c d e + 8c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (3b e - 8b c d e + 8c d e )x + (6b d e - 16b c d e + 16c d e)x +--R + +--R 2 2 2 3 2 4 +--R 3b d e - 8b c d e + 8c d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +----------+ +--R 3 2 2 2 | 2 | 2 +--R ((6b e - 12c d e )x + 10b d e - 16c d e)\|- b d e + c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 +--R (8b d e - 16b c d e + 8c d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (16b d e - 32b c d e + 16c d e)x + 8b d e - 16b c d e + 8c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R , +--R +--R 2 4 3 2 2 2 2 +--R (- 3b e + 8b c d e - 8c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 6b d e + 16b c d e - 16c d e)x - 3b d e + 8b c d e - 8c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +----------+ +--R 3 2 2 2 | 2 | 2 +--R ((3b e - 6c d e )x + 5b d e - 8c d e)\|b d e - c d \|c x + b x +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (4b d e - 8b c d e + 4c d e )x + (8b d e - 16b c d e + 8c d e)x +--R + +--R 2 4 2 5 2 6 +--R 4b d e - 8b c d e + 4c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 514 + +--S 515 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +-----------+ +-+ +--R (3b e - 8b c d e + 8c d )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 2 2 | 2 +--R (3b e - 8b c d e + 8c d )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (8b d e - 16b c d e + 8c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 2 2 2 | 2 +--R (3b e - 8b c d e + 8c d )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 2 2 +-----------+ +-+ +--R (- 6b e + 16b c d e - 16c d )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (8b d e - 16b c d e + 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ---------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1726 +r0:=3*e^2*(2*c*d-b*e)*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-2*(d+e*x)^2*_ + (b*d+(2*c*d-b*e)*x)/(b^2*sqrt(b*x+c*x^2))+e*(8*c^2*d^2-8*b*c*d*e+_ + 3*b^2*e^2)*sqrt(b*x+c*x^2)/(b^2*c^2)+2*e^2*(b*d+(2*c*d-b*e)*x)*_ + sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 3 3 2 2 | 2 x\|c +--R (- 3b e + 6b c d e )\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 3 2 3 3 2 2 2 2 3 3 2 3 +-+ +--R (b c e x + (3b e - 6b c d e + 6b c d e - 4c d )x - 2b c d )\|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R b c \|c \|c x + b x +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +----------+ +--R 3 3 2 2 | 2 | 2 +-+ +--R (3b e - 6b c d e )\|c x + b x log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 3 2 3 3 2 2 2 2 3 3 2 3 +-+ +--R (2b c e x + (6b e - 12b c d e + 12b c d e - 8c d )x - 4b c d )\|c +--R / +--R +----------+ +--R 2 2 +-+ | 2 +--R 2b c \|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 3 3 2 2 | 2 \|- c \|c x + b x +--R (- 3b e + 6b c d e )\|c x + b x atan(-------------------) +--R c x +--R + +--R 2 3 2 3 3 2 2 2 2 3 3 2 3 +---+ +--R (b c e x + (3b e - 6b c d e + 6b c d e - 4c d )x - 2b c d )\|- c +--R / +--R +----------+ +--R 2 2 +---+ | 2 +--R b c \|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 521 + +--S 522 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R 3 2 | 2 +-+ +--R (3b e - 6c d e )log(- 2c\|c x + b x + (2c x + b)\|c ) +--R + +--R +-+ +--R 3 2 x\|c +--R (6b e - 12c d e )atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R / +--R 2 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 3 2 +---+ x\|c +--R (3b e - 6c d e )\|- c atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R +----------+ +--R +---+ | 2 +--R 3 2 +-+ \|- c \|c x + b x +--R (- 3b e + 6c d e )\|c atan(-------------------) +--R c x +--R / +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1726 +r0:=2*e^2*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(d+e*x)*(b*d+_ + (2*c*d-b*e)*x)/(b^2*sqrt(b*x+c*x^2))+2*e*(2*c*d-b*e)*_ + sqrt(b*x+c*x^2)/(b^2*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 2 2 | 2 x\|c +--R 2b e \|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 2 2 2 2 2 +-+ +--R ((- 2b e + 4b c d e - 4c d )x - 2b c d )\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +----------+ +--R 2 2 | 2 | 2 +-+ +--R b e \|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 2 2 2 2 2 +-+ +--R ((- 2b e + 4b c d e - 4c d )x - 2b c d )\|c +--R / +--R +----------+ +--R 2 +-+ | 2 +--R b c\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 2 2 | 2 \|- c \|c x + b x +--R 2b e \|c x + b x atan(-------------------) +--R c x +--R + +--R 2 2 2 2 2 +---+ +--R ((- 2b e + 4b c d e - 4c d )x - 2b c d )\|- c +--R / +--R +----------+ +--R 2 +---+ | 2 +--R b c\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 528 + +--S 529 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 2 | 2 +-+ 2 x\|c +--R e log(2c\|c x + b x + (2c x + b)\|c ) - 2e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) ----------------------------------------------------------------- +--R +-+ +--R c\|c +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 2 +---+ x\|c 2 +-+ \|- c \|c x + b x +--R - 2e \|- c atanh(-------------) + 2e \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ------------------------------------------------------------------ +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 532 + +)clear all + +--S 533 of 1726 +t0:=(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1726 +r0:=-2*(b*d+(2*c*d-b*e)*x)/(b^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2b e - 4c d)x - 2b d +--R (2) --------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (2b e - 4c d)x - 2b d +--R (3) --------------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1726 +t0:=1/(b*x+c*x^2)^(3/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1726 +r0:=2/(b*sqrt(b*x+c*x^2))-4*sqrt(b*x+c*x^2)/(b^2*x) +--R +--R +--R - 4c x - 2b +--R (2) --------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1726 +a0:=integrate(t0,x) +--R +--R +--R - 4c x - 2b +--R (3) --------------- +--R +----------+ +--R 2 | 2 +--R b \|c x + b x +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R +----------+ +--R 3 2 | 2 +--R (c e x + (b e + c d)x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1726 +r0:=e^2*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*_ + sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(b*(c*d-b*e)+_ + c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 2 2 | 2 (b e - 2c d)x - b d +--R b e \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 2 +-----------+ +-+ +--R ((- 2b c e + 4c d)x - 2b e + 2b c d)\|- b e + c d \|d +--R / +--R +----------+ +--R 3 2 2 +-----------+ +-+ | 2 +--R (b d e - b c d )\|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 2 2 | 2 +--R b e \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 2 | 2 +--R ((- 2b c e + 4c d)x - 2b e + 2b c d)\|- b d e + c d +--R / +--R +--------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|- b d e + c d \|c x + b x +--R , +--R +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R 2 2 | 2 \|b d e - c d \|c x + b x +--R 2b e \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R +------------+ +--R 2 2 | 2 +--R ((- 2b c e + 4c d)x - 2b e + 2b c d)\|b d e - c d +--R / +--R +------------+ +----------+ +--R 3 2 2 | 2 | 2 +--R (b d e - b c d )\|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 545 + +--S 546 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R e \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R - e \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 | 2 +-----------+ +-+ +--R (b d e - c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 | 2 (b e - 2c d)x - b d +--R - e \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R 2e \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 +-----------+ +-+ | 2 +--R (b d e - c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R +----------+ +--R 2 4 2 3 2 2 2 | 2 +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|c x + b x +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1726 +r0:=3/2*e^2*(2*c*d-b*e)*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))-_ + 2*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*(d+e*x)*_ + sqrt(b*x+c*x^2))-e*(4*c^2*d^2-4*b*c*d*e+3*b^2*e^2)*_ + sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)) +--R +--R +--R (2) +--R +----------+ +--R 3 4 2 3 3 3 2 2 2 | 2 +--R ((3b e - 6b c d e )x + 3b d e - 6b c d e )\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 3 2 2 3 2 2 +--R (- 6b c e + 8b c d e - 8c d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (- 6b e + 4b c d e + 4b c d e - 8c d )x - 4b d e + 8b c d e +--R + +--R 2 3 +--R - 4b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 3 4 2 3 3 3 2 2 2 | 2 +--R ((3b e - 6b c d e )x + 3b d e - 6b c d e )\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 2 3 2 2 3 2 2 +--R (- 6b c e + 8b c d e - 8c d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (- 6b e + 4b c d e + 4b c d e - 8c d )x - 4b d e + 8b c d e +--R + +--R 2 3 +--R - 4b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((2b d e - 4b c d e + 2b c d e)x + 2b d e - 4b c d e + 2b c d ) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R +----------+ +--R 3 4 2 3 3 3 2 2 2 | 2 +--R ((3b e - 6b c d e )x + 3b d e - 6b c d e )\|c x + b x +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R + +--R 2 3 2 2 3 2 2 +--R (- 3b c e + 4b c d e - 4c d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 +--R (- 3b e + 2b c d e + 2b c d e - 4c d )x - 2b d e + 4b c d e +--R + +--R 2 3 +--R - 2b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 4 2 3 3 3 2 2 2 4 4 3 2 3 4 2 2 5 +--R ((b d e - 2b c d e + b c d e)x + b d e - 2b c d e + b c d ) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 552 + +--S 553 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 2 +-----------+ +-+ +--R (3b e - 6c d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 3 2 | 2 (b e - 2c d)x - b d +--R (- 3b e + 6c d e )\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (2b d e - 4b c d e + 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 3 2 | 2 (b e - 2c d)x - b d +--R (- 3b e + 6c d e )\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 3 2 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (6b e - 12c d e )\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (2b d e - 4b c d e + 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 556 + +)clear all + +--S 557 of 1726 +t0:=1/((d+e*x)^3*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1726 +r0:=3/8*e^2*(16*c^2*d^2-16*b*c*d*e+5*b^2*e^2)*atanh(1/2*(b*d+_ + (2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/_ + (d^(7/2)*(c*d-b*e)^(7/2))-2*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/_ + (b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+c*x^2))-1/2*e*(8*c^2*d^2-_ + 8*b*c*d*e+5*b^2*e^2)*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*_ + (d+e*x)^2)-1/4*e*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e+15*b^2*e^2)*_ + sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 4 6 3 5 2 2 2 4 2 +--R (15b e - 48b c d e + 48b c d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 2 4 3 3 3 +--R (30b d e - 96b c d e + 96b c d e )x + 15b d e - 48b c d e +--R + +--R 2 2 4 2 +--R 48b c d e +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 30b c e + 76b c d e - 48b c d e + 32c d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 30b e + 26b c d e + 80b c d e - 80b c d e + 64c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (- 50b d e + 112b c d e - 48b c d e - 16b c d e + 32c d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16b d e + 48b c d e - 48b c d e + 16b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 6 3 5 2 2 2 4 2 +--R (15b e - 48b c d e + 48b c d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 2 4 3 3 3 +--R (30b d e - 96b c d e + 96b c d e )x + 15b d e - 48b c d e +--R + +--R 2 2 4 2 +--R 48b c d e +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 30b c e + 76b c d e - 48b c d e + 32c d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 30b e + 26b c d e + 80b c d e - 80b c d e + 64c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (- 50b d e + 112b c d e - 48b c d e - 16b c d e + 32c d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 16b d e + 48b c d e - 48b c d e + 16b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (16b d e - 48b c d e + 48b c d e - 16b c d e)x + 8b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 24b c d e + 24b c d e - 8b c d +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 4 6 3 5 2 2 2 4 2 +--R (15b e - 48b c d e + 48b c d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 2 4 3 3 3 +--R (30b d e - 96b c d e + 96b c d e )x + 15b d e - 48b c d e +--R + +--R 2 2 4 2 +--R 48b c d e +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15b c e + 38b c d e - 24b c d e + 16c d e )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15b e + 13b c d e + 40b c d e - 40b c d e + 32c d e)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (- 25b d e + 56b c d e - 24b c d e - 8b c d e + 16c d )x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 +--R - 8b d e + 24b c d e - 24b c d e + 8b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d e )x +--R + +--R 5 4 4 4 5 3 3 2 6 2 2 3 7 5 5 3 +--R (8b d e - 24b c d e + 24b c d e - 8b c d e)x + 4b d e +--R + +--R 4 6 2 3 2 7 2 3 8 +--R - 12b c d e + 12b c d e - 4b c d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 559 + +--S 560 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 4 3 2 2 2 +-----------+ +-+ +--R (15b e - 48b c d e + 48c d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (2b d e - 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 2 4 3 2 2 2 | 2 +--R (- 15b e + 48b c d e - 48c d e )\|- b d e + c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b d e + c d \|- b e + c d +--R * +--R +-+ +--R \|d +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 2 4 3 2 2 2 | 2 +--R (- 15b e + 48b c d e - 48c d e )\|b d e - c d +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 2 4 3 2 2 2 +-----------+ +-+ +--R (30b e - 96b c d e + 96c d e )\|- b e + c d \|d +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (8b d e - 24b c d e + 24b c d e - 8c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 563 + +)clear all + +--S 564 of 1726 +t0:=(d+e*x)^4/(b*x+c*x^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R (1) -------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1726 +r0:=-2/3*(d+e*x)^3*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(3/2))+_ + 2*e^4*atanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)+4/3*(d+e*x)^2*_ + (b*d*(4*c*d-5*b*e)+(8*c^2*d^2-8*b*c*d*e-b^2*e^2)*x)/(b^4*_ + sqrt(b*x+c*x^2))-2/3*e*(2*c*d-b*e)*(16*c^2*d^2-16*b*c*d*e-_ + 3*b^2*e^2)*sqrt(b*x+c*x^2)/(b^4*c^2)-4/3*e^2*(b*d*(4*c*d-5*b*e)+_ + (8*c^2*d^2-8*b*c*d*e-b^2*e^2)*x)*sqrt(b*x+c*x^2)/(b^4*c) +--R +--R +--R (2) +--R +----------+ +-+ +--R 4 4 2 5 4 | 2 x\|c +--R (6b c e x + 6b e x)\|c x + b x atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 8b c e + 8b c d e + 24b c d e - 64b c d e + 32c d )x +--R + +--R 5 4 3 2 2 2 2 3 3 4 4 2 +--R (- 6b e + 36b c d e - 96b c d e + 48b c d )x +--R + +--R 3 2 3 2 3 4 3 2 4 +--R (- 24b c d e + 12b c d )x - 2b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +----------+ +--R 4 4 2 5 4 | 2 | 2 +-+ +--R (3b c e x + 3b e x)\|c x + b x log(2c\|c x + b x + (2c x + b)\|c ) +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 8b c e + 8b c d e + 24b c d e - 64b c d e + 32c d )x +--R + +--R 5 4 3 2 2 2 2 3 3 4 4 2 +--R (- 6b e + 36b c d e - 96b c d e + 48b c d )x +--R + +--R 3 2 3 2 3 4 3 2 4 +--R (- 24b c d e + 12b c d )x - 2b c d +--R * +--R +-+ +--R \|c +--R / +--R +----------+ +--R 4 3 2 5 2 +-+ | 2 +--R (3b c x + 3b c x)\|c \|c x + b x +--R , +--R +--R +----------+ +--R +----------+ +---+ | 2 +--R 4 4 2 5 4 | 2 \|- c \|c x + b x +--R (6b c e x + 6b e x)\|c x + b x atan(-------------------) +--R c x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 8b c e + 8b c d e + 24b c d e - 64b c d e + 32c d )x +--R + +--R 5 4 3 2 2 2 2 3 3 4 4 2 +--R (- 6b e + 36b c d e - 96b c d e + 48b c d )x +--R + +--R 3 2 3 2 3 4 3 2 4 +--R (- 24b c d e + 12b c d )x - 2b c d +--R * +--R +---+ +--R \|- c +--R / +--R +----------+ +--R 4 3 2 5 2 +---+ | 2 +--R (3b c x + 3b c x)\|- c \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 566 + +--S 567 of 1726 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R 4 | 2 +-+ 4 x\|c +--R e log(2c\|c x + b x + (2c x + b)\|c ) - 2e atanh(-------------) +--R +----------+ +--R | 2 +--R \|c x + b x +--R (4) ----------------------------------------------------------------- +--R 2 +-+ +--R c \|c +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1726 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R 4 +---+ x\|c 4 +-+ \|- c \|c x + b x +--R - 2e \|- c atanh(-------------) + 2e \|c atan(-------------------) +--R +----------+ c x +--R | 2 +--R \|c x + b x +--R (6) ------------------------------------------------------------------ +--R 2 +---+ +-+ +--R c \|- c \|c +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1726 +t0:=(d+e*x)^3/(b*x+c*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1726 +r0:=-2/3*(d+e*x)^2*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(3/2))+_ + 16/3*d*(c*d-b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (2b e + 12b c d e - 48b c d e + 32c d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (18b d e - 72b c d e + 48b c d )x + (- 18b d e + 12b c d )x - 2b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 +--R (2b e + 12b c d e - 48b c d e + 32c d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (18b d e - 72b c d e + 48b c d )x + (- 18b d e + 12b c d )x - 2b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1726 +t0:=(d+e*x)^2/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1726 +r0:=-2/3*(b+2*c*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))+_ + 8/3*(2*c*d-b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R (4b c e - 32b c d e + 32c d )x + (6b e - 48b c d e + 48b c d )x +--R + +--R 3 2 2 3 2 +--R (- 12b d e + 12b c d )x - 2b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R (4b c e - 32b c d e + 32c d )x + (6b e - 48b c d e + 48b c d )x +--R + +--R 3 2 2 3 2 +--R (- 12b d e + 12b c d )x - 2b d +--R / +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1726 +t0:=(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1726 +r0:=-2/3*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(3/2))-_ + 8/3*(2*c*d-b*e)/(b^3*sqrt(b*x+c*x^2))+16/3*(2*c*d-b*e)*_ + sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 3 +--R (- 16b c e + 32c d)x + (- 24b c e + 48b c d)x + (- 6b e + 12b c d)x - 2b d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 3 +--R (- 16b c e + 32c d)x + (- 24b c e + 48b c d)x + (- 6b e + 12b c d)x - 2b d +--R ---------------------------------------------------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1726 +t0:=1/(b*x+c*x^2)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1726 +r0:=2/3/(b*(b*x+c*x^2)^(3/2))+4/(b^2*x*sqrt(b*x+c*x^2))-_ + 16/3*sqrt(b*x+c*x^2)/(b^3*x^2)+32/3*c*sqrt(b*x+c*x^2)/(b^4*x) +--R +--R +--R 3 3 2 2 2 3 +--R 32c x + 48b c x + 12b c x - 2b +--R (2) --------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 32c x + 48b c x + 12b c x - 2b +--R (3) --------------------------------- +--R +----------+ +--R 4 2 5 | 2 +--R (3b c x + 3b x)\|c x + b x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1726 +t0:=1/((d+e*x)*(b*x+c*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------------- +--R +----------+ +--R 2 5 2 4 2 3 2 2 | 2 +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|c x + b x +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1726 +r0:=-2/3*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*_ + (b*x+c*x^2)^(3/2))+e^4*atanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*_ + sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+_ + 2/3*(b*(c*d-b*e)*(8*c^2*d^2-4*b*c*d*e-3*b^2*e^2)+c*(2*c*d-b*e)*_ + (8*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2)) +--R +--R +--R (2) +--R +----------+ +--R 4 4 2 5 4 | 2 +--R (- 3b c e x - 3b e x)\|c x + b x +--R * +--R (b e - 2c d)x - b d +--R atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (6b c e + 4b c d e - 48b c d e + 32c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 +--R (12b c e + 6b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 3 2 2 2 3 3 5 2 4 2 3 2 3 +--R (6b e - 18b c d e + 12b c d )x - 2b d e + 4b c d e - 2b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------+ +--R 4 4 2 5 4 | 2 +--R (3b c e x + 3b e x)\|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (6b c e + 4b c d e - 48b c d e + 32c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 +--R (12b c e + 6b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 3 2 2 2 3 3 5 2 4 2 3 2 3 +--R (6b e - 18b c d e + 12b c d )x - 2b d e + 4b c d e - 2b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R 4 4 2 5 4 | 2 \|b d e - c d \|c x + b x +--R (- 6b c e x - 6b e x)\|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 3 +--R (6b c e + 4b c d e - 48b c d e + 32c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 2 +--R (12b c e + 6b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 3 2 2 2 3 3 5 2 4 2 3 2 3 +--R (6b e - 18b c d e + 12b c d )x - 2b d e + 4b c d e - 2b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 6 2 2 5 2 3 4 3 4 2 7 2 2 6 3 5 2 4 +--R ((3b c d e - 6b c d e + 3b c d )x + (3b d e - 6b c d e + 3b c d )x) +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 593 + +--S 594 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 +-----------+ +-+ +--R e \|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 4 | 2 (b e - 2c d)x - b d +--R e \|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 2 2 2 3 2 4 | 2 +-----------+ +-+ +--R (b d e - 2b c d e + c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 4 | 2 (b e - 2c d)x - b d +--R e \|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 4 +-----------+ +-+ \|b d e - c d \|c x + b x +--R - 2e \|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 2 2 2 3 2 4 +-----------+ +-+ | 2 +--R (b d e - 2b c d e + c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1726 +t0:=1/((d+e*x)^2*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1726 +r0:=-2/3*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*(d+e*x)*_ + (b*x+c*x^2)^(3/2))+5/2*e^4*(2*c*d-b*e)*atanh(1/2*(b*d+(2*c*d-_ + b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*_ + (c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*(8*c^2*d^2-2*b*c*d*e-5*b^2*e^2)+_ + c*(2*c*d-b*e)*(8*c^2*d^2-8*b*c*d*e-5*b^2*e^2)*x)/(b^4*d^2*_ + (c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*(32*c^4*d^4-_ + 64*b*c^3*d^3*e+12*b^2*c^2*d^2*e^2+20*b^3*c*d*e^3-15*b^4*e^4)*_ + sqrt(b*x+c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)) +--R +--R +--R (2) +--R 5 6 4 2 5 3 6 6 5 5 4 2 2 4 2 +--R (- 15b c e + 30b c d e )x + (- 15b e + 15b c d e + 30b c d e )x +--R + +--R 6 5 5 2 4 +--R (- 15b d e + 30b c d e )x +--R * +--R +----------+ +--R | 2 (b e - 2c d)x - b d +--R \|c x + b x atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 4 +--R (30b c e - 40b c d e - 24b c d e + 128b c d e - 64c d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 60b c e - 60b c d e - 76b c d e + 168b c d e + 32b c d e +--R + +--R 6 5 +--R - 64c d +--R * +--R 3 +--R x +--R + +--R 6 5 4 2 2 3 3 3 3 2 2 4 4 5 5 2 +--R (30b e - 84b c d e + 12b c d e + 168b c d e - 96b c d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R (20b d e - 36b c d e - 12b c d e + 52b c d e - 24b c d )x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4b d e + 12b c d e - 12b c d e + 4b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +----------+ +--R +-----------+ +-+ | 2 +--R \|- b e + c d \|d \|c x + b x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 6 4 2 5 3 6 6 5 5 4 2 2 4 2 +--R (15b c e - 30b c d e )x + (15b e - 15b c d e - 30b c d e )x +--R + +--R 6 5 5 2 4 +--R (15b d e - 30b c d e )x +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 4 +--R (30b c e - 40b c d e - 24b c d e + 128b c d e - 64c d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 60b c e - 60b c d e - 76b c d e + 168b c d e + 32b c d e +--R + +--R 6 5 +--R - 64c d +--R * +--R 3 +--R x +--R + +--R 6 5 4 2 2 3 3 3 3 2 2 4 4 5 5 2 +--R (30b e - 84b c d e + 12b c d e + 168b c d e - 96b c d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R (20b d e - 36b c d e - 12b c d e + 52b c d e - 24b c d )x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 4b d e + 12b c d e - 12b c d e + 4b c d +--R * +--R +--------------+ +--R | 2 +--R \|- b d e + c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +--------------+ +----------+ +--R | 2 | 2 +--R \|- b d e + c d \|c x + b x +--R , +--R +--R 5 6 4 2 5 3 +--R (- 15b c e + 30b c d e )x +--R + +--R 6 6 5 5 4 2 2 4 2 6 5 5 2 4 +--R (- 15b e + 15b c d e + 30b c d e )x + (- 15b d e + 30b c d e )x +--R * +--R +------------+ +----------+ +--R +----------+ | 2 | 2 +--R | 2 \|b d e - c d \|c x + b x +--R \|c x + b x atan(----------------------------) +--R (b e - c d)x +--R + +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 4 +--R (15b c e - 20b c d e - 12b c d e + 64b c d e - 32c d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 30b c e - 30b c d e - 38b c d e + 84b c d e + 16b c d e +--R + +--R 6 5 +--R - 32c d +--R * +--R 3 +--R x +--R + +--R 6 5 4 2 2 3 3 3 3 2 2 4 4 5 5 2 +--R (15b e - 42b c d e + 6b c d e + 84b c d e - 48b c d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R (10b d e - 18b c d e - 6b c d e + 26b c d e - 12b c d )x +--R + +--R 6 2 3 5 3 2 4 2 4 3 3 5 +--R - 2b d e + 6b c d e - 6b c d e + 2b c d +--R * +--R +------------+ +--R | 2 +--R \|b d e - c d +--R / +--R 7 3 4 6 2 4 3 5 3 5 2 4 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 8 3 4 7 4 3 5 3 6 4 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 8 4 3 7 5 2 6 2 6 5 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +------------+ +----------+ +--R | 2 | 2 +--R \|b d e - c d \|c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 600 + +--S 601 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 4 +-----------+ +-+ +--R (5b e - 10c d e )\|- b e + c d \|d +--R * +--R log +--R +----------+ +--R 2 | 2 +--R (- 2b d e + 2c d )\|c x + b x +--R + +--R +--------------+ +--R | 2 +--R ((- b e + 2c d)x + b d)\|- b d e + c d +--R / +--R e x + d +--R + +--R +--------------+ +--R 5 4 | 2 (b e - 2c d)x - b d +--R (5b e - 10c d e )\|- b d e + c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R / +--R +--------------+ +--R 3 3 3 2 4 2 2 5 3 6 | 2 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b d e + c d \|- b e + c d \|d +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +------------+ +--R 5 4 | 2 (b e - 2c d)x - b d +--R (5b e - 10c d e )\|b d e - c d atanh(--------------------------------) +--R +----------+ +--R +-----------+ +-+ | 2 +--R 2\|- b e + c d \|d \|c x + b x +--R + +--R +------------+ +----------+ +--R | 2 | 2 +--R 5 4 +-----------+ +-+ \|b d e - c d \|c x + b x +--R (- 10b e + 20c d e )\|- b e + c d \|d atan(----------------------------) +--R (b e - c d)x +--R / +--R +------------+ +--R 3 3 3 2 4 2 2 5 3 6 +-----------+ +-+ | 2 +--R (2b d e - 6b c d e + 6b c d e - 2c d )\|- b e + c d \|d \|b d e - c d +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 604 + +)clear all + +--S 605 of 1726 +t0:=1/((2+x)*sqrt(2*x+x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-------+ +--R | 2 +--R (x + 2)\|x + 2x +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1726 +r0:=sqrt(2*x+x^2)/(2+x) +--R +--R +--R +-------+ +--R | 2 +--R \|x + 2x +--R (2) ---------- +--R x + 2 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - ------------------ +--R +-------+ +--R | 2 +--R \|x + 2x - x - 2 +--R Type: Union(Expression(Integer),...) +--E 607 + +--S 608 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 1 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1726 +t0:=(d+e*x)^(7/2)*(b*x+c*x^2) +--R +--R +--R (1) +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1726 +r0:=2/9*d*(c*d-b*e)*(d+e*x)^(9/2)/e^3-2/11*(2*c*d-b*e)*(d+e*x)^(11/2)/e^3+_ + 2/13*c*(d+e*x)^(13/2)/e^3 +--R +--R +--R (2) +--R 6 6 6 5 5 5 2 4 4 +--R 198c e x + (234b e + 720c d e )x + (884b d e + 916c d e )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (1196b d e + 424c d e )x + (624b d e + 6c d e )x +--R + +--R 4 2 5 5 6 +--R (26b d e - 8c d e)x - 52b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 5 2 4 4 +--R 198c e x + (234b e + 720c d e )x + (884b d e + 916c d e )x +--R + +--R 2 4 3 3 3 3 3 4 2 2 +--R (1196b d e + 424c d e )x + (624b d e + 6c d e )x +--R + +--R 4 2 5 5 6 +--R (26b d e - 8c d e)x - 52b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 612 + +--S 613 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1726 +t0:=(d+e*x)^(5/2)*(b*x+c*x^2) +--R +--R +--R 2 4 2 3 2 2 2 +-------+ +--R (1) (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1726 +r0:=2/7*d*(c*d-b*e)*(d+e*x)^(7/2)/e^3-2/9*(2*c*d-b*e)*(d+e*x)^(9/2)/e^3+_ + 2/11*c*(d+e*x)^(11/2)/e^3 +--R +--R +--R (2) +--R 5 5 5 4 4 4 2 3 3 +--R 126c e x + (154b e + 322c d e )x + (418b d e + 226c d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (330b d e + 6c d e )x + (22b d e - 8c d e)x - 44b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 4 2 3 3 +--R 126c e x + (154b e + 322c d e )x + (418b d e + 226c d e )x +--R + +--R 2 3 3 2 2 3 2 4 4 5 +--R (330b d e + 6c d e )x + (22b d e - 8c d e)x - 44b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 617 + +--S 618 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +)clear all + +--S 620 of 1726 +t0:=(d+e*x)^(3/2)*(b*x+c*x^2) +--R +--R +--R 3 2 +-------+ +--R (1) (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1726 +r0:=2/5*d*(c*d-b*e)*(d+e*x)^(5/2)/e^3-2/7*(2*c*d-b*e)*(d+e*x)^(7/2)/e^3+_ + 2/9*c*(d+e*x)^(9/2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 3 3 2 2 2 +--R 70c e x + (90b e + 100c d e )x + (144b d e + 6c d e )x +--R + +--R 2 2 3 3 4 +--R (18b d e - 8c d e)x - 36b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 3 2 2 2 +--R 70c e x + (90b e + 100c d e )x + (144b d e + 6c d e )x +--R + +--R 2 2 3 3 4 +--R (18b d e - 8c d e)x - 36b d e + 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 622 + +--S 623 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 1726 +t0:=(b*x+c*x^2)*sqrt(d+e*x) +--R +--R +--R 2 +-------+ +--R (1) (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1726 +r0:=2/3*d*(c*d-b*e)*(d+e*x)^(3/2)/e^3-2/5*(2*c*d-b*e)*(d+e*x)^(5/2)/e^3+_ + 2/7*c*(d+e*x)^(7/2)/e^3 +--R +--R +--R (2) +--R 3 3 3 2 2 2 2 2 +--R 30c e x + (42b e + 6c d e )x + (14b d e - 8c d e)x - 28b d e +--R + +--R 3 +--R 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 2 2 2 +--R 30c e x + (42b e + 6c d e )x + (14b d e - 8c d e)x - 28b d e +--R + +--R 3 +--R 16c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 627 + +--S 628 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 629 + +)clear all + +--S 630 of 1726 +t0:=(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R 2 +--R c x + b x +--R (1) ---------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1726 +r0:=-2/3*(2*c*d-b*e)*(d+e*x)^(3/2)/e^3+2/5*c*(d+e*x)^(5/2)/e^3+_ + 2*d*(c*d-b*e)*sqrt(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 +-------+ +--R (6c e x + (10b e - 8c d e)x - 20b d e + 16c d )\|e x + d +--R (2) ----------------------------------------------------------- +--R 3 +--R 15e +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +-------+ +--R (6c e x + (10b e - 8c d e)x - 20b d e + 16c d )\|e x + d +--R (3) ----------------------------------------------------------- +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 632 + +--S 633 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 634 + +)clear all + +--S 635 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R 2 +--R c x + b x +--R (1) ------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1726 +r0:=2/3*c*(d+e*x)^(3/2)/e^3-2*d*(c*d-b*e)/(e^3*sqrt(d+e*x))-_ + 2*(2*c*d-b*e)*sqrt(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 +--R 2c e x + (6b e - 8c d e)x + 12b d e - 16c d +--R (2) ---------------------------------------------- +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R 2c e x + (6b e - 8c d e)x + 12b d e - 16c d +--R (3) ---------------------------------------------- +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 637 + +--S 638 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R 2 +--R c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1726 +r0:=-2/3*d*(c*d-b*e)/(e^3*(d+e*x)^(3/2))+2*(2*c*d-b*e)/(e^3*sqrt(d+e*x))+_ + 2*c*sqrt(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 +--R 6c e x + (- 6b e + 24c d e)x - 4b d e + 16c d +--R (2) ------------------------------------------------ +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R 6c e x + (- 6b e + 24c d e)x - 4b d e + 16c d +--R (3) ------------------------------------------------ +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 642 + +--S 643 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 644 + +)clear all + +--S 645 of 1726 +t0:=(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R 2 +--R c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1726 +r0:=-2/5*d*(c*d-b*e)/(e^3*(d+e*x)^(5/2))+2/3*(2*c*d-b*e)/_ + (e^3*(d+e*x)^(3/2))-2*c/(e^3*sqrt(d+e*x)) +--R +--R +--R 2 2 2 2 +--R - 30c e x + (- 10b e - 40c d e)x - 4b d e - 16c d +--R (2) ---------------------------------------------------- +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R - 30c e x + (- 10b e - 40c d e)x - 4b d e - 16c d +--R (3) ---------------------------------------------------- +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 647 + +--S 648 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 649 + +)clear all + +--S 650 of 1726 +t0:=(d+e*x)^(7/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1726 +r0:=2/9*d^2*(c*d-b*e)^2*(d+e*x)^(9/2)/e^5-4/11*d*(c*d-b*e)*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^5+2/13*(6*c^2*d^2-6*b*c*d*e+_ + b^2*e^2)*(d+e*x)^(13/2)/e^5-4/15*c*(2*c*d-b*e)*(d+e*x)^(15/2)/_ + e^5+2/17*c^2*(d+e*x)^(17/2)/e^5 +--R +--R +--R (2) +--R 2 8 8 8 2 7 7 +--R 12870c e x + (29172b c e + 44616c d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (16830b e + 103224b c d e + 52932c d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (61200b d e + 126072b c d e + 21816c d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (77860b d e + 54400b c d e + 70c d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (36040b d e + 340b c d e - 80c d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (510b d e - 408b c d e + 96c d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 +--R (- 680b d e + 544b c d e - 128c d e)x + 1360b d e - 1088b c d e +--R + +--R 2 8 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 8 2 7 7 +--R 12870c e x + (29172b c e + 44616c d e )x +--R + +--R 2 8 7 2 2 6 6 +--R (16830b e + 103224b c d e + 52932c d e )x +--R + +--R 2 7 2 6 2 3 5 5 +--R (61200b d e + 126072b c d e + 21816c d e )x +--R + +--R 2 2 6 3 5 2 4 4 4 +--R (77860b d e + 54400b c d e + 70c d e )x +--R + +--R 2 3 5 4 4 2 5 3 3 +--R (36040b d e + 340b c d e - 80c d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 +--R (510b d e - 408b c d e + 96c d e )x +--R + +--R 2 5 3 6 2 2 7 2 6 2 7 +--R (- 680b d e + 544b c d e - 128c d e)x + 1360b d e - 1088b c d e +--R + +--R 2 8 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 652 + +--S 653 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1726 +t0:=(d+e*x)^(5/2)*(b*x+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1726 +r0:=2/7*d^2*(c*d-b*e)^2*(d+e*x)^(7/2)/e^5-4/9*d*(c*d-b*e)*(2*c*d-b*e)*_ + (d+e*x)^(9/2)/e^5+2/11*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*_ + (d+e*x)^(11/2)/e^5-4/13*c*(2*c*d-b*e)*(d+e*x)^(13/2)/e^5+_ + 2/15*c^2*(d+e*x)^(15/2)/e^5 +--R +--R +--R (2) +--R 2 7 7 7 2 6 6 +--R 6006c e x + (13860b c e + 14322c d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (8190b