diff --git a/changelog b/changelog index 7219234..d594f03 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100610 tpd src/axiom-website/patches.html 20100610.03.tpd.patch +20100610 tpd src/input/Makefile rule-based trig integration +20100610 tpd src/input/richtrig500-599.input rule-based trig integration 20100610 tpd src/axiom-website/patches.html 20100610.02.tpd.patch 20100610 tpd src/input/Makefile rule-based trig integration 20100610 tpd src/input/richtrig400-499.input rule-based trig integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index b4cfca1..b8c72a5 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2876,6 +2876,8 @@ src/input/richtrig300-399.input rule-based trig integration
books/bookvol10.5 start of numeric analysis of BLAS/LAPACK
20100610.02.tpd.patch src/input/richtrig400-499.input rule-based trig integration
+20100610.03.tpd.patch +src/input/richtrig500-599.input rule-based trig integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 55b758c..446be95 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -381,6 +381,7 @@ REGRES= ackermann.regress \ richtrig200-299.regress \ richtrig300-399.regress \ richtrig400-499.regress \ + richtrig500-599.regress \ robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ @@ -705,6 +706,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richtrig200-299.input \ ${OUT}/richtrig300-399.input \ ${OUT}/richtrig400-499.input \ + ${OUT}/richtrig500-599.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1058,6 +1060,7 @@ DOCFILES= \ ${DOC}/richtrig200-299.input.dvi \ ${DOC}/richtrig300-399.input.dvi \ ${DOC}/richtrig400-499.input.dvi \ + ${DOC}/richtrig500-599.input.dvi \ ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ diff --git a/src/input/richtrig500-599.input.pamphlet b/src/input/richtrig500-599.input.pamphlet new file mode 100644 index 0000000..93bea58 --- /dev/null +++ b/src/input/richtrig500-599.input.pamphlet @@ -0,0 +1,42825 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richtrig500-599.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig500-599.output +)spool richtrig500-599.output +)set message auto off +)clear all + +--S 1 of 586 +t0500:= cos(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R cos(x) +--R (1) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 1 + +--S 2 of 586 +r0500:= -1/8*%i*x-1/4*cos(x)^4-1/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)^3*sin(x) +--R +--R +--R 1 3 1 1 4 1 +--R (2) (- %i cos(x) - - %i cos(x))sin(x) - - cos(x) - - %i x +--R 4 8 4 8 +--R Type: Expression Complex Fraction Integer +--E 2 + +--S 3 of 586 +--a0500:= integrate(t0500,x) +--E 3 + +--S 4 of 586 +--m0500:= a0500-r0500 +--E 4 + +--S 5 of 586 +--d0500:= D(m0500,x) +--E 5 + +--S 6 of 586 +t0501:= cos(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R cos(x) +--R (3) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 6 + +--S 7 of 586 +r0501:= -1/5*cos(x)^5-1/3*%i*sin(x)^3+1/5*%i*sin(x)^5 +--R +--R +--R 1 5 1 3 1 5 +--R (4) - %i sin(x) - - %i sin(x) - - cos(x) +--R 5 3 5 +--R Type: Expression Complex Fraction Integer +--E 7 + +--S 8 of 586 +--a0501:= integrate(t0501,x) +--E 8 + +--S 9 of 586 +--m0501:= a0501-r0501 +--E 9 + +--S 10 of 586 +--d0501:= D(m0501,x) +--E 10 + +--S 11 of 586 +t0502:= cos(x)^4/(%i+cot(x)) +--R +--R +--R 4 +--R cos(x) +--R (5) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 11 + +--S 12 of 586 +r0502:= -1/16*%i*x-1/6*cos(x)^6-1/16*%i*cos(x)*sin(x)-1/24*%i*cos(x)^3*sin(x)+1/6*%i*cos(x)^5*sin(x) +--R +--R +--R (6) +--R 1 5 1 3 1 1 6 1 +--R (- %i cos(x) - -- %i cos(x) - -- %i cos(x))sin(x) - - cos(x) - -- %i x +--R 6 24 16 6 16 +--R Type: Expression Complex Fraction Integer +--E 12 + +--S 13 of 586 +--a0502:= integrate(t0502,x) +--E 13 + +--S 14 of 586 +--m0502:= a0502-r0502 +--E 14 + +--S 15 of 586 +--d0502:= D(m0502,x) +--E 15 + +--S 16 of 586 +t0503:= tan(x)/(%i+cot(x)) +--R +--R +--R tan(x) +--R (7) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 16 + +--S 17 of 586 +r0503:= 1/2*x+%i*log(cos(x))+1/(2*%i-2*tan(x)) +--R +--R +--R (2%i tan(x) + 2)log(cos(x)) + x tan(x) - %i x - 1 +--R (8) ------------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression Complex Integer +--E 17 + +--S 18 of 586 +a0503:= integrate(t0503,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 18 + +--S 19 of 586 +m0503:= a0503-r0503 +--R +--R +--R (9) +--R (- 2%i tan(x) - 2)log(cos(x)) + (- x + 2a0503)tan(x) + %i x - 2%i a0503 + 1 +--R --------------------------------------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression Complex Integer +--E 19 + +--S 20 of 586 +d0503:= D(m0503,x) +--R +--R +--R (%i sin(x) - cos(x))tan(x) + sin(x) +--R (10) ----------------------------------- +--R cos(x)tan(x) - %i cos(x) +--R Type: Expression Complex Integer +--E 20 + +--S 21 of 586 +t0504:= tan(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R tan(x) +--R (11) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 21 + +--S 22 of 586 +r0504:= 3/2*%i*x-log(cos(x))+%i/(2*%i-2*tan(x))-%i*tan(x) +--R +--R +--R 2 +--R 3%i (- 2tan(x) + 2%i)log(cos(x)) - 2%i tan(x) - 2tan(x) - %i +--R (12) --- x + --------------------------------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 22 + +--S 23 of 586 +a0504:= integrate(t0504,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 23 + +--S 24 of 586 +m0504:= a0504-r0504 +--R +--R +--R (13) +--R 3%i +--R - --- x +--R 2 +--R + +--R 2 +--R (2tan(x) - 2%i)log(cos(x)) + 2%i tan(x) + (2a0504 + 2)tan(x) +--R + +--R - 2%i a0504 + %i +--R / +--R 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 24 + +--S 25 of 586 +d0504:= D(m0504,x) +--R +--R +--R (14) +--R 3 2 +--R %i cos(x)tan(x) + cos(x)tan(x) + (- sin(x) - %i cos(x))tan(x) + %i sin(x) +--R --------------------------------------------------------------------------- +--R cos(x)tan(x) - %i cos(x) +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 25 + +--S 26 of 586 +t0505:= cot(x)/(%i+cot(x)) +--R +--R +--R cot(x) +--R (15) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 26 + +--S 27 of 586 +r0505:= 1/2*x+%i/(2+2*%i*tan(x)) +--R +--R +--R x tan(x) - %i x + 1 +--R (16) ------------------- +--R 2tan(x) - 2%i +--R Type: Expression Complex Integer +--E 27 + +--S 28 of 586 +a0505:= integrate(t0505,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 28 + +--S 29 of 586 +m0505:= a0505-r0505 +--R +--R +--R (- x + 2a0505)tan(x) + %i x - 2%i a0505 - 1 +--R (17) ------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression Complex Integer +--E 29 + +--S 30 of 586 +d0505:= D(m0505,x) +--R +--R +--R %i +--R (18) ----------- +--R tan(x) - %i +--R Type: Expression Complex Integer +--E 30 + +--S 31 of 586 +t0506:= cot(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R cot(x) +--R (19) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 31 + +--S 32 of 586 +r0506:= -1/2*%i*x+log(sin(x))+%i/(2*%i-2*tan(x)) +--R +--R +--R %i (2tan(x) - 2%i)log(sin(x)) - %i +--R (20) - -- x + ------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 32 + +--S 33 of 586 +a0506:= integrate(t0506,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 33 + +--S 34 of 586 +m0506:= a0506-r0506 +--R +--R +--R %i (- 2tan(x) + 2%i)log(sin(x)) + 2a0506 tan(x) - 2%i a0506 + %i +--R (21) -- x + ------------------------------------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 34 + +--S 35 of 586 +d0506:= D(m0506,x) +--R +--R +--R - cos(x)tan(x) + sin(x) + %i cos(x) +--R (22) ----------------------------------- +--R sin(x)tan(x) - %i sin(x) +--R Type: UnivariatePolynomial(x,Expression Complex Integer) +--E 35 + +--S 36 of 586 +t0507:= sec(x)/(%i+cot(x)) +--R +--R +--R sec(x) +--R (23) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 36 + +--S 37 of 586 +r0507:= -%i*atanh(sin(x))-cos(x)+%i*sin(x) +--R +--R +--R (24) - %i atanh(sin(x)) + %i sin(x) - cos(x) +--R Type: Expression Complex Integer +--E 37 + +--S 38 of 586 +a0507:= integrate(t0507,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 38 + +--S 39 of 586 +m0507:= a0507-r0507 +--R +--R +--R (25) %i atanh(sin(x)) - %i sin(x) + cos(x) + a0507 +--R Type: Expression Complex Integer +--E 39 + +--S 40 of 586 +d0507:= D(m0507,x) +--R +--R +--R 3 2 +--R - sin(x) - %i cos(x)sin(x) + sin(x) +--R (26) ------------------------------------- +--R 2 +--R sin(x) - 1 +--R Type: Expression Complex Integer +--E 40 + +--S 41 of 586 +t0508:= sec(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R sec(x) +--R (27) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 41 + +--S 42 of 586 +r0508:= 1/2*%i*atanh(sin(x))+sec(x)-1/2*%i*sec(x)*tan(x) +--R +--R +--R 1 1 +--R (28) - %i atanh(sin(x)) - - %i sec(x)tan(x) + sec(x) +--R 2 2 +--R Type: Expression Complex Fraction Integer +--E 42 + +--S 43 of 586 +a0508:= integrate(t0508,x) +--R +--R +--R 2 sin(x) + cos(x) + 1 2 +--R %i cos(x) log(-------------------) - %i sin(x) + 2cos(x) + 2cos(x) +--R sin(x) - cos(x) - 1 +--R (29) ------------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression Complex Integer,...) +--E 43 + +--S 44 of 586 +m0508:= a0508-r0508 +--R +--R +--R (30) +--R 1 2 sin(x) + cos(x) + 1 1 2 +--R - %i cos(x) log(-------------------) - - %i cos(x) atanh(sin(x)) +--R 2 sin(x) - cos(x) - 1 2 +--R + +--R 1 2 1 2 2 +--R - %i cos(x) sec(x)tan(x) - - %i sin(x) - cos(x) sec(x) + cos(x) + cos(x) +--R 2 2 +--R / +--R 2 +--R cos(x) +--R Type: Expression Complex Fraction Integer +--E 44 + +--S 45 of 586 +d0508:= D(m0508,x) +--R +--R +--R (31) +--R 3 4 +--R %i cos(x) sec(x)sin(x) +--R + +--R 5 4 3 2 +--R (- %i cos(x) - 2%i cos(x) - 2%i cos(x) )sec(x)sin(x) +--R + +--R 5 4 3 +--R (%i cos(x) + 2%i cos(x) + %i cos(x) )sec(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 5 4 3 2 +--R - cos(x) sec(x)sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sec(x)sin(x) +--R + +--R 5 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) +--R * +--R tan(x) +--R + +--R 6 5 +--R - %i sin(x) + cos(x)sin(x) +--R + +--R 1 3 3 1 2 +--R (- %i cos(x) sec(x) - %i cos(x) + - %i cos(x) + 2%i cos(x) + 2%i) +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 +--R (- cos(x) - 2cos(x) - 2cos(x))sin(x) +--R + +--R 1 5 4 3 5 +--R (- - %i cos(x) - %i cos(x) - %i cos(x) )sec(x) - %i cos(x) +--R 2 +--R + +--R 3 +--R 2%i cos(x) - 2%i cos(x) - %i +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) + cos(x))sin(x) +--R + +--R 1 5 4 1 3 1 6 +--R (- %i cos(x) + %i cos(x) + - %i cos(x) )sec(x) - - %i cos(x) +--R 2 2 2 +--R + +--R 3 1 2 +--R - %i cos(x) - - %i cos(x) +--R 2 +--R / +--R 3 4 5 4 3 2 5 +--R cos(x) sin(x) + (- cos(x) - 2cos(x) - 2cos(x) )sin(x) + cos(x) +--R + +--R 4 3 +--R 2cos(x) + cos(x) +--R Type: Expression Complex Fraction Integer +--E 45 + +--S 46 of 586 +t0509:= csc(x)/(%i+cot(x)) +--R +--R +--R csc(x) +--R (32) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 46 + +--S 47 of 586 +r0509:= %i*cos(x)+sin(x) +--R +--R +--R (33) sin(x) + %i cos(x) +--R Type: Expression Complex Integer +--E 47 + +--S 48 of 586 +a0509:= integrate(t0509,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 586 +m0509:= a0509-r0509 +--R +--R +--R (34) - sin(x) - %i cos(x) + a0509 +--R Type: Expression Complex Integer +--E 49 + +--S 50 of 586 +d0509:= D(m0509,x) +--R +--R +--R (35) %i sin(x) - cos(x) +--R Type: Expression Complex Integer +--E 50 + +--S 51 of 586 +t0510:= csc(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R