e + 34020b c d e + 8946c d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (20930b d e + 22260b c d e + 70c d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (14690b d e + 300b c d e - 80c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (390b d e - 360b c d e + 96c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 +--R (- 520b d e + 480b c d e - 128c d e)x + 1040b d e - 960b c d e +--R + +--R 2 7 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 7 2 6 6 +--R 6006c e x + (13860b c e + 14322c d e )x +--R + +--R 2 7 6 2 2 5 5 +--R (8190b e + 34020b c d e + 8946c d e )x +--R + +--R 2 6 2 5 2 3 4 4 +--R (20930b d e + 22260b c d e + 70c d e )x +--R + +--R 2 2 5 3 4 2 4 3 3 +--R (14690b d e + 300b c d e - 80c d e )x +--R + +--R 2 3 4 4 3 2 5 2 2 +--R (390b d e - 360b c d e + 96c d e )x +--R + +--R 2 4 3 5 2 2 6 2 5 2 6 +--R (- 520b d e + 480b c d e - 128c d e)x + 1040b d e - 960b c d e +--R + +--R 2 7 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 657 + +--S 658 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 659 + +)clear all + +--S 660 of 1726 +t0:=(d+e*x)^(3/2)*(b*x+c*x^2)^2 +--R +--R +--R 2 5 2 4 2 3 2 2 +-------+ +--R (1) (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1726 +r0:=2/5*d^2*(c*d-b*e)^2*(d+e*x)^(5/2)/e^5-4/7*d*(c*d-b*e)*(2*c*d-b*e)*_ + (d+e*x)^(7/2)/e^5+2/9*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*_ + (d+e*x)^(9/2)/e^5-4/11*c*(2*c*d-b*e)*(d+e*x)^(11/2)/e^5+_ + 2/13*c^2*(d+e*x)^(13/2)/e^5 +--R +--R +--R (2) +--R 2 6 6 6 2 5 5 +--R 6930c e x + (16380b c e + 8820c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (10010b e + 21840b c d e + 210c d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (14300b d e + 780b c d e - 240c d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (858b d e - 936b c d e + 288c d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 +--R (- 1144b d e + 1248b c d e - 384c d e)x + 2288b d e - 2496b c d e +--R + +--R 2 6 +--R 768c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 6 2 5 5 +--R 6930c e x + (16380b c e + 8820c d e )x +--R + +--R 2 6 5 2 2 4 4 +--R (10010b e + 21840b c d e + 210c d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (14300b d e + 780b c d e - 240c d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (858b d e - 936b c d e + 288c d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 +--R (- 1144b d e + 1248b c d e - 384c d e)x + 2288b d e - 2496b c d e +--R + +--R 2 6 +--R 768c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 662 + +--S 663 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1726 +t0:=(b*x+c*x^2)^2*sqrt(d+e*x) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (1) (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1726 +r0:=2/3*d^2*(c*d-b*e)^2*(d+e*x)^(3/2)/e^5-4/5*d*(c*d-b*e)*(2*c*d-b*e)*_ + (d+e*x)^(5/2)/e^5+2/7*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*_ + (d+e*x)^(7/2)/e^5-4/9*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^5+_ + 2/11*c^2*(d+e*x)^(11/2)/e^5 +--R +--R +--R (2) +--R 2 5 5 5 2 4 4 +--R 630c e x + (1540b c e + 70c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (990b e + 220b c d e - 80c d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (198b d e - 264b c d e + 96c d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 +--R (- 264b d e + 352b c d e - 128c d e)x + 528b d e - 704b c d e +--R + +--R 2 5 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 5 2 4 4 +--R 630c e x + (1540b c e + 70c d e )x +--R + +--R 2 5 4 2 2 3 3 +--R (990b e + 220b c d e - 80c d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (198b d e - 264b c d e + 96c d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 +--R (- 264b d e + 352b c d e - 128c d e)x + 528b d e - 704b c d e +--R + +--R 2 5 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1726 +t0:=(b*x+c*x^2)^2/sqrt(d+e*x) +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) --------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1726 +r0:=-4/3*d*(c*d-b*e)*(2*c*d-b*e)*(d+e*x)^(3/2)/e^5+2/5*(6*c^2*d^2-_ + 6*b*c*d*e+b^2*e^2)*(d+e*x)^(5/2)/e^5-4/7*c*(2*c*d-b*e)*_ + (d+e*x)^(7/2)/e^5+2/9*c^2*(d+e*x)^(9/2)/e^5+2*d^2*(c*d-b*e)^2*_ + sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 70c e x + (180b c e - 80c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126b e - 216b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (- 168b d e + 288b c d e - 128c d e)x + 336b d e - 576b c d e +--R + +--R 2 4 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 70c e x + (180b c e - 80c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (126b e - 216b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 +--R (- 168b d e + 288b c d e - 128c d e)x + 336b d e - 576b c d e +--R + +--R 2 4 +--R 256c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 672 + +--S 673 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +)clear all + +--S 675 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^(3/2) +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) --------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1726 +r0:=2/3*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*(d+e*x)^(3/2)/e^5-_ + 4/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^5+2/7*c^2*(d+e*x)^(7/2)/e^5-_ + 2*d^2*(c*d-b*e)^2/(e^5*sqrt(d+e*x))-4*d*(c*d-b*e)*(2*c*d-b*e)*_ + sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R 30c e x + (84b c e - 48c d e )x + (70b e - 168b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 280b d e + 672b c d e - 384c d e)x - 560b d e + 1344b c d e - 768c d +--R / +--R 5 +-------+ +--R 105e \|e x + d +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R 30c e x + (84b c e - 48c d e )x + (70b e - 168b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 280b d e + 672b c d e - 384c d e)x - 560b d e + 1344b c d e - 768c d +--R / +--R 5 +-------+ +--R 105e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 677 + +--S 678 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 679 + +)clear all + +--S 680 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1726 +r0:=-2/3*d^2*(c*d-b*e)^2/(e^5*(d+e*x)^(3/2))-4/3*c*(2*c*d-b*e)*_ + (d+e*x)^(3/2)/e^5+2/5*c^2*(d+e*x)^(5/2)/e^5+4*d*(c*d-b*e)*_ + (2*c*d-b*e)/(e^5*sqrt(d+e*x))+2*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)*_ + sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R 6c e x + (20b c e - 16c d e )x + (30b e - 120b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (120b d e - 480b c d e + 384c d e)x + 80b d e - 320b c d e + 256c d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 2 4 3 2 2 2 2 +--R 6c e x + (20b c e - 16c d e )x + (30b e - 120b c d e + 96c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (120b d e - 480b c d e + 384c d e)x + 80b d e - 320b c d e + 256c d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 682 + +--S 683 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1726 +t0:=(b*x+c*x^2)^2/(d+e*x)^(7/2) +--R +--R +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1726 +r0:=-2/5*d^2*(c*d-b*e)^2/(e^5*(d+e*x)^(5/2))+4/3*d*(c*d-b*e)*_ + (2*c*d-b*e)/(e^5*(d+e*x)^(3/2))+2/3*c^2*(d+e*x)^(3/2)/e^5-_ + 2*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)/(e^5*sqrt(d+e*x))-_ + 4*c*(2*c*d-b*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 4 2 3 3 +--R 10c e x + (60b c e - 80c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (- 30b e + 360b c d e - 480c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 40b d e + 480b c d e - 640c d e)x - 16b d e + 192b c d e - 256c d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 2 3 3 +--R 10c e x + (60b c e - 80c d e )x +--R + +--R 2 4 3 2 2 2 2 +--R (- 30b e + 360b c d e - 480c d e )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 40b d e + 480b c d e - 640c d e)x - 16b d e + 192b c d e - 256c d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 687 + +--S 688 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 689 + +)clear all + +--S 690 of 1726 +t0:=(d+e*x)^(7/2)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 9 2 3 3 2 8 2 3 2 2 3 2 7 +--R c e x + (3b c e + 3c d e )x + (3b c e + 9b c d e + 3c d e)x +--R + +--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 5 +--R (b e + 9b c d e + 9b c d e + c d )x + (3b d e + 9b c d e + 3b c d )x +--R + +--R 3 2 2 3 4 3 3 3 +--R (3b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1726 +r0:=2/9*d^3*(c*d-b*e)^3*(d+e*x)^(9/2)/e^7-6/11*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*(d+e*x)^(11/2)/e^7+6/13*d*(c*d-b*e)*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(13/2)/e^7-2/15*(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(15/2)/e^7+6/17*c*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(17/2)/e^7-6/19*c^2*_ + (2*c*d-b*e)*(d+e*x)^(19/2)/e^7+2/21*c^3*(d+e*x)^(21/2)/e^7 +--R +--R +--R (2) +--R 3 10 10 2 10 3 9 9 +--R 1385670c e x + (4594590b c e + 4667520c d e )x +--R + +--R 2 10 2 9 3 2 8 8 +--R (5135130b c e + 15675660b c d e + 5328180c d e )x +--R + +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (1939938b e + 17801784b c d e + 18198180b c d e + 2076360c d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (6864396b d e + 21119868b c d e + 7262640b c d e + 2310c d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (8383788b d e + 8704584b c d e + 13230b c d e - 2520c d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3617600b d e + 27930b c d e - 14700b c d e + 2800c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (22610b d e - 31920b c d e + 16800b c d e - 3200c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (- 27132b d e + 38304b c d e - 20160b c d e + 3840c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 +--R (36176b d e - 51072b c d e + 26880b c d e - 5120c d e)x +--R + +--R 3 7 3 2 8 2 2 9 3 10 +--R - 72352b d e + 102144b c d e - 53760b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 14549535e +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 10 10 2 10 3 9 9 +--R 1385670c e x + (4594590b c e + 4667520c d e )x +--R + +--R 2 10 2 9 3 2 8 8 +--R (5135130b c e + 15675660b c d e + 5328180c d e )x +--R + +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (1939938b e + 17801784b c d e + 18198180b c d e + 2076360c d e )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (6864396b d e + 21119868b c d e + 7262640b c d e + 2310c d e )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (8383788b d e + 8704584b c d e + 13230b c d e - 2520c d e )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (3617600b d e + 27930b c d e - 14700b c d e + 2800c d e )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (22610b d e - 31920b c d e + 16800b c d e - 3200c d e )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (- 27132b d e + 38304b c d e - 20160b c d e + 3840c d e )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 +--R (36176b d e - 51072b c d e + 26880b c d e - 5120c d e)x +--R + +--R 3 7 3 2 8 2 2 9 3 10 +--R - 72352b d e + 102144b c d e - 53760b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 14549535e +--R Type: Union(Expression(Integer),...) +--E 692 + +--S 693 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 694 + +)clear all + +--S 695 of 1726 +t0:=(d+e*x)^(5/2)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1726 +r0:=2/7*d^3*(c*d-b*e)^3*(d+e*x)^(7/2)/e^7-2/3*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*(d+e*x)^(9/2)/e^7+6/11*d*(c*d-b*e)*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(11/2)/e^7-2/13*(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(13/2)/e^7+2/5*c*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(15/2)/e^7-6/17*c^2*_ + (2*c*d-b*e)*(d+e*x)^(17/2)/e^7+2/19*c^3*(d+e*x)^(19/2)/e^7 +--R +--R +--R (2) +--R 3 9 9 2 9 3 8 8 +--R 510510c e x + (1711710b c e + 1171170c d e )x +--R + +--R 2 9 2 8 3 2 7 7 +--R (1939938b c e + 3993990b c d e + 690690c d e )x +--R + +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (746130b e + 4626006b c d e + 2413950b c d e + 2310c d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (1831410b d e + 2889558b c d e + 11970b c d e - 2520c d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (1198330b d e + 22610b c d e - 13300b c d e + 2800c d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (16150b d e - 25840b c d e + 15200b c d e - 3200c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (- 19380b d e + 31008b c d e - 18240b c d e + 3840c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 +--R (25840b d e - 41344b c d e + 24320b c d e - 5120c d e)x +--R + +--R 3 6 3 2 7 2 2 8 3 9 +--R - 51680b d e + 82688b c d e - 48640b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 4849845e +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 9 2 9 3 8 8 +--R 510510c e x + (1711710b c e + 1171170c d e )x +--R + +--R 2 9 2 8 3 2 7 7 +--R (1939938b c e + 3993990b c d e + 690690c d e )x +--R + +--R 3 9 2 8 2 2 7 3 3 6 6 +--R (746130b e + 4626006b c d e + 2413950b c d e + 2310c d e )x +--R + +--R 3 8 2 2 7 2 3 6 3 4 5 5 +--R (1831410b d e + 2889558b c d e + 11970b c d e - 2520c d e )x +--R + +--R 3 2 7 2 3 6 2 4 5 3 5 4 4 +--R (1198330b d e + 22610b c d e - 13300b c d e + 2800c d e )x +--R + +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (16150b d e - 25840b c d e + 15200b c d e - 3200c d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (- 19380b d e + 31008b c d e - 18240b c d e + 3840c d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 +--R (25840b d e - 41344b c d e + 24320b c d e - 5120c d e)x +--R + +--R 3 6 3 2 7 2 2 8 3 9 +--R - 51680b d e + 82688b c d e - 48640b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 4849845e +--R Type: Union(Expression(Integer),...) +--E 697 + +--S 698 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1726 +t0:=(d+e*x)^(3/2)*(b*x+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1726 +r0:=2/5*d^3*(c*d-b*e)^3*(d+e*x)^(5/2)/e^7-6/7*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*(d+e*x)^(7/2)/e^7+2/3*d*(c*d-b*e)*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(9/2)/e^7-2/11*(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(11/2)/e^7+6/13*c*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(13/2)/e^7-2/5*c^2*_ + (2*c*d-b*e)*(d+e*x)^(15/2)/e^7+2/17*c^3*(d+e*x)^(17/2)/e^7 +--R +--R +--R (2) +--R 3 8 8 2 8 3 7 7 +--R 30030c e x + (102102b c e + 36036c d e )x +--R + +--R 2 8 2 7 3 2 6 6 +--R (117810b c e + 125664b c d e + 462c d e )x +--R + +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (46410b e + 149940b c d e + 2142b c d e - 504c d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (61880b d e + 3570b c d e - 2380b c d e + 560c d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (2210b d e - 4080b c d e + 2720b c d e - 640c d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (- 2652b d e + 4896b c d e - 3264b c d e + 768c d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (3536b d e - 6528b c d e + 4352b c d e - 1024c d e)x - 7072b d e +--R + +--R 2 6 2 2 7 3 8 +--R 13056b c d e - 8704b c d e + 2048c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 255255e +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 2 8 3 7 7 +--R 30030c e x + (102102b c e + 36036c d e )x +--R + +--R 2 8 2 7 3 2 6 6 +--R (117810b c e + 125664b c d e + 462c d e )x +--R + +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (46410b e + 149940b c d e + 2142b c d e - 504c d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (61880b d e + 3570b c d e - 2380b c d e + 560c d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (2210b d e - 4080b c d e + 2720b c d e - 640c d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (- 2652b d e + 4896b c d e - 3264b c d e + 768c d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (3536b d e - 6528b c d e + 4352b c d e - 1024c d e)x - 7072b d e +--R + +--R 2 6 2 2 7 3 8 +--R 13056b c d e - 8704b c d e + 2048c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 255255e +--R Type: Union(Expression(Integer),...) +--E 702 + +--S 703 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 704 + +)clear all + +--S 705 of 1726 +t0:=(b*x+c*x^2)^3*sqrt(d+e*x) +--R +--R +--R 3 6 2 5 2 4 3 3 +-------+ +--R (1) (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1726 +r0:=2/3*d^3*(c*d-b*e)^3*(d+e*x)^(3/2)/e^7-6/5*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*(d+e*x)^(5/2)/e^7+6/7*d*(c*d-b*e)*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(7/2)/e^7-2/9*(2*c*d-b*e)*(10*_ + c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(9/2)/e^7+6/11*c*(5*c^2*_ + d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(11/2)/e^7-6/13*c^2*(2*c*d-_ + b*e)*(d+e*x)^(13/2)/e^7+2/15*c^3*(d+e*x)^(15/2)/e^7 +--R +--R +--R (2) +--R 3 7 7 2 7 3 6 6 +--R 6006c e x + (20790b c e + 462c d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (24570b c e + 1890b c d e - 504c d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (10010b e + 2730b c d e - 2100b c d e + 560c d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (1430b d e - 3120b c d e + 2400b c d e - 640c d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (- 1716b d e + 3744b c d e - 2880b c d e + 768c d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (2288b d e - 4992b c d e + 3840b c d e - 1024c d e)x - 4576b d e +--R + +--R 2 5 2 2 6 3 7 +--R 9984b c d e - 7680b c d e + 2048c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 2 7 3 6 6 +--R 6006c e x + (20790b c e + 462c d e )x +--R + +--R 2 7 2 6 3 2 5 5 +--R (24570b c e + 1890b c d e - 504c d e )x +--R + +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (10010b e + 2730b c d e - 2100b c d e + 560c d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (1430b d e - 3120b c d e + 2400b c d e - 640c d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (- 1716b d e + 3744b c d e - 2880b c d e + 768c d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (2288b d e - 4992b c d e + 3840b c d e - 1024c d e)x - 4576b d e +--R + +--R 2 5 2 2 6 3 7 +--R 9984b c d e - 7680b c d e + 2048c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 707 + +--S 708 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 709 + +)clear all + +--S 710 of 1726 +t0:=(b*x+c*x^2)^3/sqrt(d+e*x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1726 +r0:=-2*d^2*(c*d-b*e)^2*(2*c*d-b*e)*(d+e*x)^(3/2)/e^7+6/5*d*(c*d-b*e)*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(5/2)/e^7-2/7*(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(7/2)/e^7+2/3*c*(5*c^2*d^2-_ + 5*b*c*d*e+b^2*e^2)*(d+e*x)^(9/2)/e^7-6/11*c^2*(2*c*d-b*e)*_ + (d+e*x)^(11/2)/e^7+2/13*c^3*(d+e*x)^(13/2)/e^7+2*d^3*(c*d-b*e)^3*_ + sqrt(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 2310c e x + (8190b c e - 2520c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (10010b c e - 9100b c d e + 2800c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (4290b e - 11440b c d e + 10400b c d e - 3200c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 5148b d e + 13728b c d e - 12480b c d e + 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (6864b d e - 18304b c d e + 16640b c d e - 5120c d e)x - 13728b d e +--R + +--R 2 4 2 2 5 3 6 +--R 36608b c d e - 33280b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 15015e +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 2310c e x + (8190b c e - 2520c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (10010b c e - 9100b c d e + 2800c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (4290b e - 11440b c d e + 10400b c d e - 3200c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 5148b d e + 13728b c d e - 12480b c d e + 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (6864b d e - 18304b c d e + 16640b c d e - 5120c d e)x - 13728b d e +--R + +--R 2 4 2 2 5 3 6 +--R 36608b c d e - 33280b c d e + 10240c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 712 + +--S 713 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^(3/2) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1726 +r0:=2*d*(c*d-b*e)*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(3/2)/e^7-_ + 2/5*(2*c*d-b*e)*(10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(5/2)/e^7+_ + 6/7*c*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(7/2)/e^7-_ + 2/3*c^2*(2*c*d-b*e)*(d+e*x)^(9/2)/e^7+2/11*c^3*(d+e*x)^(11/2)/e^7-_ + 2*d^3*(c*d-b*e)^3/(e^7*sqrt(d+e*x))-6*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)*sqrt(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 210c e x + (770b c e - 280c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (990b c e - 1100b c d e + 400c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (462b e - 1584b c d e + 1760b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 924b d e + 3168b c d e - 3520b c d e + 1280c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (3696b d e - 12672b c d e + 14080b c d e - 5120c d e)x + 7392b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 25344b c d e + 28160b c d e - 10240c d +--R / +--R 7 +-------+ +--R 1155e \|e x + d +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 210c e x + (770b c e - 280c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (990b c e - 1100b c d e + 400c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (462b e - 1584b c d e + 1760b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 924b d e + 3168b c d e - 3520b c d e + 1280c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (3696b d e - 12672b c d e + 14080b c d e - 5120c d e)x + 7392b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 25344b c d e + 28160b c d e - 10240c d +--R / +--R 7 +-------+ +--R 1155e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 717 + +--S 718 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 719 + +)clear all + +--S 720 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^(5/2) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1726 +r0:=-2/3*d^3*(c*d-b*e)^3/(e^7*(d+e*x)^(3/2))-2/3*(2*c*d-b*e)*_ + (10*c^2*d^2-10*b*c*d*e+b^2*e^2)*(d+e*x)^(3/2)/e^7+6/5*c*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*(d+e*x)^(5/2)/e^7-6/7*c^2*_ + (2*c*d-b*e)*(d+e*x)^(7/2)/e^7+2/9*c^3*(d+e*x)^(9/2)/e^7+_ + 6*d^2*(c*d-b*e)^2*(2*c*d-b*e)/(e^7*sqrt(d+e*x))+6*d*(c*d-b*e)*_ + (5*c^2*d^2-5*b*c*d*e+b^2*e^2)*sqrt(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 70c e x + (270b c e - 120c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (378b c e - 540b c d e + 240c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (210b e - 1008b c d e + 1440b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 1260b d e + 6048b c d e - 8640b c d e + 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 5040b d e + 24192b c d e - 34560b c d e + 15360c d e)x - 3360b d e +--R + +--R 2 4 2 2 5 3 6 +--R 16128b c d e - 23040b c d e + 10240c d +--R / +--R 8 7 +-------+ +--R (315e x + 315d e )\|e x + d +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 70c e x + (270b c e - 120c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (378b c e - 540b c d e + 240c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (210b e - 1008b c d e + 1440b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (- 1260b d e + 6048b c d e - 8640b c d e + 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (- 5040b d e + 24192b c d e - 34560b c d e + 15360c d e)x - 3360b d e +--R + +--R 2 4 2 2 5 3 6 +--R 16128b c d e - 23040b c d e + 10240c d +--R / +--R 8 7 +-------+ +--R (315e x + 315d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 722 + +--S 723 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1726 +t0:=(b*x+c*x^2)^3/(d+e*x)^(7/2) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1726 +r0:=-2/5*d^3*(c*d-b*e)^3/(e^7*(d+e*x)^(5/2))+2*d^2*(c*d-b*e)^2*_ + (2*c*d-b*e)/(e^7*(d+e*x)^(3/2))+2*c*(5*c^2*d^2-5*b*c*d*e+_ + b^2*e^2)*(d+e*x)^(3/2)/e^7-6/5*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^7+_ + 2/7*c^3*(d+e*x)^(7/2)/e^7-6*d*(c*d-b*e)*(5*c^2*d^2-5*b*c*_ + d*e+b^2*e^2)/(e^7*sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2-_ + 10*b*c*d*e+b^2*e^2)*sqrt(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 6 2 6 3 5 5 +--R 10c e x + (42b c e - 24c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (70b c e - 140b c d e + 80c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (70b e - 560b c d e + 1120b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (420b d e - 3360b c d e + 6720b c d e - 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (560b d e - 4480b c d e + 8960b c d e - 5120c d e)x + 224b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 1792b c d e + 3584b c d e - 2048c d +--R / +--R 9 2 8 2 7 +-------+ +--R (35e x + 70d e x + 35d e )\|e x + d +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 2 6 3 5 5 +--R 10c e x + (42b c e - 24c d e )x +--R + +--R 2 6 2 5 3 2 4 4 +--R (70b c e - 140b c d e + 80c d e )x +--R + +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (70b e - 560b c d e + 1120b c d e - 640c d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (420b d e - 3360b c d e + 6720b c d e - 3840c d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (560b d e - 4480b c d e + 8960b c d e - 5120c d e)x + 224b d e +--R + +--R 2 4 2 2 5 3 6 +--R - 1792b c d e + 3584b c d e - 2048c d +--R / +--R 9 2 8 2 7 +-------+ +--R (35e x + 70d e x + 35d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1726 +t0:=(d+e*x)^(7/2)/(b*x+c*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1726 +r0:=2/3*e*(2*c*d-b*e)*(d+e*x)^(3/2)/c^2+2/5*e*(d+e*x)^(5/2)/c-_ + 2*d^(7/2)*atanh(sqrt(d+e*x)/sqrt(d))/b+2*(c*d-b*e)^(7/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+_ + 2*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2)*sqrt(d+e*x)/c^3 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 30b e + 90b c d e - 90b c d e + 30c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 +-+ +-+ \|e x + d +--R - 30c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 3 2 2 3 3 2 2 +--R 6b c e x + (- 10b c e + 32b c d e )x + 30b e - 100b c d e +--R + +--R 2 2 +--R 116b c d e +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 +-+ +--R 15b c \|c +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- b e + c d +--R (15b e - 45b c d e + 45b c d e - 15c d ) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 3 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 15c d \|d log(----------------------------) +--R x +--R + +--R 2 3 2 2 3 2 2 3 3 2 2 +--R 6b c e x + (- 10b c e + 32b c d e )x + 30b e - 100b c d e +--R + +--R 2 2 +--R 116b c d e +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-+ +-------+ +--R 3 3 +-+ - 2\|d \|e x + d + e x + 2d +--R 15c d \|d log(----------------------------) +--R x +--R + +--R +---------+ +--R 3 3 2 2 2 2 3 3 |b e - c d +--R (- 30b e + 90b c d e - 90b c d e + 30c d ) |--------- +--R \| c +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 3 2 2 3 3 2 2 +--R 6b c e x + (- 10b c e + 32b c d e )x + 30b e - 100b c d e +--R + +--R 2 2 +--R 116b c d e +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- b e + c d +--R (15b e - 45b c d e + 45b c d e - 15c d ) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R 3 3 +---+ \|e x + d +--R - 30c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 3 2 2 3 2 2 3 3 2 2 +--R 6b c e x + (- 10b c e + 32b c d e )x + 30b e - 100b c d e +--R + +--R 2 2 +--R 116b c d e +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R , +--R +--R +-------+ +--R 3 3 +---+ \|e x + d +--R - 30c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +--R 3 3 2 2 2 2 3 3 |b e - c d +--R (- 30b e + 90b c d e - 90b c d e + 30c d ) |--------- +--R \| c +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 3 2 2 3 2 2 3 3 2 2 +--R 6b c e x + (- 10b c e + 32b c d e )x + 30b e - 100b c d e +--R + +--R 2 2 +--R 116b c d e +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- b e + c d +-+ +--R (b e - 3b c d e + 3b c d e - c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 3 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|c \|e x + d +--R (2b e - 6b c d e + 6b c d e - 2c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 +-+ +-+ \|e x + d +--R 2c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|c \|e x + d +--R (2b e - 6b c d e + 6b c d e - 2c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 +-+ +-+ \|e x + d +--R 2c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 3 3 2 2 2 2 3 3 +-+ |b e - c d \|e x + d +--R (- 2b e + 6b c d e - 6b c d e + 2c d )\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1726 +t0:=(d+e*x)^(5/2)/(b*x+c*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1726 +r0:=2/3*e*(d+e*x)^(3/2)/c-2*d^(5/2)*atanh(sqrt(d+e*x)/sqrt(d))/b+_ + 2*(c*d-b*e)^(5/2)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b*c^(5/2))+2*e*(2*c*d-b*e)*sqrt(d+e*x)/c^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (6b e - 12b c d e + 6c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|e x + d +--R - 6c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 2 +-+ +-------+ +--R (2b c e x - 6b e + 14b c d e)\|c \|e x + d +--R / +--R 2 +-+ +--R 3b c \|c +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- b e + c d +--R (3b e - 6b c d e + 3c d ) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3c d \|d log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (2b c e x - 6b e + 14b c d e)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-+ +-------+ +--R 2 2 +-+ - 2\|d \|e x + d + e x + 2d +--R 3c d \|d log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |b e - c d \|e x + d +--R (6b e - 12b c d e + 6c d ) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 +-------+ +--R (2b c e x - 6b e + 14b c d e)\|e x + d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-----------+ +--R 2 2 2 2 |- b e + c d +--R (3b e - 6b c d e + 3c d ) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R 2 2 +---+ \|e x + d 2 2 2 +-------+ +--R - 6c d \|- d atan(----------) + (2b c e x - 6b e + 14b c d e)\|e x + d +--R +---+ +--R \|- d +--R / +--R 2 +--R 3b c +--R , +--R +--R +-------+ +--R 2 2 +---+ \|e x + d +--R - 6c d \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |b e - c d \|e x + d +--R (6b e - 12b c d e + 6c d ) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 2 +-------+ +--R (2b c e x - 6b e + 14b c d e)\|e x + d +--R / +--R 2 +--R 3b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 739 + +--S 740 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- b e + c d +-+ +--R (b e - 2b c d e + c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 2b e + 4b c d e - 2c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|e x + d +--R 2c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 2b e + 4b c d e - 2c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|e x + d +--R 2c d \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |b e - c d \|e x + d +--R (2b e - 4b c d e + 2c d )\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 2 +-+ +--R b c \|c +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1726 +t0:=(d+e*x)^(3/2)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1726 +r0:=-2*d^(3/2)*atanh(sqrt(d+e*x)/sqrt(d))/b+2*(c*d-b*e)^(3/2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(3/2))+2*e*sqrt(d+e*x)/c +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (- 2b e + 2c d)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +-+ +-------+ +--R - 2c d\|c \|d atanh(----------) + 2b e\|c \|e x + d +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- b e + c d +--R (b e - c d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +-------+ +--R c d\|d log(----------------------------) + 2b e\|e x + d +--R x +--R / +--R b c +--R , +--R +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R c d\|d log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R |b e - c d \|e x + d +-------+ +--R (- 2b e + 2c d) |--------- atan(------------) + 2b e\|e x + d +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R b c +--R , +--R +--R +-----------+ +--R |- b e + c d +--R (b e - c d) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R +---+ \|e x + d +-------+ +--R - 2c d\|- d atan(----------) + 2b e\|e x + d +--R +---+ +--R \|- d +--R / +--R b c +--R , +--R +--R +-------+ +--R +---+ \|e x + d +--R - 2c d\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +-------+ +--R |b e - c d \|e x + d +-------+ +--R (- 2b e + 2c d) |--------- atan(------------) + 2b e\|e x + d +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R b c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 746 + +--S 747 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- b e + c d +-+ +--R (b e - c d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2b e - 2c d)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +--R 2c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R c d\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (2b e - 2c d)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +--R 2c d\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R (- 2b e + 2c d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R +-+ +--R b c\|c +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1726 +t0:=sqrt(d+e*x)/(b*x+c*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ---------- +--R 2 +--R c x + b x +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1726 +r0:=-2*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b+2*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*sqrt(c)) +--R +--R +--R +-+ +-------+ +-------+ +--R +-----------+ \|c \|e x + d +-+ +-+ \|e x + d +--R 2\|- b e + c d atanh(--------------) - 2\|c \|d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R (2) ----------------------------------------------------------------- +--R +-+ +--R b\|c +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R / +--R b +--R , +--R +-+ +-------+ +---------+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d |b e - c d \|e x + d +--R \|d log(----------------------------) + 2 |--------- atan(------------) +--R x \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R -----------------------------------------------------------------------, +--R b +--R +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-------+ +--R +---+ \|e x + d +--R - 2\|- d atan(----------) +--R +---+ +--R \|- d +--R / +--R b +--R , +--R +-------+ +---------+ +-------+ +--R +---+ \|e x + d |b e - c d \|e x + d +--R - 2\|- d atan(----------) + 2 |--------- atan(------------) +--R +---+ \| c +---------+ +--R \|- d |b e - c d +--R |--------- +--R \| c +--R -----------------------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 753 + +--S 754 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d +-+ \| c +--R |----------- \|c log(-----------------------------------------------) +--R \| c c x + b +--R + +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +-------+ +--R +-----------+ \|c \|e x + d +-+ +-+ \|e x + d +--R - 2\|- b e + c d atanh(--------------) + 2\|c \|d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R +-+ +--R b\|c +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R \|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +-------+ +--R +-----------+ \|c \|e x + d +-+ +-+ \|e x + d +--R - 2\|- b e + c d atanh(--------------) + 2\|c \|d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R + +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R 2\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R +-+ +--R b\|c +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 757 + +)clear all + +--S 758 of 1726 +t0:=1/((b*x+c*x^2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 +-------+ +--R (c x + b x)\|e x + d +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1726 +r0:=-2*atanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))+2*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*sqrt(c*d-b*e)) +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ +-+ \|c \|e x + d +-----------+ \|e x + d +--R 2\|c \|d atanh(--------------) - 2\|- b e + c d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R (2) ----------------------------------------------------------------- +--R +-----------+ +-+ +--R b\|- b e + c d \|d +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R / +--R +-+ +--R b\|d +--R , +--R +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R - 2 |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R +-+ +--R b\|d +--R , +--R +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +---+ +-------+ +--R \|- d \|e x + d +--R - 2atan(----------------) +--R d +--R / +--R +---+ +--R b\|- d +--R , +--R +---+ +-------+ +---------+ +-------+ +--R \|- d \|e x + d +---+ | c c\|e x + d +--R - 2atan(----------------) - 2\|- d |--------- atan(-----------------------) +--R d \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R ---------------------------------------------------------------------------- +--R +---+ +--R b\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 760 + +--S 761 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R +-----------+ | c +-+ +--R \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +-------+ +--R +-+ +-+ \|c \|e x + d +-----------+ \|e x + d +--R - 2\|c \|d atanh(--------------) + 2\|- b e + c d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R +-----------+ +-+ +--R b\|- b e + c d \|d +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +-------+ +--R +-+ +-+ \|c \|e x + d +-----------+ \|e x + d +--R - 2\|c \|d atanh(--------------) + 2\|- b e + c d atanh(----------) +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R + +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R - 2\|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R +-----------+ +-+ +--R b\|- b e + c d \|d +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 764 + +)clear all + +--S 765 of 1726 +t0:=1/((d+e*x)^(3/2)*(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ------------------------------------------ +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1726 +r0:=-2*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))+2*c^(3/2)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(3/2))-_ + 2*e/(d*(c*d-b*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R - 2c d\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R (- 2b e + 2c d)\|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R +-----------+ +-+ +--R 2b e\|- b e + c d \|d +--R / +--R 2 2 +-----------+ +-+ +-------+ +--R (b d e - b c d )\|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R | c +-+ +-------+ +--R c d |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +-+ +--R (b e - c d)\|e x + d log(-------------------------------) + 2b e\|d +--R x +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R (b e - c d)\|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +-+ +--R 2c d |--------- \|d \|e x + d atan(-----------------------) + 2b e\|d +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 2 2 +-+ +-------+ +--R (b d e - b c d )\|d \|e x + d +--R , +--R +--R +-----------+ +--R +---+ | c +-------+ +--R c d\|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +---+ +--R (- 2b e + 2c d)\|e x + d atan(----------------) + 2b e\|- d +--R d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R , +--R +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R (- 2b e + 2c d)\|e x + d atan(----------------) +--R d +--R + +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R 2c d\|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R +---+ +--R 2b e\|- d +--R / +--R 2 2 +---+ +-------+ +--R (b d e - b c d )\|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 767 + +--S 768 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | c +-+ +--R c d\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (b e - c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R 2c d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2b e - 2c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (b e - c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R 2c d\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2b e - 2c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R 2c d\|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 2 2 +-----------+ +-+ +--R (b d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 771 + +)clear all + +--S 772 of 1726 +t0:=1/((d+e*x)^(5/2)*(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------ +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1726 +r0:=-2/3*e/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b*d^(5/2))+2*c^(5/2)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b*(c*d-b*e)^(5/2))-2*e*(2*c*d-b*e)/(d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 3 +-+ +-+ +-------+ \|c \|e x + d +--R (6c d e x + 6c d )\|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6b e + 12b c d e - 6c d e)x - 6b d e + 12b c d e - 6c d ) +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 3 2 2 2 2 +-----------+ +-+ +--R ((6b e - 12b c d e )x + 8b d e - 14b c d e)\|- b e + c d \|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 6b c d e + 3c d e)x + 3b d e - 6b c d e + 3c d ) +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 3 | c +-+ +-------+ +--R (3c d e x + 3c d ) |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 +-+ +--R ((6b e - 12b c d e )x + 8b d e - 14b c d e)\|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 2 3 +--R ((3b e - 6b c d e + 3c d e)x + 3b d e - 6b c d e + 3c d ) +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 3 | c +-+ +-------+ +--R (- 6c d e x - 6c d ) |--------- \|d \|e x + d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +-+ +--R ((6b e - 12b c d e )x + 8b d e - 14b c d e)\|d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +-+ +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d )\|d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R +-----------+ +--R 2 2 2 3 +---+ | c +-------+ +--R (3c d e x + 3c d )\|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6b e + 12b c d e - 6c d e)x - 6b d e + 12b c d e - 6c d ) +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 2 3 2 2 2 2 +---+ +--R ((6b e - 12b c d e )x + 8b d e - 14b c d e)\|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6b e + 12b c d e - 6c d e)x - 6b d e + 12b c d e - 6c d ) +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R +---------+ +--R 2 2 2 3 +---+ | c +-------+ +--R (- 6c d e x - 6c d )\|- d |--------- \|e x + d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 3 2 2 2 2 +---+ +--R ((6b e - 12b c d e )x + 8b d e - 14b c d e)\|- d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R ((3b d e - 6b c d e + 3b c d e)x + 3b d e - 6b c d e + 3b c d ) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 774 + +--S 775 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +-----------+ +--R (b e - 2b c d e + c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 +-----------+ | c +-+ +--R c d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R - 2c d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2b e - 4b c d e + 2c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 +-----------+ +--R (b e - 2b c d e + c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R - 2c d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (2b e - 4b c d e + 2c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 +-----------+ | c +-+ c\|e x + d +--R - 2c d \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 3 2 2 2 3 2 4 +-----------+ +-+ +--R (b d e - 2b c d e + b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1726 +t0:=1/((d+e*x)^(7/2)*(b*x+c*x^2)) +--R +--R +--R (1) +--R 1 +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R c e x + (b e + 3c d e )x + (3b d e + 3c d e)x + (3b d e + c d )x +--R + +--R 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1726 +r0:=-2/5*e/(d*(c*d-b*e)*(d+e*x)^(5/2))-2/3*e*(2*c*d-b*e)/(d^2*(c*d-b*e)^2*_ + (d+e*x)^(3/2))-2*atanh(sqrt(d+e*x)/sqrt(d))/(b*d^(7/2))+_ + 2*c^(7/2)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b*(c*d-b*e)^(7/2))-2*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2)/_ + (d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 3 2 2 3 4 3 5 +-+ +-+ +-------+ +--R (- 30c d e x - 60c d e x - 30c d )\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30b e + 90b c d e - 90b c d e + 30c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 60b d e + 180b c d e - 180b c d e + 60c d e)x - 30b d e +--R + +--R 2 3 2 2 4 3 5 +--R 90b c d e - 90b c d e + 30c d +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 5 2 4 2 2 3 2 +--R (30b e - 90b c d e + 90b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 +--R (70b d e - 210b c d e + 200b c d e )x + 46b d e - 132b c d e +--R + +--R 2 4 +--R 116b c d e +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 3 4 3 5 | c +-+ +-------+ +--R (15c d e x + 30c d e x + 15c d ) |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 45b c d e + 45b c d e - 15c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 90b c d e + 90b c d e - 30c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45b c d e + 45b c d e - 15c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 3 5 2 4 2 2 3 2 +--R (30b e - 90b c d e + 90b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 +--R (70b d e - 210b c d e + 200b c d e )x + 46b d e - 132b c d e +--R + +--R 2 4 +--R 116b c d e +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15b e - 45b c d e + 45b c d e - 15c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (30b d e - 90b c d e + 90b c d e - 30c d e)x + 15b d e +--R + +--R 2 3 2 2 4 3 5 +--R - 45b c d e + 45b c d e - 15c d +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R +---------+ +--R 3 3 2 2 3 4 3 5 | c +-+ +-------+ +--R (30c d e x + 60c d e x + 30c d ) |--------- \|d \|e x + d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 +--R (30b e - 90b c d e + 90b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 +--R (70b d e - 210b c d e + 200b c d e )x + 46b d e - 132b c d e +--R + +--R 2 4 +--R 116b c d e +--R * +--R +-+ +--R \|d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R +-----------+ +--R 3 3 2 2 3 4 3 5 +---+ | c +-------+ +--R (15c d e x + 30c d e x + 15c d )\|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30b e + 90b c d e - 90b c d e + 30c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 60b d e + 180b c d e - 180b c d e + 60c d e)x - 30b d e +--R + +--R 2 3 2 2 4 3 5 +--R 90b c d e - 90b c d e + 30c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 5 2 4 2 2 3 2 +--R (30b e - 90b c d e + 90b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 +--R (70b d e - 210b c d e + 200b c d e )x + 46b d e - 132b c d e +--R + +--R 2 4 +--R 116b c d e +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 30b e + 90b c d e - 90b c d e + 30c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 60b d e + 180b c d e - 180b c d e + 60c d e)x - 30b d e +--R + +--R 2 3 2 2 4 3 5 +--R 90b c d e - 90b c d e + 30c d +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R +---------+ +--R 3 3 2 2 3 4 3 5 +---+ | c +-------+ +--R (30c d e x + 60c d e x + 30c d )\|- d |--------- \|e x + d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 5 2 4 2 2 3 2 +--R (30b e - 90b c d e + 90b c d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 +--R (70b d e - 210b c d e + 200b c d e )x + 46b d e - 132b c d e +--R + +--R 2 4 +--R 116b c d e +--R * +--R +---+ +--R \|- d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (15b d e - 45b c d e + 45b c d e - 15b c d e )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 +--R (30b d e - 90b c d e + 90b c d e - 30b c d e)x + 15b d e +--R + +--R 3 6 2 2 2 7 3 8 +--R - 45b c d e + 45b c d e - 15b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 781 + +--S 782 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 +-----------+ | c +-+ +--R c d \|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (b e - 3b c d e + 3b c d e - c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 +-+ +-+ \|c \|e x + d +--R 2c d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|e x + d +--R (2b e - 6b c d e + 6b c d e - 2c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (b e - 3b c d e + 3b c d e - c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 +-+ +-+ \|c \|e x + d +--R 2c d \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|e x + d +--R (2b e - 6b c d e + 6b c d e - 2c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 3 3 +-----------+ | c +-+ c\|e x + d +--R 2c d \|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 3 3 4 2 2 2 5 3 6 +-----------+ +-+ +--R (b d e - 3b c d e + 3b c d e - b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1726 +t0:=(d+e*x)^(9/2)/(b*x+c*x^2)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1726 +r0:=1/3*e*(6*c^2*d^2-6*b*c*d*e+5*b^2*e^2)*(d+e*x)^(3/2)/(b^2*c^2)+_ + e*(2*c*d-b*e)*(d+e*x)^(5/2)/(b^2*c)-2*(c*d-b*e)*(d+e*x)^(7/2)/_ + (b^2*(b+c*x))-(d+e*x)^(9/2)/(b*x*(b+c*x))+d^(7/2)*(4*c*d-9*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/b^3-(c*d-b*e)^(7/2)*(4*c*d+5*b*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+_ + e*(2*c*d-b*e)*(c^2*d^2-b*c*d*e+5*b^2*e^2)*sqrt(d+e*x)/(b^2*c^3) +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (15b e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 3 5 4 2 2 3 3 4 4 +-+ +-+ +--R ((- 27b c d e + 12c d )x + (- 27b c d e + 12b c d )x)\|c \|d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 4 3 4 4 3 2 3 2 +--R 2b c e x + (- 10b c e + 26b c d e )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 2 3 4 +--R (- 15b e + 38b c d e - 18b c d e + 12b c d e - 6b c d )x - 3b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 3 4 2 4 3 +-+ +--R (3b c x + 3b c x)\|c +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (15b e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 4 3 5 4 2 2 3 3 4 4 +-+ +--R ((27b c d e - 12c d )x + (27b c d e - 12b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 2 4 3 4 4 3 2 3 2 +--R 4b c e x + (- 20b c e + 52b c d e )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 30b e + 76b c d e - 36b c d e + 24b c d e - 12b c d )x +--R + +--R 2 3 4 +--R - 6b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 3 5 4 2 2 3 3 4 4 +-+ +--R ((27b c d e - 12c d )x + (27b c d e - 12b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (30b c e - 66b c d e + 18b c d e + 42b c d e - 24c d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (30b e - 66b c d e + 18b c d e + 42b c d e - 24b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 3 4 4 3 2 3 2 +--R 4b c e x + (- 20b c e + 52b c d e )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 30b e + 76b c d e - 36b c d e + 24b c d e - 12b c d )x +--R + +--R 2 3 4 +--R - 6b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (15b e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 4 3 5 4 2 2 3 3 4 4 +---+ +--R ((- 54b c d e + 24c d )x + (- 54b c d e + 24b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 4 3 4 4 3 2 3 2 +--R 4b c e x + (- 20b c e + 52b c d e )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 30b e + 76b c d e - 36b c d e + 24b c d e - 12b c d )x +--R + +--R 2 3 4 +--R - 6b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 6b c x + 6b c x +--R , +--R +--R 4 3 5 4 2 2 3 3 4 4 +---+ +--R ((- 27b c d e + 12c d )x + (- 27b c d e + 12b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R (15b e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 4 3 4 4 3 2 3 2 +--R 2b c e x + (- 10b c e + 26b c d e )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 2 3 4 +--R (- 15b e + 38b c d e - 18b c d e + 12b c d e - 6b c d )x - 3b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 4 2 4 3 +--R 3b c x + 3b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 788 + +--S 789 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 4 3 3 2 2 2 2 3 3 4 4 |- b e + c d +-+ +--R (5b e - 11b c d e + 3b c d e + 7b c d e - 4c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (9b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10b e + 22b c d e - 6b c d e - 14b c d e + 8c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 4 4 +-+ +-+ \|e x + d +--R (18b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (9b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10b e + 22b c d e - 6b c d e - 14b c d e + 8c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 4 4 +-+ +-+ \|e x + d +--R (18b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ |b e - c d +--R (10b e - 22b c d e + 6b c d e + 14b c d e - 8c d )\|c |--------- +--R \| c +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 3 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1726 +t0:=(d+e*x)^(7/2)/(b*x+c*x^2)^2 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1726 +r0:=e*(2*c*d-b*e)*(d+e*x)^(3/2)/(b^2*c)-2*(c*d-b*e)*(d+e*x)^(5/2)/_ + (b^2*(b+c*x))-(d+e*x)^(7/2)/(b*x*(b+c*x))+d^(5/2)*(4*c*d-7*b*e)*_ + atanh(sqrt(d+e*x)/sqrt(d))/b^3-(c*d-b*e)^(5/2)*(4*c*d+3*b*e)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+_ + e*(2*c^2*d^2-2*b*c*d*e+3*b^2*e^2)*sqrt(d+e*x)/(b^2*c^2) +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 3b c e + 2b c d e + 5b c d e - 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (- 3b e + 2b c d e + 5b c d e - 4b c d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 4 3 2 2 2 2 3 3 +-+ +-+ +--R ((- 7b c d e + 4c d )x + (- 7b c d e + 4b c d )x)\|c \|d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 4 3 3 2 2 2 2 3 3 2 2 3 +-+ +--R (2b c e x + (3b e - 3b c d e + 3b c d e - 2b c d )x - b c d )\|c +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 3 2 4 3 2 2 2 2 3 3 +-+ +--R ((7b c d e - 4c d )x + (7b c d e - 4b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 3 2 4 3 3 2 2 2 2 3 3 2 2 3 +--R (4b c e x + (6b e - 6b c d e + 6b c d e - 4b c d )x - 2b c d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 2 4 3 2 2 2 2 3 3 +-+ +--R ((7b c d e - 4c d )x + (7b c d e - 4b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 6b c e + 4b c d e + 10b c d e - 8c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (- 6b e + 4b c d e + 10b c d e - 8b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 2 4 3 3 2 2 2 2 3 3 2 2 3 +--R (4b c e x + (6b e - 6b c d e + 6b c d e - 4b c d )x - 2b c d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ - 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-------------------------------------------------) +--R \| c c x + b +--R + +--R 3 2 4 3 2 2 2 2 3 3 +---+ +--R ((- 14b c d e + 8c d )x + (- 14b c d e + 8b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 2 4 3 3 2 2 2 2 3 3 2 2 3 +--R (4b c e x + (6b e - 6b c d e + 6b c d e - 4b c d )x - 2b c d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R 2b c x + 2b c x +--R , +--R +--R 3 2 4 3 2 2 2 2 3 3 +---+ +--R ((- 7b c d e + 4c d )x + (- 7b c d e + 4b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 3b c e + 2b c d e + 5b c d e - 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (- 3b e + 2b c d e + 5b c d e - 4b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 3 2 4 3 3 2 2 2 2 3 3 2 2 3 +--R (2b c e x + (3b e - 3b c d e + 3b c d e - 2b c d )x - b c d ) +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 4 2 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 795 + +--S 796 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- b e + c d +-+ +--R (3b e - 2b c d e - 5b c d e + 4c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R - 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (7b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (6b e - 4b c d e - 10b c d e + 8c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 3 3 +-+ +-+ \|e x + d +--R (14b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (7b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (6b e - 4b c d e - 10b c d e + 8c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 3 3 +-+ +-+ \|e x + d +--R (14b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 3 3 2 2 2 2 3 3 +-+ |b e - c d \|e x + d +--R (- 6b e + 4b c d e + 10b c d e - 8c d )\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 2 +-+ +--R 2b c \|c +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1726 +t0:=(d+e*x)^(5/2)/(b*x+c*x^2)^2 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1726 +r0:=-2*(c*d-b*e)*(d+e*x)^(3/2)/(b^2*(b+c*x))-(d+e*x)^(5/2)/(b*x*(b+c*x))+_ + d^(3/2)*(4*c*d-5*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/b^3-_ + (c*d-b*e)^(3/2)*(4*c*d+b*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))/(b^3*c^(3/2))+e*(2*c*d-b*e)*sqrt(d+e*x)/(b^2*c) +--R +--R +--R (2) +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5b c d e + 4c d )x + (- 5b c d e + 4b c d )x)\|c \|d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 2 2 2 +-+ +-------+ +--R ((- b e + 2b c d e - 2b c d )x - b c d )\|c \|e x + d +--R / +--R 3 2 2 4 +-+ +--R (b c x + b c x)\|c +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 2 2 2 +-+ +--R ((5b c d e - 4c d )x + (5b c d e - 4b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2b e + 4b c d e - 4b c d )x - 2b c d )\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 2 2 2 +-+ +--R ((5b c d e - 4c d )x + (5b c d e - 4b c d )x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2b c e + 6b c d e - 8c d )x + (2b e + 6b c d e - 8b c d )x) +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2b e + 4b c d e - 4b c d )x - 2b c d )\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 2 2 2 2 +---+ +--R ((- 10b c d e + 8c d )x + (- 10b c d e + 8b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2b e + 4b c d e - 4b c d )x - 2b c d )\|e x + d +--R / +--R 3 2 2 4 +--R 2b c x + 2b c x +--R , +--R +--R 2 3 2 2 2 2 2 +---+ +--R ((- 5b c d e + 4c d )x + (- 5b c d e + 4b c d )x)\|- d +--R * +--R +-------+ +--R \|e x + d +--R atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- b e + 2b c d e - 2b c d )x - b c d )\|e x + d +--R / +--R 3 2 2 4 +--R b c x + b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- b e + c d +-+ +--R (b e + 3b c d e - 4c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (5b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 2b e - 6b c d e + 8c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|e x + d +--R (10b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (5b c d e - 4c d )\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 2b e - 6b c d e + 8c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|e x + d +--R (10b c d e - 8c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |b e - c d \|e x + d +--R (2b e + 6b c d e - 8c d )\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R 2b c\|c +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1726 +t0:=(d+e*x)^(3/2)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1726 +r0:=-(d+e*x)^(3/2)/(b*x*(b+c*x))+(4*c*d-3*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))*sqrt(d)/b^3-(4*c*d-b*e)*atanh(sqrt(c)*sqrt(d+e*x)/_ + sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b^3*sqrt(c))-2*(c*d-b*e)*_ + sqrt(d+e*x)/(b^2*(b+c*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|c \|e x + d +--R ((b c e - 4c d)x + (b e - 4b c d)x)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 +-+ +-+ \|e x + d +--R ((- 3b c e + 4c d)x + (- 3b e + 4b c d)x)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 +-+ +-------+ +--R ((b e - 2b c d)x - b d)\|c \|e x + d +--R / +--R 3 2 4 +-+ +--R (b c x + b x)\|c +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- b e + c d +--R ((b c e - 4c d)x + (b e - 4b c d)x) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R 2 2 2 +-+ +--R ((3b c e - 4c d)x + (3b e - 4b c d)x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 2 2 +-------+ +--R ((2b e - 4b c d)x - 2b d)\|e x + d +--R / +--R 3 2 4 +--R 2b c x + 2b x +--R , +--R +--R 2 2 2 +-+ +--R ((3b c e - 4c d)x + (3b e - 4b c d)x)\|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 |b e - c d \|e x + d +--R ((2b c e - 8c d)x + (2b e - 8b c d)x) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 +-------+ +--R ((2b e - 4b c d)x - 2b d)\|e x + d +--R / +--R 3 2 4 +--R 2b c x + 2b x +--R , +--R +--R +-----------+ +--R 2 2 2 |- b e + c d +--R ((b c e - 4c d)x + (b e - 4b c d)x) |----------- +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-------+ +--R 2 2 2 +---+ \|e x + d +--R ((- 6b c e + 8c d)x + (- 6b e + 8b c d)x)\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 +-------+ +--R ((2b e - 4b c d)x - 2b d)\|e x + d +--R / +--R 3 2 4 +--R 2b c x + 2b x +--R , +--R +--R +-------+ +--R 2 2 2 +---+ \|e x + d +--R ((- 3b c e + 4c d)x + (- 3b e + 4b c d)x)\|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R +---------+ +-------+ +--R 2 2 2 |b e - c d \|e x + d +--R ((b c e - 4c d)x + (b e - 4b c d)x) |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 2 2 +-------+ +--R ((b e - 2b c d)x - b d)\|e x + d +--R / +--R 3 2 4 +--R b c x + b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- b e + c d +-+ +--R (b e - 4c d) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3b e - 4c d)\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (- 2b e + 8c d)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +--R (6b e - 8c d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-+ +--R 2b \|c +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (3b e - 4c d)\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R (- 2b e + 8c d)\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-+ +-+ \|e x + d +--R (6b e - 8c d)\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-+ |b e - c d \|e x + d +--R (2b e - 8c d)\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 3 +-+ +--R 2b \|c +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1726 +t0:=sqrt(d+e*x)/(b*x+c*x^2)^2 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) --------------------- +--R 2 4 3 2 2 +--R c x + 2b c x + b x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1726 +r0:=(4*c*d-b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))-_ + (4*c*d-3*b*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c)/(b^3*sqrt(c*d-b*e))-2*c*sqrt(d+e*x)/(b^2*(b+c*x))-_ + sqrt(d+e*x)/(b*x*(b+c*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-+ +-+ \|c \|e x + d +--R ((3b c e - 4c d)x + (3b e - 4b c d)x)\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 +-----------+ \|e x + d +--R ((- b c e + 4c d)x + (- b e + 4b c d)x)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 +-----------+ +-+ +-------+ +--R (- 2b c x - b )\|- b e + c d \|d \|e x + d +--R / +--R 3 2 4 +-----------+ +-+ +--R (b c x + b x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R ((b c e - 4c d)x + (b e - 4b c d)x) +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 | c +-+ +--R ((3b c e - 4c d)x + (3b e - 4b c d)x) |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 +-+ +-------+ +--R (- 4b c x - 2b )\|d \|e x + d +--R / +--R 3 2 4 +-+ +--R (2b c x + 2b x)\|d +--R , +--R +--R 2 2 2 +--R ((b c e - 4c d)x + (b e - 4b c d)x) +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 | c +-+ +--R ((- 6b c e + 8c d)x + (- 6b e + 8b c d)x) |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 +-+ +-------+ +--R (- 4b c x - 2b )\|d \|e x + d +--R / +--R 3 2 4 +-+ +--R (2b c x + 2b x)\|d +--R , +--R +--R +-----------+ +--R 2 2 2 +---+ | c +--R ((3b c e - 4c d)x + (3b e - 4b c d)x)\|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +---+ +-------+ +--R 2 2 2 \|- d \|e x + d +--R ((- 2b c e + 8c d)x + (- 2b e + 8b c d)x)atan(----------------) +--R d +--R + +--R 2 +---+ +-------+ +--R (- 4b c x - 2b )\|- d \|e x + d +--R / +--R 3 2 4 +---+ +--R (2b c x + 2b x)\|- d +--R , +--R +--R +---+ +-------+ +--R 2 2 2 \|- d \|e x + d +--R ((- b c e + 4c d)x + (- b e + 4b c d)x)atan(----------------) +--R d +--R + +--R +---------+ +--R 2 2 2 +---+ | c +--R ((- 3b c e + 4c d)x + (- 3b e + 4b c d)x)\|- d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 +---+ +-------+ +--R (- 2b c x - b )\|- d \|e x + d +--R / +--R 3 2 4 +---+ +--R (b c x + b x)\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 816 + +--S 817 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (b e - 4c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R +-----------+ | c +-+ +--R (3b e - 4c d)\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (- 6b e + 8c d)\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2b e - 8c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 3 +-----------+ +-+ +--R 2b \|- b e + c d \|d +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R (b e - 4c d)\|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R (- 6b e + 8c d)\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R +-----------+ \|e x + d +--R (2b e - 8c d)\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R +-----------+ | c +-+ c\|e x + d +--R (- 6b e + 8c d)\|- b e + c d |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 3 +-----------+ +-+ +--R 2b \|- b e + c d \|d +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1726 +t0:=1/((b*x+c*x^2)^2*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (c x + 2b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1726 +r0:=(4*c*d+b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))-_ + c^(3/2)*(4*c*d-5*b*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-_ + b*e))/(b^3*(c*d-b*e)^(3/2))-c*(2*c*d-b*e)*sqrt(d+e*x)/_ + (b^2*d*(c*d-b*e)*(b+c*x))-sqrt(d+e*x)/(b*d*x*(b+c*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5b c d e + 4c d )x + (- 5b c d e + 4b c d )x)\|c \|d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 2 +-----------+ +-+ +-------+ +--R ((- b c e + 2b c d)x - b e + b c d)\|- b e + c d \|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- b e + c d \|d +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 3 2 2 2 2 2 | c +-+ +--R ((5b c d e - 4c d )x + (5b c d e - 4b c d )x) |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2b c e + 4b c d)x - 2b e + 2b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 | c +-+ +--R ((10b c d e - 8c d )x + (10b c d e - 8b c d )x) |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2b c e + 4b c d)x - 2b e + 2b c d)\|d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|d +--R , +--R +--R +-----------+ +--R 2 3 2 2 2 2 2 +---+ | c +--R ((5b c d e - 4c d )x + (5b c d e - 4b c d )x)\|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2b c e + 6b c d e - 8c d )x + (2b e + 6b c d e - 8b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- 2b c e + 4b c d)x - 2b e + 2b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((2b c d e - 2b c d )x + (2b d e - 2b c d )x)\|- d +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((b c e + 3b c d e - 4c d )x + (b e + 3b c d e - 4b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 +---+ | c +--R ((5b c d e - 4c d )x + (5b c d e - 4b c d )x)\|- d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- b c e + 2b c d)x - b e + b c d)\|- d \|e x + d +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((b c d e - b c d )x + (b d e - b c d )x)\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 823 + +--S 824 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | c +-+ +--R (5b c d e - 4c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R (b e + 3b c d e - 4c d )\|- b e + c d log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (10b c d e - 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (- 2b e - 6b c d e + 8c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R (b e + 3b c d e - 4c d )\|- b e + c d log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|e x + d +--R (10b c d e - 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (- 2b e - 6b c d e + 8c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 +-----------+ | c +-+ +--R (10b c d e - 8c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 4 3 2 +-----------+ +-+ +--R (2b d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1726 +t0:=1/((d+e*x)^(3/2)*(b*x+c*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1726 +r0:=(4*c*d+3*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))-c^(5/2)*_ + (4*c*d-7*b*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/_ + (b^3*(c*d-b*e)^(5/2))-e*(2*c^2*d^2-2*b*c*d*e+3*b^2*e^2)/_ + (b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x))-c*(2*c*d-b*e)/(b^2*d*_ + (c*d-b*e)*(b+c*x)*sqrt(d+e*x))+(-1)/(b*d*x*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 4 3 2 2 2 2 3 3 +-+ +-+ +-------+ +--R ((7b c d e - 4c d )x + (7b c d e - 4b c d )x)\|c \|d \|e x + d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3b c e + 2b c d e - 2b c d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3 +--R (- 3b e + b c d e + b c d e - 2b c d )x - b d e + 2b c d e - b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 | c +-+ +--R ((7b c d e - 4c d )x + (7b c d e - 4b c d )x) |- --------- \|d +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6b c e + 4b c d e - 4b c d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6b e + 2b c d e + 2b c d e - 4b c d )x - 2b d e + 4b c d e +--R + +--R 2 2 3 +--R - 2b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 | c +-+ +--R ((- 14b c d e + 8c d )x + (- 14b c d e + 8b c d )x) |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6b c e + 4b c d e - 4b c d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6b e + 2b c d e + 2b c d e - 4b c d )x - 2b d e + 4b c d e +--R + +--R 2 2 3 +--R - 2b c d +--R * +--R +-+ +--R \|d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | c +--R ((7b c d e - 4c d )x + (7b c d e - 4b c d )x)\|- d |- --------- +--R \| b e - c d +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (6b c e - 4b c d e - 10b c d e + 8c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (6b e - 4b c d e - 10b c d e + 8b c d )x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6b c e + 4b c d e - 4b c d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6b e + 2b c d e + 2b c d e - 4b c d )x - 2b d e + 4b c d e +--R + +--R 2 2 3 +--R - 2b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2b c d e - 4b c d e + 2b c d )x + (2b d e - 4b c d e + 2b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3b c e - 2b c d e - 5b c d e + 4c d )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3b e - 2b c d e - 5b c d e + 4b c d )x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | c +--R ((- 7b c d e + 4c d )x + (- 7b c d e + 4b c d )x)\|- d |--------- +--R \|b e - c d +--R * +--R +-------+ +--R +-------+ c\|e x + d +--R \|e x + d atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3b c e + 2b c d e - 2b c d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 3b e + b c d e + b c d e - 2b c d )x - b d e + 2b c d e +--R + +--R 2 2 3 +--R - b c d +--R * +--R +---+ +--R \|- d +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((b c d e - 2b c d e + b c d )x + (b d e - 2b c d e + b c d )x) +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 830 + +--S 831 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3b e - 2b c d e - 5b c d e + 4c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 3 3 +-----------+ | c +-+ +--R (7b c d e - 4c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|c \|e x + d +--R (- 14b c d e + 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|e x + d +--R (- 6b e + 4b c d e + 10b c d e - 8c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3b e - 2b c d e - 5b c d e + 4c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|c \|e x + d +--R (- 14b c d e + 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|e x + d +--R (- 6b e + 4b c d e + 10b c d e - 8c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 3 3 +-----------+ | c +-+ +--R (- 14b c d e + 8c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2b d e - 4b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 834 + +)clear all + +--S 835 of 1726 +t0:=1/((d+e*x)^(5/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R c e x + (2b c e + 2c d e)x + (b e + 4b c d e + c d )x +--R + +--R 2 2 3 2 2 2 +--R (2b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1726 +r0:=-1/3*e*(6*c^2*d^2-6*b*c*d*e+5*b^2*e^2)/(b^2*d^2*(c*d-b*e)^2*_ + (d+e*x)^(3/2))-c*(2*c*d-b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + (d+e*x)^(3/2))+(-1)/(b*d*x*(b+c*x)*(d+e*x)^(3/2))+(4*c*d+_ + 5*b*e)*atanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(7/2))-c^(7/2)*_ + (4*c*d-9*b*e)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*_ + (c*d-b*e)^(7/2))-e*(2*c*d-b*e)*(c^2*d^2-b*c*d*e+5*b^2*e^2)/_ + (b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (- 27b c d e + 12c d e)x + (- 27b c d e - 15b c d e + 12c d )x +--R + +--R 2 3 4 4 5 +--R (- 27b c d e + 12b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (15b e - 18b c d e - 24b c d e + 30b c d e + 9b c d e - 12c d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15b d e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15b c e + 33b c d e - 9b c d e + 6b c d e )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15b e + 13b c d e + 35b c d e - 15b c d e + 12b c d e)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 5 2 3 +--R (- 20b d e + 41b c d e - 9b c d e - 3b c d e + 6b c d )x - 3b d e +--R + +--R 4 3 2 3 2 4 2 3 5 +--R 9b c d e - 9b c d e + 3b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27b c d e - 12c d e)x + (27b c d e + 15b c d e - 12c d )x +--R + +--R 2 3 4 4 5 +--R (27b c d e - 12b c d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15b e - 18b c d e - 24b c d e + 30b c d e + 9b c d e +--R + +--R 5 5 +--R - 12c d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15b d e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30b c e + 66b c d e - 18b c d e + 12b c d e )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30b e + 26b c d e + 70b c d e - 30b c d e + 24b c d e)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40b d e + 82b c d e - 18b c d e - 6b c d e + 12b c d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6b d e + 18b c d e - 18b c d e + 6b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15b e - 18b c d e - 24b c d e + 30b c d e + 9b c d e +--R + +--R 5 5 +--R - 12c d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15b d e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (54b c d e - 24c d e)x + (54b c d e + 30b c d e - 24c d )x +--R + +--R 2 3 4 4 5 +--R (54b c d e - 24b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30b c e + 66b c d e - 18b c d e + 12b c d e )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30b e + 26b c d e + 70b c d e - 30b c d e + 24b c d e)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40b d e + 82b c d e - 18b c d e - 6b c d e + 12b c d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6b d e + 18b c d e - 18b c d e + 6b c d +--R * +--R +-+ +--R \|d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27b c d e - 12c d e)x + (27b c d e + 15b c d e - 12c d )x +--R + +--R 2 3 4 4 5 +--R (27b c d e - 12b c d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (30b c e - 66b c d e + 18b c d e + 42b c d e - 24c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 30b e - 36b c d e - 48b c d e + 60b c d e + 18b c d e +--R + +--R 5 5 +--R - 24c d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (30b d e - 66b c d e + 18b c d e + 42b c d e - 24b c d )x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30b c e + 66b c d e - 18b c d e + 12b c d e )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30b e + 26b c d e + 70b c d e - 30b c d e + 24b c d e)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40b d e + 82b c d e - 18b c d e - 6b c d e + 12b c d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6b d e + 18b c d e - 18b c d e + 6b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6b c d e - 18b c d e + 18b c d e - 6b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6b d e - 12b c d e + 12b c d e - 6b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6b d e - 18b c d e + 18b c d e - 6b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15b c e - 33b c d e + 9b c d e + 21b c d e - 12c d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15b e - 18b c d e - 24b c d e + 30b c d e + 9b c d e +--R + +--R 5 5 +--R - 12c d +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15b d e - 33b c d e + 9b c d e + 21b c d e - 12b c d )x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27b c d e - 12c d e)x + (27b c d e + 15b c d e - 12c d )x +--R + +--R 2 3 4 4 5 +--R (27b c d e - 12b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15b c e + 33b c d e - 9b c d e + 6b c d e )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15b e + 13b c d e + 35b c d e - 15b c d e + 12b c d e)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 20b d e + 41b c d e - 9b c d e - 3b c d e + 6b c d )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3b d e + 9b c d e - 9b c d e + 3b c d +--R * +--R +---+ +--R \|- d +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3b c d e - 9b c d e + 9b c d e - 3b c d e)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3b d e - 6b c d e + 6b c d e - 3b c d )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3b d e - 9b c d e + 9b c d e - 3b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 837 + +--S 838 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 4 4 +-----------+ | c +-+ +--R (9b c d e - 4c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5b e - 11b c d e + 3b c d e + 7b c d e - 4c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|c \|e x + d +--R (18b c d e - 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10b e + 22b c d e - 6b c d e - 14b c d e + 8c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5b e - 11b c d e + 3b c d e + 7b c d e - 4c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|c \|e x + d +--R (18b c d e - 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10b e + 22b c d e - 6b c d e - 14b c d e + 8c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 3 3 4 4 +-----------+ | c +-+ +--R (18b c d e - 8c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2b d e - 6b c d e + 6b c d e - 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 841 + +)clear all + +--S 842 of 1726 +t0:=1/((d+e*x)^(7/2)*(b*x+c*x^2)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R c e x + (2b c e + 3c d e )x + (b e + 6b c d e + 3c d e)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3b d e + 6b c d e + c d )x + (3b d e + 2b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1726 +r0:=-1/5*e*(10*c^2*d^2-10*b*c*d*e+7*b^2*e^2)/(b^2*d^2*(c*d-b*e)^2*_ + (d+e*x)^(5/2))-c*(2*c*d-b*e)/(b^2*d*(c*d-b*e)*(b+c*x)*_ + (d+e*x)^(5/2))+(-1)/(b*d*x*(b+c*x)*(d+e*x)^(5/2))-1/3*e*_ + (2*c*d-b*e)*(3*c^2*d^2-3*b*c*d*e+7*b^2*e^2)/(b^2*d^3*_ + (c*d-b*e)^3*(d+e*x)^(3/2))+(4*c*d+7*b*e)*atanh(sqrt(d+e*x)/_ + sqrt(d))/(b^3*d^(9/2))-c^(9/2)*(4*c*d-11*b*e)*atanh(sqrt(c)*_ + sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(9/2))-e*(2*c^4*d^4-_ + 4*b*c^3*d^3*e+26*b^2*c^2*d^2*e^2-24*b^3*c*d*e^3+7*b^4*e^4)/_ + (b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 +--R (165b c d e - 60c d e )x + (165b c d e + 270b c d e - 120c d e)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (330b c d e + 45b c d e - 60c d )x + (165b c d e - 60b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 105b c e - 360b c d e + 390b c d e - 60b c d e - 135b c d e +--R + +--R 6 5 2 +--R 60c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R 105b e - 150b c d e - 330b c d e + 720b c d e - 255b c d e +--R + +--R 5 5 2 6 6 +--R - 210b c d e + 120c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R 210b d e - 615b c d e + 420b c d e + 270b c d e - 330b c d e +--R + +--R 5 6 6 7 +--R - 15b c d e + 60c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 105b d e - 360b c d e + 390b c d e - 60b c d e - 135b c d e +--R + +--R 5 7 +--R 60b c d +--R * +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 4 +--R (- 105b c e + 360b c d e - 390b c d e + 60b c d e - 30b c d e )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 105b e + 115b c d e + 450b c d e - 850b c d e + 165b c d e +--R + +--R 5 5 2 +--R - 90b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 245b d e + 679b c d e - 358b c d e - 436b c d e +--R + +--R 2 4 5 2 5 6 +--R 135b c d e - 90b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R - 161b d e + 537b c d e - 556b c d e + 90b c d e + 15b c d e +--R + +--R 5 7 +--R - 30b c d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15b d e + 60b c d e - 90b c d e + 60b c d e - 15b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 105b c e - 360b c d e + 390b c d e - 60b c d e +--R + +--R 5 4 3 6 5 2 +--R - 135b c d e + 60c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R 105b e - 150b c d e - 330b c d e + 720b c d e - 255b c d e +--R + +--R 5 5 2 6 6 +--R - 210b c d e + 120c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 210b d e - 615b c d e + 420b c d e + 270b c d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 330b c d e - 15b c d e + 60c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 105b d e - 360b c d e + 390b c d e - 60b c d e - 135b c d e +--R + +--R 5 7 +--R 60b c d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 4 3 6 5 2 4 +--R (165b c d e - 60c d e )x +--R + +--R 2 4 4 3 5 5 2 6 6 3 +--R (165b c d e + 270b c d e - 120c d e)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (330b c d e + 45b c d e - 60c d )x + (165b c d e - 60b c d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 210b c e + 720b c d e - 780b c d e + 120b c d e +--R + +--R 5 4 3 +--R - 60b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 210b e + 230b c d e + 900b c d e - 1700b c d e +--R + +--R 2 4 4 3 5 5 2 +--R 330b c d e - 180b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 490b d e + 1358b c d e - 716b c d e - 872b c d e +--R + +--R 2 4 5 2 5 6 +--R 270b c d e - 180b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R - 322b d e + 1074b c d e - 1112b c d e + 180b c d e +--R + +--R 2 4 6 5 7 +--R 30b c d e - 60b c d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 30b d e + 120b c d e - 180b c d e + 120b c d e - 30b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 105b c e - 360b c d e + 390b c d e - 60b c d e +--R + +--R 5 4 3 6 5 2 +--R - 135b c d e + 60c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R 105b e - 150b c d e - 330b c d e + 720b c d e - 255b c d e +--R + +--R 5 5 2 6 6 +--R - 210b c d e + 120c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 210b d e - 615b c d e + 420b c d e + 270b c d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 330b c d e - 15b c d e + 60c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 105b d e - 360b c d e + 390b c d e - 60b c d e - 135b c d e +--R + +--R 5 7 +--R 60b c d +--R * +--R x +--R * +--R +-------+ +-+ +--R +-------+ 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-----------------------------) +--R x +--R + +--R 5 4 3 6 5 2 4 +--R (- 330b c d e + 120c d e )x +--R + +--R 2 4 4 3 5 5 2 6 6 3 +--R (- 330b c d e - 540b c d e + 240c d e)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 660b c d e - 90b c d e + 120c d )x + (- 330b c d e + 120b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 210b c e + 720b c d e - 780b c d e + 120b c d e +--R + +--R 5 4 3 +--R - 60b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 210b e + 230b c d e + 900b c d e - 1700b c d e +--R + +--R 2 4 4 3 5 5 2 +--R 330b c d e - 180b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 490b d e + 1358b c d e - 716b c d e - 872b c d e +--R + +--R 2 4 5 2 5 6 +--R 270b c d e - 180b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R - 322b d e + 1074b c d e - 1112b c d e + 180b c d e +--R + +--R 2 4 6 5 7 +--R 30b c d e - 60b c d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 30b d e + 120b c d e - 180b c d e + 120b c d e - 30b c d +--R * +--R +-+ +--R \|d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 4 3 6 5 2 4 +--R (165b c d e - 60c d e )x +--R + +--R 2 4 4 3 5 5 2 6 6 3 +--R (165b c d e + 270b c d e - 120c d e)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (330b c d e + 45b c d e - 60c d )x + (165b c d e - 60b c d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 210b c e - 720b c d e + 780b c d e - 120b c d e +--R + +--R 5 4 3 6 5 2 +--R - 270b c d e + 120c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R 210b e - 300b c d e - 660b c d e + 1440b c d e +--R + +--R 2 4 4 3 5 5 2 6 6 +--R - 510b c d e - 420b c d e + 240c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 420b d e - 1230b c d e + 840b c d e + 540b c d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 660b c d e - 30b c d e + 120c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R 210b d e - 720b c d e + 780b c d e - 120b c d e +--R + +--R 2 4 6 5 7 +--R - 270b c d e + 120b c d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 210b c e + 720b c d e - 780b c d e + 120b c d e +--R + +--R 5 4 3 +--R - 60b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 210b e + 230b c d e + 900b c d e - 1700b c d e +--R + +--R 2 4 4 3 5 5 2 +--R 330b c d e - 180b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 490b d e + 1358b c d e - 716b c d e - 872b c d e +--R + +--R 2 4 5 2 5 6 +--R 270b c d e - 180b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R - 322b d e + 1074b c d e - 1112b c d e + 180b c d e +--R + +--R 2 4 6 5 7 +--R 30b c d e - 60b c d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 30b d e + 120b c d e - 180b c d e + 120b c d e - 30b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (30b c d e - 120b c d e + 180b c d e - 120b c d e + 30b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 30b d e - 60b c d e - 60b c d e + 240b c d e - 210b c d e +--R + +--R 3 5 9 +--R 60b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 60b d e - 210b c d e + 240b c d e - 60b c d e - 60b c d e +--R + +--R 3 5 10 +--R 30b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (30b d e - 120b c d e + 180b c d e - 120b c d e + 30b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R 105b c e - 360b c d e + 390b c d e - 60b c d e +--R + +--R 5 4 3 6 5 2 +--R - 135b c d e + 60c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R 105b e - 150b c d e - 330b c d e + 720b c d e - 255b c d e +--R + +--R 5 5 2 6 6 +--R - 210b c d e + 120c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R 210b d e - 615b c d e + 420b c d e + 270b c d e +--R + +--R 2 4 5 2 5 6 6 7 +--R - 330b c d e - 15b c d e + 60c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 +--R 105b d e - 360b c d e + 390b c d e - 60b c d e - 135b c d e +--R + +--R 5 7 +--R 60b c d +--R * +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 4 3 6 5 2 4 +--R (- 165b c d e + 60c d e )x +--R + +--R 2 4 4 3 5 5 2 6 6 3 +--R (- 165b c d e - 270b c d e + 120c d e)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 330b c d e - 45b c d e + 60c d )x + (- 165b c d e + 60b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 +--R - 105b c e + 360b c d e - 390b c d e + 60b c d e +--R + +--R 5 4 3 +--R - 30b c d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 +--R - 105b e + 115b c d e + 450b c d e - 850b c d e +--R + +--R 2 4 4 3 5 5 2 +--R 165b c d e - 90b c d e +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 +--R - 245b d e + 679b c d e - 358b c d e - 436b c d e +--R + +--R 2 4 5 2 5 6 +--R 135b c d e - 90b c d e +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 +--R - 161b d e + 537b c d e - 556b c d e + 90b c d e +--R + +--R 2 4 6 5 7 +--R 15b c d e - 30b c d +--R * +--R x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 15b d e + 60b c d e - 90b c d e + 60b c d e - 15b c d +--R * +--R +---+ +--R \|- d +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (15b c d e - 60b c d e + 90b c d e - 60b c d e + 15b c d e )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 15b d e - 30b c d e - 30b c d e + 120b c d e - 105b c d e +--R + +--R 3 5 9 +--R 30b c d e +--R * +--R 3 +--R x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 +--R 30b d e - 105b c d e + 120b c d e - 30b c d e - 30b c d e +--R + +--R 3 5 10 +--R 15b c d +--R * +--R 2 +--R x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (15b d e - 60b c d e + 90b c d e - 60b c d e + 15b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 844 + +--S 845 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (7b e - 24b c d e + 26b c d e - 4b c d e - 9b c d e + 4c d ) +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 4 4 5 5 +-----------+ | c +-+ +--R (11b c d e - 4c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 4 4 5 5 +-+ +-+ \|c \|e x + d +--R (- 22b c d e + 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 14b e + 48b c d e - 52b c d e + 8b c d e + 18b c d e - 8c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (7b e - 24b c d e + 26b c d e - 4b c d e - 9b c d e + 4c d ) +--R * +--R +-------+ +-+ +--R +-----------+ 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 4 4 5 5 +-+ +-+ \|c \|e x + d +--R (- 22b c d e + 8c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 14b e + 48b c d e - 52b c d e + 8b c d e + 18b c d e - 8c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 4 4 5 5 +-----------+ | c +-+ +--R (- 22b c d e + 8c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +-----------+ +-+ +--R (2b d e - 8b c d e + 12b c d e - 8b c d e + 2b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 848 + +)clear all + +--S 849 of 1726 +t0:=(d+e*x)^(9/2)/(b*x+c*x^2)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R (1) -------------------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1726 +r0:=1/4*(c*d-b*e)*(24*c^2*d^2-24*b*c*d*e-b^2*e^2)*(d+e*x)^(3/2)/_ + (b^4*c*(b+c*x))+1/4*(12*c*d-13*b*e)*(c*d-b*e)*(d+e*x)^(5/2)/_ + (b^3*(b+c*x)^2)+1/4*(8*c*d-9*b*e)*(d+e*x)^(7/2)/(b^2*x*_ + (b+c*x)^2)-1/2*(d+e*x)^(9/2)/(b*x^2*(b+c*x)^2)-3/4*d^(5/2)*_ + (16*c^2*d^2-36*b*c*d*e+21*b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/_ + b^5+3/4*(c*d-b*e)^(5/2)*(16*c^2*d^2+4*b*c*d*e+b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*c^(5/2))-_ + 3/4*e*(2*c*d-b*e)*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)*sqrt(d+e*x)/(b^4*c^2) +--R +--R +--R (2) +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (3b c e + 6b c d e + 27b c d e - 84b c d e + 48c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (6b c e + 12b c d e + 54b c d e - 168b c d e + 96b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (3b e + 6b c d e + 27b c d e - 84b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (- 63b c d e + 108b c d e - 48c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (- 126b c d e + 216b c d e - 96b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (- 63b c d e + 108b c d e - 48b c d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (- 5b c e + 3b c d e + 21b c d e - 48b c d e + 24b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 3b e - 5b c d e + 33b c d e - 73b c d e + 36b c d )x +--R + +--R 4 2 3 3 3 4 4 2 4 +--R (- 17b c d e + 8b c d )x - 2b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 4 4 6 3 3 7 2 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1726 value stack overflow +--a0:=integrate(t0,x) +--E 851 + +--S 852 of 1726 +--m0:=a0-r0 +--E 852 + +--S 853 of 1726 +--d0:=D(m0,x) +--E 853 + +)clear all + +--S 854 of 1726 +t0:=(d+e*x)^(7/2)/(b*x+c*x^2)^3 +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1726 +r0:=1/4*(12*c*d-11*b*e)*(c*d-b*e)*(d+e*x)^(3/2)/(b^3*(b+c*x)^2)+_ + 1/4*(8*c*d-7*b*e)*(d+e*x)^(5/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*(d+e*x)^(7/2)/(b*x^2*(b+c*x)^2)-1/4*d^(3/2)*(48*c^2*d^2-_ + 84*b*c*d*e+35*b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/b^5+_ + 1/4*(c*d-b*e)^(3/2)*(48*c^2*d^2-12*b*c*d*e-b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*c^(3/2))+_ + 1/4*(c*d-b*e)*(24*c^2*d^2-24*b*c*d*e+b^2*e^2)*sqrt(d+e*x)/(b^4*c*(b+c*x)) +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 3 2 4 2 5 3 4 +--R (- 35b c d e + 84b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 70b c d e + 168b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 35b c d e + 84b c d e - 48b c d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (b c e + 10b c d e - 36b c d e + 24b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- b e + 16b c d e - 55b c d e + 36b c d )x +--R + +--R 4 2 3 2 3 4 3 +--R (- 13b c d e + 8b c d )x - 2b c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +-+ +--R (4b c x + 8b c x + 4b c x )\|c +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 5 3 4 +--R (35b c d e - 84b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (70b c d e - 168b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (35b c d e - 84b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 20b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- 2b e + 32b c d e - 110b c d e + 72b c d )x +--R + +--R 4 2 3 2 3 4 3 +--R (- 26b c d e + 16b c d )x - 4b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 5 3 4 +--R (35b c d e - 84b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (70b c d e - 168b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (35b c d e - 84b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (2b c e + 22b c d e - 120b c d e + 96c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (4b c e + 44b c d e - 240b c d e + 192b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (2b e + 22b c d e - 120b c d e + 96b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 20b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- 2b e + 32b c d e - 110b c d e + 72b c d )x +--R + +--R 4 2 3 2 3 4 3 +--R (- 26b c d e + 16b c d )x - 4b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 3 2 4 2 5 3 4 +--R (- 70b c d e + 168b c d e - 96c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 140b c d e + 336b c d e - 192b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 70b c d e + 168b c d e - 96b c d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 20b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- 2b e + 32b c d e - 110b c d e + 72b c d )x +--R + +--R 4 2 3 2 3 4 3 +--R (- 26b c d e + 16b c d )x - 4b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 8b c x + 16b c x + 8b c x +--R , +--R +--R 2 3 2 4 2 5 3 4 +--R (- 35b c d e + 84b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 70b c d e + 168b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 35b c d e + 84b c d e - 48b c d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (b c e + 10b c d e - 36b c d e + 24b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- b e + 16b c d e - 55b c d e + 36b c d )x +--R + +--R 4 2 3 2 3 4 3 +--R (- 13b c d e + 8b c d )x - 2b c d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 3 4 6 2 3 7 2 +--R 4b c x + 8b c x + 4b c x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 856 + +--S 857 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 2 2 2 2 3 3 |- b e + c d +-+ +--R (b e + 11b c d e - 60b c d e + 48c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R 2 2 2 2 3 3 +-+ +-+ +--R (35b c d e - 84b c d e + 48c d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 2b e - 22b c d e + 120b c d e - 96c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 3 3 +-+ +-+ \|e x + d +--R (70b c d e - 168b c d e + 96c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 3 3 +-+ +-+ +--R (35b c d e - 84b c d e + 48c d )\|c \|d +--R * +--R +-+ +-------+ +--R - 2\|d \|e x + d + e x + 2d +--R log(----------------------------) +--R x +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 2b e - 22b c d e + 120b c d e - 96c d )\|- b e + c d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 3 3 +-+ +-+ \|e x + d +--R (70b c d e - 168b c d e + 96c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 3 3 2 2 2 2 3 3 +-+ |b e - c d +--R (2b e + 22b c d e - 120b c d e + 96c d )\|c |--------- +--R \| c +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 +-+ +--R 8b c\|c +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1726 +t0:=(d+e*x)^(5/2)/(b*x+c*x^2)^3 +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1726 +r0:=1/4*(8*c*d-5*b*e)*(d+e*x)^(3/2)/(b^2*x*(b+c*x)^2)-_ + 1/2*(d+e*x)^(5/2)/(b*x^2*(b+c*x)^2)-3/4*(16*c^2*d^2-_ + 20*b*c*d*e+5*b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^5+_ + 3/4*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)*atanh(sqrt(c)*sqrt(d+_ + e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b^5*sqrt(c))+3/4*(4*c*d-_ + 3*b*e)*(c*d-b*e)*sqrt(d+e*x)/(b^3*(b+c*x)^2)+3/4*(8*c^2*d^2-_ + 8*b*c*d*e+b^2*e^2)*sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R (3b c e - 36b c d e + 48c d )x + (6b c e - 72b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (3b e - 36b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-----------+ \|c \|e x + d +--R \|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 4 2 4 +--R (- 15b c e + 60b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 30b c e + 120b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 15b e + 60b c d e - 48b c d )x +--R * +--R +-------+ +--R +-+ +-+ \|e x + d +--R \|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (3b c e - 24b c d e + 24b c d )x + (5b e - 37b c d e + 36b c d )x +--R + +--R 4 3 2 4 2 +--R (- 9b d e + 8b c d )x - 2b d +--R * +--R +-+ +-------+ +--R \|c \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-+ +--R (4b c x + 8b c x + 4b x )\|c +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 4 2 4 +--R (3b c e - 36b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (6b c e - 72b c d e + 96b c d )x + (3b e - 36b c d e + 48b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 3 4 2 4 +--R (15b c e - 60b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (30b c e - 120b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (15b e - 60b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 3 2 2 2 3 2 3 +--R (6b c e - 48b c d e + 48b c d )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (10b e - 74b c d e + 72b c d )x + (- 18b d e + 16b c d )x - 4b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 2 4 6 3 7 2 +--R 8b c x + 16b c x + 8b x +--R , +--R +--R 2 2 2 3 4 2 4 +--R (15b c e - 60b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (30b c e - 120b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (15b e - 60b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|d \|e x + d + e x + 2d +--R \|d log(----------------------------) +--R x +--R + +--R 2 2 2 3 4 2 4 +--R (6b c e - 72b c d e + 96c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (12b c e - 144b c d e + 192b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (6b e - 72b c d e + 96b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 2 3 2 3 +--R (6b c e - 48b c d e + 48b c d )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (10b e - 74b c d e + 72b c d )x + (- 18b d e + 16b c d )x - 4b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 2 4 6 3 7 2 +--R 8b c x + 16b c x + 8b x +--R , +--R +--R 2 2 2 3 4 2 4 +--R (3b c e - 36b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (6b c e - 72b c d e + 96b c d )x + (3b e - 36b c d e + 48b c d )x +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R +-----------+ 2c |----------- \|e x + d + c e x - b e + 2c d +--R |- b e + c d \| c +--R |----------- log(-----------------------------------------------) +--R \| c c x + b +--R + +--R 2 2 2 3 4 2 4 +--R (- 30b c e + 120b c d e - 96c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 60b c e + 240b c d e - 192b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 30b e + 120b c d e - 96b c d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 3 2 2 2 3 2 3 +--R (6b c e - 48b c d e + 48b c d )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (10b e - 74b c d e + 72b c d )x + (- 18b d e + 16b c d )x - 4b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 2 4 6 3 7 2 +--R 8b c x + 16b c x + 8b x +--R , +--R +--R 2 2 2 3 4 2 4 +--R (- 15b c e + 60b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 30b c e + 120b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 15b e + 60b c d e - 48b c d )x +--R * +--R +-------+ +--R +---+ \|e x + d +--R \|- d atan(----------) +--R +---+ +--R \|- d +--R + +--R 2 2 2 3 4 2 4 +--R (3b c e - 36b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (6b c e - 72b c d e + 96b c d )x + (3b e - 36b c d e + 48b c d )x +--R * +--R +---------+ +-------+ +--R |b e - c d \|e x + d +--R |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R + +--R 3 2 2 2 3 2 3 +--R (3b c e - 24b c d e + 24b c d )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (5b e - 37b c d e + 36b c d )x + (- 9b d e + 8b c d )x - 2b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 2 4 6 3 7 2 +--R 4b c x + 8b c x + 4b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 863 + +--S 864 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- b e + c d +-+ +--R (3b e - 36b c d e + 48c d ) |----------- \|c +--R \| c +--R * +--R +-----------+ +--R |- b e + c d +-------+ +--R 2c |----------- \|e x + d + c e x - b e + 2c d +--R \| c +--R log(-----------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (15b e - 60b c d e + 48c d )\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 6b e + 72b c d e - 96c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|e x + d +--R (30b e - 120b c d e + 96c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 +-+ +--R 8b \|c +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|d \|e x + d + e x + 2d +--R (15b e - 60b c d e + 48c d )\|c \|d log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|c \|e x + d +--R (- 6b e + 72b c d e - 96c d )\|- b e + c d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|e x + d +--R (30b e - 120b c d e + 96c d )\|c \|d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |b e - c d \|e x + d +--R (6b e - 72b c d e + 96c d )\|c |--------- atan(------------) +--R \| c +---------+ +--R |b e - c d +--R |--------- +--R \| c +--R / +--R 5 +-+ +--R 8b \|c +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1726 +t0:=(d+e*x)^(3/2)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1726 +r0:=-1/2*(d+e*x)^(3/2)/(b*x^2*(b+c*x)^2)-3/4*(16*c^2*d^2-12*b*c*d*e+_ + b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/(b^5*sqrt(d))+3/4*(16*c^2*d^2-_ + 20*b*c*d*e+5*b^2*e^2)*atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*_ + sqrt(c)/(b^5*sqrt(c*d-b*e))+1/4*c*(12*c*d-7*b*e)*sqrt(d+e*x)/_ + (b^3*(b+c*x)^2)+1/4*(8*c*d-3*b*e)*sqrt(d+e*x)/(b^2*x*(b+c*x)^2)+_ + 3*c*(2*c*d-b*e)*sqrt(d+e*x)/(b^4*(b+c*x)) +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 +--R (15b c e - 60b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (30b c e - 120b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (15b e - 60b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 2 2 2 3 4 2 4 +--R (- 3b c e + 36b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6b c e + 72b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 3b e + 36b c d e - 48b c d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12b c e + 24b c d)x + (- 19b c e + 36b c d)x +--R + +--R 4 3 4 +--R (- 5b e + 8b c d)x - 2b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-----------+ +-+ +--R (4b c x + 8b c x + 4b x )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 4 2 4 +--R (3b c e - 36b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (6b c e - 72b c d e + 96b c d )x + (3b e - 36b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 4 2 4 +--R (15b c e - 60b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (30b c e - 120b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (15b e - 60b c d e + 48b c d )x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 24b c e + 48b c d)x + (- 38b c e + 72b c d)x +--R + +--R 4 3 4 +--R (- 10b e + 16b c d)x - 4b d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-+ +--R (8b c x + 16b c x + 8b x )\|d +--R , +--R +--R 2 2 2 3 4 2 4 +--R (3b c e - 36b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (6b c e - 72b c d e + 96b c d )x + (3b e - 36b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 4 2 4 +--R (- 30b c e + 120b c d e - 96c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 60b c e + 240b c d e - 192b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 30b e + 120b c d e - 96b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 24b c e + 48b c d)x + (- 38b c e + 72b c d)x +--R + +--R 4 3 4 +--R (- 10b e + 16b c d)x - 4b d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +-+ +--R (8b c x + 16b c x + 8b x )\|d +--R , +--R +--R 2 2 2 3 4 2 4 +--R (15b c e - 60b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (30b c e - 120b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (15b e - 60b c d e + 48b c d )x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 2 2 2 3 4 2 4 +--R (- 6b c e + 72b c d e - 96c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 12b c e + 144b c d e - 192b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 6b e + 72b c d e - 96b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 24b c e + 48b c d)x + (- 38b c e + 72b c d)x +--R + +--R 4 3 4 +--R (- 10b e + 16b c d)x - 4b d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +---+ +--R (8b c x + 16b c x + 8b x )\|- d +--R , +--R +--R 2 2 2 3 4 2 4 +--R (- 3b c e + 36b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6b c e + 72b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 3b e + 36b c d e - 48b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 2 2 3 4 2 4 +--R (- 15b c e + 60b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 30b c e + 120b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 2 +--R (- 15b e + 60b c d e - 48b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 12b c e + 24b c d)x + (- 19b c e + 36b c d)x +--R + +--R 4 3 4 +--R (- 5b e + 8b c d)x - 2b d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 5 2 4 6 3 7 2 +---+ +--R (4b c x + 8b c x + 4b x )\|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 870 + +--S 871 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 +-----------+ +--R (3b e - 36b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 2 +-----------+ | c +-+ +--R (15b e - 60b c d e + 48c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ \|c \|e x + d +--R (- 30b e + 120b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (6b e - 72b c d e + 96c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 5 +-----------+ +-+ +--R 8b \|- b e + c d \|d +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 +-----------+ +--R (3b e - 36b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ \|c \|e x + d +--R (- 30b e + 120b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|e x + d +--R (6b e - 72b c d e + 96c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 2 2 +-----------+ | c +-+ +--R (- 30b e + 120b c d e - 96c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 5 +-----------+ +-+ +--R 8b \|- b e + c d \|d +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 874 + +)clear all + +--S 875 of 1726 +t0:=sqrt(d+e*x)/(b*x+c*x^2)^3 +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R c x + 3b c x + 3b c x + b x +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1726 +r0:=-1/4*(48*c^2*d^2-12*b*c*d*e-b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*d^(3/2))+1/4*c^(3/2)*(48*c^2*d^2-84*b*c*d*e+35*b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(3/2))+_ + 1/4*c*(12*c*d-b*e)*sqrt(d+e*x)/(b^3*d*(b+c*x)^2)-_ + 1/2*sqrt(d+e*x)/(b*x^2*(b+c*x)^2)+1/4*(8*c*d-b*e)*_ + sqrt(d+e*x)/(b^2*d*x*(b+c*x)^2)+1/4*c*(24*c^2*d^2-24*b*c*d*e+_ + b^2*e^2)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b+c*x)) +--R +--R +--R (2) +--R 2 3 2 4 2 5 3 4 +--R (- 35b c d e + 84b c d e - 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 70b c d e + 168b c d e - 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 35b c d e + 84b c d e - 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 3 2 2 2 3 4 2 3 +--R (- b c e + 24b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 3 2 2 5 2 4 3 2 2 +--R (- 2b c e + 37b c d e - 36b c d )x + (- b e + 9b c d e - 8b c d )x +--R + +--R 5 4 2 +--R - 2b d e + 2b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 8 7 2 2 +--R ((4b c d e - 4b c d )x + (8b c d e - 8b c d )x + (4b d e - 4b c d )x ) +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 4 2 5 3 4 +--R (35b c d e - 84b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (70b c d e - 