csc(x) +--R (36) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 51 + +--S 52 of 586 +r0510:= -log(%i+cot(x)) +--R +--R +--R (37) - log(cot(x) + %i) +--R Type: Expression Complex Integer +--E 52 + +--S 53 of 586 +a0510:= integrate(t0510,x) +--R +--R +--R sin(x) 2 +--R (38) log(----------) - log(----------) - %i x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression Complex Integer,...) +--E 53 + +--S 54 of 586 +m0510:= a0510-r0510 +--R +--R +--R sin(x) 2 +--R (39) log(----------) + log(cot(x) + %i) - log(----------) - %i x +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression Complex Integer +--E 54 + +--S 55 of 586 +d0510:= D(m0510,x) +--R +--R +--R - cot(x)sin(x) + cos(x) +--R (40) ----------------------- +--R sin(x) +--R Type: Expression Complex Integer +--E 55 + +--S 56 of 586 +t0511:= csc(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R csc(x) +--R (41) ----------- +--R cot(x) + %i +--R Type: Expression Complex Integer +--E 56 + +--S 57 of 586 +r0511:= %i*atanh(cos(x))-csc(x) +--R +--R +--R (42) %i atanh(cos(x)) - csc(x) +--R Type: Expression Complex Integer +--E 57 + +--S 58 of 586 +a0511:= integrate(t0511,x) +--R +--R +--R sin(x) +--R - %i sin(x)log(----------) - 1 +--R cos(x) + 1 +--R (43) ------------------------------ +--R sin(x) +--R Type: Union(Expression Complex Integer,...) +--E 58 + +--S 59 of 586 +m0511:= a0511-r0511 +--R +--R +--R (44) +--R sin(x) +--R - %i sin(x)log(----------) - %i sin(x)atanh(cos(x)) + csc(x)sin(x) - 1 +--R cos(x) + 1 +--R ---------------------------------------------------------------------- +--R sin(x) +--R Type: Expression Complex Integer +--E 59 + +--S 60 of 586 +d0511:= D(m0511,x) +--R +--R +--R (45) +--R 3 2 2 +--R - %i cos(x)sin(x) + (- cos(x) + 1)cot(x)csc(x)sin(x) +--R + +--R 3 3 +--R (- %i cos(x) + %i cos(x))sin(x) + cos(x) - cos(x) +--R / +--R 2 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression Complex Integer +--E 60 + +--S 61 of 586 +t0512:= sin(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R sin(x) +--R (46) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 61 + +--S 62 of 586 +r0512:= 1/2/a^3*(a^2*x-2*b^2*x+4*b*(a^2-b^2)^(1/2)*atanh((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))+2*a*b*sin(x)-cos(x)*sin(x)*a^2) +--R +--R +--R (47) +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a 2 +--R - 4b\|- b + a atanh(---------------------) + (- a cos(x) + 2a b)sin(x) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression Integer +--E 62 + +--S 63 of 586 +a0512:= integrate(t0512,x) +--R +--R +--R (48) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R 2b\|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R 2 2 2 +--R (- a cos(x) + 2a b)sin(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a 2 +--R - 4b\|b - a atan(----------------------) + (- a cos(x) + 2a b)sin(x) +--R (b - a)sin(x) +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 63 + +--S 64 of 586 +m0512a:= a0512.1-r0512 +--R +--R +--R (49) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R b\|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2b\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 3 +--R a +--R Type: Expression Integer +--E 64 + +--S 65 of 586 +d0512a:= D(m0512a,x) +--R +--R +--R (50) +--R 3 3 4 3 2 2 3 3 +--R ((- 2a b + 2a b)cos(x) - b + a b + a b - a b)sin(x) +--R + +--R 3 3 3 4 3 2 2 3 2 +--R (- 2a b + 2a b)cos(x) + (- b + a b + a b - a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (2a b - 2a b)cos(x) + b - a b - a b + a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 4 +--R (- a b - a b + a b + a b)sin(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 2 +--R ((b + a b - a b - a b )cos(x) + a b + a b - a b - a b)sin(x) +--R + +--R 4 2 3 3 2 4 4 5 4 2 3 3 2 3 +--R (a b + a b - a b - a b)cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 2 4 2 5 4 2 3 3 2 +--R (- a b - a b + a b + a b)cos(x) + (- b - a b + a b + a b )cos(x) +--R / +--R 4 5 3 2 4 3 +--R ((a b + a )cos(x) + a b + a b)sin(x) +--R + +--R 4 5 3 3 2 4 5 2 +--R (a b - a )cos(x) + (a b - 3a b + 2a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (- 2a b + 3a b - a )cos(x) + a b - a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 5 2 3 3 4 2 5 6 4 2 5 +--R ((- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) - a b - a b) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 4 3 3 4 2 5 6 3 +--R (- a b + a b)cos(x) + (- a b + 3a b - 3a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 5 6 +--R (2a b - 4a b + 4a b - 2a )cos(x) + (- a b + 3a b - 3a b + a )cos(x) +--R + +--R 4 2 5 +--R - a b + a b +--R Type: Expression Integer +--E 65 + +--S 66 of 586 +m0512b:= a0512.2-r0512 +--R +--R +--R (51) +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2b\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2b\|b - a atan(----------------------) +--R (b - a)sin(x) +--R / +--R 3 +--R a +--R Type: Expression Integer +--E 66 + +--S 67 of 586 +d0512b:= D(m0512b,x) +--R +--R +--R (52) +--R 3 3 4 4 2 2 3 3 2 +--R (4a b - 4a b)sin(x) + ((- 4b + 4a b )cos(x) - 4a b + 4a b)sin(x) +--R + +--R 3 3 4 4 2 2 3 3 3 2 +--R (- 4a b + 4a b)cos(x) + (- 4b + 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 2 +--R (4b - 4a b )cos(x) +--R / +--R 3 2 5 4 +--R (a b - a )sin(x) +--R + +--R 3 2 5 2 4 3 2 5 2 +--R ((2a b + 2a )cos(x) + 8a b cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (a b - a )cos(x) + (- 2a b + 2a )cos(x) + a b - a +--R Type: Expression Integer +--E 67 + +--S 68 of 586 +t0513:= sin(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R sin(x) +--R (53) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 68 + +--S 69 of 586 +r0513:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5-2*b*(a^2-b^2)^(3/2)*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^5+b*sin(x)/a^2-b^3*sin(x)/a^4-5/8*cos(x)*sin(x)/a+1/2*b^2*cos(x)*sin(x)/a^3+1/4*cos(x)^3*sin(x)/a+1/3*b*sin(x)^3/a^2 +--R +--R +--R (54) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 3 3 +--R (- 48b + 48a b)\|- b + a atanh(-------------) + 8a b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (12a b - 15a )cos(x) - 24a b + 24a b)sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression Integer +--E 69 + +--S 70 of 586 +a0513:= integrate(t0513,x) +--R +--R +--R (55) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (24b - 24a b)\|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (6a cos(x) - 8a b cos(x) + (12a b - 15a )cos(x) - 24a b + 32a b) +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a +--R (48b - 48a b)\|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (6a cos(x) - 8a b cos(x) + (12a b - 15a )cos(x) - 24a b + 32a b) +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R ] +--R Type: Union(List Expression Integer,...) +--E 70 + +--S 71 of 586 +m0513a:= a0513.1-r0513 +--R +--R +--R (56) +--R +---------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (3b - 3a b)\|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 3 3 +--R (6b - 6a b)\|- b + a atanh(-------------) - a b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (- a b cos(x) + a b)sin(x) +--R / +--R 5 +--R 3a +--R Type: Expression Integer +--E 71 + +--S 72 of 586 +d0513a:= D(m0513a,x) +--R +--R +--R (57) +--R 3 2 4 2 2 3 3 2 3 +--R ((- a b + a b)cos(x) + (- a b + a b )cos(x))sin(x) +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- a b + a b)cos(x) + (- a b + a b )cos(x) +--R + +--R 3 2 4 2 5 2 3 3 2 4 5 +--R (a b - a b)cos(x) + (3b - 5a b - a b + 3a b)cos(x) + 3b +--R + +--R 2 3 4 +--R - 6a b + 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 2 2 3 3 2 3 +--R ((- a b - a b)cos(x) + (- a b - a b )cos(x))sin(x) +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- a b - a b)cos(x) + (- a b - a b )cos(x) +--R + +--R 3 2 4 2 5 2 3 3 2 4 5 +--R (a b + a b)cos(x) + (3b - 5a b + a b + 3a b)cos(x) - 3b +--R + +--R 2 3 4 +--R 6a b - 3a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 6 5 2 4 3 3 4 2 5 +--R (- a b + a b )cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (3a b + a b - 7a b + a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 4 +--R (3b + 3a b - 6a b - 5a b + 2a b + 3a b)cos(x) + 3b - 6a b +--R + +--R 4 2 +--R 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 3 3 4 2 6 5 2 4 3 3 4 2 5 +--R (- a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 3a b + a b + 7a b + a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 4 4 2 +--R (- 3b + 3a b + 6a b - 5a b - 2a b + 3a b)cos(x) + 3b - 6a b + 3a b +--R / +--R 5 6 4 2 5 x 2 +--R ((3a b - 3a )cos(x) + 3a b - 3a b)sin(x)tan(-) +--R 2 +--R + +--R 5 6 4 2 5 +--R ((3a b + 3a )cos(x) + 3a b + 3a b)sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) + 3a b +--R + +--R 6 +--R - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 6 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b + 3a b +--R Type: Expression Integer +--E 72 + +--S 73 of 586 +m0513b:= a0513.2-r0513 +--R +--R +--R (58) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R (6b - 6a b)\|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a 3 3 +--R (6b - 6a b)\|b - a atan(----------------------) - a b sin(x) +--R (b - a)sin(x) +--R + +--R 3 2 3 +--R (- a b cos(x) + a b)sin(x) +--R / +--R 5 +--R 3a +--R Type: Expression Integer +--E 73 + +--S 74 of 586 +d0513b:= D(m0513b,x) +--R +--R +--R (59) +--R 3 3 4 2 5 4 +--R (- a b + 2a b - a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 5 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 2 5 6 5 2 4 3 3 4 2 5 +--R (- 2a b + 2a b)cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 3b + 9a b + 6a b - 16a b - 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 6 5 2 4 3 3 4 2 +--R (12a b - 23a b + 11a b)cos(x) + 3b + 3a b - 6a b - 6a b + 3a b +--R + +--R 5 +--R 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 4 +--R (- a b + a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 4 2 5 2 +--R (- 2a b - 2a b )cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 4 2 5 6 5 2 4 3 3 4 2 5 +--R (- 2a b - 2a b)cos(x) - 3b - 9a b + 6a b + 18a b - 3a b - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 5 3 3 4 2 5 4 +--R (- a b - 2a b - a b)cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 3b - 3a b + 6a b + 8a b + a b - a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 5 +--R (a b + 2a b + a b)cos(x) + 3b + 3a b - 6a b - 6a b + 3a b + 3a b +--R / +--R 5 2 6 7 2 5 2 7 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 5 2 7 5 2 7 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 7 2 5 2 6 7 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 5 2 6 7 5 2 6 7 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression Integer +--E 74 + +--S 75 of 586 +t0514:= cos(x)/(a+b*sec(x)) +--R +--R +--R cos(x) +--R (60) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 75 + +--S 76 of 586 +r0514:= -b*x/a^2+2*b^2*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)+sin(x)/a +--R +--R +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R - 2b atanh(-------------) + (a sin(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (61) -------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 76 + +--S 77 of 586 +a0514:= integrate(t0514,x) +--R +--R +--R (62) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - b x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R 2 sin(x)\|b - a | 2 2 +--R 2b atan(---------------------) + (a sin(x) - b x)\|b - a +--R (b + a)cos(x) + b + a +--R -----------------------------------------------------------] +--R +-------+ +--R 2 | 2 2 +--R a \|b - a +--R Type: Union(List Expression Integer,...) +--E 77 + +--S 78 of 586 +m0514a:= a0514.1-r0514 +--R +--R +--R (63) +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 2 2 +--R 2b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 78 + +--S 79 of 586 +d0514a:= D(m0514a,x) +--R +--R +--R (64) +--R 3 2 2 2 2 3 2 3 x 2 +--R ((b - a b )sin(x) - a b cos(x) + (- b - a b )cos(x) - b )tan(-) +--R 2 +--R + +--R 3 2 2 2 2 3 2 3 +--R (b + a b )sin(x) + a b cos(x) + (b - a b )cos(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 4 2 2 x 2 +--R ((b - a b )cos(x) + b - a b )sin(x)tan(-) +--R 2 +--R + +--R 4 2 2 4 2 2 +--R ((b - a b )cos(x) - b + a b )sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R ((a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b + a b + a b - a )cos(x) - a b + a b + a b - a b)sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b - a b + a b + a )cos(x) - a b - a b + a b + a b)sin(x) +--R Type: Expression Integer +--E 79 + +--S 80 of 586 +m0514b:= a0514.2-r0514 +--R +--R +--R (65) +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 sin(x)\|b - a +--R 2b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression Integer +--E 80 + +--S 81 of 586 +d0514b:= D(m0514b,x) +--R +--R +--R (66) +--R 3 2 2 3 2 2 2 3 2 +--R ((b - a b )sin(x) + (b - 3a b )cos(x) - 4a b cos(x) - b - a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 3 2 +--R (b + 3a b )sin(x) + (b + a b )cos(x) - b - a b +--R / +--R 2 2 3 4 2 2 2 4 2 2 2 4 +--R (a b - 2a b + a )sin(x) + (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 4 +--R a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 2 3 4 2 +--R (a b - a )sin(x) + (a b + 2a b + a )cos(x) +--R + +--R 2 2 3 4 2 2 3 4 +--R (2a b + 4a b + 2a )cos(x) + a b + 2a b + a +--R Type: Expression Integer +--E 81 + +--S 82 of 586 +t0515:= cos(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R cos(x) +--R (67) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 82 + +--S 83 of 586 +r0515:= 1/2*x/a+b^2*x/a^3-2*b^3*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)-b*sin(x)/a^2+1/2*cos(x)*sin(x)/a +--R +--R +--R (68) +--R x +--R (b - a)tan(-) +---------+ +--R 3 2 2 2 2 | 2 2 +--R 4b atanh(-------------) + ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression Integer +--E 83 + +--S 84 of 586 +a0515:= integrate(t0515,x) +--R +--R +--R (69) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 3 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 sin(x)\|b - a +--R - 4b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 84 + +--S 85 of 586 +m0515a:= a0515.1-r0515 +--R +--R +--R (70) +--R +---------+ +--R | 2 2 2 2 +--R 3 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 3 2 +--R - 2b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 85 + +--S 86 of 586 +d0515a:= D(m0515a,x) +--R +--R +--R (71) +--R 4 3 2 3 2 4 3 4 x 2 +--R ((- b + a b )sin(x) + a b cos(x) + (b + a b )cos(x) + b )tan(-) +--R 2 +--R + +--R 4 3 2 3 2 4 3 4 +--R (- b - a b )sin(x) - a b cos(x) + (- b + a b )cos(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 5 2 3 x 2 +--R ((b - a b )cos(x) + b - a b )sin(x)tan(-) +--R 2 +--R + +--R 5 2 3 5 2 3 +--R ((b - a b )cos(x) - b + a b )sin(x) +--R / +--R 3 2 4 2 2 3 3 2 4 5 3 2 4 +--R ((a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 2 2 3 3 2 4 5 3 2 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 x 2 +--R ((a b - a b - a b + a )cos(x) + a b - a b - a b + a b)sin(x)tan(-) +--R 2 +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 +--R ((a b + a b - a b - a )cos(x) + a b + a b - a b - a b)sin(x) +--R Type: Expression Integer +--E 86 + +--S 87 of 586 +m0515b:= a0515.2-r0515 +--R +--R +--R (72) +--R x +--R +-------+ (b - a)tan(-) +--R 3 | 2 2 2 +--R - 2b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 | 2 2 sin(x)\|b - a +--R - 2b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression Integer +--E 87 + +--S 88 of 586 +d0515b:= D(m0515b,x) +--R +--R +--R (73) +--R 4 3 2 4 3 2 3 4 +--R (- b + a b )sin(x) + (- b + 3a b )cos(x) + 4a b cos(x) + b +--R + +--R 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 3 2 4 3 +--R (- b - 3a b )sin(x) + (- b - a b )cos(x) + b + a b +--R / +--R 3 2 4 5 2 3 2 5 2 3 2 5 +--R (a b - 2a b + a )sin(x) + (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 +--R a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 4 5 2 +--R (a b - a )sin(x) + (a b + 2a b + a )cos(x) +--R + +--R 3 2 4 5 3 2 4 5 +--R (2a b + 4a b + 2a )cos(x) + a b + 2a b + a +--R Type: Expression Integer +--E 88 + +--S 89 of 586 +t0516:= cos(x)^3/(a+b*sec(x)) +--R +--R +--R 3 +--R cos(x) +--R (74) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 89 + +--S 90 of 586 +r0516:= -1/2*b*x/a^2-b^3*x/a^4+2*b^4*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+sin(x)/a+b^2*sin(x)/a^3-1/2*b*cos(x)*sin(x)/a^2-1/3*sin(x)^3/a +--R +--R +--R (75) +--R x +--R (b - a)tan(-) +--R 4 2 +--R - 12b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 2 3 3 2 +--R (- 2a sin(x) + (- 3a b cos(x) + 6a b + 6a )sin(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression Integer +--E 90 + +--S 91 of 586 +a0516:= integrate(t0516,x) +--R +--R +--R (76) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 4 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R 6b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R 3 2 2 2 3 3 2 +--R ((2a cos(x) - 3a b cos(x) + 6a b + 4a )sin(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 4 sin(x)\|b - a +--R 12b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 3 2 2 2 3 3 2 +--R ((2a cos(x) - 3a b cos(x) + 6a b + 4a )sin(x) + (- 6b - 3a b)x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 91 + +--S 92 of 586 +m0516a:= a0516.1-r0516 +--R +--R +--R (77) +--R +---------+ +--R | 2 2 2 2 +--R 4 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R 3b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +---------+ +--R 4 2 3 3 3 2 3 | 2 2 +--R 6b atanh(-------------) + (a sin(x) + (a cos(x) - a )sin(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 3a \|- b + a +--R Type: Expression Integer +--E 92 + +--S 93 of 586 +d0516a:= D(m0516a,x) +--R +--R +--R (78) +--R 3 2 4 3 2 3 3 2 4 5 2 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 5 4 +--R (a b - a b)cos(x) + 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 3a b - a b + a b - a b + a )cos(x) +--R + +--R 5 4 3 2 4 5 +--R (- 3b - 3a b - a b + a b)cos(x) - 3b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 3 2 3 3 2 4 5 2 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 3 2 4 5 4 +--R (a b + a b)cos(x) + 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (3a b - a b - a b - a b - a )cos(x) +--R + +--R 5 4 3 2 4 5 +--R (3b - 3a b - a b - a b)cos(x) - 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 5 6 2 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- a b + a b + a b - a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 4 +--R (3b - 2a b - a b - a b + a b)cos(x) + 3b - 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- a b - a b + a b + a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 4 +--R (3b - 2a b + a b - a b - a b)cos(x) - 3b + 3a b +--R * +--R sin(x) +--R / +--R 4 2 5 2 3 3 4 2 5 6 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) +--R + +--R 4 2 5 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 3 4 2 5 6 4 2 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b +--R + +--R 5 +--R 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 5 2 6 7 3 4 4 3 5 2 6 +--R ((- 3a b + 3a b + 3a b - 3a )cos(x) - 3a b + 3a b + 3a b - 3a b) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 4 3 5 2 6 7 3 4 4 3 5 2 6 +--R ((- 3a b - 3a b + 3a b + 3a )cos(x) - 3a b - 3a b + 3a b + 3a b)sin(x) +--R Type: Expression Integer +--E 93 + +--S 94 of 586 +m0516b:= a0516.2-r0516 +--R +--R +--R (79) +--R x +--R +-------+ (b - a)tan(-) +--R 4 | 2 2 2 +--R 6b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 4 | 2 2 sin(x)\|b - a +--R 6b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (a sin(x) + (a cos(x) - a )sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R 3a \|- b + a \|b - a +--R Type: Expression Integer +--E 94 + +--S 95 of 586 +d0516b:= D(m0516b,x) +--R +--R +--R (80) +--R 3 2 4 5 4 +--R (a b - 2a b + a )cos(x)sin(x) +--R + +--R 3 2 4 3 3 2 5 2 4 5 +--R (2a b - 2a b)cos(x) + (2a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 5 4 +--R 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 5 4 3 2 5 2 4 3 2 5 +--R (3b - 9a b - 2a b + 2a )cos(x) + (- 12a b - a b + a )cos(x) +--R + +--R 5 4 +--R - 3b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 +--R (a b - a )cos(x)sin(x) +--R + +--R 3 2 4 3 3 2 4 5 2 +--R (2a b + 2a b)cos(x) + (2a b + 4a b + 2a )cos(x) +--R + +--R 4 5 5 4 +--R (2a b + 2a )cos(x) + 3b + 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (a b + 2a b + a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 5 2 3 2 4 5 +--R (3b + 3a b - 2a b - 4a b - 2a )cos(x) + (- a b - 2a b - a )cos(x) +--R + +--R 5 4 +--R - 3b - 3a b +--R / +--R 4 2 5 6 2 4 2 6 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 4 2 6 4 2 6 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 2 4 2 5 6 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 4 2 5 6 4 2 5 6 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression Integer +--E 95 + +--S 96 of 586 +t0517:= cos(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R cos(x) +--R (81) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 96 + +--S 97 of 586 +r0517:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5-2*b^5*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)-b*sin(x)/a^2-b^3*sin(x)/a^4+3/8*cos(x)*sin(x)/a+1/2*b^2*cos(x)*sin(x)/a^3+1/4*cos(x)^3*sin(x)/a+1/3*b*sin(x)^3/a^2 +--R +--R +--R (82) +--R x +--R (b - a)tan(-) +--R 5 2 +--R 48b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 +--R 8a b sin(x) +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (12a b + 9a )cos(x) - 24a b - 24a b)sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression Integer +--E 97 + +--S 98 of 586 +a0517:= integrate(t0517,x) +--R +--R +--R (83) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 5 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 24b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R 4 3 3 2 2 2 4 3 +--R 6a cos(x) - 8a b cos(x) + (12a b + 9a )cos(x) - 24a b +--R + +--R 3 +--R - 16a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 sin(x)\|b - a +--R - 48b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 4 3 3 2 2 2 4 3 +--R 6a cos(x) - 8a b cos(x) + (12a b + 9a )cos(x) - 24a b +--R + +--R 3 +--R - 16a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 98 + +--S 99 of 586 +m0517a:= a0517.1-r0517 +--R +--R +--R (84) +--R +---------+ +--R | 2 2 2 2 +--R 5 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 3b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 5 2 +--R - 6b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 3 2 3 | 2 2 +--R (- a b sin(x) + (- a b cos(x) + a b)sin(x))\|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 3a \|- b + a +--R Type: Expression Integer +--E 99 + +--S 100 of 586 +d0517a:= D(m0517a,x) +--R +--R +--R (85) +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 6 5 +--R (- a b + a b )cos(x) - 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (3a b + a b - a b + a b - a b)cos(x) +--R + +--R 6 5 3 3 4 2 6 +--R (3b + 3a b + a b - a b )cos(x) + 3b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 3 3 4 2 6 5 +--R (- a b - a b )cos(x) - 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 3a b + a b + a b + a b + a b)cos(x) +--R + +--R 6 5 3 3 4 2 6 +--R (- 3b + 3a b + a b + a b )cos(x) + 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 4 3 5 2 6 2 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- a b + a b + a b - a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 2 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 7 2 5 +--R (3b - 2a b - a b - a b + a b )cos(x) + 3b - 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 5 2 6 2 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- a b - a b + a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 2 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 7 2 5 +--R (3b - 2a b + a b - a b - a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R / +--R 5 2 6 2 4 3 5 2 6 7 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) +--R + +--R 5 2 6 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b +--R + +--R 6 +--R 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 6 2 7 8 4 4 5 3 6 2 7 +--R ((3a b - 3a b - 3a b + 3a )cos(x) + 3a b - 3a b - 3a b + 3a b) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 5 3 6 2 7 8 4 4 5 3 6 2 7 +--R ((3a b + 3a b - 3a b - 3a )cos(x) + 3a b + 3a b - 3a b - 3a b)sin(x) +--R Type: Expression Integer +--E 100 + +--S 101 of 586 +m0517b:= a0517.2-r0517 +--R +--R +--R (86) +--R x +--R +-------+ (b - a)tan(-) +--R 5 | 2 2 2 +--R - 6b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 | 2 2 sin(x)\|b - a +--R - 6b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (- a b sin(x) + (- a b cos(x) + a b)sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 | 2 2 | 2 2 +--R 3a \|- b + a \|b - a +--R Type: Expression Integer +--E 101 + +--S 102 of 586 +d0517b:= D(m0517b,x) +--R +--R +--R (87) +--R 3 3 4 2 5 4 +--R (- a b + 2a b - a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 5 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 2 5 6 5 +--R (- 2a b + 2a b)cos(x) - 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 6 5 3 3 5 2 5 3 3 5 +--R (- 3b + 9a b + 2a b - 2a b)cos(x) + (12a b + a b - a b)cos(x) +--R + +--R 6 5 +--R 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 4 +--R (- a b + a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 4 2 5 2 +--R (- 2a b - 2a b )cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 4 2 5 6 5 +--R (- 2a b - 2a b)cos(x) - 3b - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 5 3 3 4 2 5 4 +--R (- a b - 2a b - a b)cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (- 3b - 3a b + 2a b + 4a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (a b + 2a b + a b)cos(x) + 3b + 3a b +--R / +--R 5 2 6 7 2 5 2 7 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 5 2 7 5 2 7 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 7 2 5 2 6 7 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 5 2 6 7 5 2 6 7 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression Integer +--E 102 + +--S 103 of 586 +t0518:= tan(x)/(a+b*sec(x)) +--R +--R +--R tan(x) +--R (88) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 103 + +--S 104 of 586 +r0518:= -log(b+a*cos(x))/a +--R +--R +--R log(a cos(x) + b) +--R (89) - ----------------- +--R a +--R Type: Expression Integer +--E 104 + +--S 105 of 586 +a0518:= integrate(t0518,x) +--R +--R +--R 2a cos(x) + 2b 2 +--R - log(--------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (90) --------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 105 + +--S 106 of 586 +m0518:= a0518-r0518 +--R +--R +--R 2a cos(x) + 2b 2 +--R log(a cos(x) + b) - log(--------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (91) --------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 106 + +--S 107 of 586 +d0518:= D(m0518,x) +--R +--R +--R (92) 0 +--R Type: Expression Integer +--E 107 + +--S 108 of 586 +t0519:= tan(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R tan(x) +--R (93) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 108 + +--S 109 of 586 +r0519:= 1/a/b*(-b*x+a*atanh(sin(x))+2*(a^2-b^2)^(1/2)*atanh((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))) +--R +--R +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R a atanh(sin(x)) - 2\|- b + a atanh(---------------------) - b x +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R (94) ----------------------------------------------------------------- +--R a b +--R Type: Expression Integer +--E 109 + +--S 110 of 586 +a0519:= integrate(t0519,x) +--R +--R +--R (95) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R \|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - b x +--R cos(x) + 1 cos(x) + 1 +--R / +--R a b +--R , +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(----------------------) - b x +--R (b - a)sin(x) +--R / +--R a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 110 + +--S 111 of 586 +m0519a:= a0519.1-r0519 +--R +--R +--R (96) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R \|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - a atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R a b +--R Type: Expression Integer +--E 111 + +--S 112 of 586 +d0519a:= D(m0519a,x) +--R +--R +--R (97) +--R 2 2 3 2 2 3 7 +--R ((- 2a b - 2a b)cos(x) - b - a b - a b - a )sin(x) +--R + +--R 2 3 2 3 2 3 2 2 +--R - 4a b cos(x) + (3a b - 9a )cos(x) + (2b + 7a b - 7a b)cos(x) +--R + +--R 3 2 2 3 +--R 3b - 3a b + a b + 3a +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (2a b - 2a b)cos(x) + (b + a b + 3a b - 7a )cos(x) +--R + +--R 3 2 3 2 2 3 2 +--R (2b - 4a b)cos(x) + (- 6a b - 6a b + 14a )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 4b - 6a b + 12a b)cos(x) - 3b + 5a b + a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 6 2 2 5 +--R (- a b + a )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- b - a b - a b + 3a )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (2a b + 3a b - 5a )cos(x) + (2b + a b - 3a b)cos(x) + b +--R + +--R 2 2 3 +--R - a b - a b + a +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 4 8 +--R (- a b - a b + a b + a )sin(x) +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 +--R (a b + 3a b + a b - a )cos(x) + (b + 5a b + 3a b - a b)cos(x) +--R + +--R 3 2 2 3 4 +--R 3a b + 5a b - a b - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 3 +--R (a b + 5a b - a b - a )cos(x) + (4a b - 3a b + 9a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 8a b + 8a b - 2a b + 8a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R (- 3b - 7a b - 8a b + 12a b)cos(x) - 3a b - 3a b - a b + 3a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R (- a b + a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - a b - 5a b + 9a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 3 3 +--R (- 2b - 5a b + 5a b + a b + 5a )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b + 11a b - 11a b + a b - 9a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R (3b + 3a b + 5a b - 13a b)cos(x) + a b - a b + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b - a b)cos(x) + (2a b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 5 4 3 2 2 3 4 +--R (b + a b + 4a b - 6a b)cos(x) + (2b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 2 3 3 4 3 2 2 4 2 +--R (- 5a b + 5a b)cos(x) + (- 2b - 4a b + 4a b + 2a )cos(x) +--R + +--R 4 3 3 +--R (- b - a b + 2a b)cos(x) +--R / +--R 2 2 3 3 2 2 7 +--R ((a b + a b)cos(x) + a b + a b )sin(x) +--R + +--R 3 3 2 2 2 3 2 2 3 +--R - 2a b cos(x) - 6a b cos(x) + (- 4a b - a b - 3a b)cos(x) +--R + +--R 3 2 2 +--R - a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 4 2 2 3 +--R (- a b + a b)cos(x) + (- a b + a b )cos(x) + 2a b cos(x) +--R + +--R 3 2 2 2 3 2 2 3 3 2 2 +--R (2a b + 4a b )cos(x) + (4a b - a b + 3a b)cos(x) - a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 4 +--R (a b - a b)cos(x) + (a b - a b )cos(x) +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 2 3 3 2 2 +--R (a b - a b)cos(x) + a b - a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 4 2 3 3 2 4 2 3 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) - a b +--R + +--R 3 2 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 2 3 4 3 4 2 3 3 2 2 +--R 2a b cos(x) + (6a b + 2a b)cos(x) + (4a b + a b + 9a b )cos(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (a b + 7a b + a b + 3a b)cos(x) + a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 6 4 2 3 3 2 4 5 +--R (a b - a b )cos(x) + (a b - a b + a b - a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 3 +--R (- a b - a b )cos(x) + (- 2a b - 4a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 2 4 +--R (- 4a b - a b - 7a b )cos(x) + (a b - 7a b + a b - 3a b)cos(x) +--R + +--R 2 3 3 2 +--R a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 6 4 2 3 3 2 4 5 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 4 2 3 3 2 +--R (a b - a b )cos(x) + (- a b + a b - a b + a b)cos(x) - a b + a b +--R Type: Expression Integer +--E 112 + +--S 113 of 586 +m0519b:= a0519.2-r0519 +--R +--R +--R (98) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - a atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(----------------------) +--R (b - a)sin(x) +--R / +--R a b +--R Type: Expression Integer +--E 113 + +--S 114 of 586 +d0519b:= D(m0519b,x) +--R +--R +--R (99) +--R 2 3 8 +--R (2a b - 2a )sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 10a b + 2a )cos(x) + (- 4b - 9a b - 12a b + 9a )cos(x) +--R + +--R 2 3 +--R - 14a b + 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 2 2 3 3 +--R (- 10a b + 2a )cos(x) + (- 3a b - 16a b - a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b + 16a b - 16a b - 16a )cos(x) +--R + +--R 3 2 2 3 2 3 +--R (12b + 15a b + 4a b - 19a )cos(x) + 14a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 3 2 2 3 5 +--R (2a b - 2a )cos(x) + (4b + 5a b - 4a b - 9a )cos(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (8b + 10a b - 16a b - 10a )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 16b - 18a b + 24a b + 18a )cos(x) +--R + +--R 3 2 2 3 2 3 +--R (- 12b - 7a b + 12a b + 11a )cos(x) - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 3 6 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 5 3 2 4 +--R (- 4b - 5a b + 4a b + 5a )cos(x) + (- 8b + 8a b)cos(x) +--R + +--R 2 3 3 3 2 2 3 2 +--R (5a b - 5a )cos(x) + (8b + 4a b - 8a b - 4a )cos(x) +--R + +--R 3 2 2 3 +--R (4b + a b - 4a b - a )cos(x) +--R / +--R 3 3 8 +--R (a b - a b)sin(x) +--R + +--R 3 3 2 3 2 2 3 3 6 +--R ((a b + 3a b)cos(x) + (- 2a b + 8a b + 2a b)cos(x) + 4a b)sin(x) +--R + +--R 3 3 4 3 2 2 3 3 +--R (- a b - 3a b)cos(x) + (- 4a b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 7a b - 16a b - 5a b)cos(x) + (- 2a b - 16a b - 6a b)cos(x) +--R + +--R 3 3 +--R - 2a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 6 3 3 5 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (2a b + 2a b)cos(x) + (8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 3 +--R (7a b + 16a b + a b)cos(x) + (2a b + 8a b + 6a b)cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 