168b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (35b c d e - 84b c d e + 48b c d )x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 3 2 2 2 3 4 2 3 +--R (- 2b c e + 48b c d e - 48b c d )x +--R + +--R 4 2 3 2 2 3 2 2 +--R (- 4b c e + 74b c d e - 72b c d )x +--R + +--R 5 2 4 3 2 2 5 4 2 +--R (- 2b e + 18b c d e - 16b c d )x - 4b d e + 4b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R 2 3 2 4 2 5 3 4 +--R (70b c d e - 168b c d e + 96c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (140b c d e - 336b c d e + 192b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (70b c d e - 168b c d e + 96b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 4 2 3 +--R (- 2b c e + 48b c d e - 48b c d )x +--R + +--R 4 2 3 2 2 3 2 2 +--R (- 4b c e + 74b c d e - 72b c d )x +--R + +--R 5 2 4 3 2 2 5 4 2 +--R (- 2b e + 18b c d e - 16b c d )x - 4b d e + 4b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 3 2 4 2 5 3 4 +--R (35b c d e - 84b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (70b c d e - 168b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (35b c d e - 84b c d e + 48b c d )x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (2b c e + 22b c d e - 120b c d e + 96c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (4b c e + 44b c d e - 240b c d e + 192b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (2b e + 22b c d e - 120b c d e + 96b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 3 2 2 2 3 4 2 3 +--R (- 2b c e + 48b c d e - 48b c d )x +--R + +--R 4 2 3 2 2 3 2 2 +--R (- 4b c e + 74b c d e - 72b c d )x +--R + +--R 5 2 4 3 2 2 5 4 2 +--R (- 2b e + 18b c d e - 16b c d )x - 4b d e + 4b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (8b c d e - 8b c d )x + (16b c d e - 16b c d )x +--R + +--R 8 7 2 2 +--R (8b d e - 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 3 2 3 2 3 2 4 2 5 3 4 +--R (b c e + 11b c d e - 60b c d e + 48c d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 3 +--R (2b c e + 22b c d e - 120b c d e + 96b c d )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (b e + 11b c d e - 60b c d e + 48b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 3 2 4 2 5 3 4 +--R (35b c d e - 84b c d e + 48c d )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (70b c d e - 168b c d e + 96b c d )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (35b c d e - 84b c d e + 48b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 3 2 2 2 3 4 2 3 +--R (- b c e + 24b c d e - 24b c d )x +--R + +--R 4 2 3 2 2 3 2 2 +--R (- 2b c e + 37b c d e - 36b c d )x +--R + +--R 5 2 4 3 2 2 5 4 2 +--R (- b e + 9b c d e - 8b c d )x - 2b d e + 2b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 6 2 5 3 2 4 7 6 2 2 3 +--R (4b c d e - 4b c d )x + (8b c d e - 8b c d )x +--R + +--R 8 7 2 2 +--R (4b d e - 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 877 + +--S 878 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 3 3 +-----------+ | c +-+ +--R (35b c d e - 84b c d e + 48c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (b e + 11b c d e - 60b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 3 3 +-+ +-+ \|c \|e x + d +--R (70b c d e - 168b c d e + 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|e x + d +--R (- 2b e - 22b c d e + 120b c d e - 96c d )\|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (b e + 11b c d e - 60b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R 2d\|e x + d + (e x + 2d)\|d +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 3 3 +-+ +-+ \|c \|e x + d +--R (70b c d e - 168b c d e + 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (- 2b e - 22b c d e + 120b c d e - 96c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 2 2 3 3 +-----------+ | c +-+ +--R (70b c d e - 168b c d e + 96c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 6 5 2 +-----------+ +-+ +--R (8b d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 881 + +)clear all + +--S 882 of 1726 +t0:=1/((b*x+c*x^2)^3*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 6 2 5 2 4 3 3 +-------+ +--R (c x + 3b c x + 3b c x + b x )\|e x + d +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1726 +r0:=-3/4*(16*c^2*d^2+4*b*c*d*e+b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*d^(5/2))+3/4*c^(5/2)*(16*c^2*d^2-36*b*c*d*e+21*b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(5/2))+_ + 1/4*c*(12*c^2*d^2-7*b*c*d*e-3*b^2*e^2)*sqrt(d+e*x)/(b^3*_ + d^2*(c*d-b*e)*(b+c*x)^2)-1/2*sqrt(d+e*x)/(b*d*x^2*(b+c*x)^2)+_ + 1/4*(8*c*d+3*b*e)*sqrt(d+e*x)/(b^2*d^2*x*(b+c*x)^2)+3/4*c*_ + (2*c*d-b*e)*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)*sqrt(d+e*x)/(b^4*_ + d^2*(c*d-b*e)^2*(b+c*x)) +--R +--R +--R (2) +--R 2 4 2 2 5 3 6 4 4 +--R (63b c d e - 108b c d e + 48c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (126b c d e - 216b c d e + 96b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (63b c d e - 108b c d e + 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ \|c \|e x + d +--R \|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (- 3b c e - 6b c d e - 27b c d e + 84b c d e - 48c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (- 6b c e - 12b c d e - 54b c d e + 168b c d e - 96b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 3b e - 6b c d e - 27b c d e + 84b c d e - 48b c d )x +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 3 +--R (3b c e + 6b c d e - 36b c d e + 24b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 2 +--R (6b c e + 10b c d e - 55b c d e + 36b c d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 6 2 5 2 +--R (3b e + 2b c d e - 13b c d e + 8b c d )x - 2b d e + 4b c d e +--R + +--R 4 2 3 +--R - 2b c d +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (3b c e + 6b c d e + 27b c d e - 84b c d e + 48c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (6b c e + 12b c d e + 54b c d e - 168b c d e + 96b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (3b e + 6b c d e + 27b c d e - 84b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (63b c d e - 108b c d e + 48c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (126b c d e - 216b c d e + 96b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (63b c d e - 108b c d e + 48b c d )x +--R * +--R +-----------+ +--R | c +-+ +--R |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 3 +--R (6b c e + 12b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 2 +--R (12b c e + 20b c d e - 110b c d e + 72b c d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 6 2 5 2 +--R (6b e + 4b c d e - 26b c d e + 16b c d )x - 4b d e + 8b c d e +--R + +--R 4 2 3 +--R - 4b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (3b c e + 6b c d e + 27b c d e - 84b c d e + 48c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (6b c e + 12b c d e + 54b c d e - 168b c d e + 96b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (3b e + 6b c d e + 27b c d e - 84b c d e + 48b c d )x +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (- 126b c d e + 216b c d e - 96c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (- 252b c d e + 432b c d e - 192b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (- 126b c d e + 216b c d e - 96b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ c\|e x + d +--R |--------- \|d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 3 +--R (6b c e + 12b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 2 +--R (12b c e + 20b c d e - 110b c d e + 72b c d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 6 2 5 2 +--R (6b e + 4b c d e - 26b c d e + 16b c d )x - 4b d e + 8b c d e +--R + +--R 4 2 3 +--R - 4b c d +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +-+ +--R \|d +--R , +--R +--R 2 4 2 2 5 3 6 4 4 +--R (63b c d e - 108b c d e + 48c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (126b c d e - 216b c d e + 96b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (63b c d e - 108b c d e + 48b c d )x +--R * +--R +-----------+ +--R +---+ | c +--R \|- d |- --------- +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (- 6b c e - 12b c d e - 54b c d e + 168b c d e - 96c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (- 12b c e - 24b c d e - 108b c d e + 336b c d e - 192b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 6b e - 12b c d e - 54b c d e + 168b c d e - 96b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 3 +--R (6b c e + 12b c d e - 72b c d e + 48b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 2 +--R (12b c e + 20b c d e - 110b c d e + 72b c d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 6 2 5 2 +--R (6b e + 4b c d e - 26b c d e + 16b c d )x - 4b d e + 8b c d e +--R + +--R 4 2 3 +--R - 4b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (8b c d e - 16b c d e + 8b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 +--R (16b c d e - 32b c d e + 16b c d )x +--R + +--R 9 2 2 8 3 7 2 4 2 +--R (8b d e - 16b c d e + 8b c d )x +--R * +--R +---+ +--R \|- d +--R , +--R +--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4 +--R (- 3b c e - 6b c d e - 27b c d e + 84b c d e - 48c d )x +--R + +--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 3 +--R (- 6b c e - 12b c d e - 54b c d e + 168b c d e - 96b c d )x +--R + +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 3b e - 6b c d e - 27b c d e + 84b c d e - 48b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R atan(----------------) +--R d +--R + +--R 2 4 2 2 5 3 6 4 4 +--R (- 63b c d e + 108b c d e - 48c d )x +--R + +--R 3 3 2 2 2 4 3 5 4 3 +--R (- 126b c d e + 216b c d e - 96b c d )x +--R + +--R 4 2 2 2 3 3 3 2 4 4 2 +--R (- 63b c d e + 108b c d e - 48b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c c\|e x + d +--R \|- d |--------- atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 3 +--R (3b c e + 6b c d e - 36b c d e + 24b c d )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 2 +--R (6b c e + 10b c d e - 55b c d e + 36b c d )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 6 2 5 2 +--R (3b e + 2b c d e - 13b c d e + 8b c d )x - 2b d e + 4b c d e +--R + +--R 4 2 3 +--R - 2b c d +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R / +--R 7 2 2 2 6 3 3 5 4 4 4 +--R (4b c d e - 8b c d e + 4b c d )x +--R + +--R 8 2 2 7 2 3 6 3 4 3 9 2 2 8 3 7 2 4 2 +--R (8b c d e - 16b c d e + 8b c d )x + (4b d e - 8b c d e + 4b c d )x +--R * +--R +---+ +--R \|- d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 884 + +--S 885 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (3b e + 6b c d e + 27b c d e - 84b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 2 3 3 4 4 +-----------+ | c +-+ +--R (63b c d e - 108b c d e + 48c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 2 2 2 3 3 4 4 +-+ +-+ \|c \|e x + d +--R (- 126b c d e + 216b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (6b e + 12b c d e + 54b c d e - 168b c d e + 96c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (3b e + 6b c d e + 27b c d e - 84b c d e + 48c d )\|- b e + c d +--R * +--R +-------+ +-+ +--R - 2d\|e x + d + (e x + 2d)\|d +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 3 3 4 4 +-+ +-+ \|c \|e x + d +--R (- 126b c d e + 216b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (6b e + 12b c d e + 54b c d e - 168b c d e + 96c d )\|- b e + c d +--R * +--R +-------+ +--R \|e x + d +--R atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 2 2 2 3 3 4 4 +-----------+ | c +-+ +--R (- 126b c d e + 216b c d e - 96c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 7 2 2 6 3 5 2 4 +-----------+ +-+ +--R (8b d e - 16b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1726 +t0:=1/((d+e*x)^(3/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 7 2 3 6 2 2 5 3 2 4 +--R c e x + (3b c e + c d)x + (3b c e + 3b c d)x + (b e + 3b c d)x +--R + +--R 3 3 +--R b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1726 +r0:=-3/4*(16*c^2*d^2+12*b*c*d*e+5*b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*d^(7/2))+3/4*c^(7/2)*(16*c^2*d^2-44*b*c*d*e+33*b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+_ + 3/4*e*(c^2*d^2-b*c*d*e-b^2*e^2)*(8*c^2*d^2-8*b*c*d*e+5*b^2*e^2)/_ + (b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x))+1/4*c*(12*c^2*d^2-5*b*c*d*e-_ + 5*b^2*e^2)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*sqrt(d+e*x))+(-1/2)/_ + (b*d*x^2*(b+c*x)^2*sqrt(d+e*x))+1/4*(8*c*d+5*b*e)/(b^2*d^2*_ + x*(b+c*x)^2*sqrt(d+e*x))+1/4*c*(2*c*d-b*e)*(12*c^2*d^2-12*b*c*d*e-_ + 5*b^2*e^2)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 5 3 2 6 4 7 5 4 +--R (- 99b c d e + 132b c d e - 48c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (- 198b c d e + 264b c d e - 96b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (- 99b c d e + 132b c d e - 48b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 15b c e + 9b c d e + 15b c d e + 51b c d e - 108b c d e +--R + +--R 7 5 +--R 48c d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R - 30b c e + 18b c d e + 30b c d e + 102b c d e - 216b c d e +--R + +--R 6 5 +--R 96b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 15b e + 9b c d e + 15b c d e + 51b c d e - 108b c d e +--R + +--R 2 5 5 +--R 48b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 4 +--R (15b c e - 9b c d e - 15b c d e + 48b c d e - 24b c d e)x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 30b c e - 13b c d e - 33b c d e + 58b c d e + 12b c d e +--R + +--R 6 5 +--R - 24b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (15b e + b c d e - 23b c d e - 7b c d e + 65b c d e - 36b c d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (5b d e - 7b c d e - 9b c d e + 19b c d e - 8b c d )x - 2b d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R 6b c d e - 6b c d e + 2b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 5 3 2 6 4 7 5 4 +--R (99b c d e - 132b c d e + 48c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (198b c d e - 264b c d e + 96b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (99b c d e - 132b c d e + 48b c d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 15b c e - 9b c d e - 15b c d e - 51b c d e + 108b c d e +--R + +--R 7 5 +--R - 48c d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 30b c e - 18b c d e - 30b c d e - 102b c d e + 216b c d e +--R + +--R 6 5 +--R - 96b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 15b e - 9b c d e - 15b c d e - 51b c d e + 108b c d e +--R + +--R 2 5 5 +--R - 48b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 4 +--R (30b c e - 18b c d e - 30b c d e + 96b c d e - 48b c d e)x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 60b c e - 26b c d e - 66b c d e + 116b c d e + 24b c d e +--R + +--R 6 5 +--R - 48b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 30b e + 2b c d e - 46b c d e - 14b c d e + 130b c d e +--R + +--R 2 5 5 +--R - 72b c d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 +--R (10b d e - 14b c d e - 18b c d e + 38b c d e - 16b c d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 4b d e + 12b c d e - 12b c d e + 4b c d +--R * +--R +-+ +--R \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (16b c d e - 48b c d e + 48b c d e - 16b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R 15b c e - 9b c d e - 15b c d e - 51b c d e + 108b c d e +--R + +--R 7 5 +--R - 48c d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 30b c e - 18b c d e - 30b c d e - 102b c d e + 216b c d e +--R + +--R 6 5 +--R - 96b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 15b e - 9b c d e - 15b c d e - 51b c d e + 108b c d e +--R + +--R 2 5 5 +--R - 48b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (198b c d e - 264b c d e + 96c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (396b c d e - 528b c d e + 192b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (198b c d e - 264b c d e + 96b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 4 +--R (30b c e - 18b c d e - 30b c d e + 96b c d e - 48b c d e)x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 60b c e - 26b c d e - 66b c d e + 116b c d e + 24b c d e +--R + +--R 6 5 +--R - 48b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 30b e + 2b c d e - 46b c d e - 14b c d e + 130b c d e +--R + +--R 2 5 5 +--R - 72b c d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 +--R (10b d e - 14b c d e - 18b c d e + 38b c d e - 16b c d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 4b d e + 12b c d e - 12b c d e + 4b c d +--R * +--R +-+ +--R \|d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (16b c d e - 48b c d e + 48b c d e - 16b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 2 5 3 2 6 4 7 5 4 +--R (99b c d e - 132b c d e + 48c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (198b c d e - 264b c d e + 96b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (99b c d e - 132b c d e + 48b c d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 30b c e + 18b c d e + 30b c d e + 102b c d e - 216b c d e +--R + +--R 7 5 +--R 96c d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R - 60b c e + 36b c d e + 60b c d e + 204b c d e - 432b c d e +--R + +--R 6 5 +--R 192b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 30b e + 18b c d e + 30b c d e + 102b c d e - 216b c d e +--R + +--R 2 5 5 +--R 96b c d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 4 +--R (30b c e - 18b c d e - 30b c d e + 96b c d e - 48b c d e)x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 60b c e - 26b c d e - 66b c d e + 116b c d e + 24b c d e +--R + +--R 6 5 +--R - 48b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 30b e + 2b c d e - 46b c d e - 14b c d e + 130b c d e +--R + +--R 2 5 5 +--R - 72b c d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 +--R (10b d e - 14b c d e - 18b c d e + 38b c d e - 16b c d )x +--R + +--R 7 2 3 6 3 2 5 2 4 4 3 5 +--R - 4b d e + 12b c d e - 12b c d e + 4b c d +--R * +--R +---+ +--R \|- d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (16b c d e - 48b c d e + 48b c d e - 16b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (8b d e - 24b c d e + 24b c d e - 8b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 +--R - 15b c e + 9b c d e + 15b c d e + 51b c d e - 108b c d e +--R + +--R 7 5 +--R 48c d +--R * +--R 4 +--R x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R - 30b c e + 18b c d e + 30b c d e + 102b c d e - 216b c d e +--R + +--R 6 5 +--R 96b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 15b e + 9b c d e + 15b c d e + 51b c d e - 108b c d e +--R + +--R 2 5 5 +--R 48b c d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 2 5 3 2 6 4 7 5 4 +--R (99b c d e - 132b c d e + 48c d )x +--R + +--R 3 4 3 2 2 5 4 6 5 3 +--R (198b c d e - 264b c d e + 96b c d )x +--R + +--R 4 3 3 2 3 4 4 2 5 5 2 +--R (99b c d e - 132b c d e + 48b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2 6 4 4 +--R (15b c e - 9b c d e - 15b c d e + 48b c d e - 24b c d e)x +--R + +--R 6 5 5 2 4 4 3 2 3 3 4 3 2 2 5 4 +--R 30b c e - 13b c d e - 33b c d e + 58b c d e + 12b c d e +--R + +--R 6 5 +--R - 24b c d +--R * +--R 3 +--R x +--R + +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R 15b e + b c d e - 23b c d e - 7b c d e + 65b c d e +--R + +--R 2 5 5 +--R - 36b c d +--R * +--R 2 +--R x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (5b d e - 7b c d e - 9b c d e + 19b c d e - 8b c d )x - 2b d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R 6b c d e - 6b c d e + 2b c d +--R * +--R +---+ +--R \|- d +--R / +--R 8 2 3 3 7 3 4 2 6 4 5 5 5 6 4 +--R (4b c d e - 12b c d e + 12b c d e - 4b c d )x +--R + +--R 9 3 3 8 2 4 2 7 3 5 6 4 6 3 +--R (8b c d e - 24b c d e + 24b c d e - 8b c d )x +--R + +--R 10 3 3 9 4 2 8 2 5 7 3 6 2 +--R (4b d e - 12b c d e + 12b c d e - 4b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 891 + +--S 892 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 3 3 2 4 4 5 5 +-----------+ | c +-+ +--R (99b c d e - 132b c d e + 48c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (2b e - 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(----------------------------------------------------------) +--R c x + b +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (15b e - 9b c d e - 15b c d e - 51b c d e + 108b c d e - 48c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 3 3 2 4 4 5 5 +-+ +-+ \|c \|e x + d +--R (198b c d e - 264b c d e + 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (30b e - 18b c d e - 30b c d e - 102b c d e + 216b c d e - 96c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 8 3 3 7 4 2 6 2 5 5 3 6 +-----------+ +-+ +--R (8b d e - 24b c d e + 24b c d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (15b e - 9b c d e - 15b c d e - 51b c d e + 108b c d e - 48c d ) +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 3 3 2 4 4 5 5 +-+ +-+ \|c \|e x + d +--R (198b c d e - 264b c d e + 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (30b e - 18b c d e - 30b c d e - 102b c d e + 216b c d e - 96c d ) +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 3 3 2 4 4 5 5 +-----------+ | c +-+ +--R (198b c d e - 264b c d e + 96c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 8 3 3 7 4 2 6 2 5 5 3 6 +-----------+ +-+ +--R (8b d e - 24b c d e + 24b c d e - 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1726 +t0:=1/((d+e*x)^(5/2)*(b*x+c*x^2)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 2 8 2 2 3 7 2 2 2 3 2 6 +--R c e x + (3b c e + 2c d e)x + (3b c e + 6b c d e + c d )x +--R + +--R 3 2 2 2 2 5 3 2 2 4 3 2 3 +--R (b e + 6b c d e + 3b c d )x + (2b d e + 3b c d )x + b d x +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1726 +r0:=1/12*e*(72*c^4*d^4-144*b*c^3*d^3*e+27*b^2*c^2*d^2*e^2+45*b^3*c*d*e^3-_ + 35*b^4*e^4)/(b^4*d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/4*c*(12*c^2*d^2-_ + 3*b*c*d*e-7*b^2*e^2)/(b^3*d^2*(c*d-b*e)*(b+c*x)^2*(d+e*x)^(3/2))+_ + (-1/2)/(b*d*x^2*(b+c*x)^2*(d+e*x)^(3/2))+1/4*(8*c*d+7*b*e)/_ + (b^2*d^2*x*(b+c*x)^2*(d+e*x)^(3/2))+1/4*c*(2*c*d-b*e)*(12*c^2*d^2-_ + 12*b*c*d*e-7*b^2*e^2)/(b^4*d^2*(c*d-b*e)^2*(b+c*x)*(d+e*x)^(3/2))-_ + 1/4*(48*c^2*d^2+60*b*c*d*e+35*b^2*e^2)*atanh(sqrt(d+e*x)/sqrt(d))/_ + (b^5*d^(9/2))+1/4*c^(9/2)*(48*c^2*d^2-156*b*c*d*e+143*b^2*e^2)*_ + atanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+_ + 1/4*e*(2*c*d-b*e)*(12*c^4*d^4-24*b*c^3*d^3*e+2*b^2*c^2*d^2*e^2+_ + 10*b^3*c*d*e^3-35*b^4*e^4)/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 6 4 3 7 5 2 8 6 5 +--R (429b c d e - 468b c d e + 144c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (858b c d e - 507b c d e - 180b c d e + 144c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (429b c d e + 390b c d e - 792b c d e + 288b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (429b c d e - 468b c d e + 144b c d )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|c \|e x + d +--R \|c \|d \|e x + d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R - 105b c e + 240b c d e - 54b c d e - 84b c d e - 249b c d e +--R + +--R 7 5 2 8 6 +--R 396b c d e - 144c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R - 210b c e + 375b c d e + 132b c d e - 222b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 +--R - 582b c d e + 543b c d e + 108b c d e - 144c d +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R - 105b e + 30b c d e + 426b c d e - 192b c d e - 417b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 102b c d e + 648b c d e - 288b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R - 105b d e + 240b c d e - 54b c d e - 84b c d e - 249b c d e +--R + +--R 3 5 6 2 6 7 +--R 396b c d e - 144b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +--R +-----------+ +-------+ \|e x + d +--R \|- b e + c d \|e x + d atanh(----------) +--R +-+ +--R \|d +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R 105b c e - 240b c d e + 54b c d e + 84b c d e - 180b c d e +--R + +--R 7 5 2 +--R 72b c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 3 5 4 3 +--R 210b c e - 340b c d e - 212b c d e + 240b c d e - 105b c d e +--R + +--R 2 6 5 2 7 6 +--R - 252b c d e + 144b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 105b e + 40b c d e - 565b c d e + 180b c d e + 255b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 438b c d e + 36b c d e + 72b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 3 5 6 +--R 140b d e - 278b c d e - 30b c d e + 180b c d e - 225b c d e +--R + +--R 2 6 7 +--R 108b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 21b d e - 60b c d e + 30b c d e + 60b c d e - 75b c d e +--R + +--R 3 5 7 +--R 24b c d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6b d e + 24b c d e - 36b c d e + 24b c d e - 6b c d +--R * +--R +-----------+ +-+ +--R \|- b e + c d \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- b e + c d \|d \|e x + d +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R 105b c e - 240b c d e + 54b c d e + 84b c d e + 249b c d e +--R + +--R 7 5 2 8 6 +--R - 396b c d e + 144c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 210b c e - 375b c d e - 132b c d e + 222b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 +--R 582b c d e - 543b c d e - 108b c d e + 144c d +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 105b e - 30b c d e - 426b c d e + 192b c d e + 417b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R 102b c d e - 648b c d e + 288b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R 105b d e - 240b c d e + 54b c d e + 84b c d e + 249b c d e +--R + +--R 3 5 6 2 6 7 +--R - 396b c d e + 144b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 2 6 4 3 7 5 2 8 6 5 +--R (429b c d e - 468b c d e + 144c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (858b c d e - 507b c d e - 180b c d e + 144c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (429b c d e + 390b c d e - 792b c d e + 288b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (429b c d e - 468b c d e + 144b c d )x +--R * +--R +-----------+ +--R | c +-+ +-------+ +--R |- --------- \|d \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 +--R 210b c e - 480b c d e + 108b c d e + 168b c d e +--R + +--R 2 6 4 3 7 5 2 +--R - 360b c d e + 144b c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 420b c e - 680b c d e - 424b c d e + 480b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 +--R - 210b c d e - 504b c d e + 288b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 210b e + 80b c d e - 1130b c d e + 360b c d e + 510b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 876b c d e + 72b c d e + 144b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 3 5 6 +--R 280b d e - 556b c d e - 60b c d e + 360b c d e - 450b c d e +--R + +--R 2 6 7 +--R 216b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 42b d e - 120b c d e + 60b c d e + 120b c d e - 150b c d e +--R + +--R 3 5 7 +--R 48b c d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 12b d e + 48b c d e - 72b c d e + 48b c d e - 12b c d +--R * +--R +-+ +--R \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (24b c d e - 96b c d e + 144b c d e - 96b c d e + 24b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 48b c d e - 168b c d e + 192b c d e - 48b c d e - 48b c d e +--R + +--R 5 6 9 +--R 24b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 24b d e - 48b c d e - 48b c d e + 192b c d e - 168b c d e +--R + +--R 6 5 9 +--R 48b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (24b d e - 96b c d e + 144b c d e - 96b c d e + 24b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R 105b c e - 240b c d e + 54b c d e + 84b c d e + 249b c d e +--R + +--R 7 5 2 8 6 +--R - 396b c d e + 144c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 210b c e - 375b c d e - 132b c d e + 222b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 +--R 582b c d e - 543b c d e - 108b c d e + 144c d +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 105b e - 30b c d e - 426b c d e + 192b c d e + 417b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R 102b c d e - 648b c d e + 288b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 4 4 5 2 +--R 105b d e - 240b c d e + 54b c d e + 84b c d e + 249b c d e +--R + +--R 3 5 6 2 6 7 +--R - 396b c d e + 144b c d +--R * +--R 2 +--R x +--R * +--R +-------+ +-+ +--R +-------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|e x + d log(-------------------------------) +--R x +--R + +--R 2 6 4 3 7 5 2 8 6 5 +--R (- 858b c d e + 936b c d e - 288c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (- 1716b c d e + 1014b c d e + 360b c d e - 288c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (- 858b c d e - 780b c d e + 1584b c d e - 576b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (- 858b c d e + 936b c d e - 288b c d )x +--R * +--R +---------+ +-------+ +--R | c +-+ +-------+ c\|e x + d +--R |--------- \|d \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 +--R 210b c e - 480b c d e + 108b c d e + 168b c d e +--R + +--R 2 6 4 3 7 5 2 +--R - 360b c d e + 144b c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 420b c e - 680b c d e - 424b c d e + 480b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 +--R - 210b c d e - 504b c d e + 288b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 210b e + 80b c d e - 1130b c d e + 360b c d e + 510b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 876b c d e + 72b c d e + 144b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 3 5 6 +--R 280b d e - 556b c d e - 60b c d e + 360b c d e - 450b c d e +--R + +--R 2 6 7 +--R 216b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 42b d e - 120b c d e + 60b c d e + 120b c d e - 150b c d e +--R + +--R 3 5 7 +--R 48b c d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 12b d e + 48b c d e - 72b c d e + 48b c d e - 12b c d +--R * +--R +-+ +--R \|d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (24b c d e - 96b c d e + 144b c d e - 96b c d e + 24b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 48b c d e - 168b c d e + 192b c d e - 48b c d e - 48b c d e +--R + +--R 5 6 9 +--R 24b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 24b d e - 48b c d e - 48b c d e + 192b c d e - 168b c d e +--R + +--R 6 5 9 +--R 48b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (24b d e - 96b c d e + 144b c d e - 96b c d e + 24b c d )x +--R * +--R +-+ +-------+ +--R \|d \|e x + d +--R , +--R +--R 2 6 4 3 7 5 2 8 6 5 +--R (429b c d e - 468b c d e + 144c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (858b c d e - 507b c d e - 180b c d e + 144c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (429b c d e + 390b c d e - 792b c d e + 288b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (429b c d e - 468b c d e + 144b c d )x +--R * +--R +-----------+ +--R +---+ | c +-------+ +--R \|- d |- --------- \|e x + d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 +--R - 210b c e + 480b c d e - 108b c d e - 168b c d e +--R + +--R 2 6 4 3 7 5 2 8 6 +--R - 498b c d e + 792b c d e - 288c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R - 420b c e + 750b c d e + 264b c d e - 444b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 +--R - 1164b c d e + 1086b c d e + 216b c d e - 288c d +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 +--R - 210b e + 60b c d e + 852b c d e - 384b c d e +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 +--R - 834b c d e - 204b c d e + 1296b c d e - 576b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 +--R - 210b d e + 480b c d e - 108b c d e - 168b c d e +--R + +--R 4 4 5 2 3 5 6 2 6 7 +--R - 498b c d e + 792b c d e - 288b c d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 +--R 210b c e - 480b c d e + 108b c d e + 168b c d e +--R + +--R 2 6 4 3 7 5 2 +--R - 360b c d e + 144b c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 420b c e - 680b c d e - 424b c d e + 480b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 +--R - 210b c d e - 504b c d e + 288b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 210b e + 80b c d e - 1130b c d e + 360b c d e + 510b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 876b c d e + 72b c d e + 144b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 3 5 6 +--R 280b d e - 556b c d e - 60b c d e + 360b c d e - 450b c d e +--R + +--R 2 6 7 +--R 216b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 42b d e - 120b c d e + 60b c d e + 120b c d e - 150b c d e +--R + +--R 3 5 7 +--R 48b c d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 12b d e + 48b c d e - 72b c d e + 48b c d e - 12b c d +--R * +--R +---+ +--R \|- d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (24b c d e - 96b c d e + 144b c d e - 96b c d e + 24b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 48b c d e - 168b c d e + 192b c d e - 48b c d e - 48b c d e +--R + +--R 5 6 9 +--R 24b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 24b d e - 48b c d e - 48b c d e + 192b c d e - 168b c d e +--R + +--R 6 5 9 +--R 48b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (24b d e - 96b c d e + 144b c d e - 96b c d e + 24b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R , +--R +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 +--R - 105b c e + 240b c d e - 54b c d e - 84b c d e +--R + +--R 2 6 4 3 7 5 2 8 6 +--R - 249b c d e + 396b c d e - 144c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R - 210b c e + 375b c d e + 132b c d e - 222b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 +--R - 582b c d e + 543b c d e + 108b c d e - 144c d +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 +--R - 105b e + 30b c d e + 426b c d e - 192b c d e +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 +--R - 417b c d e - 102b c d e + 648b c d e - 288b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 +--R - 105b d e + 240b c d e - 54b c d e - 84b c d e +--R + +--R 4 4 5 2 3 5 6 2 6 7 +--R - 249b c d e + 396b c d e - 144b c d +--R * +--R 2 +--R x +--R * +--R +---+ +-------+ +--R +-------+ \|- d \|e x + d +--R \|e x + d atan(----------------) +--R d +--R + +--R 2 6 4 3 7 5 2 8 6 5 +--R (- 429b c d e + 468b c d e - 144c d e)x +--R + +--R 3 5 4 3 2 6 5 2 7 6 8 7 4 +--R (- 858b c d e + 507b c d e + 180b c d e - 144c d )x +--R + +--R 4 4 4 3 3 5 5 2 2 6 6 7 7 3 +--R (- 429b c d e - 390b c d e + 792b c d e - 288b c d )x +--R + +--R 4 4 5 2 3 5 6 2 6 7 2 +--R (- 429b c d e + 468b c d e - 144b c d )x +--R * +--R +---------+ +-------+ +--R +---+ | c +-------+ c\|e x + d +--R \|- d |--------- \|e x + d atan(-----------------------) +--R \|b e - c d +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R + +--R 6 2 7 5 3 6 4 4 2 5 3 5 3 4 2 6 4 3 +--R 105b c e - 240b c d e + 54b c d e + 84b c d e - 180b c d e +--R + +--R 7 5 2 +--R 72b c d e +--R * +--R 5 +--R x +--R + +--R 7 7 6 2 6 5 3 2 5 4 4 3 4 +--R 210b c e - 340b c d e - 212b c d e + 240b c d e +--R + +--R 3 5 4 3 2 6 5 2 7 6 +--R - 105b c d e - 252b c d e + 144b c d e +--R * +--R 4 +--R x +--R + +--R 8 7 7 6 6 2 2 5 5 3 3 4 4 4 4 3 +--R 105b e + 40b c d e - 565b c d e + 180b c d e + 255b c d e +--R + +--R 3 5 5 2 2 6 6 7 7 +--R - 438b c d e + 36b c d e + 72b c d +--R * +--R 3 +--R x +--R + +--R 8 6 7 2 5 6 2 3 4 5 3 4 3 3 5 6 +--R 140b d e - 278b c d e - 30b c d e + 180b c d e - 225b c d e +--R + +--R 2 6 7 +--R 108b c d +--R * +--R 2 +--R x +--R + +--R 8 2 5 7 3 4 6 2 4 3 5 3 5 2 4 4 6 +--R 21b d e - 60b c d e + 30b c d e + 60b c d e - 75b c d e +--R + +--R 3 5 7 +--R 24b c d +--R * +--R x +--R + +--R 8 3 4 7 4 3 6 2 5 2 5 3 6 4 4 7 +--R - 6b d e + 24b c d e - 36b c d e + 24b c d e - 6b c d +--R * +--R +---+ +--R \|- d +--R / +--R 9 2 4 5 8 3 5 4 7 4 6 3 6 5 7 2 5 6 8 5 +--R (12b c d e - 48b c d e + 72b c d e - 48b c d e + 12b c d e)x +--R + +--R 10 4 5 9 2 5 4 8 3 6 3 7 4 7 2 6 5 8 +--R 24b c d e - 84b c d e + 96b c d e - 24b c d e - 24b c d e +--R + +--R 5 6 9 +--R 12b c d +--R * +--R 4 +--R x +--R + +--R 11 4 5 10 5 4 9 2 6 3 8 3 7 2 7 4 8 +--R 12b d e - 24b c d e - 24b c d e + 96b c d e - 84b c d e +--R + +--R 6 5 9 +--R 24b c d +--R * +--R 3 +--R x +--R + +--R 11 5 4 10 6 3 9 2 7 2 8 3 8 7 4 9 2 +--R (12b d e - 48b c d e + 72b c d e - 48b c d e + 12b c d )x +--R * +--R +---+ +-------+ +--R \|- d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 898 + +--S 899 of 1726 