6 3 3 5 3 3 4 +--R (a b - a b)cos(x) + (2a b - 2a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 4a b + 4a b)cos(x) + (- a b + a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R Type: Expression Integer +--E 114 + +--S 115 of 586 +t0520:= tan(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R tan(x) +--R (100) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 115 + +--S 116 of 586 +r0520:= x/a+a^2*atanh(sin(x))/b^3-3/2*atanh(sin(x))/b-2*(a^2-b^2)^(3/2)*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a/b^3-a*tan(x)/b^2+1/2*sec(x)*tan(x)/b +--R +--R +--R (101) +--R 2 3 +--R (- 3a b + 2a )atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 2 2 +--R (- 4b + 4a )\|- b + a atanh(-------------) + (a b sec(x) - 2a b)tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 +--R 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression Integer +--E 116 + +--S 117 of 586 +a0520:= integrate(t0520,x) +--R +--R +--R (102) +--R [ +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (2b - 2a )cos(x) \|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 2 2 3 2 +--R (- 2a b cos(x) + a b )sin(x) + 2b x cos(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R , +--R +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R (4b - 4a )cos(x) \|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 2 2 3 2 +--R (- 2a b cos(x) + a b )sin(x) + 2b x cos(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R ] +--R Type: Union(List Expression Integer,...) +--E 117 + +--S 118 of 586 +m0520a:= a0520.1-r0520 +--R +--R +--R (103) +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (2b - 2a )cos(x) \|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 2 3 2 +--R (3a b - 2a )cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 2 | 2 2 2 +--R (4b - 4a )cos(x) \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 2 2 +--R (- a b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a b )sin(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R Type: Expression Integer +--E 118 + +--S 119 of 586 +d0520a:= D(m0520a,x) +--R +--R +--R (104) +--R 3 2 2 4 4 3 3 +--R ((- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) )sec(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 4 2 2 4 4 3 3 +--R (4b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (- 2b - 2a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 4b + 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (2a b - 2a b)cos(x) + (2a b + 2a b - 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 3 +--R ((- 2a b - 2a b )cos(x) + (- 2b - 2a b )cos(x) )sec(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (2a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (4b + 8a b + 4a b )cos(x) + (4b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 6a b - 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (- 4a b - 8a b - 4a b)cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 4b - 6a b - 2a b )cos(x) + (- 2b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 2 4 3 7 +--R ((- 2a b + 2a b)cos(x) + 2b - 2a b )sin(x) +--R + +--R 3 2 2 4 4 3 3 +--R ((- a b + a b )cos(x) + (- b + a b )cos(x) )sec(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b + 6a b - 8a b - 6a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (8b - 5a b - 5a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- b + a b + 4a b - 4a b)cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 3 +--R - 4b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (a b - a b )cos(x) + (b + a b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 3 3 +--R (2b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 2b + 6a b - 2a b - 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 4a b + 6a b + 2a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 6b - 10a b + 20a b + 8a b - 12a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (- 12b + 6a b + 10a b - 4a )cos(x) +--R + +--R 2 2 3 2 4 3 4 3 +--R (- 2a b + 2a b)cos(x) + (4b - 4a b )cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- a b + a b )cos(x) + (- b - a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 2b + a b + a b )cos(x) + (- b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 4 7 +--R (3a b - 3a b - 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (5b - 3a b - 6a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (6b - 2a b - 10a b + 2a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 4a b - 12a b - 2a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 3 4 3 2 +--R (4b - a b - 5a b + 2a )cos(x) + (b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 4 3 7 +--R ((- 2a b - 2a b)cos(x) + 2b + 2a b )sin(x) +--R + +--R 3 2 2 4 4 3 3 +--R ((- a b - a b )cos(x) + (- b - a b )cos(x) )sec(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b + 6a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (4b + 7a b + 5a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 4 +--R (- b - a b + 4a b + 4a b)cos(x) + (- 4b - 4a b )cos(x) - 4b +--R + +--R 3 +--R - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (a b + a b )cos(x) + (b + 3a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (2b + 4a b + 2a b )cos(x) + (2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 2b + 6a b + 10a b - 4a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 8a b + 2a b - 6a b - 4a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (2b - 6a b - 12a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 3 2 +--R (- 4b - 10a b - 10a b + 4a )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 4 3 4 3 +--R (4b + 4a b )cos(x) + 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 2b - 3a b - a b )cos(x) + (- b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 4 7 +--R (3a b + 3a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (5b + 3a b - 6a b - 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b - 2a b - 6a b + 2a b + 4a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (- 4b + 8a b + 2a b - 2a )cos(x) +--R + +--R 3 2 2 4 3 4 3 2 +--R (3a b + 5a b - 2a )cos(x) + (b + a b )cos(x) +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 5 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b - 2a b + 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 2a b - 2a b - 4a b )cos(x) +--R + +--R 5 3 2 4 4 2 3 3 +--R (4b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 3 2 5 +--R (- 4b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b - 2a b )cos(x) + (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 4 4 5 4 2 3 3 2 4 4 +--R (4a b - 4a b)cos(x) + (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 4 +--R (2a b + 2a b )cos(x) + (2a b + 2a b + 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 10a b + 10a b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (4b + 8a b + 8a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 10a b - 10a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b + 2a b )cos(x) + (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 8a b + 8a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 6a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b + 2a b + 2a b - 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b + 2a b)cos(x) + (2b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b + a b )cos(x) + (- b + a b - a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 6a b - 8a b - 6a b + 6a b)cos(x) +--R + +--R 5 4 2 3 5 4 +--R (12b - 7a b - 7a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (5b + 3a b - 13a b + 3a b + 6a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b + 3a b + a b + 4a b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 3 +--R (- 4b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b - a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 3 2 4 +--R (2b + a b - a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 4 5 7 +--R (4a b - 6a b + 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 10a b + 4a b + 8a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 6b - 10a b + 16a b + 14a b - 10a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 20b + 8a b + 16a b + 4a b - 4a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 3 +--R (- 6b - 6a b + 16a b - 6a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 2 5 4 2 3 +--R (4b - 4a b - 2a b + 2a b)cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 4 2 3 +--R 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 5 3 2 5 5 4 2 3 3 2 4 +--R (- 2b + 2a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (3a b - 3a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (3b - a b + a b - 5a b - 2a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (2b + 7a b - 5a b - 12a b + 2a b + 6a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + 10a b - 14a b - 12a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (8b - a b - 9a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (3b + a b - 5a b - a b + 2a b)cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b - 2a b + 2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b - 2a b)cos(x) + (2b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 6a b + 4a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (8b + 13a b + 3a b - 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (5b + 9a b - a b - 3a b + 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b - 5a b - a b + 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 4 2 3 +--R (- 4b - 8a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 5a b + 5a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (2b + 4a b + 4a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (8a b + 6a b - 8a b - 4a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 5 6 +--R (8b + 10a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 2a b - 4a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 12b - 16a b + 4a b - 4a b - 4a )cos(x) +--R + +--R 5 4 4 5 3 +--R (- 6b - 10a b - 6a b - 2a )cos(x) +--R + +--R 5 4 3 2 4 2 5 4 2 3 +--R (4b + 4a b - 2a b - 2a b)cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 4 2 3 +--R 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 2b - 4a b - 4a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- b - 3a b - 3a b - a b )cos(x) + (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (3a b + 3a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (3b + a b + a b + 5a b - 2a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 2b - a b + 5a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (- 4b + 2a b + 6a b - 4a b + 4a )cos(x) +--R + +--R 5 4 2 3 4 5 4 +--R (4b + 3a b - 3a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (3b + 3a b - a b + a b + 2a b)cos(x) + (a b + a b )cos(x) +--R / +--R 4 2 3 4 5 4 3 5 +--R ((2a b - 2a b )cos(x) + (2b - 2a b )cos(x) )sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (- 2a b + 2a b )cos(x) + (- 2b - 2a b + 4a b )cos(x) +--R + +--R 5 2 3 4 5 4 3 +--R (- 4b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (4b - 2a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 5 4 3 5 +--R ((2a b + 2a b )cos(x) + (2b + 2a b )cos(x) )sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (- 4b - 8a b - 4a b )cos(x) + (- 4b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (4b + 6a b + 2a b )cos(x) + (2b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b + 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b + 2a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 