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 35b e - 80b c d e + 18b c d e + 28b c d e + 83b c d e +--R + +--R 5 5 6 6 +--R - 132b c d e + 48c d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 4 4 2 5 5 6 6 +-----------+ | c +-+ +--R (143b c d e - 156b c d e + 48c d )\|- b e + c d |- --------- \|d +--R \| b e - c d +--R * +--R +-----------+ +--R | c +-------+ +--R (- 2b e + 2c d) |- --------- \|e x + d + c e x - b e + 2c d +--R \| b e - c d +--R log(------------------------------------------------------------) +--R c x + b +--R + +--R +-+ +-------+ +--R 2 4 4 2 5 5 6 6 +-+ +-+ \|c \|e x + d +--R (- 286b c d e + 312b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 70b e - 160b c d e + 36b c d e + 56b c d e + 166b c d e +--R + +--R 5 5 6 6 +--R - 264b c d e + 96c d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R / +--R 9 4 4 8 5 3 7 2 6 2 6 3 7 5 4 8 +-----------+ +-+ +--R (8b d e - 32b c d e + 48b c d e - 32b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1726 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1726 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 35b e - 80b c d e + 18b c d e + 28b c d e + 83b c d e +--R + +--R 5 5 6 6 +--R - 132b c d e + 48c d +--R * +--R +-------+ +-+ +--R +-----------+ - 2d\|e x + d + (e x + 2d)\|d +--R \|- b e + c d log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 4 4 2 5 5 6 6 +-+ +-+ \|c \|e x + d +--R (- 286b c d e + 312b c d e - 96c d )\|c \|d atanh(--------------) +--R +-----------+ +--R \|- b e + c d +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 70b e - 160b c d e + 36b c d e + 56b c d e + 166b c d e +--R + +--R 5 5 6 6 +--R - 264b c d e + 96c d +--R * +--R +-------+ +--R +-----------+ \|e x + d +--R \|- b e + c d atanh(----------) +--R +-+ +--R \|d +--R + +--R +---------+ +--R 2 4 4 2 5 5 6 6 +-----------+ | c +-+ +--R (- 286b c d e + 312b c d e - 96c d )\|- b e + c d |--------- \|d +--R \|b e - c d +--R * +--R +-------+ +--R c\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | c +--R (b e - c d) |--------- +--R \|b e - c d +--R / +--R 9 4 4 8 5 3 7 2 6 2 6 3 7 5 4 8 +-----------+ +-+ +--R (8b d e - 32b c d e + 48b c d e - 32b c d e + 8b c d )\|- b e + c d \|d +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1726 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1726 +t0:=(d+e*x)^(3/2)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1726 +--r0:=2/7*e*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(2*c*d-b*e)*_ +-- (3*c^2*d^2-3*b*c*d*e+8*b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^3*e^(3/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/105*(-b)^(3/2)*(c*d-b*e)*(3*c^2*d^2-15*b*c*d*e+8*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(3*c^2*d^2+9*b*c*d*e-4*b^2*e^2+_ +-- 12*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e) +--E 904 + +--S 905 of 1726 +--a0:=integrate(t0,x) +--E 905 + +--S 906 of 1726 +--m0:=a0-r0 +--E 906 + +--S 907 of 1726 +--d0:=D(m0,x) +--E 907 + +)clear all + +--S 908 of 1726 +t0:=sqrt(d+e*x)*sqrt(b*x+c*x^2) +--R +--R +--R +----------+ +--R +-------+ | 2 +--R (1) \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1726 +--r0:=-4/15*(c^2*d^2-b*c*d*e+b^2*e^2)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(3/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/15*(-b)^(3/2)*(c*d-2*b*e)*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/e-_ +-- 2/15*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e) +--E 909 + +--S 910 of 1726 +--a0:=integrate(t0,x) +--E 910 + +--S 911 of 1726 +--m0:=a0-r0 +--E 911 + +--S 912 of 1726 +--d0:=D(m0,x) +--E 912 + +)clear all + +--S 913 of 1726 +t0:=sqrt(b*x+c*x^2)/sqrt(d+e*x) +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1726 +--r0:=-2/3*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(3/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(-b)^(3/2)*_ +-- (c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*e*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*sqrt(d+e*x)*sqrt(b*x+c*x^2)/e +--E 914 + +--S 915 of 1726 +--a0:=integrate(t0,x) +--E 915 + +--S 916 of 1726 +--m0:=a0-r0 +--E 916 + +--S 917 of 1726 +--d0:=D(m0,x) +--E 917 + +)clear all + +--S 918 of 1726 +t0:=sqrt(b*x+c*x^2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1726 +--r0:=4*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(e^(3/2)*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(-b)^(3/2)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(e*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2*sqrt(b*x+c*x^2)/(e*sqrt(d+e*x)) +--E 919 + +--S 920 of 1726 +--a0:=integrate(t0,x) +--E 920 + +--S 921 of 1726 +--m0:=a0-r0 +--E 921 + +--S 922 of 1726 +--d0:=D(m0,x) +--E 922 + +)clear all + +--S 923 of 1726 +t0:=sqrt(b*x+c*x^2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1726 +--r0:=2/3*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(3/2)*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(-b)^(3/2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*sqrt(b*x+c*x^2)/(e*(d+e*x)^(3/2))+_ +-- 2/3*(2*c*d-b*e)*sqrt(b*x+c*x^2)/(d*e*(c*d-b*e)*sqrt(d+e*x)) +--E 924 + +--S 925 of 1726 +--a0:=integrate(t0,x) +--E 925 + +--S 926 of 1726 +--m0:=a0-r0 +--E 926 + +--S 927 of 1726 +--d0:=D(m0,x) +--E 927 + +)clear all + +--S 928 of 1726 +t0:=sqrt(b*x+c*x^2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R | 2 +--R \|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1726 +--r0:=-4/15*(c^2*d^2-b*c*d*e+b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*_ +-- e^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/15*(-b)^(3/2)*(c*d-2*b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*e*(c*d-b*e)*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/5*sqrt(b*x+c*x^2)/_ +-- (e*(d+e*x)^(5/2))+2/15*(2*c*d-b*e)*sqrt(b*x+c*x^2)/(d*e*(c*d-b*e)*_ +-- (d+e*x)^(3/2))+4/15*(c^2*d^2-b*c*d*e+b^2*e^2)*sqrt(b*x+c*x^2)/_ +-- (d^2*e*(c*d-b*e)^2*sqrt(d+e*x)) +--E 929 + +--S 930 of 1726 +--a0:=integrate(t0,x) +--E 930 + +--S 931 of 1726 +--m0:=a0-r0 +--E 931 + +--S 932 of 1726 +--d0:=D(m0,x) +--E 932 + +)clear all + +--S 933 of 1726 +t0:=(d+e*x)^(3/2)*(b*x+c*x^2)^(3/2) +--R +--R +--R +----------+ +--R 3 2 +-------+ | 2 +--R (1) (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1726 +--r0:=2/231*(c^2*d^2+13*b*c*d*e-6*b^2*e^2+14*c*e*(2*c*d-b*e)*x)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x)/(c^2*e)+2/11*e*(b*x+c*x^2)^(5/2)*_ +-- sqrt(d+e*x)/c-16/1155*(2*c*d-b*e)*(c^4*d^4-2*b*c^3*d^3*e+b^3*c*d*_ +-- e^3-2*b^4*e^4)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c^4*e^(7/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/1155*(-b)^(3/2)*_ +-- (c*d-b*e)*(8*c^4*d^4-13*b*c^3*d^3*e-3*b^2*c^2*d^2*e^2+32*b^3*c*_ +-- d*e^3-16*b^4*e^4)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*e^3*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/1155*(8*c^4*d^4-19*b*c^3*d^3*e+_ +-- 6*b^2*c^2*d^2*e^2-19*b^3*c*d*e^3+8*b^4*e^4-3*c*e*(2*c*d-b*e)*_ +-- (c^2*d^2-b*c*d*e+8*b^2*e^2)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^3*e^3) +--E 934 + +--S 935 of 1726 +--a0:=integrate(t0,x) +--E 935 + +--S 936 of 1726 +--m0:=a0-r0 +--E 936 + +--S 937 of 1726 +--d0:=D(m0,x) +--E 937 + +)clear all + +--S 938 of 1726 +t0:=(b*x+c*x^2)^(3/2)*sqrt(d+e*x) +--R +--R +--R +----------+ +--R 2 +-------+ | 2 +--R (1) (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1726 +--r0:=2/9*(d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)/e-2/21*(2*c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x)/(c*e)-2/315*(16*c^4*d^4-32*b*c^3*_ +-- d^3*e+9*b^2*c^2*d^2*e^2+7*b^3*c*d*e^3-8*b^4*e^4)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*e^(7/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/315*(-b)^(3/2)*(c*d-b*e)*(8*c^3*d^3-9*b*c^2*_ +-- d^2*e-3*b^2*c*d*e^2+8*b^3*e^3)*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(7/2)*e^3*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/315*(8*c^3*d^3-_ +-- 15*b*c^2*d^2*e+3*b^2*c*d*e^2-4*b^3*e^3-6*c*e*(c^2*d^2-b*c*d*e+_ +-- 2*b^2*e^2)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^3) +--E 939 + +--S 940 of 1726 +--a0:=integrate(t0,x) +--E 940 + +--S 941 of 1726 +--m0:=a0-r0 +--E 941 + +--S 942 of 1726 +--d0:=D(m0,x) +--E 942 + +)clear all + +--S 943 of 1726 +t0:=(b*x+c*x^2)^(3/2)/sqrt(d+e*x) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1726 +--r0:=2/7*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e-4/35*(2*c*d-b*e)*_ +-- (4*c^2*d^2-4*b*c*d*e-b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (c^2*e^(7/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/35*(-b)^(3/2)*(c*d-b*e)*(8*c^2*d^2-5*b*c*d*e-2*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*e^3*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/35*(8*c^2*d^2-11*b*c*d*e+b^2*e^2-_ +-- 3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^3) +--E 944 + +--S 945 of 1726 +--a0:=integrate(t0,x) +--E 945 + +--S 946 of 1726 +--m0:=a0-r0 +--E 946 + +--S 947 of 1726 +--d0:=D(m0,x) +--E 947 + +)clear all + +--S 948 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1726 +--r0:=-2*(b*x+c*x^2)^(3/2)/(e*sqrt(d+e*x))+2/5*(16*c^2*d^2-_ +-- 16*b*c*d*e+b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(c*e^(7/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(-b)^(3/2)*_ +-- (c*d-b*e)*(8*c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*_ +-- e^3*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/5*(8*c*d-7*b*e-6*c*e*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/e^3 +--E 949 + +--S 950 of 1726 +--a0:=integrate(t0,x) +--E 950 + +--S 951 of 1726 +--m0:=a0-r0 +--E 951 + +--S 952 of 1726 +--d0:=D(m0,x) +--E 952 + +)clear all + +--S 953 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1726 +--r0:=-2/3*(b*x+c*x^2)^(3/2)/(e*(d+e*x)^(3/2))-16/3*(2*c*d-b*e)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(e^(7/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*(-b)^(3/2)*(8*c*d-5*b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(e^3*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(b*x+c*x^2)/_ +-- (e^3*sqrt(d+e*x)) +--E 954 + +--S 955 of 1726 +--a0:=integrate(t0,x) +--E 955 + +--S 956 of 1726 +--m0:=a0-r0 +--E 956 + +--S 957 of 1726 +--d0:=D(m0,x) +--E 957 + +)clear all + +--S 958 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1726 +--r0:=-2/5*(b*x+c*x^2)^(3/2)/(e*(d+e*x)^(5/2))-2/5*(16*c^2*d^2-_ +-- 16*b*c*d*e+b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(7/2)*(c*d-b*e)*sqrt(-d)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(-b)^(3/2)*_ +-- (8*c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*e^3*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*(8*c*d-b*e+6*c*e*x)*sqrt(b*x+c*x^2)/_ +-- (e^3*(d+e*x)^(3/2))-2/5*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)*_ +-- sqrt(b*x+c*x^2)/(d*e^3*(c*d-b*e)*sqrt(d+e*x)) +--E 959 + +--S 960 of 1726 +--a0:=integrate(t0,x) +--E 960 + +--S 961 of 1726 +--m0:=a0-r0 +--E 961 + +--S 962 of 1726 +--d0:=D(m0,x) +--E 962 + +)clear all + +--S 963 of 1726 +t0:=(b*x+c*x^2)^(3/2)/(d+e*x)^(9/2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1726 +--r0:=-2/7*(b*x+c*x^2)^(3/2)/(e*(d+e*x)^(7/2))-4/35*(2*c*d-b*e)*_ +-- (4*c^2*d^2-4*b*c*d*e-b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*_ +-- e^(7/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/35*(-b)^(3/2)*(8*c^2*d^2-5*b*c*d*e-2*b^2*e^2)*elliptic_f(asin(_ +-- sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d^2*e^3*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+_ +-- c*x^2))+2/35*(16*c^2*d^2-16*b*c*d*e-b^2*e^2)*sqrt(b*x+c*x^2)/_ +-- (d*e^3*(c*d-b*e)*(d+e*x)^(3/2))-6/35*(8*c*d+b*e+10*c*e*x)*_ +-- sqrt(b*x+c*x^2)/(e^3*(d+e*x)^(5/2))+4/35*(2*c*d-b*e)*(4*c^2*d^2-_ +-- 4*b*c*d*e-b^2*e^2)*sqrt(b*x+c*x^2)/(d^2*e^3*(c*d-b*e)^2*sqrt(d+e*x)) +--E 964 + +--S 965 of 1726 +--a0:=integrate(t0,x) +--E 965 + +--S 966 of 1726 +--m0:=a0-r0 +--E 966 + +--S 967 of 1726 +--d0:=D(m0,x) +--E 967 + +)clear all + +--S 968 of 1726 +t0:=(b*x+c*x^2)^(5/2)*sqrt(d+e*x) +--R +--R +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (1) (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1726 +--r0:=2/13*(d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)/e+10/9009*(16*c^3*d^3-_ +-- 31*b*c^2*d^2*e+9*b^2*c*d*e^2-18*b^3*e^3-14*c*e*(c^2*d^2-b*c*d*e+_ +-- 3*b^2*e^2)*x)*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/(c^2*e^3)-_ +-- 10/143*(2*c*d-b*e)*(b*x+c*x^2)^(5/2)*sqrt(d+e*x)/(c*e)-4/9009*_ +-- (128*c^6*d^6-384*b*c^5*d^5*e+343*b^2*c^4*d^4*e^2-46*b^3*c^3*d^3*_ +-- e^3-21*b^4*c^2*d^2*e^4-20*b^5*c*d*e^5+24*b^6*e^6)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^4*e^(11/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/9009*(-b)^(3/2)*(c*d-b*e)*(128*c^5*d^5-272*b*_ +-- c^4*d^4*e+111*b^2*c^3*d^3*e^2+41*b^3*c^2*d^2*e^3+16*b^4*c*d*e^4-_ +-- 48*b^5*e^5)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*e^5*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/9009*(128*c^5*d^5-368*b*c^4*d^4*e+303*b^2*c^3*_ +-- d^3*e^2-22*b^3*c^2*d^2*e^3-17*b^4*c*d*e^4+24*b^5*e^5-3*c*e*(32*c^4*d^4-_ +-- 64*b*c^3*d^3*e+21*b^2*c^2*d^2*e^2+11*b^3*c*d*e^3-24*b^4*e^4)*x)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^3*e^5) +--E 969 + +--S 970 of 1726 +--a0:=integrate(t0,x) +--E 970 + +--S 971 of 1726 +--m0:=a0-r0 +--E 971 + +--S 972 of 1726 +--d0:=D(m0,x) +--E 972 + +)clear all + +--S 973 of 1726 +t0:=(b*x+c*x^2)^(5/2)/sqrt(d+e*x) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1726 +--r0:=10/693*(16*c^2*d^2-23*b*c*d*e+3*b^2*e^2-7*c*e*(2*c*d-b*e)*x)*_ +-- (b*x+c*x^2)^(3/2)*sqrt(d+e*x)/(c*e^3)+2/11*(b*x+c*x^2)^(5/2)*_ +-- sqrt(d+e*x)/e-2/693*(2*c*d-b*e)*(128*c^4*d^4-256*b*c^3*d^3*e+99*_ +-- b^2*c^2*d^2*e^2+29*b^3*c*d*e^3+8*b^4*e^4)*(b+c*x)*elliptic_e(_ +-- asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(c^3*e^(11/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/693*(-b)^(3/2)*(c*d-b*e)*(128*c^4*d^4-_ +-- 208*b*c^3*d^3*e+51*b^2*c^2*d^2*e^2+17*b^3*c*d*e^3+8*b^4*e^4)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*e^5*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/693*(128*c^4*d^4-304*b*c^3*d^3*e+195*b^2*_ +-- c^2*d^2*e^2-7*b^3*c*d*e^3-4*b^4*e^4-12*c*e*(2*c*d-b*e)*(4*c^2*d^2-_ +-- 4*b*c*d*e-b^2*e^2)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^5) +--E 974 + +--S 975 of 1726 +--a0:=integrate(t0,x) +--E 975 + +--S 976 of 1726 +--m0:=a0-r0 +--E 976 + +--S 977 of 1726 +--d0:=D(m0,x) +--E 977 + +)clear all + +--S 978 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^(3/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1726 +--r0:=-2*(b*x+c*x^2)^(5/2)/(e*sqrt(d+e*x))-10/63*(16*c*d-15*b*e-_ +-- 14*c*e*x)*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^3+4/63*(128*c^4*d^4-_ +-- 256*b*c^3*d^3*e+135*b^2*c^2*d^2*e^2-7*b^3*c*d*e^3-b^4*e^4)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^2*e^(11/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/63*(-b)^(3/2)*(c*d-b*e)*(128*c^3*d^3-144*b*c^2*_ +-- d^2*e+15*b^2*c*d*e^2+2*b^3*e^3)*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- (c^(5/2)*e^5*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/63*(128*c^3*d^3-_ +-- 240*b*c^2*d^2*e+111*b^2*c*d*e^2-b^3*e^3-3*c*e*(32*c^2*d^2-32*b*_ +-- c*d*e+b^2*e^2)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^5) +--E 979 + +--S 980 of 1726 +--a0:=integrate(t0,x) +--E 980 + +--S 981 of 1726 +--m0:=a0-r0 +--E 981 + +--S 982 of 1726 +--d0:=D(m0,x) +--E 982 + +)clear all + +--S 983 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^(5/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ------------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1726 +--r0:=-2/3*(b*x+c*x^2)^(5/2)/(e*(d+e*x)^(3/2))+10/21*(16*c*d-7*b*e+_ +-- 2*c*e*x)*(b*x+c*x^2)^(3/2)/(e^3*sqrt(d+e*x))-2/21*(2*c*d-b*e)*_ +-- (128*c^2*d^2-128*b*c*d*e+3*b^2*e^2)*(b+c*x)*elliptic_e(asin(_ +-- sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(c*e^(11/2)*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/21*(-b)^(3/2)*(c*d-b*e)*(128*c^2*d^2-80*b*c*d*_ +-- e+3*b^2*e^2)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*e^5*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/21*(128*c^2*d^2-176*b*c*d*e+51*b^2*e^2-48*c*_ +-- e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/e^5 +--E 984 + +--S 985 of 1726 +--a0:=integrate(t0,x) +--E 985 + +--S 986 of 1726 +--m0:=a0-r0 +--E 986 + +--S 987 of 1726 +--d0:=D(m0,x) +--E 987 + +)clear all + +--S 988 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^(7/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1726 +--r0:=2/15*(16*c*d-5*b*e+6*c*e*x)*(b*x+c*x^2)^(3/2)/(e^3*(d+e*x)^(3/2))-_ +-- 2/5*(b*x+c*x^2)^(5/2)/(e*(d+e*x)^(5/2))+4/15*(128*c^2*d^2-_ +-- 128*b*c*d*e+23*b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(x)*sqrt((d+e*x)/d)/(e^(11/2)*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/15*(-b)^(3/2)*_ +-- (128*c^2*d^2-144*b*c*d*e+31*b^2*e^2)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(e^5*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(128*c^2*d^2-_ +-- 112*b*c*d*e+15*b^2*e^2+16*c*e*(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/_ +-- (e^5*sqrt(d+e*x)) +--E 989 + +--S 990 of 1726 +--a0:=integrate(t0,x) +--E 990 + +--S 991 of 1726 +--m0:=a0-r0 +--E 991 + +--S 992 of 1726 +--d0:=D(m0,x) +--E 992 + +)clear all + +--S 993 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^(9/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1726 +--r0:=2/21*(16*c*d-3*b*e+10*c*e*x)*(b*x+c*x^2)^(3/2)/(e^3*(d+e*x)^(5/2))-_ +-- 2/7*(b*x+c*x^2)^(5/2)/(e*(d+e*x)^(7/2))+2/21*(2*c*d-b*e)*(128*c^2*d^2-_ +-- 128*b*c*d*e+3*b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(x)*sqrt((d+e*x)/d)/(e^(11/2)*(c*d-b*e)*_ +-- sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/21*(-b)^(3/2)*(128*c^2*d^2-80*b*c*d*e+3*b^2*e^2)*elliptic_f(_ +-- asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(d*e^5*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/21*(128*c^2*d^2-80*b*c*d*e+3*b^2*e^2+48*c*e*(2*c*d-b*e)*x)*_ +-- sqrt(b*x+c*x^2)/(e^5*(d+e*x)^(3/2))+2/21*(2*c*d-b*e)*(128*c^2*d^2-_ +-- 128*b*c*d*e+3*b^2*e^2)*sqrt(b*x+c*x^2)/(d*e^5*(c*d-b*e)*sqrt(d+e*x)) +--E 994 + +--S 995 of 1726 +--a0:=integrate(t0,x) +--E 995 + +--S 996 of 1726 +--m0:=a0-r0 +--E 996 + +--S 997 of 1726 +--d0:=D(m0,x) +--E 997 + +)clear all + +--S 998 of 1726 +t0:=(b*x+c*x^2)^(5/2)/(d+e*x)^(11/2) +--R +--R +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1726 +--r0:=10/63*(16*c*d-b*e+14*c*e*x)*(b*x+c*x^2)^(3/2)/(e^3*(d+e*x)^(7/2))-_ +-- 2/9*(b*x+c*x^2)^(5/2)/(e*(d+e*x)^(9/2))+4/63*(128*c^4*d^4-_ +-- 256*b*c^3*d^3*e+135*b^2*c^2*d^2*e^2-7*b^3*c*d*e^3-b^4*e^4)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(x)*_ +-- sqrt((d+e*x)/d)/((-d)^(3/2)*e^(11/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/63*(-b)^(3/2)*(128*c^3*d^3-_ +-- 144*b*c^2*d^2*e+15*b^2*c*d*e^2+2*b^3*e^3)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+_ +-- e*x)/d)/(d^2*e^5*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-_ +-- 2/63*(2*c*d-b*e)*(128*c^2*d^2-128*b*c*d*e-b^2*e^2)*sqrt(b*x+_ +-- c*x^2)/(d*e^5*(c*d-b*e)*(d+e*x)^(3/2))+2/21*(128*c^2*d^2-48*b*c*_ +-- d*e-b^2*e^2+80*c*e*(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(e^5*(d+_ +-- e*x)^(5/2))-4/63*(128*c^4*d^4-256*b*c^3*d^3*e+135*b^2*c^2*d^2*e^2-_ +-- 7*b^3*c*d*e^3-b^4*e^4)*sqrt(b*x+c*x^2)/(d^2*e^5*(c*d-b*e)^2*sqrt(d+e*x)) +--E 999 + +--S 1000 of 1726 +--a0:=integrate(t0,x) +--E 1000 + +--S 1001 of 1726 +--m0:=a0-r0 +--E 1001 + +--S 1002 of 1726 +--d0:=D(m0,x) +--E 1002 + +)clear all + +--S 1003 of 1726 +t0:=(d+e*x)^(7/2)/sqrt(b*x+c*x^2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1726 +--r0:=16/105*(2*c*d-b*e)*(11*c^2*d^2-11*b*c*d*e+6*b^2*e^2)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(c^4*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/105*(7*c*d-4*b*e)*(c*d-b*e)*(15*c^2*d^2-19*b*_ +-- c*d*e+12*b^2*e^2)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/_ +-- (c*d))*sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(9/2)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+12/35*e*(2*c*d-b*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2)/c^2+2/7*e*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+_ +-- 2/105*e*(71*c^2*d^2-71*b*c*d*e+24*b^2*e^2)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3 +--E 1004 + +--S 1005 of 1726 +--a0:=integrate(t0,x) +--E 1005 + +--S 1006 of 1726 +--m0:=a0-r0 +--E 1006 + +--S 1007 of 1726 +--d0:=D(m0,x) +--E 1007 + +)clear all + +--S 1008 of 1726 +t0:=(d+e*x)^(5/2)/sqrt(b*x+c*x^2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1726 +--r0:=2/15*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)*(b+c*x)*elliptic_e(_ +-- asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/15*(c*d-b*e)*(15*c^2*d^2-19*b*c*d*e+8*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/5*e*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/c+8/15*e*_ +-- (2*c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^2 +--E 1009 + +--S 1010 of 1726 +--a0:=integrate(t0,x) +--E 1010 + +--S 1011 of 1726 +--m0:=a0-r0 +--E 1011 + +--S 1012 of 1726 +--d0:=D(m0,x) +--E 1012 + +)clear all + +--S 1013 of 1726 +t0:=(d+e*x)^(3/2)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1726 +--r0:=4/3*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(c^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(3*c*d-2*b*e)*_ +-- (c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(-b)*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(5/2)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c +--E 1014 + +--S 1015 of 1726 +--a0:=integrate(t0,x) +--E 1015 + +--S 1016 of 1726 +--m0:=a0-r0 +--E 1016 + +--S 1017 of 1726 +--d0:=D(m0,x) +--E 1017 + +)clear all + +--S 1018 of 1726 +t0:=sqrt(d+e*x)/sqrt(b*x+c*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1726 +--r0:=2*elliptic_e(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt(d+e*x)/(sqrt(c)*sqrt((d+e*x)/d)*_ +-- sqrt(b*x+c*x^2)) +--E 1019 + +--S 1020 of 1726 +--a0:=integrate(t0,x) +--E 1020 + +--S 1021 of 1726 +--m0:=a0-r0 +--E 1021 + +--S 1022 of 1726 +--d0:=D(m0,x) +--E 1022 + +)clear all + +--S 1023 of 1726 +t0:=1/(sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +----------+ +--R +-------+ | 2 +--R \|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1726 +--r0:=2*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 1024 + +--S 1025 of 1726 +--a0:=integrate(t0,x) +--E 1025 + +--S 1026 of 1726 +--m0:=a0-r0 +--E 1026 + +--S 1027 of 1726 +--d0:=D(m0,x) +--E 1027 + +)clear all + +--S 1028 of 1726 +t0:=1/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +----------+ +--R +-------+ | 2 +--R (e x + d)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1726 +--r0:=2*elliptic_e(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(c)*sqrt(x)*sqrt((b+c*x)/b)*sqrt(d+e*x)/(d*(c*d-b*e)*_ +-- sqrt((d+e*x)/d)*sqrt(b*x+c*x^2))-2*e*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- sqrt(d+e*x)) +--E 1029 + +--S 1030 of 1726 +--a0:=integrate(t0,x) +--E 1030 + +--S 1031 of 1726 +--m0:=a0-r0 +--E 1031 + +--S 1032 of 1726 +--d0:=D(m0,x) +--E 1032 + +)clear all + +--S 1033 of 1726 +t0:=1/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R +----------+ +--R 2 2 2 +-------+ | 2 +--R (e x + 2d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1726 +--r0:=4/3*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/((-d)^(3/2)*(c*d-b*e)^2*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(3*c*d-2*b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(3/2))-4/3*e*(2*c*d-b*e)*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*_ +-- sqrt(d+e*x)) +--E 1034 + +--S 1035 of 1726 +--a0:=integrate(t0,x) +--E 1035 + +--S 1036 of 1726 +--m0:=a0-r0 +--E 1036 + +--S 1037 of 1726 +--d0:=D(m0,x) +--E 1037 + +)clear all + +--S 1038 of 1726 +t0:=1/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R +----------+ +--R 3 3 2 2 2 3 +-------+ | 2 +--R (e x + 3d e x + 3d e x + d )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1726 +--r0:=-2/15*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)*(b+c*x)*elliptic_e(_ +-- asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/((-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/15*(15*c^2*d^2-19*b*c*d*e+8*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(-b)*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*e)^2*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/5*e*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*_ +-- (d+e*x)^(5/2))-8/15*e*(2*c*d-b*e)*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*_ +-- (d+e*x)^(3/2))-2/15*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)*sqrt(b*x+_ +-- c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 1039 + +--S 1040 of 1726 +--a0:=integrate(t0,x) +--E 1040 + +--S 1041 of 1726 +--m0:=a0-r0 +--E 1041 + +--S 1042 of 1726 +--d0:=D(m0,x) +--E 1042 + +)clear all + +--S 1043 of 1726 +t0:=(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1726 +--r0:=-2*(d+e*x)^(5/2)*(b*d+(2*c*d-b*e)*x)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2/3*(2*c*d-b*e)*(3*c^2*d^2-3*b*c*d*e+8*b^2*e^2)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c^3*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2/3*e*(c*d-b*e)*(3*c^2*d^2-15*b*c*d*e+8*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(7/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/_ +-- (b^2*c)+4/3*e*(3*c^2*d^2-3*b*c*d*e+2*b^2*e^2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^2*c^2) +--E 1044 + +--S 1045 of 1726 +--a0:=integrate(t0,x) +--E 1045 + +--S 1046 of 1726 +--m0:=a0-r0 +--E 1046 + +--S 1047 of 1726 +--d0:=D(m0,x) +--E 1047 + +)clear all + +--S 1048 of 1726 +t0:=(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------ +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1726 +--r0:=-2*(d+e*x)^(3/2)*(b*d+(2*c*d-b*e)*x)/(b^2*sqrt(b*x+c*x^2))+_ +-- 4*(c^2*d^2-b*c*d*e+b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*_ +-- sqrt((d+e*x)/d)/(b^2*c^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*(c*d-2*b*e)*(c*d-b*e)*elliptic_f(asin(sqrt(c)*_ +-- sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*_ +-- sqrt((d+e*x)/d)/(c^(5/2)*sqrt(-b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2*e*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c) +--E 1049 + +--S 1050 of 1726 +--a0:=integrate(t0,x) +--E 1050 + +--S 1051 of 1726 +--m0:=a0-r0 +--E 1051 + +--S 1052 of 1726 +--d0:=D(m0,x) +--E 1052 + +)clear all + +--S 1053 of 1726 +t0:=(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1726 +--r0:=-2*(b*d+(2*c*d-b*e)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))+_ +-- 2*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*e*(c*d-b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(c^(3/2)*sqrt(-b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 1054 + +--S 1055 of 1726 +--a0:=integrate(t0,x) +--E 1055 + +--S 1056 of 1726 +--m0:=a0-r0 +--E 1056 + +--S 1057 of 1726 +--d0:=D(m0,x) +--E 1057 + +)clear all + +--S 1058 of 1726 +t0:=sqrt(d+e*x)/(b*x+c*x^2)^(3/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------- +--R +----------+ +--R 2 | 2 +--R (c x + b x)\|c x + b x +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1726 +--r0:=-2*(b+2*c*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))+4*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(-d)*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+2*e*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(sqrt(-b)*_ +-- sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1059 + +--S 1060 of 1726 +--a0:=integrate(t0,x) +--E 1060 + +--S 1061 of 1726 +--m0:=a0-r0 +--E 1061 + +--S 1062 of 1726 +--d0:=D(m0,x) +--E 1062 + +)clear all + +--S 1063 of 1726 +t0:=1/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R +----------+ +--R 2 +-------+ | 2 +--R (c x + b x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1726 +--r0:=-2*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*_ +-- sqrt(b*x+c*x^2))-2*(2*c*d-b*e)*(b+c*x)*elliptic_e(asin(sqrt(e)*_ +-- sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*_ +-- (c*d-b*e)*sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+_ +-- 2*e*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 1064 + +--S 1065 of 1726 +--a0:=integrate(t0,x) +--E 1065 + +--S 1066 of 1726 +--m0:=a0-r0 +--E 1066 + +--S 1067 of 1726 +--d0:=D(m0,x) +--E 1067 + +)clear all + +--S 1068 of 1726 +t0:=1/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R +----------+ +--R 3 2 +-------+ | 2 +--R (c e x + (b e + c d)x + b d x)\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1726 +--r0:=-2*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))+4*(c^2*d^2-b*c*d*e+b^2*e^2)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(3/2)*(c*d-b*e)^2*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*e*(c*d-2*b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^2*(c*d-b*e)*sqrt(-b)*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-4*e*(c^2*d^2-b*c*d*e+b^2*e^2)*_ +-- sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x)) +--E 1069 + +--S 1070 of 1726 +--a0:=integrate(t0,x) +--E 1070 + +--S 1071 of 1726 +--m0:=a0-r0 +--E 1071 + +--S 1072 of 1726 +--d0:=D(m0,x) +--E 1072 + +)clear all + +--S 1073 of 1726 +t0:=1/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 4 2 3 2 2 2 +-------+ +--R (c e x + (b e + 2c d e)x + (2b d e + c d )x + b d x)\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1726 +--r0:=-2*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*(d+e*x)^(3/2)*_ +-- sqrt(b*x+c*x^2))-2/3*(2*c*d-b*e)*(3*c^2*d^2-3*b*c*d*e+8*b^2*e^2)*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^2*(-d)^(5/2)*(c*d-b*e)^3*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(3*c^2*d^2-_ +-- 15*b*c*d*e+8*b^2*e^2)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/(d^3*(c*d-b*_ +-- e)^2*sqrt(-b)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-4/3*e*(3*c^2*_ +-- d^2-3*b*c*d*e+2*b^2*e^2)*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*_ +-- (d+e*x)^(3/2))-2/3*e*(2*c*d-b*e)*(3*c^2*d^2-3*b*c*d*e+8*b^2*e^2)*_ +-- sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 1074 + +--S 1075 of 1726 +--a0:=integrate(t0,x) +--E 1075 + +--S 1076 of 1726 +--m0:=a0-r0 +--E 1076 + +--S 1077 of 1726 +--d0:=D(m0,x) +--E 1077 + +)clear all + +--S 1078 of 1726 +t0:=(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R (1) ---------------------------------------- +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1726 +--r0:=-2/3*(d+e*x)^(5/2)*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(3/2))+_ +-- 2/3*(d+e*x)^(3/2)*(b*d*(8*c*d-9*b*e)+(16*c^2*d^2-16*b*c*d*e-_ +-- b^2*e^2)*x)/(b^4*sqrt(b*x+c*x^2))-4/3*(2*c*d-b*e)*(4*c^2*d^2-_ +-- 4*b*c*d*e-b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/_ +-- (b^4*c^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (c*d-b*e)*(8*c^2*d^2-5*b*c*d*e-2*b^2*e^2)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*c^(5/2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2))-2/3*e*(16*c^2*d^2-16*b*c*d*e-b^2*e^2)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)/(b^4*c) +--E 1079 + +--S 1080 of 1726 +--a0:=integrate(t0,x) +--E 1080 + +--S 1081 of 1726 +--m0:=a0-r0 +--E 1081 + +--S 1082 of 1726 +--d0:=D(m0,x) +--E 1082 + +)clear all + +--S 1083 of 1726 +t0:=(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1726 +--r0:=-2/3*(d+e*x)^(3/2)*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(3/2))+_ +-- 2/3*(b*d*(8*c*d-7*b*e)+(16*c^2*d^2-16*b*c*d*e+b^2*e^2)*x)*_ +-- sqrt(d+e*x)/(b^4*sqrt(b*x+c*x^2))-2/3*(16*c^2*d^2-16*b*c*d*e+_ +-- b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*c*_ +-- sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(c*d-b*e)*_ +-- (8*c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*c^(3/2)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1084 + +--S 1085 of 1726 +--a0:=integrate(t0,x) +--E 1085 + +--S 1086 of 1726 +--m0:=a0-r0 +--E 1086 + +--S 1087 of 1726 +--d0:=D(m0,x) +--E 1087 + +)clear all + +--S 1088 of 1726 +t0:=(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R (e x + d)\|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1726 +--r0:=-2/3*(b*d+(2*c*d-b*e)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))+_ +-- 2/3*(b*(8*c*d-5*b*e)*(c*d-b*e)+8*c*(c*d-b*e)*(2*c*d-b*e)*x)*_ +-- sqrt(d+e*x)/(b^4*(c*d-b*e)*sqrt(b*x+c*x^2))-16/3*(2*c*d-b*e)*_ +-- (b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*_ +-- sqrt(-d)*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*c*d-5*b*e)*_ +-- elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*sqrt(x)*_ +-- sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*sqrt(c)*sqrt(d+e*x)*_ +-- sqrt(b*x+c*x^2)) +--E 1089 + +--S 1090 of 1726 +--a0:=integrate(t0,x) +--E 1090 + +--S 1091 of 1726 +--m0:=a0-r0 +--E 1091 + +--S 1092 of 1726 +--d0:=D(m0,x) +--E 1092 + +)clear all + +--S 1093 of 1726 +t0:=sqrt(d+e*x)/(b*x+c*x^2)^(5/2) +--R +--R +--R +-------+ +--R \|e x + d +--R (1) ------------------------------------ +--R +----------+ +--R 2 4 3 2 2 | 2 +--R (c x + 2b c x + b x )\|c x + b x +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1726 +--r0:=-2/3*(b+2*c*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))+_ +-- 2/3*(b*(c*d-b*e)*(8*c*d-b*e)+c*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)*x)*_ +-- sqrt(d+e*x)/(b^4*d*(c*d-b*e)*sqrt(b*x+c*x^2))+2/3*(16*c^2*d^2-_ +-- 16*b*c*d*e+b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/_ +-- sqrt(-d)),c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(c*d-_ +-- b*e)*sqrt(-d)*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*_ +-- e*(8*c*d-b*e)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),b*e/(c*d))*_ +-- sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*d*sqrt(c)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1094 + +--S 1095 of 1726 +--a0:=integrate(t0,x) +--E 1095 + +--S 1096 of 1726 +--m0:=a0-r0 +--E 1096 + +--S 1097 of 1726 +--d0:=D(m0,x) +--E 1097 + +)clear all + +--S 1098 of 1726 +t0:=1/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R +----------+ +--R 2 4 3 2 2 +-------+ | 2 +--R (c x + 2b c x + b x )\|e x + d \|c x + b x +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1726 +--r0:=-2/3*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*_ +-- (b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*c^2*d^2-5*b*c*d*e-2*b^2*e^2)+_ +-- 2*c*(2*c*d-b*e)*(4*c^2*d^2-4*b*c*d*e-b^2*e^2)*x)*sqrt(d+e*x)/_ +-- (b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-4/3*(2*c*d-b*e)*(4*c^2*d^2-_ +-- 4*b*c*d*e-b^2*e^2)*(b+c*x)*elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),_ +-- c*d/(b*e))*sqrt(e)*sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(3/2)*_ +-- (c*d-b*e)^2*sqrt((b+c*x)/b)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*_ +-- (8*c^2*d^2-5*b*c*d*e-2*b^2*e^2)*elliptic_f(asin(sqrt(c)*sqrt(x)/_ +-- sqrt(-b)),b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/_ +-- ((-b)^(5/2)*d^2*(c*d-b*e)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2)) +--E 1099 + +--S 1100 of 1726 +--a0:=integrate(t0,x) +--E 1100 + +--S 1101 of 1726 +--m0:=a0-r0 +--E 1101 + +--S 1102 of 1726 +--d0:=D(m0,x) +--E 1102 + +)clear all + +--S 1103 of 1726 +t0:=1/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 5 2 4 2 3 2 2 +-------+ +--R (c e x + (2b c e + c d)x + (b e + 2b c d)x + b d x )\|e x + d +--R * +--R +----------+ +--R | 2 +--R \|c x + b x +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1726 +--r0:=-2/3*(b*(c*d-b*e)+c*(2*c*d-b*e)*x)/(b^2*d*(c*d-b*e)*(b*x+_ +-- c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*c^2*d^2-3*b*c*d*e-_ +-- 4*b^2*e^2)+4*c*(4*c^3*d^3-6*b*c^2*d^2*e+b^3*e^3)*x)/(b^4*d^2*(c*d-_ +-- b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(16*c^4*d^4-32*b*c^3*d^3*e+_ +-- 9*b^2*c^2*d^2*e^2+7*b^3*c*d*e^3-8*b^4*e^4)*(b+c*x)*_ +-- elliptic_e(asin(sqrt(e)*sqrt(x)/sqrt(-d)),c*d/(b*e))*sqrt(e)*_ +-- sqrt(x)*sqrt((d+e*x)/d)/(b^4*(-d)^(5/2)*(c*d-b*e)^3*sqrt((b+c*x)/b)*_ +-- sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(8*c^3*d^3-9*b*c^2*d^2*e-_ +-- 3*b^2*c*d*e^2+8*b^3*e^3)*elliptic_f(asin(sqrt(c)*sqrt(x)/sqrt(-b)),_ +-- b*e/(c*d))*sqrt(x)*sqrt((b+c*x)/b)*sqrt((d+e*x)/d)/((-b)^(5/2)*_ +-- d^3*(c*d-b*e)^2*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*_ +-- (16*c^4*d^4-32*b*c^3*d^3*e+9*b^2*c^2*d^2*e^2+7*b^3*c*d*e^3-_ +-- 8*b^4*e^4)*sqrt(b*x+c*x^2)/(b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x)) +--E 1104 + +--S 1105 of 1726 +--a0:=integrate(t0,x) +--E 1105 + +--S 1106 of 1726 +--m0:=a0-r0 +--E 1106 + +--S 1107 of 1726 +--d0:=D(m0,x) +--E 1107 + +)clear all + +--S 1108 of 1726 +t0:=(d+e*x)^m*(c*d*x+c*e*x^2)^3 +--R +--R +--R 3 3 6 3 2 5 3 2 4 3 3 3 m +--R (1) (c e x + 3c d e x + 3c d e x + c d x )(e x + d) +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1726 +r0:=-c^3*d^3*(d+e*x)^(4+m)/(e^4*(4+m))+3*c^3*d^2*(d+e*x)^(5+m)/_ + (e^4*(5+m))-3*c^3*d*(d+e*x)^(6+m)/(e^4*(6+m))+_ + c^3*(d+e*x)^(7+m)/(e^4*(7+m)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 7 +--R (c m + 15c m + 74c m + 120c )(e x + d) +--R + +--R 3 3 3 2 3 3 m + 6 +--R (- 3c d m - 48c d m - 249c d m - 420c d)(e x + d) +--R + +--R 3 2 3 3 2 2 3 2 3 2 m + 5 +--R (3c d m + 51c d m + 282c d m + 504c d )(e x + d) +--R + +--R 3 3 3 3 3 2 3 3 3 3 m + 4 +--R (- c d m - 18c d m - 107c d m - 210c d )(e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 22e m + 179e m + 638e m + 840e +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 3 3 7 2 3 7 3 7 7 +--R (c e m + 15c e m + 74c e m + 120c e )x +--R + +--R 3 6 3 3 6 2 3 6 3 6 6 +--R (4c d e m + 57c d e m + 269c d e m + 420c d e )x +--R + +--R 3 2 5 3 3 2 5 2 3 2 5 3 2 5 5 +--R (6c d e m + 78c d e m + 342c d e m + 504c d e )x +--R + +--R 3 3 4 3 3 3 4 2 3 3 4 3 3 4 4 +--R (4c d e m + 42c d e m + 158c d e m + 210c d e )x +--R + +--R 3 4 3 3 3 4 3 2 3 4 3 3 3 5 2 2 3 5 2 2 +--R (c d e m + 3c d e m + 2c d e m)x + (- 3c d e m - 3c d e m)x +--R + +--R 3 6 3 7 +--R 6c d e m x - 6c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 22e m + 179e m + 638e m + 840e +--R Type: Union(Expression(Integer),...) +--E 1110 + +--S 1111 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 3 3 7 2 3 7 3 7 7 +--R (c e m + 15c e m + 74c e m + 120c e )x +--R + +--R 3 6 3 3 6 2 3 6 3 6 6 +--R (4c d e m + 57c d e m + 269c d e m + 420c d e )x +--R + +--R 3 2 5 3 3 2 5 2 3 2 5 3 2 5 5 +--R (6c d e m + 78c d e m + 342c d e m + 504c d e )x +--R + +--R 3 3 4 3 3 3 4 2 3 3 4 3 3 4 4 +--R (4c d e m + 42c d e m + 158c d e m + 210c d e )x +--R + +--R 3 4 3 3 3 4 3 2 3 4 3 3 3 5 2 2 3 5 2 2 +--R (c d e m + 3c d e m + 2c d e m)x + (- 3c d e m - 3c d e m)x +--R + +--R 3 6 3 7 +--R 6c d e m x - 6c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 3 3 2 3 3 m + 7 +--R (- c m - 15c m - 74c m - 120c )(e x + d) +--R + +--R 3 3 3 2 3 3 m + 6 +--R (3c d m + 48c d m + 249c d m + 420c d)(e x + d) +--R + +--R 3 2 3 3 2 2 3 2 3 2 m + 5 +--R (- 3c d m - 51c d m - 282c d m - 504c d )(e x + d) +--R + +--R 3 3 3 3 3 2 3 3 3 3 m + 4 +--R (c d m + 18c d m + 107c d m + 210c d )(e x + d) +--R / +--R 4 4 4 3 4 2 4 4 +--R e m + 22e m + 179e m + 638e m + 840e +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1112 + +)clear all + +--S 1113 of 1726 +t0:=(d+e*x)^m*(c*d*x+c*e*x^2)^2 +--R +--R +--R 2 2 4 2 3 2 2 2 m +--R (1) (c e x + 2c d e x + c d x )(e x + d) +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1726 +r0:=c^2*d^2*(d+e*x)^(3+m)/(e^3*(3+m))-2*c^2*d*(d+e*x)^(4+m)/(e^3*(4+m))+_ + c^2*(d+e*x)^(5+m)/(e^3*(5+m)) +--R +--R +--R (2) +--R 2 2 2 2 m + 5 +--R (c m + 7c m + 12c )(e x + d) +--R + +--R 2 2 2 2 m + 4 +--R (- 2c d m - 16c d m - 30c d)(e x + d) +--R + +--R 2 2 2 2 2 2 2 m + 3 +--R (c d m + 9c d m + 20c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 12e m + 47e m + 60e +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 2 5 2 5 5 2 4 2 2 4 2 4 4 +--R (c e m + 7c e m + 12c e )x + (3c d e m + 19c d e m + 30c d e )x +--R + +--R 2 2 3 2 2 2 3 2 2 3 3 2 3 2 2 2 3 2 2 +--R (3c d e m + 15c d e m + 20c d e )x + (c d e m + c d e m)x +--R + +--R 2 4 2 5 +--R - 2c d e m x + 2c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 12e m + 47e m + 60e +--R Type: Union(Expression(Integer),...) +--E 1115 + +--S 1116 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 2 2 5 2 5 5 2 4 2 2 4 2 4 4 +--R (c e m + 7c e m + 12c e )x + (3c d e m + 19c d e m + 30c d e )x +--R + +--R 2 2 3 2 2 2 3 2 2 3 3 2 3 2 2 2 3 2 2 +--R (3c d e m + 15c d e m + 20c d e )x + (c d e m + c d e m)x +--R + +--R 2 4 2 5 +--R - 2c d e m x + 2c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 2 2 2 m + 5 +--R (- c m - 7c m - 12c )(e x + d) +--R + +--R 2 2 2 2 m + 4 +--R (2c d m + 16c d m + 30c d)(e x + d) +--R + +--R 2 2 2 2 2 2 2 m + 3 +--R (- c d m - 9c d m - 20c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 12e m + 47e m + 60e +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1117 + +)clear all + +--S 1118 of 1726 +t0:=(d+e*x)^m*(c*d*x+c*e*x^2) +--R +--R +--R 2 m +--R (1) (c e x + c d x)(e x + d) +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1726 +r0:=-c*d*(d+e*x)^(2+m)/(e^2*(2+m))+c*(d+e*x)^(3+m)/(e^2*(3+m)) +--R +--R +--R m + 3 m + 2 +--R (c m + 2c)(e x + d) + (- c d m - 3c d)(e x + d) +--R (2) --------------------------------------------------------- +--R 2 2 2 2 +--R e m + 5e m + 6e +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 2 2 3 +--R ((c e m + 2c e )x + (2c d e m + 3c d e )x + c d e m x - c d ) +--R * +--R m log(e x + d) +--R %e +--R / +--R 2 2 2 2 +--R e m + 5e m + 6e +--R Type: Union(Expression(Integer),...) +--E 1120 + +--S 1121 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 2 2 2 3 +--R ((c e m + 2c e )x + (2c d e m + 3c d e )x + c d e m x - c d ) +--R * +--R m log(e x + d) +--R %e +--R + +--R m + 3 m + 2 +--R (- c m - 2c)(e x + d) + (c d m + 3c d)(e x + d) +--R / +--R 2 2 2 2 +--R e m + 5e m + 6e +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1122 + +)clear all + +--S 1123 of 1726 +t0:=(d+e*x)^m +--R +--R +--R m +--R (1) (e x + d) +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1726 +r0:=(d+e*x)^(1+m)/(e*(1+m)) +--R +--R +--R m + 1 +--R (e x + d) +--R (2) -------------- +--R e m + e +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1726 +a0:=integrate(t0,x) +--R +--R +--R m log(e x + d) +--R (e x + d)%e +--R (3) ------------------------- +--R e m + e +--R Type: Union(Expression(Integer),...) +--E 1125 + +--S 1126 of 1726 +m0:=a0-r0 +--R +--R +--R m log(e x + d) m + 1 +--R (e x + d)%e - (e x + d) +--R (4) ------------------------------------------ +--R e m + e +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1127 + +)clear all + +--S 1128 of 1726 +t0:=(d+e*x)^m/(c*d*x+c*e*x^2) +--R +--R +--R m +--R (e x + d) +--R (1) -------------- +--R 2 +--R c e x + c d x +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1726 +--r0:=-(d+e*x)^m/(c*d*m)-(d+e*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,(d+e*x)/d)/(c*d^2*(1+m)) +--E 1129 + +--S 1130 of 1726 +--a0:=integrate(t0,x) +--E 1130 + +--S 1131 of 1726 +--m0:=a0-r0 +--E 1131 + +--S 1132 of 1726 +--d0:=D(m0,x) +--E 1132 + +)clear all + +--S 1133 of 1726 +t0:=(d+e*x)^m*(a+c*x^2) +--R +--R +--R 2 m +--R (1) (c x + a)(e x + d) +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1726 +r0:=(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^3*(1+m))-2*c*d*(d+e*x)^(2+m)/(e^3*(2+m))+_ + c*(d+e*x)^(3+m)/(e^3*(3+m)) +--R +--R +--R (2) +--R 2 m + 3 +--R (c m + 3c m + 2c)(e x + d) +--R + +--R 2 m + 2 +--R (- 2c d m - 8c d m - 6c d)(e x + d) +--R + +--R 2 2 2 2 2 2 2 m + 1 +--R ((a e + c d )m + (5a e + 5c d )m + 6a e + 6c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 2 2 2 2 +--R (c e m + 3c e m + 2c e )x + (c d e m + c d e m)x +--R + +--R 3 2 3 2 3 2 2 2 2 +--R (a e m + (5a e - 2c d e)m + 6a e )x + a d e m + 5a d e m + 6a d e +--R + +--R 3 +--R 2c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Union(Expression(Integer),...) +--E 1135 + +--S 1136 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 2 2 2 2 +--R (c e m + 3c e m + 2c e )x + (c d e m + c d e m)x +--R + +--R 3 2 3 2 3 2 2 2 2 +--R (a e m + (5a e - 2c d e)m + 6a e )x + a d e m + 5a d e m + 6a d e +--R + +--R 3 +--R 2c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 m + 3 +--R (- c m - 3c m - 2c)(e x + d) +--R + +--R 2 m + 2 +--R (2c d m + 8c d m + 6c d)(e x + d) +--R + +--R 2 2 2 2 2 2 2 m + 1 +--R ((- a e - c d )m + (- 5a e - 5c d )m - 6a e - 6c d )(e x + d) +--R / +--R 3 3 3 2 3 3 +--R e m + 6e m + 11e m + 6e +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1137 + +)clear all + +--S 1138 of 1726 +t0:=(d+e*x)^4*(a+c*x^2) +--R +--R +--R (1) +--R 4 6 3 5 4 2 2 4 3 3 3 +--R c e x + 4c d e x + (a e + 6c d e )x + (4a d e + 4c d e)x +--R + +--R 2 2 4 2 3 4 +--R (6a d e + c d )x + 4a d e x + a d +--R Type: Polynomial(Integer) +--E 1138 + +--S 1139 of 1726 +r0:=1/5*(c*d^2+a*e^2)*(d+e*x)^5/e^3-1/3*c*d*(d+e*x)^6/e^3+1/7*c*(d+e*x)^7/e^3 +--R +--R +--R (2) +--R 1 7 7 2 6 6 1 7 6 2 5 5 6 3 4 4 +--R - c e x + - c d e x + (- a e + - c d e )x + (a d e + c d e )x +--R 7 3 5 5 +--R + +--R 2 5 1 4 3 3 3 4 2 4 3 1 5 2 1 7 +--R (2a d e + - c d e )x + 2a d e x + a d e x + - a d e + --- c d +--R 3 5 105 +--R / +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1139 + +--S 1140 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 4 7 2 3 6 1 4 6 2 2 5 3 3 4 +--R - c e x + - c d e x + (- a e + - c d e )x + (a d e + c d e)x +--R 7 3 5 5 +--R + +--R 2 2 1 4 3 3 2 4 +--R (2a d e + - c d )x + 2a d e x + a d x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1140 + +--S 1141 of 1726 +m0:=a0-r0 +--R +--R +--R 1 5 2 1 7 +--R - - a d e - --- c d +--R 5 105 +--R (4) --------------------- +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1141 + +--S 1142 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1142 + +)clear all + +--S 1143 of 1726 +t0:=(d+e*x)^3*(a+c*x^2) +--R +--R +--R (1) +--R 3 5 2 4 3 2 3 2 3 2 2 3 +--R c e x + 3c d e x + (a e + 3c d e)x + (3a d e + c d )x + 3a d e x + a d +--R Type: Polynomial(Integer) +--E 1143 + +--S 1144 of 1726 +r0:=1/4*(c*d^2+a*e^2)*(d+e*x)^4/e^3-2/5*c*d*(d+e*x)^5/e^3+1/6*c*(d+e*x)^6/e^3 +--R +--R +--R (2) +--R 1 6 6 3 5 5 1 6 3 2 4 4 5 1 3 3 3 +--R - c e x + - c d e x + (- a e + - c d e )x + (a d e + - c d e )x +--R 6 5 4 4 3 +--R + +--R 3 2 4 2 3 3 1 4 2 1 6 +--R - a d e x + a d e x + - a d e + -- c d +--R 2 4 60 +--R / +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1144 + +--S 1145 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 6 3 2 5 1 3 3 2 4 2 1 3 3 +--R - c e x + - c d e x + (- a e + - c d e)x + (a d e + - c d )x +--R 6 5 4 4 3 +--R + +--R 3 2 2 3 +--R - a d e x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1145 + +--S 1146 of 1726 +m0:=a0-r0 +--R +--R +--R 1 4 2 1 6 +--R - - a d e - -- c d +--R 4 60 +--R (4) -------------------- +--R 3 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1146 + +--S 1147 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1147 + +)clear all + +--S 1148 of 1726 +t0:=(d+e*x)^2*(a+c*x^2) +--R +--R +--R 2 4 3 2 2 2 2 +--R (1) c e x + 2c d e x + (a e + c d )x + 2a d e x + a d +--R Type: Polynomial(Integer) +--E 1148 + +--S 1149 of 1726 +r0:=a*d^2*x+a*d*e*x^2+1/3*(c*d^2+a*e^2)*x^3+1/2*c*d*e*x^4+1/5*c*e^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 1 2 3 2 2 +--R (2) - c e x + - c d e x + (- a e + - c d )x + a d e x + a d x +--R 5 2 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1149 + +--S 1150 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 1 4 1 2 1 2 3 2 2 +--R (3) - c e x + - c d e x + (- a e + - c d )x + a d e x + a d x +--R 5 2 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1150 + +--S 1151 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1151 + +--S 1152 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1152 + +)clear all + +--S 1153 of 1726 +t0:=(d+e*x)*(a+c*x^2) +--R +--R +--R 3 2 +--R (1) c e x + c d x + a e x + a d +--R Type: Polynomial(Integer) +--E 1153 + +--S 1154 of 1726 +r0:=a*d*x+1/2*a*e*x^2+1/3*c*d*x^3+1/4*c*e*x^4 +--R +--R +--R 1 4 1 3 1 2 +--R (2) - c e x + - c d x + - a e x + a d x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1154 + +--S 1155 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 3 1 2 +--R (3) - c e x + - c d x + - a e x + a d x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1155 + +--S 1156 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1156 + +--S 1157 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1157 + +)clear all + +--S 1158 of 1726 +t0:=a+c*x^2 +--R +--R +--R 2 +--R (1) c x + a +--R Type: Polynomial(Integer) +--E 1158 + +--S 1159 of 1726 +r0:=a*x+1/3*c*x^3 +--R +--R +--R 1 3 +--R (2) - c x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1159 + +--S 1160 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 3 +--R (3) - c x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1160 + +--S 1161 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1161 + +--S 1162 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1162 + +)clear all + +--S 1163 of 1726 +t0:=(a+c*x^2)/(d+e*x) +--R +--R +--R 2 +--R c x + a +--R (1) -------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1163 + +--S 1164 of 1726 +r0:=-c*d*x/e^2+1/2*c*x^2/e+(c*d^2+a*e^2)*log(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 +--R (2a e + 2c d )log(e x + d) + c e x - 2c d e x +--R (2) ----------------------------------------------- +--R 3 +--R 2e +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (2a e + 2c d )log(e x + d) + c e x - 2c d e x +--R (3) ----------------------------------------------- +--R 3 +--R 2e +--R Type: Union(Expression(Integer),...) +--E 1165 + +--S 1166 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1167 + +)clear all + +--S 1168 of 1726 +t0:=(a+c*x^2)/(d+e*x)^2 +--R +--R +--R 2 +--R c x + a +--R (1) ------------------ +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1168 + +--S 1169 of 1726 +r0:=c*x/e^2+(-c*d^2-a*e^2)/(e^3*(d+e*x))-2*c*d*log(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 2 +--R (- 2c d e x - 2c d )log(e x + d) + c e x + c d e x - a e - c d +--R (2) ----------------------------------------------------------------- +--R 4 3 +--R e x + d e +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R (- 2c d e x - 2c d )log(e x + d) + c e x + c d e x - a e - c d +--R (3) ----------------------------------------------------------------- +--R 4 3 +--R e x + d e +--R Type: Union(Expression(Integer),...) +--E 1170 + +--S 1171 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1172 + +)clear all + +--S 1173 of 1726 +t0:=(a+c*x^2)/(d+e*x)^3 +--R +--R +--R 2 +--R c x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1173 + +--S 1174 of 1726 +r0:=1/2*(-c*d^2-a*e^2)/(e^3*(d+e*x)^2)+2*c*d/(e^3*(d+e*x))+c*log(d+e*x)/e^3 +--R +--R +--R 2 2 2 2 2 +--R (2c e x + 4c d e x + 2c d )log(e x + d) + 4c d e x - a e + 3c d +--R (2) ------------------------------------------------------------------ +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R (2c e x + 4c d e x + 2c d )log(e x + d) + 4c d e x - a e + 3c d +--R (3) ------------------------------------------------------------------ +--R 5 2 4 2 3 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1175 + +--S 1176 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1177 + +)clear all + +--S 1178 of 1726 +t0:=(a+c*x^2)/(d+e*x)^4 +--R +--R +--R 2 +--R c x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1178 + +--S 1179 of 1726 +r0:=1/3*(-c*d^2-a*e^2)/(e^3*(d+e*x)^3)+c*d/(e^3*(d+e*x)^2)-c/(e^3*(d+e*x)) +--R +--R +--R 2 2 1 2 1 2 +--R - c e x - c d e x - - a e - - c d +--R 3 3 +--R (2) ------------------------------------ +--R 6 3 5 2 2 4 3 3 +--R e x + 3d e x + 3d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1179 + +--S 1180 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R - 3c e x - 3c d e x - a e - c d +--R (3) ---------------------------------- +--R 6 3 5 2 2 4 3 3 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1180 + +--S 1181 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1182 + +)clear all + +--S 1183 of 1726 +t0:=(a+c*x^2)/(d+e*x)^5 +--R +--R +--R 2 +--R c x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1183 + +--S 1184 of 1726 +r0:=1/4*(-c*d^2-a*e^2)/(e^3*(d+e*x)^4)+2/3*c*d/(e^3*(d+e*x)^3)-_ + 1/2*c/(e^3*(d+e*x)^2) +--R +--R +--R 1 2 2 1 1 2 1 2 +--R - - c e x - - c d e x - - a e - -- c d +--R 2 3 4 12 +--R (2) ----------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R e x + 4d e x + 6d e x + 4d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1184 + +--S 1185 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R - 6c e x - 4c d e x - 3a e - c d +--R (3) ----------------------------------------------- +--R 7 4 6 3 2 5 2 3 4 4 3 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1185 + +--S 1186 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1187 + +)clear all + +--S 1188 of 1726 +t0:=(d+e*x)^m*(a+c*x^2)^2 +--R +--R +--R 2 4 2 2 m +--R (1) (c x + 2a c x + a )(e x + d) +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1726 +r0:=(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^5*(1+m))-4*c*d*(c*d^2+a*e^2)*_ + (d+e*x)^(2+m)/(e^5*(2+m))+2*c*(3*c*d^2+a*e^2)*(d+e*x)^(3+m)/_ + (e^5*(3+m))-4*c^2*d*(d+e*x)^(4+m)/(e^5*(4+m))+_ + c^2*(d+e*x)^(5+m)/(e^5*(5+m)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 m + 5 +--R (c m + 10c m + 35c m + 50c m + 24c )(e x + d) +--R + +--R 2 4 2 3 2 2 2 2 m + 4 +--R (- 4c d m - 44c d m - 164c d m - 244c d m - 120c d)(e x + d) +--R + +--R 2 2 2 4 2 2 2 3 2 2 2 2 +--R (2a c e + 6c d )m + (24a c e + 72c d )m + (98a c e + 294c d )m +--R + +--R 2 2 2 2 2 2 +--R (156a c e + 468c d )m + 80a c e + 240c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 4a c d e - 4c d )m + (- 52a c d e - 52c d )m +--R + +--R 2 2 3 2 2 2 3 +--R (- 236a c d e - 236c d )m + (- 428a c d e - 428c d )m +--R + +--R 2 2 3 +--R - 240a c d e - 240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 4 2 2 2 4 4 2 4 2 2 2 4 3 +--R (a e + 2a c d e + c d )m + (14a e + 28a c d e + 14c d )m +--R + +--R 2 4 2 2 2 4 2 +--R (71a e + 142a c d e + 71c d )m +--R + +--R 2 4 2 2 2 4 2 4 2 2 2 4 +--R (154a e + 308a c d e + 154c d )m + 120a e + 240a c d e + 120c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 2 5 3 2 5 2 2 5 2 5 5 +--R (c e m + 10c e m + 35c e m + 50c e m + 24c e )x +--R + +--R 2 4 4 2 4 3 2 4 2 2 4 4 +--R (c d e m + 6c d e m + 11c d e m + 6c d e m)x +--R + +--R 5 4 5 2 2 3 3 5 2 2 3 2 +--R 2a c e m + (24a c e - 4c d e )m + (98a c e - 12c d e )m +--R + +--R 5 2 2 3 5 +--R (156a c e - 8c d e )m + 80a c e +--R * +--R 3 +--R x +--R + +--R 4 4 4 3 4 2 3 2 2 +--R 2a c d e m + 20a c d e m + (58a c d e + 12c d e )m +--R + +--R 4 2 3 2 +--R (40a c d e + 12c d e )m +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 5 2 3 3 2 5 2 3 2 +--R a e m + (14a e - 4a c d e )m + (71a e - 36a c d e )m +--R + +--R 2 5 2 3 2 4 2 5 +--R (154a e - 80a c d e - 24c d e)m + 120a e +--R * +--R x +--R + +--R 2 4 4 2 4 3 2 4 3 2 2 +--R a d e m + 14a d e m + (71a d e + 4a c d e )m +--R + +--R 2 4 3 2 2 4 3 2 2 5 +--R (154a d e + 36a c d e )m + 120a d e + 80a c d e + 24c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Union(Expression(Integer),...) +--E 1190 + +--S 1191 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 4 2 5 3 2 5 2 2 5 2 5 5 +--R (c e m + 10c e m + 35c e m + 50c e m + 24c e )x +--R + +--R 2 4 4 2 4 3 2 4 2 2 4 4 +--R (c d e m + 6c d e m + 11c d e m + 6c d e m)x +--R + +--R 5 4 5 2 2 3 3 5 2 2 3 2 +--R 2a c e m + (24a c e - 4c d e )m + (98a c e - 12c d e )m +--R + +--R 5 2 2 3 5 +--R (156a c e - 8c d e )m + 80a c e +--R * +--R 3 +--R x +--R + +--R 4 4 4 3 4 2 3 2 2 +--R 2a c d e m + 20a c d e m + (58a c d e + 12c d e )m +--R + +--R 4 2 3 2 +--R (40a c d e + 12c d e )m +--R * +--R 2 +--R x +--R + +--R 2 5 4 2 5 2 3 3 2 5 2 3 2 +--R a e m + (14a e - 4a c d e )m + (71a e - 36a c d e )m +--R + +--R 2 5 2 3 2 4 2 5 +--R (154a e - 80a c d e - 24c d e)m + 120a e +--R * +--R x +--R + +--R 2 4 4 2 4 3 2 4 3 2 2 +--R a d e m + 14a d e m + (71a d e + 4a c d e )m +--R + +--R 2 4 3 2 2 4 3 2 2 5 +--R (154a d e + 36a c d e )m + 120a d e + 80a c d e + 24c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 2 4 2 3 2 2 2 2 m + 5 +--R (- c m - 10c m - 35c m - 50c m - 24c )(e x + d) +--R + +--R 2 4 2 3 2 2 2 2 m + 4 +--R (4c d m + 44c d m + 164c d m + 244c d m + 120c d)(e x + d) +--R + +--R 2 2 2 4 2 2 2 3 +--R (- 2a c e - 6c d )m + (- 24a c e - 72c d )m +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 98a c e - 294c d )m + (- 156a c e - 468c d )m - 80a c e +--R + +--R 2 2 +--R - 240c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 2 3 4 2 2 3 3 +--R (4a c d e + 4c d )m + (52a c d e + 52c d )m +--R + +--R 2 2 3 2 2 2 3 2 +--R (236a c d e + 236c d )m + (428a c d e + 428c d )m + 240a c d e +--R + +--R 2 3 +--R 240c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 2 4 2 2 2 4 4 2 4 2 2 2 4 3 +--R (- a e - 2a c d e - c d )m + (- 14a e - 28a c d e - 14c d )m +--R + +--R 2 4 2 2 2 4 2 +--R (- 71a e - 142a c d e - 71c d )m +--R + +--R 2 4 2 2 2 4 2 4 2 2 2 4 +--R (- 154a e - 308a c d e - 154c d )m - 120a e - 240a c d e - 120c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R e m + 15e m + 85e m + 225e m + 274e m + 120e +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1192 + +)clear all + +--S 1193 of 1726 +t0:=(d+e*x)^4*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 4 8 2 3 7 4 2 2 2 6 3 2 3 5 +--R c e x + 4c d e x + (2a c e + 6c d e )x + (8a c d e + 4c d e)x +--R + +--R 2 4 2 2 2 4 4 2 3 3 3 +--R (a e + 12a c d e + c d )x + (4a d e + 8a c d e)x +--R + +--R 2 2 2 4 2 2 3 2 4 +--R (6a d e + 2a c d )x + 4a d e x + a d +--R Type: Polynomial(Integer) +--E 1193 + +--S 1194 of 1726 +r0:=1/5*(c*d^2+a*e^2)^2*(d+e*x)^5/e^5-2/3*c*d*(c*d^2+a*e^2)*(d+e*x)^6/e^5+_ + 2/7*c*(3*c*d^2+a*e^2)*(d+e*x)^7/e^5-1/2*c^2*d*(d+e*x)^8/e^5+_ + 1/9*c^2*(d+e*x)^9/e^5 +--R +--R +--R (2) +--R 1 2 9 9 1 2 8 8 2 9 6 2 2 7 7 +--R - c e x + - c d e x + (- a c e + - c d e )x +--R 9 2 7 7 +--R + +--R 4 8 2 2 3 6 6 1 2 9 12 2 7 1 2 4 5 5 +--R (- a c d e + - c d e )x + (- a e + -- a c d e + - c d e )x +--R 3 3 5 5 5 +--R + +--R 2 8 3 6 4 2 2 7 2 4 5 3 2 3 6 2 2 4 5 +--R (a d e + 2a c d e )x + (2a d e + - a c d e )x + 2a d e x + a d e x +--R 3 +--R + +--R 1 2 5 4 2 7 2 1 2 9 +--R - a d e + --- a c d e + --- c d +--R 5 105 630 +--R / +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1194 + +--S 1195 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 4 9 1 2 3 8 2 4 6 2 2 2 7 4 3 2 2 3 6 +--R - c e x + - c d e x + (- a c e + - c d e )x + (- a c d e + - c d e)x +--R 9 2 7 7 3 3 +--R + +--R 1 2 4 12 2 2 1 2 4 5 2 3 3 4 +--R (- a e + -- a c d e + - c d )x + (a d e + 2a c d e)x +--R 5 5 5 +--R + +--R 2 2 2 2 4 3 2 3 2 2 4 +--R (2a d e + - a c d )x + 2a d e x + a d x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1195 + +--S 1196 of 1726 +m0:=a0-r0 +--R +--R +--R 1 2 5 4 2 7 2 1 2 9 +--R - - a d e - --- a c d e - --- c d +--R 5 105 630 +--R (4) ------------------------------------ +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1196 + +--S 1197 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1197 + +)clear all + +--S 1198 of 1726 +t0:=(d+e*x)^3*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 3 7 2 2 6 3 2 2 5 2 2 3 4 +--R c e x + 3c d e x + (2a c e + 3c d e)x + (6a c d e + c d )x +--R + +--R 2 3 2 3 2 2 3 2 2 2 2 3 +--R (a e + 6a c d e)x + (3a d e + 2a c d )x + 3a d e x + a d +--R Type: Polynomial(Integer) +--E 1198 + +--S 1199 of 1726 +r0:=1/4*(c*d^2+a*e^2)^2*(d+e*x)^4/e^5-4/5*c*d*(c*d^2+a*e^2)*(d+e*x)^5/e^5+_ + 1/3*c*(3*c*d^2+a*e^2)*(d+e*x)^6/e^5-4/7*c^2*d*(d+e*x)^7/e^5+_ + 1/8*c^2*(d+e*x)^8/e^5 +--R +--R +--R (2) +--R 1 2 8 8 3 2 7 7 1 8 1 2 2 6 6 +--R - c e x + - c d e x + (- a c e + - c d e )x +--R 8 7 3 2 +--R + +--R 6 7 1 2 3 5 5 1 2 8 3 2 6 4 +--R (- a c d e + - c d e )x + (- a e + - a c d e )x +--R 5 5 4 2 +--R + +--R 2 7 2 3 5 3 3 2 2 6 2 2 3 5 1 2 4 4 1 6 2 +--R (a d e + - a c d e )x + - a d e x + a d e x + - a d e + -- a c d e +--R 3 2 4 30 +--R + +--R 1 2 8 +--R --- c d +--R 280 +--R / +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1199 + +--S 1200 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 3 8 3 2 2 7 1 3 1 2 2 6 6 2 1 2 3 5 +--R - c e x + - c d e x + (- a c e + - c d e)x + (- a c d e + - c d )x +--R 8 7 3 2 5 5 +--R + +--R 1 2 3 3 2 4 2 2 2 3 3 3 2 2 2 2 3 +--R (- a e + - a c d e)x + (a d e + - a c d )x + - a d e x + a d x +--R 4 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1200 + +--S 1201 of 1726 +m0:=a0-r0 +--R +--R +--R 1 2 4 4 1 6 2 1 2 8 +--R - - a d e - -- a c d e - --- c d +--R 4 30 280 +--R (4) ----------------------------------- +--R 5 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1201 + +--S 1202 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1202 + +)clear all + +--S 1203 of 1726 +t0:=(d+e*x)^2*(a+c*x^2)^2 +--R +--R +--R (1) +--R 2 2 6 2 5 2 2 2 4 3 2 2 2 2 +--R c e x + 2c d e x + (2a c e + c d )x + 4a c d e x + (a e + 2a c d )x +--R + +--R 2 2 2 +--R 2a d e x + a d +--R Type: Polynomial(Integer) +--E 1203 + +--S 1204 of 1726 +r0:=a^2*d^2*x+a^2*d*e*x^2+1/3*a*(2*c*d^2+a*e^2)*x^3+a*c*d*e*x^4+_ + 1/5*c*(c*d^2+2*a*e^2)*x^5+1/3*c^2*d*e*x^6+1/7*c^2*e^2*x^7 +--R +--R +--R (2) +--R 1 2 2 7 1 2 6 2 2 1 2 2 5 4 +--R - c e x + - c d e x + (- a c e + - c d )x + a c d e x +--R 7 3 5 5 +--R + +--R 1 2 2 2 2 3 2 2 2 2 +--R (- a e + - a c d )x + a d e x + a d x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1204 + +--S 1205 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 2 7 1 2 6 2 2 1 2 2 5 4 +--R - c e x + - c d e x + (- a c e + - c d )x + a c d e x +--R 7 3 5 5 +--R + +--R 1 2 2 2 2 3 2 2 2 2 +--R (- a e + - a c d )x + a d e x + a d x +--R 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1205 + +--S 1206 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1206 + +--S 1207 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1207 + +)clear all + +--S 1208 of 1726 +t0:=(d+e*x)*(a+c*x^2)^2 +--R +--R +--R 2 5 2 4 3 2 2 2 +--R (1) c e x + c d x + 2a c e x + 2a c d x + a e x + a d +--R Type: Polynomial(Integer) +--E 1208 + +--S 1209 of 1726 +r0:=a^2*d*x+2/3*a*c*d*x^3+1/5*c^2*d*x^5+1/6*e*(a+c*x^2)^3/c +--R +--R +--R (2) +--R 1 3 6 1 3 5 1 2 4 2 2 3 1 2 2 2 1 3 +--R - c e x + - c d x + - a c e x + - a c d x + - a c e x + a c d x + - a e +--R 6 5 2 3 2 6 +--R ---------------------------------------------------------------------------- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1209 + +--S 1210 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 5 1 4 2 3 1 2 2 2 +--R (3) - c e x + - c d x + - a c e x + - a c d x + - a e x + a d x +--R 6 5 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1210 + +--S 1211 of 1726 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - a e +--R 6 +--R (4) - ----- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1211 + +--S 1212 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1212 + +)clear all + +--S 1213 of 1726 +t0:=(a+c*x^2)^2 +--R +--R +--R 2 4 2 2 +--R (1) c x + 2a c x + a +--R Type: Polynomial(Integer) +--E 1213 + +--S 1214 of 1726 +r0:=a^2*x+2/3*a*c*x^3+1/5*c^2*x^5 +--R +--R +--R 1 2 5 2 3 2 +--R (2) - c x + - a c x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1214 + +--S 1215 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 2 3 2 +--R (3) - c x + - a c x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1215 + +--S 1216 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1216 + +--S 1217 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1217 + +)clear all + +--S 1218 of 1726 +t0:=(a+c*x^2)^2/(d+e*x) +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1218 + +--S 1219 of 1726 +r0:=-c*d*(c*d^2+2*a*e^2)*x/e^4+1/2*c*(c*d^2+2*a*e^2)*x^2/e^3-_ + 1/3*c^2*d*x^3/e^2+1/4*c^2*x^4/e+(c*d^2+a*e^2)^2*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 4 4 2 3 3 +--R (12a e + 24a c d e + 12c d )log(e x + d) + 3c e x - 4c d e x +--R + +--R 4 2 2 2 2 3 2 3 +--R (12a c e + 6c d e )x + (- 24a c d e - 12c d e)x +--R / +--R 5 +--R 12e +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 4 4 2 3 3 +--R (12a e + 24a c d e + 12c d )log(e x + d) + 3c e x - 4c d e x +--R + +--R 4 2 2 2 2 3 2 3 +--R (12a c e + 6c d e )x + (- 24a c d e - 12c d e)x +--R / +--R 5 +--R 12e +--R Type: Union(Expression(Integer),...) +--E 1220 + +--S 1221 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1222 + +)clear all + +--S 1223 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^2 +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1223 + +--S 1224 of 1726 +r0:=c*(3*c*d^2+2*a*e^2)*x/e^4-c^2*d*x^2/e^3+1/3*c^2*x^3/e^2-_ + (c*d^2+a*e^2)^2/(e^5*(d+e*x))-4*c*d*(c*d^2+a*e^2)*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 3 2 3 2 2 2 4 2 4 4 +--R ((- 12a c d e - 12c d e)x - 12a c d e - 12c d )log(e x + d) + c e x +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 2 4 +--R - 2c d e x + (6a c e + 6c d e )x + (6a c d e + 9c d e)x - 3a e +--R + +--R 2 2 2 4 +--R - 6a c d e - 3c d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 4 2 4 4 +--R ((- 12a c d e - 12c d e)x - 12a c d e - 12c d )log(e x + d) + c e x +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 2 4 +--R - 2c d e x + (6a c e + 6c d e )x + (6a c d e + 9c d e)x - 3a e +--R + +--R 2 2 2 4 +--R - 6a c d e - 3c d +--R / +--R 6 5 +--R 3e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1225 + +--S 1226 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1227 + +)clear all + +--S 1228 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^3 +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1228 + +--S 1229 of 1726 +r0:=-3*c^2*d*x/e^4+1/2*c^2*x^2/e^3-1/2*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^2)+_ + 4*c*d*(c*d^2+a*e^2)/(e^5*(d+e*x))+2*c*(3*c*d^2+a*e^2)*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 4 2 2 2 2 3 2 3 2 2 2 4 +--R ((4a c e + 12c d e )x + (8a c d e + 24c d e)x + 4a c d e + 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 4 4 2 3 3 2 2 2 2 3 2 3 2 4 +--R c e x - 4c d e x - 11c d e x + (8a c d e + 2c d e)x - a e +--R + +--R 2 2 2 4 +--R 6a c d e + 7c d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 2 2 2 3 2 3 2 2 2 4 +--R ((4a c e + 12c d e )x + (8a c d e + 24c d e)x + 4a c d e + 12c d ) +--R * +--R log(e x + d) +--R + +--R 2 4 4 2 3 3 2 2 2 2 3 2 3 2 4 +--R c e x - 4c d e x - 11c d e x + (8a c d e + 2c d e)x - a e +--R + +--R 2 2 2 4 +--R 6a c d e + 7c d +--R / +--R 7 2 6 2 5 +--R 2e x + 4d e x + 2d e +--R Type: Union(Expression(Integer),...) +--E 1230 + +--S 1231 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1232 + +)clear all + +--S 1233 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^4 +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1233 + +--S 1234 of 1726 +r0:=c^2*x/e^4-1/3*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^3)+2*c*d*(c*d^2+a*e^2)/_ + (e^5*(d+e*x)^2)-2*c*(3*c*d^2+a*e^2)/(e^5*(d+e*x))-4*c^2*d*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 3 3 2 2 2 2 2 3 2 4 2 4 4 +--R (- 12c d e x - 36c d e x - 36c d e x - 12c d )log(e x + d) + 3c e x +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 2 4 +--R 9c d e x + (- 6a c e - 9c d e )x + (- 6a c d e - 27c d e)x - a e +--R + +--R 2 2 2 4 +--R - 2a c d e - 13c d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 2 2 3 2 4 2 4 4 +--R (- 12c d e x - 36c d e x - 36c d e x - 12c d )log(e x + d) + 3c e x +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 2 4 +--R 9c d e x + (- 6a c e - 9c d e )x + (- 6a c d e - 27c d e)x - a e +--R + +--R 2 2 2 4 +--R - 2a c d e - 13c d +--R / +--R 8 3 7 2 2 6 3 5 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1235 + +--S 1236 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^5 +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1238 + +--S 1239 of 1726 +r0:=-1/4*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^4)+4/3*c*d*(c*d^2+a*e^2)/_ + (e^5*(d+e*x)^3)-c*(3*c*d^2+a*e^2)/(e^5*(d+e*x)^2)+4*c^2*d/_ + (e^5*(d+e*x))+c^2*log(d+e*x)/e^5 +--R +--R +--R (2) +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R (12c e x + 48c d e x + 72c d e x + 48c d e x + 12c d )log(e x + d) +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 +--R 48c d e x + (- 12a c e + 108c d e )x + (- 8a c d e + 88c d e)x +--R + +--R 2 4 2 2 2 4 +--R - 3a e - 2a c d e + 25c d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R (12c e x + 48c d e x + 72c d e x + 48c d e x + 12c d )log(e x + d) +--R + +--R 2 3 3 4 2 2 2 2 3 2 3 +--R 48c d e x + (- 12a c e + 108c d e )x + (- 8a c d e + 88c d e)x +--R + +--R 2 4 2 2 2 4 +--R - 3a e - 2a c d e + 25c d +--R / +--R 9 4 8 3 2 7 2 3 6 4 5 +--R 12e x + 48d e x + 72d e x + 48d e x + 12d e +--R Type: Union(Expression(Integer),...) +--E 1240 + +--S 1241 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1242 + +)clear all + +--S 1243 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^6 +--R +--R +--R 2 4 2 2 +--R c x + 2a c x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1243 + +--S 1244 of 1726 +r0:=-1/5*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^5)+c*d*(c*d^2+a*e^2)/_ + (e^5*(d+e*x)^4)-2/3*c*(3*c*d^2+a*e^2)/(e^5*(d+e*x)^3)+_ + 2*c^2*d/(e^5*(d+e*x)^2)-c^2/(e^5*(d+e*x)) +--R +--R +--R (2) +--R 2 4 4 2 3 3 2 4 2 2 2 2 1 3 2 3 +--R - c e x - 2c d e x + (- - a c e - 2c d e )x + (- - a c d e - c d e)x +--R 3 3 +--R + +--R 1 2 4 1 2 2 1 2 4 +--R - - a e - -- a c d e - - c d +--R 5 15 5 +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1244 + +--S 1245 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 3 3 4 2 2 2 2 +--R - 15c e x - 30c d e x + (- 10a c e - 30c d e )x +--R + +--R 3 2 3 2 4 2 2 2 4 +--R (- 5a c d e - 15c d e)x - 3a e - a c d e - 3c d +--R / +--R 10 5 9 4 2 8 3 3 7 2 4 6 5 5 +--R 15e x + 75d e x + 150d e x + 150d e x + 75d e x + 15d e +--R Type: Union(Expression(Integer),...) +--E 1245 + +--S 1246 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1247 + +)clear all + +--S 1248 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^7 +--R +--R +--R (1) +--R 2 4 2 2 +--R c x + 2a c x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1248 + +--S 1249 of 1726 +r0:=-1/6*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^6)+4/5*c*d*(c*d^2+a*e^2)/_ + (e^5*(d+e*x)^5)-1/2*c*(3*c*d^2+a*e^2)/(e^5*(d+e*x)^4)+_ + 4/3*c^2*d/(e^5*(d+e*x)^3)-1/2*c^2/(e^5*(d+e*x)^2) +--R +--R +--R (2) +--R 1 2 4 4 2 2 3 3 1 4 1 2 2 2 2 +--R - - c e x - - c d e x + (- - a c e - - c d e )x +--R 2 3 2 2 +--R + +--R 1 3 1 2 3 1 2 4 1 2 2 1 2 4 +--R (- - a c d e - - c d e)x - - a e - -- a c d e - -- c d +--R 5 5 6 30 30 +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 6 5 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1249 + +--S 1250 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 3 3 4 2 2 2 2 +--R - 15c e x - 20c d e x + (- 15a c e - 15c d e )x +--R + +--R 3 2 3 2 4 2 2 2 4 +--R (- 6a c d e - 6c d e)x - 5a e - a c d e - c d +--R / +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 +--R 30e x + 180d e x + 450d e x + 600d e x + 450d e x + 180d e x +--R + +--R 6 5 +--R 30d e +--R Type: Union(Expression(Integer),...) +--E 1250 + +--S 1251 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1252 + +)clear all + +--S 1253 of 1726 +t0:=(a+c*x^2)^2/(d+e*x)^8 +--R +--R +--R (1) +--R 2 4 2 2 +--R c x + 2a c x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1253 + +--S 1254 of 1726 +r0:=-1/7*(c*d^2+a*e^2)^2/(e^5*(d+e*x)^7)+2/3*c*d*(c*d^2+a*e^2)/_ + (e^5*(d+e*x)^6)-2/5*c*(3*c*d^2+a*e^2)/(e^5*(d+e*x)^5)+_ + c^2*d/(e^5*(d+e*x)^4)-1/3*c^2/(e^5*(d+e*x)^3) +--R +--R +--R (2) +--R 1 2 4 4 1 2 3 3 2 4 1 2 2 2 2 +--R - - c e x - - c d e x + (- - a c e - - c d e )x +--R 3 3 5 5 +--R + +--R 2 3 1 2 3 1 2 4 2 2 2 1 2 4 +--R (- -- a c d e - -- c d e)x - - a e - --- a c d e - --- c d +--R 15 15 7 105 105 +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 5 7 2 6 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 5 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1254 + +--S 1255 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 3 3 4 2 2 2 2 +--R - 35c e x - 35c d e x + (- 42a c e - 21c d e )x +--R + +--R 3 2 3 2 4 2 2 2 4 +--R (- 14a c d e - 7c d e)x - 15a e - 2a c d e - c d +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105e x + 735d e x + 2205d e x + 3675d e x + 3675d e x +--R + +--R 5 7 2 6 6 7 5 +--R 2205d e x + 735d e x + 105d e +--R Type: Union(Expression(Integer),...) +--E 1255 + +--S 1256 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1257 + +)clear all + +--S 1258 of 1726 +t0:=(d+e*x)^m*(a+c*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 m +--R (1) (c x + 3a c x + 3a c x + a )(e x + d) +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1726 +r0:=(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^7*(1+m))-6*c*d*(c*d^2+a*e^2)^2*_ + (d+e*x)^(2+m)/(e^7*(2+m))+3*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)*_ + (d+e*x)^(3+m)/(e^7*(3+m))-4*c^2*d*(5*c*d^2+3*a*e^2)*_ + (d+e*x)^(4+m)/(e^7*(4+m))+3*c^2*(5*c*d^2+a*e^2)*(d+e*x)^(5+m)/_ + (e^7*(5+m))-6*c^3*d*(d+e*x)^(6+m)/(e^7*(6+m))+c^3*(d+e*x)^(7+m)/_ + (e^7*(7+m)) +--R +--R +--R (2) +--R 3 6 3 5 3 4 3 3 3 2 3 3 +--R (c m + 21c m + 175c m + 735c m + 1624c m + 1764c m + 720c ) +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 6 3 5 3 4 3 3 3 2 +--R - 6c d m - 132c d m - 1140c d m - 4920c d m - 11094c d m +--R + +--R 3 3 +--R - 12228c d m - 5040c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 2 6 2 2 3 2 5 +--R (3a c e + 15c d )m + (69a c e + 345c d )m +--R + +--R 2 2 3 2 4 2 2 3 2 3 +--R (621a c e + 3105c d )m + (2775a c e + 13875c d )m +--R + +--R 2 2 3 2 2 2 2 3 2 2 2 +--R (6432a c e + 32160c d )m + (7236a c e + 36180c d )m + 3024a c e +--R + +--R 3 2 +--R 15120c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 3 3 6 2 2 3 3 5 +--R (- 12a c d e - 20c d )m + (- 288a c d e - 480c d )m +--R + +--R 2 2 3 3 4 2 2 3 3 3 +--R (- 2712a c d e - 4520c d )m + (- 12672a c d e - 21120c d )m +--R + +--R 2 2 3 3 2 2 2 3 3 +--R (- 30540a c d e - 50900c d )m + (- 35424a c d e - 59040c d )m +--R + +--R 2 2 3 3 +--R - 15120a c d e - 25200c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 4 2 2 2 3 4 6 +--R (3a c e + 18a c d e + 15c d )m +--R + +--R 2 4 2 2 2 3 4 5 +--R (75a c e + 450a c d e + 375c d )m +--R + +--R 2 4 2 2 2 3 4 4 +--R (741a c e + 4446a c d e + 3705c d )m +--R + +--R 2 4 2 2 2 3 4 3 +--R (3657a c e + 21942a c d e + 18285c d )m +--R + +--R 2 4 2 2 2 3 4 2 +--R (9336a c e + 56016a c d e + 46680c d )m +--R + +--R 2 4 2 2 2 3 4 2 4 +--R (11388a c e + 68328a c d e + 56940c d )m + 5040a c e +--R + +--R 2 2 2 3 4 +--R 30240a c d e + 25200c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 2 3 5 6 +--R (- 6a c d e - 12a c d e - 6c d )m +--R + +--R 2 4 2 3 2 3 5 5 +--R (- 156a c d e - 312a c d e - 156c d )m +--R + +--R 2 4 2 3 2 3 5 4 +--R (- 1620a c d e - 3240a c d e - 1620c d )m +--R + +--R 2 4 2 3 2 3 5 3 +--R (- 8520a c d e - 17040a c d e - 8520c d )m +--R + +--R 2 4 2 3 2 3 5 2 +--R (- 23574a c d e - 47148a c d e - 23574c d )m +--R + +--R 2 4 2 3 2 3 5 2 4 +--R (- 31644a c d e - 63288a c d e - 31644c d )m - 15120a c d e +--R + +--R 2 3 2 3 5 +--R - 30240a c d e - 15120c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 6 2 2 4 2 4 2 3 6 6 +--R (a e + 3a c d e + 3a c d e + c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 5 +--R (27a e + 81a c d e + 81a c d e + 27c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 4 +--R (295a e + 885a c d e + 885a c d e + 295c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 3 +--R (1665a e + 4995a c d e + 4995a c d e + 1665c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 2 +--R (5104a e + 15312a c d e + 15312a c d e + 5104c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 3 6 +--R (8028a e + 24084a c d e + 24084a c d e + 8028c d )m + 5040a e +--R + +--R 2 2 4 2 4 2 3 6 +--R 15120a c d e + 15120a c d e + 5040c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 6 3 7 5 3 7 4 3 7 3 3 7 2 3 7 +--R c e m + 21c e m + 175c e m + 735c e m + 1624c e m + 1764c e m +--R + +--R 3 7 +--R 720c e +--R * +--R 7 +--R x +--R + +--R 3 6 6 3 6 5 3 6 4 3 6 3 3 6 2 +--R c d e m + 15c d e m + 85c d e m + 225c d e m + 274c d e m +--R + +--R 3 6 +--R 120c d e m +--R * +--R 6 +--R x +--R + +--R 2 7 6 2 7 3 2 5 5 2 7 3 2 5 4 +--R 3a c e m + (69a c e - 6c d e )m + (621a c e - 60c d e )m +--R + +--R 2 7 3 2 5 3 2 7 3 2 5 2 +--R (2775a c e - 210c d e )m + (6432a c e - 300c d e )m +--R + +--R 2 7 3 2 5 2 7 +--R (7236a c e - 144c d e )m + 3024a c e +--R * +--R 5 +--R x +--R + +--R 2 6 6 2 6 5 2 6 3 3 4 4 +--R 3a c d e m + 57a c d e m + (393a c d e + 30c d e )m +--R + +--R 2 6 3 3 4 3 2 6 3 3 4 2 +--R (1203a c d e + 180c d e )m + (1620a c d e + 330c d e )m +--R + +--R 2 6 3 3 4 +--R (756a c d e + 180c d e )m +--R * +--R 4 +--R x +--R + +--R 2 7 6 2 7 2 2 5 5 2 7 2 2 5 4 +--R 3a c e m + (75a c e - 12a c d e )m + (741a c e - 192a c d e )m +--R + +--R 2 7 2 2 5 3 4 3 3 +--R (3657a c e - 996a c d e - 120c d e )m +--R + +--R 2 7 2 2 5 3 4 3 2 +--R (9336a c e - 1824a c d e - 360c d e )m +--R + +--R 2 7 2 2 5 3 4 3 2 7 +--R (11388a c e - 1008a c d e - 240c d e )m + 5040a c e +--R * +--R 3 +--R x +--R + +--R 2 6 6 2 6 5 2 6 2 3 4 4 +--R 3a c d e m + 69a c d e m + (603a c d e + 36a c d e )m +--R + +--R 2 6 2 3 4 3 +--R (2451a c d e + 504a c d e )m +--R + +--R 2 6 2 3 4 3 5 2 2 +--R (4434a c d e + 1980a c d e + 360c d e )m +--R + +--R 2 6 2 3 4 3 5 2 +--R (2520a c d e + 1512a c d e + 360c d e )m +--R * +--R 2 +--R x +--R + +--R 3 7 6 3 7 2 2 5 5 3 7 2 2 5 4 +--R a e m + (27a e - 6a c d e )m + (295a e - 132a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 3 +--R (1665a e - 1074a c d e - 72a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 2 +--R (5104a e - 3828a c d e - 936a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 3 6 3 7 +--R (8028a e - 5040a c d e - 3024a c d e - 720c d e)m + 5040a e +--R * +--R x +--R + +--R 3 6 6 3 6 5 3 6 2 3 4 4 +--R a d e m + 27a d e m + (295a d e + 6a c d e )m +--R + +--R 3 6 2 3 4 3 +--R (1665a d e + 132a c d e )m +--R + +--R 3 6 2 3 4 2 5 2 2 +--R (5104a d e + 1074a c d e + 72a c d e )m +--R + +--R 3 6 2 3 4 2 5 2 3 6 2 3 4 +--R (8028a d e + 3828a c d e + 936a c d e )m + 5040a d e + 5040a c d e +--R + +--R 2 5 2 3 7 +--R 3024a c d e + 720c d +--R * +--R m log(e x + d) +--R %e +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Union(Expression(Integer),...) +--E 1260 + +--S 1261 of 1726 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 6 3 7 5 3 7 4 3 7 3 3 7 2 +--R c e m + 21c e m + 175c e m + 735c e m + 1624c e m +--R + +--R 3 7 3 7 +--R 1764c e m + 720c e +--R * +--R 7 +--R x +--R + +--R 3 6 6 3 6 5 3 6 4 3 6 3 3 6 2 +--R c d e m + 15c d e m + 85c d e m + 225c d e m + 274c d e m +--R + +--R 3 6 +--R 120c d e m +--R * +--R 6 +--R x +--R + +--R 2 7 6 2 7 3 2 5 5 2 7 3 2 5 4 +--R 3a c e m + (69a c e - 6c d e )m + (621a c e - 60c d e )m +--R + +--R 2 7 3 2 5 3 2 7 3 2 5 2 +--R (2775a c e - 210c d e )m + (6432a c e - 300c d e )m +--R + +--R 2 7 3 2 5 2 7 +--R (7236a c e - 144c d e )m + 3024a c e +--R * +--R 5 +--R x +--R + +--R 2 6 6 2 6 5 2 6 3 3 4 4 +--R 3a c d e m + 57a c d e m + (393a c d e + 30c d e )m +--R + +--R 2 6 3 3 4 3 2 6 3 3 4 2 +--R (1203a c d e + 180c d e )m + (1620a c d e + 330c d e )m +--R + +--R 2 6 3 3 4 +--R (756a c d e + 180c d e )m +--R * +--R 4 +--R x +--R + +--R 2 7 6 2 7 2 2 5 5 +--R 3a c e m + (75a c e - 12a c d e )m +--R + +--R 2 7 2 2 5 4 +--R (741a c e - 192a c d e )m +--R + +--R 2 7 2 2 5 3 4 3 3 +--R (3657a c e - 996a c d e - 120c d e )m +--R + +--R 2 7 2 2 5 3 4 3 2 +--R (9336a c e - 1824a c d e - 360c d e )m +--R + +--R 2 7 2 2 5 3 4 3 2 7 +--R (11388a c e - 1008a c d e - 240c d e )m + 5040a c e +--R * +--R 3 +--R x +--R + +--R 2 6 6 2 6 5 2 6 2 3 4 4 +--R 3a c d e m + 69a c d e m + (603a c d e + 36a c d e )m +--R + +--R 2 6 2 3 4 3 +--R (2451a c d e + 504a c d e )m +--R + +--R 2 6 2 3 4 3 5 2 2 +--R (4434a c d e + 1980a c d e + 360c d e )m +--R + +--R 2 6 2 3 4 3 5 2 +--R (2520a c d e + 1512a c d e + 360c d e )m +--R * +--R 2 +--R x +--R + +--R 3 7 6 3 7 2 2 5 5 3 7 2 2 5 4 +--R a e m + (27a e - 6a c d e )m + (295a e - 132a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 3 +--R (1665a e - 1074a c d e - 72a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 2 +--R (5104a e - 3828a c d e - 936a c d e )m +--R + +--R 3 7 2 2 5 2 4 3 3 6 3 7 +--R (8028a e - 5040a c d e - 3024a c d e - 720c d e)m + 5040a e +--R * +--R x +--R + +--R 3 6 6 3 6 5 3 6 2 3 4 4 +--R a d e m + 27a d e m + (295a d e + 6a c d e )m +--R + +--R 3 6 2 3 4 3 +--R (1665a d e + 132a c d e )m +--R + +--R 3 6 2 3 4 2 5 2 2 +--R (5104a d e + 1074a c d e + 72a c d e )m +--R + +--R 3 6 2 3 4 2 5 2 3 6 +--R (8028a d e + 3828a c d e + 936a c d e )m + 5040a d e +--R + +--R 2 3 4 2 5 2 3 7 +--R 5040a c d e + 3024a c d e + 720c d +--R * +--R m log(e x + d) +--R %e +--R + +--R 3 6 3 5 3 4 3 3 3 2 3 3 +--R (- c m - 21c m - 175c m - 735c m - 1624c m - 1764c m - 720c ) +--R * +--R m + 7 +--R (e x + d) +--R + +--R 3 6 3 5 3 4 3 3 3 2 +--R 6c d m + 132c d m + 1140c d m + 4920c d m + 11094c d m +--R + +--R 3 3 +--R 12228c d m + 5040c d +--R * +--R m + 6 +--R (e x + d) +--R + +--R 2 2 3 2 6 2 2 3 2 5 +--R (- 3a c e - 15c d )m + (- 69a c e - 345c d )m +--R + +--R 2 2 3 2 4 2 2 3 2 3 +--R (- 621a c e - 3105c d )m + (- 2775a c e - 13875c d )m +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 6432a c e - 32160c d )m + (- 7236a c e - 36180c d )m +--R + +--R 2 2 3 2 +--R - 3024a c e - 15120c d +--R * +--R m + 5 +--R (e x + d) +--R + +--R 2 2 3 3 6 2 2 3 3 5 +--R (12a c d e + 20c d )m + (288a c d e + 480c d )m +--R + +--R 2 2 3 3 4 2 2 3 3 3 +--R (2712a c d e + 4520c d )m + (12672a c d e + 21120c d )m +--R + +--R 2 2 3 3 2 2 2 3 3 +--R (30540a c d e + 50900c d )m + (35424a c d e + 59040c d )m +--R + +--R 2 2 3 3 +--R 15120a c d e + 25200c d +--R * +--R m + 4 +--R (e x + d) +--R + +--R 2 4 2 2 2 3 4 6 +--R (- 3a c e - 18a c d e - 15c d )m +--R + +--R 2 4 2 2 2 3 4 5 +--R (- 75a c e - 450a c d e - 375c d )m +--R + +--R 2 4 2 2 2 3 4 4 +--R (- 741a c e - 4446a c d e - 3705c d )m +--R + +--R 2 4 2 2 2 3 4 3 +--R (- 3657a c e - 21942a c d e - 18285c d )m +--R + +--R 2 4 2 2 2 3 4 2 +--R (- 9336a c e - 56016a c d e - 46680c d )m +--R + +--R 2 4 2 2 2 3 4 2 4 +--R (- 11388a c e - 68328a c d e - 56940c d )m - 5040a c e +--R + +--R 2 2 2 3 4 +--R - 30240a c d e - 25200c d +--R * +--R m + 3 +--R (e x + d) +--R + +--R 2 4 2 3 2 3 5 6 +--R (6a c d e + 12a c d e + 6c d )m +--R + +--R 2 4 2 3 2 3 5 5 +--R (156a c d e + 312a c d e + 156c d )m +--R + +--R 2 4 2 3 2 3 5 4 +--R (1620a c d e + 3240a c d e + 1620c d )m +--R + +--R 2 4 2 3 2 3 5 3 +--R (8520a c d e + 17040a c d e + 8520c d )m +--R + +--R 2 4 2 3 2 3 5 2 +--R (23574a c d e + 47148a c d e + 23574c d )m +--R + +--R 2 4 2 3 2 3 5 2 4 +--R (31644a c d e + 63288a c d e + 31644c d )m + 15120a c d e +--R + +--R 2 3 2 3 5 +--R 30240a c d e + 15120c d +--R * +--R m + 2 +--R (e x + d) +--R + +--R 3 6 2 2 4 2 4 2 3 6 6 +--R (- a e - 3a c d e - 3a c d e - c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 5 +--R (- 27a e - 81a c d e - 81a c d e - 27c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 4 +--R (- 295a e - 885a c d e - 885a c d e - 295c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 3 +--R (- 1665a e - 4995a c d e - 4995a c d e - 1665c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 2 +--R (- 5104a e - 15312a c d e - 15312a c d e - 5104c d )m +--R + +--R 3 6 2 2 4 2 4 2 3 6 3 6 +--R (- 8028a e - 24084a c d e - 24084a c d e - 8028c d )m - 5040a e +--R + +--R 2 2 4 2 4 2 3 6 +--R - 15120a c d e - 15120a c d e - 5040c d +--R * +--R m + 1 +--R (e x + d) +--R / +--R 7 7 7 6 7 5 7 4 7 3 7 2 7 +--R e m + 28e m + 322e m + 1960e m + 6769e m + 13132e m + 13068e m +--R + +--R 7 +--R 5040e +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1726 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1262 + +)clear all + +--S 1263 of 1726 +t0:=(d+e*x)^4*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 4 10 3 3 9 2 4 3 2 2 8 2 3 3 3 7 +--R c e x + 4c d e x + (3a c e + 6c d e )x + (12a c d e + 4c d e)x +--R + +--R 2 4 2 2 2 3 4 6 2 3 2 3 5 +--R (3a c e + 18a c d e + c d )x + (12a c d e + 12a c d e)x +--R + +--R 3 4 2 2 2 2 4 4 3 3 2 3 3 +--R (a e + 18a c d e + 3a c d )x + (4a d e + 12a c d e)x +--R + +--R 3 2 2 2 4 2 3 3 3 4 +--R (6a d e + 3a c d )x + 4a d e x + a d +--R Type: Polynomial(Integer) +--E 1263 + +--S 1264 of 1726 +r0:=1/5*(c*d^2+a*e^2)^3*(d+e*x)^5/e^7-c*d*(c*d^2+a*e^2)^2*(d+e*x)^6/e^7+_ + 3/7*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)*(d+e*x)^7/e^7-_ + 1/2*c^2*d*(5*c*d^2+3*a*e^2)*(d+e*x)^8/e^7+1/3*c^2*(5*c*d^2+a*e^2)*_ + (d+e*x)^9/e^7-3/5*c^3*d*(d+e*x)^10/e^7+1/11*c^3*(d+e*x)^11/e^7 +--R +--R +--R (2) +--R 1 3 11 11 2 3 10 10 1 2 11 2 3 2 9 9 +--R -- c e x + - c d e x + (- a c e + - c d e )x +--R 11 5 3 3 +--R + +--R 3 2 10 1 3 3 8 8 3 2 11 18 2 2 9 1 3 4 7 7 +--R (- a c d e + - c d e )x + (- a c e + -- a c d e + - c d e )x +--R 2 2 7 7 7 +--R + +--R 2 10 2 3 8 6 1 3 11 18 2 2 9 3 2 4 7 5 +--R (2a c d e + 2a c d e )x + (- a e + -- a c d e + - a c d e )x +--R 5 5 5 +--R + +--R 3 10 2 3 8 4 3 2 9 2 4 7 3 3 3 8 2 3 4 7 +--R (a d e + 3a c d e )x + (2a d e + a c d e )x + 2a d e x + a d e x +--R + +--R 1 3 5 6 1 2 7 4 1 2 9 2 1 3 11 +--R - a d e + -- a c d e + --- a c d e + ---- c d +--R 5 35 210 2310 +--R / +--R 7 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1264 + +--S 1265 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 4 11 2 3 3 10 1 2 4 2 3 2 2 9 +--R -- c e x + - c d e x + (- a c e + - c d e )x +--R 11 5 3 3 +--R + +--R 3 2 3 1 3 3 8 3 2 4 18 2 2 2 1 3 4 7 +--R (- a c d e + - c d e)x + (- a c e + -- a c d e + - c d )x +--R 2 2 7 7 7 +--R + +--R 2 3 2 3 6 1 3 4 18 2 2 2 3 2 4 5 +--R (2a c d e + 2a c d e)x + (- a e + -- a c d e + - a c d )x +--R 5 5 5 +--R + +--R 3 3 2 3 4 3 2 2 2 4 3 3 3 2 3 4 +--R (a d e + 3a c d e)x + (2a d e + a c d )x + 2a d e x + a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1265 + +--S 1266 of 1726 +m0:=a0-r0 +--R +--R +--R 1 3 5 6 1 2 7 4 1 2 9 2 1 3 11 +--R - - a d e - -- a c d e - --- a c d e - ---- c d +--R 5 35 210 2310 +--R (4) ---------------------------------------------------- +--R 7 +--R e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1266 + +--S 1267 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1267 + +)clear all + +--S 1268 of 1726 +t0:=(d+e*x)^3*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 3 9 3 2 8 2 3 3 2 7 2 2 3 3 6 +--R c e x + 3c d e x + (3a c e + 3c d e)x + (9a c d e + c d )x +--R + +--R 2 3 2 2 5 2 2 2 3 4 3 3 2 2 3 +--R (3a c e + 9a c d e)x + (9a c d e + 3a c d )x + (a e + 9a c d e)x +--R + +--R 3 2 2 3 2 3 2 3 3 +--R (3a d e + 3a c d )x + 3a d e x + a d +--R Type: Polynomial(Integer) +--E 1268 + +--S 1269 of 1726 +r0:=a^3*d^3*x+3/2*a^3*d^2*e*x^2+a^2*d*(c*d^2+a*e^2)*x^3+1/4*a^2*e*_ + (9*c*d^2+a*e^2)*x^4+3/5*a*c*d*(c*d^2+3*a*e^2)*x^5+1/2*a*c*e*_ + (3*c*d^2+a*e^2)*x^6+1/7*c^2*d*(c*d^2+9*a*e^2)*x^7+3/8*c^2*e*_ + (c*d^2+a*e^2)*x^8+1/3*c^3*d*e^2*x^9+1/10*c^3*e^3*x^10 +--R +--R +--R (2) +--R 1 3 3 10 1 3 2 9 3 2 3 3 3 2 8 9 2 2 1 3 3 7 +--R -- c e x + - c d e x + (- a c e + - c d e)x + (- a c d e + - c d )x +--R 10 3 8 8 7 7 +--R + +--R 1 2 3 3 2 2 6 9 2 2 3 2 3 5 +--R (- a c e + - a c d e)x + (- a c d e + - a c d )x +--R 2 2 5 5 +--R + +--R 1 3 3 9 2 2 4 3 2 2 3 3 3 3 2 2 3 3 +--R (- a e + - a c d e)x + (a d e + a c d )x + - a d e x + a d x +--R 4 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1269 + +--S 1270 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 3 10 1 3 2 9 3 2 3 3 3 2 8 9 2 2 1 3 3 7 +--R -- c e x + - c d e x + (- a c e + - c d e)x + (- a c d e + - c d )x +--R 10 3 8 8 7 7 +--R + +--R 1 2 3 3 2 2 6 9 2 2 3 2 3 5 +--R (- a c e + - a c d e)x + (- a c d e + - a c d )x +--R 2 2 5 5 +--R + +--R 1 3 3 9 2 2 4 3 2 2 3 3 3 3 2 2 3 3 +--R (- a e + - a c d e)x + (a d e + a c d )x + - a d e x + a d x +--R 4 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1270 + +--S 1271 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1271 + +--S 1272 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1272 + +)clear all + +--S 1273 of 1726 +t0:=(d+e*x)^2*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 2 8 3 7 2 2 3 2 6 2 5 +--R c e x + 2c d e x + (3a c e + c d )x + 6a c d e x +--R + +--R 2 2 2 2 4 2 3 3 2 2 2 2 3 3 2 +--R (3a c e + 3a c d )x + 6a c d e x + (a e + 3a c d )x + 2a d e x + a d +--R Type: Polynomial(Integer) +--E 1273 + +--S 1274 of 1726 +r0:=a^3*d^2*x+a^3*d*e*x^2+1/3*a^2*(3*c*d^2+a*e^2)*x^3+3/2*a^2*c*d*e*x^4+_ + 3/5*a*c*(c*d^2+a*e^2)*x^5+a*c^2*d*e*x^6+1/7*c^2*(c*d^2+3*a*e^2)*x^7+_ + 1/4*c^3*d*e*x^8+1/9*c^3*e^2*x^9 +--R +--R +--R (2) +--R 1 3 2 9 1 3 8 3 2 2 1 3 2 7 2 6 +--R - c e x + - c d e x + (- a c e + - c d )x + a c d e x +--R 9 4 7 7 +--R + +--R 3 2 2 3 2 2 5 3 2 4 1 3 2 2 2 3 3 2 +--R (- a c e + - a c d )x + - a c d e x + (- a e + a c d )x + a d e x +--R 5 5 2 3 +--R + +--R 3 2 +--R a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1274 + +--S 1275 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 2 9 1 3 8 3 2 2 1 3 2 7 2 6 +--R - c e x + - c d e x + (- a c e + - c d )x + a c d e x +--R 9 4 7 7 +--R + +--R 3 2 2 3 2 2 5 3 2 4 1 3 2 2 2 3 3 2 +--R (- a c e + - a c d )x + - a c d e x + (- a e + a c d )x + a d e x +--R 5 5 2 3 +--R + +--R 3 2 +--R a d x +--R Type: Polynomial(Fraction(Integer)) +--E 1275 + +--S 1276 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1276 + +--S 1277 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1277 + +)clear all + +--S 1278 of 1726 +t0:=(d+e*x)*(a+c*x^2)^3 +--R +--R +--R (1) +--R 3 7 3 6 2 5 2 4 2 3 2 2 3 3 +--R c e x + c d x + 3a c e x + 3a c d x + 3a c e x + 3a c d x + a e x + a d +--R Type: Polynomial(Integer) +--E 1278 + +--S 1279 of 1726 +r0:=a^3*d*x+a^2*c*d*x^3+3/5*a*c^2*d*x^5+1/7*c^3*d*x^7+1/8*e*(a+c*x^2)^4/c +--R +--R +--R (2) +--R 1 4 8 1 4 7 1 3 6 3 3 5 3 2 2 4 2 2 3 +--R - c e x + - c d x + - a c e x + - a c d x + - a c e x + a c d x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 1 4 +--R - a c e x + a c d x + - a e +--R 2 8 +--R / +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1279 + +--S 1280 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 7 1 2 6 3 2 5 3 2 4 2 3 +--R - c e x + - c d x + - a c e x + - a c d x + - a c e x + a c d x +--R 8 7 2 5 4 +--R + +--R 1 3 2 3 +--R - a e x + a d x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1280 + +--S 1281 of 1726 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - a e +--R 8 +--R (4) - ----- +--R c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1281 + +--S 1282 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1282 + +)clear all + +--S 1283 of 1726 +t0:=(a+c*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R (1) c x + 3a c x + 3a c x + a +--R Type: Polynomial(Integer) +--E 1283 + +--S 1284 of 1726 +r0:=a^3*x+a^2*c*x^3+3/5*a*c^2*x^5+1/7*c^3*x^7 +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (2) - c x + - a c x + a c x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1284 + +--S 1285 of 1726 +a0:=integrate(t0,x) +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (3) - c x + - a c x + a c x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1285 + +--S 1286 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1286 + +--S 1287 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1287 + +)clear all + +--S 1288 of 1726 +t0:=(a+c*x^2)^3/(d+e*x) +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) ----------------------------- +--R e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1288 + +--S 1289 of 1726 +r0:=-c*d*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x/e^6+1/2*c*(c^2*d^4+_ + 3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^5-1/3*c^2*d*(c*d^2+3*a*e^2)*x^3/e^4+_ + 1/4*c^2*(c*d^2+3*a*e^2)*x^4/e^3-1/5*c^3*d*x^5/e^2+1/6*c^3*x^6/e+_ + (c*d^2+a*e^2)^3*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 2 2 4 2 4 2 3 6 3 6 6 +--R (60a e + 180a c d e + 180a c d e + 60c d )log(e x + d) + 10c e x +--R + +--R 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R - 12c d e x + (45a c e + 15c d e )x + (- 60a c d e - 20c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (90a c e + 90a c d e + 30c d e )x +--R + +--R 2 5 2 3 3 3 5 +--R (- 180a c d e - 180a c d e - 60c d e)x +--R / +--R 7 +--R 60e +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 2 4 2 4 2 3 6 3 6 6 +--R (60a e + 180a c d e + 180a c d e + 60c d )log(e x + d) + 10c e x +--R + +--R 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R - 12c d e x + (45a c e + 15c d e )x + (- 60a c d e - 20c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (90a c e + 90a c d e + 30c d e )x +--R + +--R 2 5 2 3 3 3 5 +--R (- 180a c d e - 180a c d e - 60c d e)x +--R / +--R 7 +--R 60e +--R Type: Union(Expression(Integer),...) +--E 1290 + +--S 1291 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1292 + +)clear all + +--S 1293 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) ----------------------------- +--R 2 2 2 +--R e x + 2d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1293 + +--S 1294 of 1726 +r0:=c*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4)*x/e^6-c^2*d*(2*c*d^2+3*a*e^2)*_ + x^2/e^5+c^2*(c*d^2+a*e^2)*x^3/e^4-1/2*c^3*d*x^4/e^3+1/5*c^3*_ + x^5/e^2-(c*d^2+a*e^2)^3/(e^7*(d+e*x))-6*c*d*(c*d^2+a*e^2)^2*_ + log(d+e*x)/e^7 +--R +--R +--R (2) +--R 2 5 2 3 3 3 5 2 2 4 2 4 2 +--R (- 60a c d e - 120a c d e - 60c d e)x - 60a c d e - 120a c d e +--R + +--R 3 6 +--R - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R 2c e x - 3c d e x + (10a c e + 5c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 20a c d e - 10c d e )x + (30a c e + 60a c d e + 30c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (30a c d e + 90a c d e + 50c d e)x - 10a e - 30a c d e - 30a c d e +--R + +--R 3 6 +--R - 10c d +--R / +--R 8 7 +--R 10e x + 10d e +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 3 3 3 5 2 2 4 2 4 2 +--R (- 60a c d e - 120a c d e - 60c d e)x - 60a c d e - 120a c d e +--R + +--R 3 6 +--R - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R 2c e x - 3c d e x + (10a c e + 5c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 20a c d e - 10c d e )x + (30a c e + 60a c d e + 30c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (30a c d e + 90a c d e + 50c d e)x - 10a e - 30a c d e - 30a c d e +--R + +--R 3 6 +--R - 10c d +--R / +--R 8 7 +--R 10e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 1295 + +--S 1296 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1297 + +)clear all + +--S 1298 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) ----------------------------- +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1298 + +--S 1299 of 1726 +r0:=-c^2*d*(10*c*d^2+9*a*e^2)*x/e^6+3/2*c^2*(2*c*d^2+a*e^2)*x^2/e^5-_ + c^3*d*x^3/e^4+1/4*c^3*x^4/e^3-1/2*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^2)+_ + 6*c*d*(c*d^2+a*e^2)^2/(e^7*(d+e*x))+3*c*(c*d^2+a*e^2)*_ + (5*c*d^2+a*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 2 6 2 2 4 3 4 2 2 +--R (12a c e + 72a c d e + 60c d e )x +--R + +--R 2 5 2 3 3 3 5 2 2 4 2 4 2 +--R (24a c d e + 144a c d e + 120c d e)x + 12a c d e + 72a c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R c e x - 2c d e x + (6a c e + 5c d e )x + (- 24a c d e - 20c d e )x +--R + +--R 2 2 4 3 4 2 2 2 5 2 3 3 3 5 +--R (- 66a c d e - 68c d e )x + (24a c d e + 12a c d e - 16c d e)x +--R + +--R 3 6 2 2 4 2 4 2 3 6 +--R - 2a e + 18a c d e + 42a c d e + 22c d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 2 2 4 3 4 2 2 +--R (12a c e + 72a c d e + 60c d e )x +--R + +--R 2 5 2 3 3 3 5 2 2 4 2 4 2 +--R (24a c d e + 144a c d e + 120c d e)x + 12a c d e + 72a c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R c e x - 2c d e x + (6a c e + 5c d e )x + (- 24a c d e - 20c d e )x +--R + +--R 2 2 4 3 4 2 2 2 5 2 3 3 3 5 +--R (- 66a c d e - 68c d e )x + (24a c d e + 12a c d e - 16c d e)x +--R + +--R 3 6 2 2 4 2 4 2 3 6 +--R - 2a e + 18a c d e + 42a c d e + 22c d +--R / +--R 9 2 8 2 7 +--R 4e x + 8d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 1300 + +--S 1301 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1302 + +)clear all + +--S 1303 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R e x + 4d e x + 6d e x + 4d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1303 + +--S 1304 of 1726 +r0:=c^2*(10*c*d^2+3*a*e^2)*x/e^6-2*c^3*d*x^2/e^5+1/3*c^3*x^3/e^4-_ + 1/3*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^3)+3*c*d*(c*d^2+a*e^2)^2/(e^7*_ + (d+e*x)^2)-3*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/(e^7*(d+e*x))-_ + 4*c^2*d*(5*c*d^2+3*a*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 2 5 3 3 3 3 2 2 4 3 4 2 2 +--R (- 36a c d e - 60c d e )x + (- 108a c d e - 180c d e )x +--R + +--R 2 3 3 3 5 2 4 2 3 6 +--R (- 108a c d e - 180c d e)x - 36a c d e - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R c e x - 3c d e x + (9a c e + 15c d e )x + (27a c d e + 73c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (- 9a c e - 27a c d e + 39c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 9a c d e - 81a c d e - 51c d e)x - a e - 3a c d e - 39a c d e +--R + +--R 3 6 +--R - 37c d +--R / +--R 10 3 9 2 2 8 3 7 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 3 3 3 2 2 4 3 4 2 2 +--R (- 36a c d e - 60c d e )x + (- 108a c d e - 180c d e )x +--R + +--R 2 3 3 3 5 2 4 2 3 6 +--R (- 108a c d e - 180c d e)x - 36a c d e - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R c e x - 3c d e x + (9a c e + 15c d e )x + (27a c d e + 73c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (- 9a c e - 27a c d e + 39c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 9a c d e - 81a c d e - 51c d e)x - a e - 3a c d e - 39a c d e +--R + +--R 3 6 +--R - 37c d +--R / +--R 10 3 9 2 2 8 3 7 +--R 3e x + 9d e x + 9d e x + 3d e +--R Type: Union(Expression(Integer),...) +--E 1305 + +--S 1306 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1307 + +)clear all + +--S 1308 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R e x + 5d e x + 10d e x + 10d e x + 5d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1308 + +--S 1309 of 1726 +r0:=-5*c^3*d*x/e^6+1/2*c^3*x^2/e^5-1/4*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^4)+_ + 2*c*d*(c*d^2+a*e^2)^2/(e^7*(d+e*x)^3)-3/2*c*(c*d^2+a*e^2)*_ + (5*c*d^2+a*e^2)/(e^7*(d+e*x)^2)+4*c^2*d*(5*c*d^2+3*a*e^2)/_ + (e^7*(d+e*x))+3*c^2*(5*c*d^2+a*e^2)*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 2 6 3 2 4 4 2 5 3 3 3 3 +--R (12a c e + 60c d e )x + (48a c d e + 240c d e )x +--R + +--R 2 2 4 3 4 2 2 2 3 3 3 5 2 4 2 +--R (72a c d e + 360c d e )x + (48a c d e + 240c d e)x + 12a c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 3 2 4 4 2 5 3 3 3 3 +--R 2c e x - 12c d e x - 68c d e x + (48a c d e - 32c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (- 6a c e + 108a c d e + 132c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 4a c d e + 88a c d e + 168c d e)x - a e - a c d e + 25a c d e +--R + +--R 3 6 +--R 57c d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 2 4 4 2 5 3 3 3 3 +--R (12a c e + 60c d e )x + (48a c d e + 240c d e )x +--R + +--R 2 2 4 3 4 2 2 2 3 3 3 5 2 4 2 +--R (72a c d e + 360c d e )x + (48a c d e + 240c d e)x + 12a c d e +--R + +--R 3 6 +--R 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 3 2 4 4 2 5 3 3 3 3 +--R 2c e x - 12c d e x - 68c d e x + (48a c d e - 32c d e )x +--R + +--R 2 6 2 2 4 3 4 2 2 +--R (- 6a c e + 108a c d e + 132c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 4a c d e + 88a c d e + 168c d e)x - a e - a c d e + 25a c d e +--R + +--R 3 6 +--R 57c d +--R / +--R 11 4 10 3 2 9 2 3 8 4 7 +--R 4e x + 16d e x + 24d e x + 16d e x + 4d e +--R Type: Union(Expression(Integer),...) +--E 1310 + +--S 1311 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1312 + +)clear all + +--S 1313 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1313 + +--S 1314 of 1726 +r0:=c^3*x/e^6-1/5*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^5)+3/2*c*d*_ + (c*d^2+a*e^2)^2/(e^7*(d+e*x)^4)-c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/_ + (e^7*(d+e*x)^3)+2*c^2*d*(5*c*d^2+3*a*e^2)/(e^7*(d+e*x)^2)-_ + 3*c^2*(5*c*d^2+a*e^2)/(e^7*(d+e*x))-6*c^3*d*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 3 5 +--R - 60c d e x - 300c d e x - 600c d e x - 600c d e x - 300c d e x +--R + +--R 3 6 +--R - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R 10c e x + 50c d e x + (- 30a c e - 50c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 60a c d e - 400c d e )x + (- 10a c e - 60a c d e - 600c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 5a c d e - 30a c d e - 375c d e)x - 2a e - a c d e - 6a c d e +--R + +--R 3 6 +--R - 87c d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 10e x + 50d e x + 100d e x + 100d e x + 50d e x + 10d e +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 3 5 +--R - 60c d e x - 300c d e x - 600c d e x - 600c d e x - 300c d e x +--R + +--R 3 6 +--R - 60c d +--R * +--R log(e x + d) +--R + +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R 10c e x + 50c d e x + (- 30a c e - 50c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 60a c d e - 400c d e )x + (- 10a c e - 60a c d e - 600c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 5a c d e - 30a c d e - 375c d e)x - 2a e - a c d e - 6a c d e +--R + +--R 3 6 +--R - 87c d +--R / +--R 12 5 11 4 2 10 3 3 9 2 4 8 5 7 +--R 10e x + 50d e x + 100d e x + 100d e x + 50d e x + 10d e +--R Type: Union(Expression(Integer),...) +--E 1315 + +--S 1316 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1317 + +)clear all + +--S 1318 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^7 +--R +--R +--R (1) +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1318 + +--S 1319 of 1726 +r0:=-1/6*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^6)+6/5*c*d*(c*d^2+a*e^2)^2/_ + (e^7*(d+e*x)^5)-3/4*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/(e^7*_ + (d+e*x)^4)+4/3*c^2*d*(5*c*d^2+3*a*e^2)/(e^7*(d+e*x)^3)-_ + 3/2*c^2*(5*c*d^2+a*e^2)/(e^7*(d+e*x)^2)+6*c^3*d/(e^7*(d+e*x))+_ + c^3*log(d+e*x)/e^7 +--R +--R +--R (2) +--R 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 +--R 60c e x + 360c d e x + 900c d e x + 1200c d e x + 900c d e x +--R + +--R 3 5 3 6 +--R 360c d e x + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 6 3 2 4 4 +--R 360c d e x + (- 90a c e + 1350c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 120a c d e + 2200c d e )x + (- 45a c e - 90a c d e + 1875c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 18a c d e - 36a c d e + 822c d e)x - 10a e - 3a c d e - 6a c d e +--R + +--R 3 6 +--R 147c d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 +--R 60c e x + 360c d e x + 900c d e x + 1200c d e x + 900c d e x +--R + +--R 3 5 3 6 +--R 360c d e x + 60c d +--R * +--R log(e x + d) +--R + +--R 3 5 5 2 6 3 2 4 4 +--R 360c d e x + (- 90a c e + 1350c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 120a c d e + 2200c d e )x + (- 45a c e - 90a c d e + 1875c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 18a c d e - 36a c d e + 822c d e)x - 10a e - 3a c d e - 6a c d e +--R + +--R 3 6 +--R 147c d +--R / +--R 13 6 12 5 2 11 4 3 10 3 4 9 2 5 8 +--R 60e x + 360d e x + 900d e x + 1200d e x + 900d e x + 360d e x +--R + +--R 6 7 +--R 60d e +--R Type: Union(Expression(Integer),...) +--E 1320 + +--S 1321 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1322 + +)clear all + +--S 1323 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^8 +--R +--R +--R (1) +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1323 + +--S 1324 of 1726 +r0:=-1/7*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^7)+c*d*(c*d^2+a*e^2)^2/_ + (e^7*(d+e*x)^6)-3/5*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/(e^7*_ + (d+e*x)^5)+c^2*d*(5*c*d^2+3*a*e^2)/(e^7*(d+e*x)^4)-c^2*_ + (5*c*d^2+a*e^2)/(e^7*(d+e*x)^3)+3*c^3*d/(e^7*(d+e*x)^2)-_ + c^3/(e^7*(d+e*x)) +--R +--R +--R (2) +--R 3 6 6 3 5 5 2 6 3 2 4 4 2 5 3 3 3 3 +--R - c e x - 3c d e x + (- a c e - 5c d e )x + (- a c d e - 5c d e )x +--R + +--R 3 2 6 3 2 2 4 3 4 2 2 +--R (- - a c e - - a c d e - 3c d e )x +--R 5 5 +--R + +--R 1 2 5 1 2 3 3 3 5 1 3 6 1 2 2 4 1 2 4 2 +--R (- - a c d e - - a c d e - c d e)x - - a e - -- a c d e - -- a c d e +--R 5 5 7 35 35 +--R + +--R 1 3 6 +--R - - c d +--R 7 +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 6 8 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 7 +--R d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1324 + +--S 1325 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R - 35c e x - 105c d e x + (- 35a c e - 175c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 35a c d e - 175c d e )x + (- 21a c e - 21a c d e - 105c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 3 6 +--R (- 7a c d e - 7a c d e - 35c d e)x - 5a e - a c d e - a c d e - 5c d +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 35e x + 245d e x + 735d e x + 1225d e x + 1225d e x + 735d e x +--R + +--R 6 8 7 7 +--R 245d e x + 35d e +--R Type: Union(Expression(Integer),...) +--E 1325 + +--S 1326 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^9 +--R +--R +--R (1) +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1328 + +--S 1329 of 1726 +r0:=-1/8*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^8)+6/7*c*d*(c*d^2+a*e^2)^2/_ + (e^7*(d+e*x)^7)-1/2*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/(e^7*_ + (d+e*x)^6)+4/5*c^2*d*(5*c*d^2+3*a*e^2)/(e^7*(d+e*x)^5)-_ + 3/4*c^2*(5*c*d^2+a*e^2)/(e^7*(d+e*x)^4)+2*c^3*d/(e^7*(d+e*x)^3)-_ + 1/2*c^3/(e^7*(d+e*x)^2) +--R +--R +--R (2) +--R 1 3 6 6 3 5 5 3 2 6 5 3 2 4 4 +--R - - c e x - c d e x + (- - a c e - - c d e )x +--R 2 4 4 +--R + +--R 3 2 5 3 3 3 3 1 2 6 3 2 2 4 1 3 4 2 2 +--R (- - a c d e - c d e )x + (- - a c e - -- a c d e - - c d e )x +--R 5 2 10 2 +--R + +--R 1 2 5 3 2 3 3 1 3 5 1 3 6 1 2 2 4 +--R (- - a c d e - -- a c d e - - c d e)x - - a e - -- a c d e +--R 7 35 7 8 56 +--R + +--R 3 2 4 2 1 3 6 +--R - --- a c d e - -- c d +--R 280 56 +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 5 10 3 +--R e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x +--R + +--R 6 9 2 7 8 8 7 +--R 28d e x + 8d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1329 + +--S 1330 of 1726 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 5 5 2 6 3 2 4 4 +--R - 140c e x - 280c d e x + (- 210a c e - 350c d e )x +--R + +--R 2 5 3 3 3 3 2 6 2 2 4 3 4 2 2 +--R (- 168a c d e - 280c d e )x + (- 140a c e - 84a c d e - 140c d e )x +--R + +--R 2 5 2 3 3 3 5 3 6 2 2 4 2 4 2 +--R (- 40a c d e - 24a c d e - 40c d e)x - 35a e - 5a c d e - 3a c d e +--R + +--R 3 6 +--R - 5c d +--R / +--R 15 8 14 7 2 13 6 3 12 5 4 11 4 +--R 280e x + 2240d e x + 7840d e x + 15680d e x + 19600d e x +--R + +--R 5 10 3 6 9 2 7 8 8 7 +--R 15680d e x + 7840d e x + 2240d e x + 280d e +--R Type: Union(Expression(Integer),...) +--E 1330 + +--S 1331 of 1726 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1726 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +)clear all + +--S 1333 of 1726 +t0:=(a+c*x^2)^3/(d+e*x)^10 +--R +--R +--R (1) +--R 3 6 2 4 2 2 3 +--R c x + 3a c x + 3a c x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R e x + 10d e x + 45d e x + 120d e x + 210d e x + 252d e x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210d e x + 120d e x + 45d e x + 10d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 1333 + +--S 1334 of 1726 +r0:=-1/9*(c*d^2+a*e^2)^3/(e^7*(d+e*x)^9)+3/4*c*d*(c*d^2+a*e^2)^2/_ + (e^7*(d+e*x)^8)-3/7*c*(c*d^2+a*e^2)*(5*c*d^2+a*e^2)/(e^7*_ + (d+e*x)^7)+2/3*c^2*d*(5*c*d^2+3*a*e^2)/(e^7*(d+e*x)^6)-_ + 3/5*c^2*(5*c*d^2+a*e^2)/(e^7*(d+e*x)^5)+3/2*c^3*d/(e^7*_ + (d+e*x)^4)-1/3*c^3/(e^7*(d+e*x)^3) +--R +--R +--R (2) +--R 1 3 6 6 1 3 5 5 3 2 6 1 3 2 4 4 +--R - - c e x - - c d e x + (- - a c e - - c d e )x +--R 3 2 5 2 +--R + +--R 2 2 5 1 3 3 3 3 3 2 6 6 2 2 4 1 3 4 2 2 +--R (- - a c d e - - c d e )x + (- - a c e - -- a c d e - - c d e )x +--R 5 3 7 35 7 +--R + +--R 3 2 5 3 2 3 3 1 3 5 1 3 6 1 2 2 4 +--R (- -- a c d e - -- a c d e - -- c d e)x - - a e - -- a c d e +--R 28 70 28 9 84 +--R + +--R 1 2 4 2 1 3 6 +--R - --- a c d e - --- c d +--R 210 252 +--R / +--R 16 9 15 8 2 14 7 3 13 6 4 12 5 5 11 4 +--R e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x +--R + +--R