6 3 3 4 +--R (- 4b - 2a b + 2a b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 5 2 4 3 +--R (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 3 5 6 5 2 4 3 3 4 +--R (4b - 4a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b + 2a b )cos(x) + (2b + 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 10a b - 10a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (2b + 6a b + 6a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression Integer +--E 119 + +--S 120 of 586 +m0520b:= a0520.2-r0520 +--R +--R +--R (105) +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (3a b - 2a )cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 2 | 2 2 2 +--R (4b - 4a )cos(x) \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R (4b - 4a )cos(x) \|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (- a b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a b )sin(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R Type: Expression Integer +--E 120 + +--S 121 of 586 +d0520b:= D(m0520b,x) +--R +--R +--R (106) +--R 4 2 3 3 2 3 +--R (- 2a b + 4a b - 2a b )cos(x) sec(x) +--R + +--R 2 3 3 2 4 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b - 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b + 8a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (2a b - 2a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (12a b + 4a b - 16a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 8a b - 16a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b + 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 12a b - 4a b + 16a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 8a b - 8a b + 16a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b - 4a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 2a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 12a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (12a b - 12a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 4 3 6 +--R ((- 2a b + 2a b )cos(x) sec(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 4a b - 4a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b - 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b + 4a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 7 +--R (2a b + 4a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (8a b + 16a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (12a b + 28a b + 16a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 24a b + 16a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b + 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 4 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 12a b - 28a b - 16a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (- 8a b - 24a b - 16a b)cos(x) + (- 2a b - 8a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 7 +--R (- 2a b - 4a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 12a b - 24a b - 12a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (- 2a b - 4a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 4 7 2 3 3 2 4 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2a b - 4a b + 2a b )sin(x) +--R + +--R 4 2 3 3 2 3 +--R (- a b + 2a b - a b )cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b + 8a b - 8a b - 6a b + 10a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (a b + 2a b - 11a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 +--R (10a b - 16a b + 6a b)cos(x) - 2a b + 8a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b - 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 10a b - 16a b + 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (4b + 17a b - 4a b - 27a b + 10a )cos(x) +--R + +--R 5 4 2 3 4 5 3 +--R (6b - 10a b + 16a b - 18a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 13a b + 8a b + 21a b - 16a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (- 8a b - 6a b + 20a b - 6a b)cos(x) - 2a b - 4a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (a b - a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (6a b + 2a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (4a b + 4a b - 8a b )cos(x) + (a b + 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 3 2 4 5 7 +--R (2b - 4a b + 2a b + 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 3a b - 14a b + 17a b + 8a b - 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 26a b - 2a b + 50a b + 2a b - 24a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 8b - 32a b + 12a b + 52a b - 4a b - 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 6b - 4a b - 4a b + 14a b + 6a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (11a b - 10a b - 9a b + 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 3 2 +--R (8a b - 2a b - 8a b + 2a b)cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- a b + a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 6a b + 6a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 +--R (3a b - 5a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 2b + 12a b + 4a b - 22a b - 2a b + 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b + 21a b + 8a b - 41a b - 4a b + 20a )cos(x) +--R + +--R 4 3 2 5 5 +--R (22a b - 42a b + 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 15a b - 8a b - 25a b + 4a b + 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (2b + 6a b - 4a b - 8a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 3 2 8 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b )sin(x) +--R + +--R 4 3 2 3 +--R (- a b + a b )cos(x) sec(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 2b + 4a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 4 +--R (a b + 4a b - 5a b - 8a b)cos(x) + (10a b + 4a b - 6a b)cos(x) +--R + +--R 4 2 3 3 2 +--R - 2a b + 4a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 2a b - 2a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b - 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b + 14a b - 12a b - 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 25a b + 22a b - 9a b - 4a b + 6a )cos(x) +--R + +--R 5 4 3 2 4 5 3 +--R (6b + 6a b + 8a b + 14a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 13a b - 18a b + 11a b + 16a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (- 8a b - 22a b - 8a b + 6a b)cos(x) - 2a b - 8a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 7 4 2 3 3 2 6 +--R (a b + 2a b + a b )cos(x) + (4a b + 8a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (6a b + 14a b + 8a b )cos(x) + (4a b + 12a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b + 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (2b + 8a b + 8a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b + 21a b + 20a b - 9a b - 16a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 2a b + 2a b + 2a b - 10a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 8b - 32a b - 20a b + 12a b - 4a b - 12a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 6b - 12a b - 8a b - 6a b - 10a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (11a b + 12a b - 7a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (8a b + 14a b + 4a b - 2a b)cos(x) + 2a b + 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 7 4 2 3 3 2 6 +--R (- a b - 2a b - a b )cos(x) + (- 4a b - 8a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (- 6a b - 12a b - 6a b )cos(x) + (- 4a b - 8a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (- a b - 2a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (3a b + 6a b + a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 2b + 4a b + 16a b + 6a b - 10a b - 6a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b - 3a b + 10a b + 9a b - 4a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 2a b - 4a b + 2a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 7a b - 2a b - 3a b + 8a b + 6a )cos(x) +--R + +--R 5 4 2 3 4 5 3 4 2 3 3 2 2 +--R (2b + 6a b + 4a b + 2a b + 2a )cos(x) + (a b + 2a b + a b )cos(x) +--R / +--R 5 2 4 3 3 3 6 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 2 4 3 3 5 2 4 3 3 4 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (- 2a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 +--R (- 12a b - 4a b + 16a b )cos(x) +--R + +--R 5 2 4 3 3 4 +--R (- 8a b - 8a b + 16a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b - 4a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (2a b - 2a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (12a b - 12a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 3 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 3 6 +--R (2a b - 2a b )cos(x) sin(x) +--R + +--R 2 4 3 3 5 2 4 3 3 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b + 4a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 3 3 7 5 2 4 3 3 6 +--R (- 2a b - 4a b - 2a b )cos(x) + (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 +--R (- 12a b - 28a b - 16a b )cos(x) +--R + +--R 5 2 4 3 3 4 5 2 4 3 3 3 +--R (- 8a b - 24a b - 16a b )cos(x) + (- 2a b - 8a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 3 3 7 5 2 4 3 3 6 +--R (2a b + 4a b + 2a b )cos(x) + (8a b + 16a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 5 2 4 3 3 4 +--R (12a b + 24a b + 12a b )cos(x) + (8a b + 16a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (2a b + 4a b + 2a b )cos(x) +--R Type: Expression Integer +--E 121 + +--S 122 of 586 +t0521:= sec(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (107) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 122 + +--S 123 of 586 +r0521:= atanh(sin(x))/b-2*a*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2) +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R \|- b + a atanh(sin(x)) + 2a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (108) --------------------------------------------------- +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression Integer +--E 123 + +--S 124 of 586 +a0521:= integrate(t0521,x) +--R +--R +--R (109) +--R [ +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R a log(------------------------------------------------) +--R a cos(x) + b +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R , +--R +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b - a log(-------------------) - \|b - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R - 2a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +-------+ +--R | 2 2 +--R b\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 124 + +--S 125 of 586 +m0521a:= a0521.1-r0521 +--R +--R +--R (110) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R a log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - \|- b + a atanh(sin(x)) - 2a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression Integer +--E 125 + +--S 126 of 586 +d0521a:= D(m0521a,x) +--R +--R +--R (111) +--R 2 3 6 +--R (- a b + a )sin(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 2a b + 3a b)cos(x) + (- 2b + 2a b + a b + a )cos(x) +--R + +--R 2 2 3 +--R - 2a b + 5a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 +--R (- 2a b + 2a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2b + a b - 2a b - a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R (2b - 3a b - 3a b - 2a )cos(x) + 2a b - 5a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b + a b)cos(x) + (- b + a b - a b + 2a )cos(x) +--R + +--R 2 3 3 3 2 2 3 2 +--R (a b + 3a )cos(x) + (b - a b + 4a b + 2a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + 2a b + a )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 6 +--R (- a b - a )sin(x) +--R + +--R 2 2 2 3 2 2 3 2 +--R (- 2a b - a b)cos(x) + (- 2b - 2a b - a b + a )cos(x) - 2a b +--R + +--R 2 3 +--R a b + 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- 2a b - 2a b + a )cos(x) + (- 2b - 3a b - 2a b - a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - a b - a b - 2a )cos(x) + (2b + a b - a b - 2a )cos(x) +--R + +--R 2 2 3 +--R 2a b - a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b - a b)cos(x) + (- b - a b - a b - 2a )cos(x) +--R + +--R 2 3 3 3 2 3 2 +--R (- a b - a )cos(x) + (b + a b + 2a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + 2a b + a )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (- 2a b + 3a b + 2a b - 3a )cos(x) - 2b + 2a b + 3a b - 2a b +--R + +--R 4 +--R - a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 3 4 3 +--R (- 2a b + a b + 2a b - a )cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b + a b - a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (- b + 3a b - 5a b - 3a b + 6a )cos(x) + 2b - 2a b - 4a b +--R + +--R 3 4 +--R 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b + a b + 2a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 2 4 +--R (b - a b + 2a b + a b - 3a )cos(x) + a b - a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 4 4 3 2 2 3 4 +--R ((- 2a b - a b + 2a b + a )cos(x) - 2b - 2a b + a b + 2a b + a ) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 3 4 3 +--R (- 2a b - 3a b + 2a b + 3a )cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 4 +--R (- b + a b + 3a b - a b - 2a )cos(x) + 2b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b - a b + 2a b + a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 2 4 +--R (b + a b - 2a b - a b + a )cos(x) - a b + a +--R * +--R sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b)cos(x) + a b +--R + +--R 2 2 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 2b - a b + a b + 2a b)cos(x) + (- 2b + 2a b)cos(x) +--R + +--R 3 2 2 +--R - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b + a b - a b - a b)cos(x) +--R + +--R 4 3 2 4 3 2 2 3 3 2 2 +--R (2b - 2a b)cos(x) + (b + a b - a b - a b)cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b + a b )cos(x) + (b + a b + a b + a b)cos(x) + a b +--R + +--R 2 2 +--R a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 2b - 5a b - 5a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + 4a b + 4a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 5 +--R ((a b - a b - a b + a b)cos(x) + b - a b - a b + a b )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b - a b + 3a b + a b - 2a b)cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 +--R (- 2b + 4a b - 2a b)cos(x) - 2b + 2a b + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + a b - 3a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (2b - a b - 3a b + a b + a b)cos(x) + b - a b - a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 5 +--R ((a b + a b - a b - a b)cos(x) + b + a b - a b - a b )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b - 3a b - a b + 3a b + 2a b)cos(x) +--R + +--R 5 4 3 2 4 5 4 2 3 3 2 +--R (- 2b - 4a b + 4a b + 2a b)cos(x) - 2b - 2a b + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + 3a b + a b - 3a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (2b + 3a b - a b - 3a b - a b)cos(x) + b + a b - a b - a b +--R * +--R sin(x) +--R Type: Expression Integer +--E 126 + +--S 127 of 586 +m0521b:= a0521.2-r0521 +--R +--R +--R (112) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R x +--R +---------+ +-------+ +-------+ (b - a)tan(-) +--R | 2 2 | 2 2 | 2 2 2 +--R - \|- b + a \|b - a atanh(sin(x)) - 2a\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|b - a +--R - 2a\|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- b + a \|b - a +--R Type: Expression Integer +--E 127 + +--S 128 of 586 +d0521b:= D(m0521b,x) +--R +--R +--R (113) +--R 2 2 6 +--R (- 2b + 3a b - a )sin(x) +--R + +--R 2 2 2 2 2 +--R (- 4b + 4a b + 2a )cos(x) + (- 5b + 4a b + 5a )cos(x) - a b +--R + +--R 2 +--R 3a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a b - a )cos(x) + (- 6b + 4a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 2b - 12a )cos(x) + (4b - 6a b - 10a )cos(x) + 2b - 3a b +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b + a )cos(x) + (- 2b - a b + 5a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2a b + 10a )cos(x) + (2b + 10a )cos(x) +--R + +--R 2 2 2 +--R (b + 2a b + 5a )cos(x) + a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 6 +--R (- 2b - a b - a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 4b - 4a b + 2a )cos(x) + (- 5b - 6a b + 3a )cos(x) - a b + 3a ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - 3a b - a )cos(x) + (- 6b - 8a b - 2a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 2b - 4a b - 4a )cos(x) + (4b + 2a b - 6a )cos(x) + 2b + a b +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b - 2a b - a )cos(x) + (- 2b - 5a b - 3a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2a b - 2a )cos(x) + (2b + 4a b + 2a )cos(x) +--R + +--R 2 2 2 +--R (b + 4a b + 3a )cos(x) + a b + a +--R / +--R 3 2 2 6 +--R (b - 2a b + a b)sin(x) +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) - b + 4a b - 3a b) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- b + a b)cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (- 6b - 2a b + 8a b)cos(x) + (- 4b - 4a b + 8a b)cos(x) - b +--R + +--R 2 2 +--R - 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (b - a b)cos(x) + (4b - 4a b)cos(x) + (6b - 6a b)cos(x) +--R + +--R 3 2 3 2 +--R (4b - 4a b)cos(x) + b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 6 +--R (b - a b)sin(x) +--R + +--R 2 2 2 2 2 3 2 2 4 +--R ((2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) - b + 2a b + 3a b)sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- b - 2a b - a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (- 6b - 14a b - 8a b)cos(x) + (- 4b - 12a b - 8a b)cos(x) - b +--R + +--R 2 2 +--R - 4a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (b + 2a b + a b)cos(x) + (4b + 8a b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 2 +--R (6b + 12a b + 6a b)cos(x) + (4b + 8a b + 4a b)cos(x) + b + 2a b +--R + +--R 2 +--R a b +--R Type: Expression Integer +--E 128 + +--S 129 of 586 +t0522:= sec(x)^3/(a+b*sec(x)) +--R +--R +--R 3 +--R sec(x) +--R (114) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 129 + +--S 130 of 586 +r0522:= -a*atanh(sin(x))/b^2+2*a^2*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+tan(x)/b +--R +--R +--R (115) +--R x +--R +---------+ (b - a)tan(-) +---------+ +--R | 2 2 2 2 | 2 2 +--R - a\|- b + a atanh(sin(x)) - 2a atanh(-------------) + b tan(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 130 + +--S 131 of 586 +a0522:= integrate(t0522,x) +--R +--R +--R (116) +--R [ +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R a cos(x)log(----------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 +--R b sin(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b cos(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +-------+ +--R 2 sin(x)\|b - a | 2 2 +--R 2a cos(x)atan(---------------------) + b sin(x)\|b - a +--R (b + a)cos(x) + b + a +--R / +--R +-------+ +--R 2 | 2 2 +--R b cos(x)\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 131 + +--S 132 of 586 +m0522a:= a0522.1-r0522 +--R +--R +--R (117) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R a cos(x)log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 2 +--R a cos(x)\|- b + a atanh(sin(x)) + 2a cos(x)atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b cos(x)tan(x) + b sin(x))\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b cos(x)\|- b + a +--R Type: Expression Integer +--E 132 + +--S 133 of 586 +d0522a:= D(m0522a,x) +--R +--R +--R (118) +--R 3 2 2 4 +--R (- a b + a b )cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (- b + a b - a b + a b)cos(x) + (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (a b - a b )cos(x) + (b + a b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 +--R (2b + a b - a b - 2a b)cos(x) + (2b - 2a b)cos(x) +--R + +--R 3 2 2 2 +--R (2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 4 4 3 2 2 3 3 +--R (- 2b + 2a b)cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 3 2 2 2 +--R (- a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b)cos(x) +--R + +--R 3 2 2 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 5a b + 5a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (2b + 4a b + 4a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (- b - 3a b - 3a b - a b)cos(x) + (- a b - a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R (a b - a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b - a b + a b - a b)cos(x) + a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- a b + 3a b - 3a b)cos(x) +--R + +--R 4 3 2 2 4 3 +--R (- b + a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - a b + 3a b - 3a b + 2a )cos(x) +--R + +--R 4 3 3 2 2 +--R (- 2b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 +--R (2a b - 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (2a b - a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b - 2a b + 5a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b - a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 4 2 2 3 4 2 +--R (2b - 2a b + 3a b - a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + a b - a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b - a b)cos(x) + (a b - a b + a b - 2a )cos(x) +--R + +--R 3 4 5 3 2 2 3 4 4 +--R (- a b - 3a )cos(x) + (- a b + a b - 4a b - 2a )cos(x) +--R + +--R 2 2 3 4 3 3 2 +--R (- a b - 2a b - a )cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 +--R (a b + a b + a b + a )cos(x) + (b + a b + a b + a b)cos(x) +--R + +--R 3 2 2 +--R a b + a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 4 3 +--R (- a b + a b + a b)cos(x) + (- b - a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 5a b - 3a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (2a b + 2a b - a )cos(x) + (2a b + 3a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 2a b + a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 4a b + 2a b + 3a b + a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b + a b)cos(x) + (a b + a b + a b + 2a )cos(x) +--R + +--R 3 4 5 3 2 2 4 4 +--R (a b + a )cos(x) + (- a b - a b - 2a )cos(x) +--R + +--R 2 2 3 4 3 3 2 +--R (- a b - 2a b - a )cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b - a b - a b + a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- b - a b + 3a b + a b - 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 2b + 4a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + a b - 3a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b - a b - 3a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b - a b - a b + a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- b - 3a b - a b + 3a b + 2a b)cos(x) +--R + +--R 5 4 3 2 4 3 +--R (- 2b - 4a b + 4a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + 3a b + a b - 3a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b + 3a b - a b - 3a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 7 +--R ((- a b + a b + a b - a b)cos(x) - b + a b + a b - a b )sin(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b - 3a b + 2a b + 3a b - 3a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (b - a b - a b + 2a b - a )cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 +--R (2b - 4a b + 2a b)cos(x) + 2b - 2a b - 2a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b + a b + 2a b - a )cos(x) +--R + +--R 4 2 3 4 5 4 +--R (- 2a b + a b - a b + 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 2a b + 4a b - 4a b - 4a b + 6a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (- b + a b + a b - 3a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- 2b + a b + 3a b - a b - a b)cos(x) - b + a b + a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- a b + a b + 2a b - a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 5 2 +--R (a b - a b + 2a b + a b - 3a )cos(x) + (a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 7 +--R ((- a b - a b + a b + a b)cos(x) - b - a b + a b + a b )sin(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b - a b - 2a b + a b + a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (b + a b - a b - 2a b + a )cos(x) +--R + +--R 5 4 3 2 4 5 4 2 3 3 2 +--R (2b + 4a b - 4a b - 2a b)cos(x) + 2b + 2a b - 2a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b - 3a b + 2a b + 3a )cos(x) +--R + +--R 4 2 3 4 5 4 +--R (- 2a b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (- b - a b + a b + 3a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- 2b - 3a b + a b + 3a b + a b)cos(x) - b - a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- a b - a b + 2a b + a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 5 2 +--R (a b + a b - 2a b - a b + a )cos(x) + (- a b + a )cos(x) +--R * +--R sin(x) +--R / +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 2 3 +--R (- 2b - a b + a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 4 2 3 2 +--R (- 2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (a b - a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 5 3 2 4 5 4 2 3 3 2 3 +--R (2b - 2a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (a b + a b )cos(x) + (b + a b + a b + a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 5a b - 5a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (- 2b - 4a b - 4a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + 4a b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (b + 3a b + 3a b + a b )cos(x) + (a b + a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (a b - a b - a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b + a b - 3a b - a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 3 6 5 2 4 3 3 2 +--R (2b - 4a b + 2a b )cos(x) + (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b - a b + 3a b + a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 2b + a b + 3a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (a b + a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b + 3a b + a b - 3a b - 2a b )cos(x) +--R + +--R 6 5 3 3 4 2 3 +--R (2b + 4a b - 4a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b - 3a b - a b + 3a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 2b - 3a b + a b + 3a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 133 + +--S 134 of 586 +m0522b:= a0522.2-r0522 +--R +--R +--R (119) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a cos(x)\|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2a cos(x)\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 sin(x)\|b - a +--R 2a cos(x)\|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (- b cos(x)tan(x) + b sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b cos(x)\|- b + a \|b - a +--R Type: Expression Integer +--E 134 + +--S 135 of 586 +d0522b:= D(m0522b,x) +--R +--R +--R (120) +--R 3 2 2 2 6 +--R (- b + 2a b - a b)cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (b - 4a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 6 3 2 5 +--R (b - a b)cos(x) + (4b - 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 2a b - 8a b)cos(x) + (4b + 4a b - 8a b)cos(x) +--R + +--R 3 2 2 2 +--R (b + 2a b - 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 6 3 2 5 +--R (- b + a b)cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 6b + 6a b)cos(x) + (- 4b + 4a b)cos(x) + (- b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 6 +--R (- b + a b)cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (b - 2a b - 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b + 2a b + a b)cos(x) + (4b + 8a b + 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 14a b + 8a b)cos(x) + (4b + 12a b + 8a b)cos(x) +--R + +--R 3 2 2 2 +--R (b + 4a b + 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (- b - 2a b - a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 6b - 12a b - 6a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 8 +--R (b - 2a b + a b)sin(x) +--R + +--R 2 2 3 2 2 2 3 2 +--R (4a b - 5a b + a )cos(x) + (4a b - 4a b)cos(x) - b + 4a b +--R + +--R 2 +--R - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- b + 4a b - 3a b - 2a )cos(x) + (- 4b + 5a b - 5a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 2a b + 9a b - 3a )cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- 4b - 4a b + 8a b)cos(x) - b - 2a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (2a b - a b + a )cos(x) + (6a b - 4a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 +--R (b + 2a b - a b + 12a )cos(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b + 2a b + 10a )cos(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R (6b - 2a b - 3a b + 3a )cos(x) + (4b - 4a b)cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 2 3 6 +--R (a b - a )cos(x) + (2a b + a b - 5a )cos(x) +--R + +--R 2 3 5 2 3 4 +--R (2a b - 10a )cos(x) + (- 2a b - 10a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - 2a b - 5a )cos(x) + (- a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 8 +--R (b - a b)sin(x) +--R + +--R 2 2 3 2 2 2 3 2 2 +--R ((4a b + 3a b + a )cos(x) + (4a b + 4a b)cos(x) - b + 2a b + 3a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- b + 2a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 3a b + 2a b - 3a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b - 14a b - 7a b - 3a )cos(x) + (- 4b - 12a b - 8a b)cos(x) +--R + +--R 3 2 2 +--R - b - 4a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (2a b + 3a b + a )cos(x) + (6a b + 8a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (b + 4a b + 5a b + 4a )cos(x) + (4b + 4a b + 2a b + 6a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b + 10a b + 5a b + 3a )cos(x) + (4b + 8a b + 4a b)cos(x) + b +--R + +--R 2 2 +--R 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 2 2 3 6 +--R (a b + 2a b + a )cos(x) + (2a b + 5a b + 3a )cos(x) +--R + +--R 2 3 5 2 2 3 4 +--R (2a b + 2a )cos(x) + (- 2a b - 4a b - 2a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - 4a b - 3a )cos(x) + (- a b - a )cos(x) +--R / +--R 4 3 2 2 2 6 +--R (b - 2a b + a b )cos(x) sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 6 4 2 2 5 +--R (- b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 6b - 2a b + 8a b )cos(x) + (- 4b - 4a b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b - 2a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 6 4 2 2 5 4 2 2 4 +--R (b - a b )cos(x) + (4b - 4a b )cos(x) + (6b - 6a b )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (4b - 4a b )cos(x) + (b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 6 +--R (b - a b )cos(x) sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2a b + 2a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b + 2a b + 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 5 +--R (- b - 2a b - a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 6b - 14a b - 8a b )cos(x) + (- 4b - 12a b - 8a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b - 4a b - 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 5 +--R (b + 2a b + a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (6b + 12a b + 6a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (b + 2a b + a b )cos(x) +--R Type: Expression Integer +--E 135 + +--S 136 of 586 +t0523:= sec(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R sec(x) +--R (121) ------------ +--R b sec(x) + a +--R Type: Expression Integer +--E 136 + +--S 137 of 586 +r0523:= a^2*atanh(sin(x))/b^3+1/2*atanh(sin(x))/b-2*a^3*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-a*tan(x)/b^2+1/2*sec(x)*tan(x)/b +--R +--R +--R (122) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 3 2 +--R (b + 2a )\|- b + a atanh(sin(x)) + 4a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (b sec(x) - 2a b)tan(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression Integer +--E 137 + +--S 138 of 586 +a0523:= integrate(t0523,x) +--R +--R +--R (123) +--R [ +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 3 2 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2a cos(x) log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + b )sin(x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|- b + a +--R , +--R +--R +-------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R 3 2 sin(x)\|b - a +--R - 4a cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + b )sin(x)\|b - a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 138 + +--S 139 of 586 +m0523a:= a0523.1-r0523 +--R +--R +--R (124) +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 3 2 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2a cos(x) log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b - 2a )cos(x) \|- b + a atanh(sin(x)) +--R + +--R x +--R (b - a)tan(-) +--R 3 2 2 +--R - 4a cos(x) atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + b )sin(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|- b + a +--R Type: Expression Integer +--E 139 + +--S 140 of 586 +d0523a:= D(m0523a,x) +--R +--R +--R (125) +--R 4 2 3 5 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 2a b - 2a b - 4a b )cos(x) +--R + +--R 5 3 2 4 4 2 3 3 +--R (4b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 3 2 5 +--R (- 4b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 4 4 5 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b + 2a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 10a b + 10a b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 4 2 3 3 +--R (4a b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 10a b - 10a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b + 2a b )cos(x) + (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 8a b + 8a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 6a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b + 2a b)cos(x) + (2b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 +--R (- a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- b + a b - a b + a b )cos(x) + (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 2a b + 4a b - 6a b + 6a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (- 2b + 3a b - 3a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- b - a b + 7a b - 5a b + 6a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b + 3a b + a b + 4a b - 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a b + a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- b + a b - 3a b + 3a b - 2a b + 4a )cos(x) +--R + +--R 4 2 3 4 5 6 +--R (a b - a b + 2a b + 6a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (2b + 2a b - 4a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 4 5 4 +--R (2b + a b - a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (b + a b - a b - a b + 2a b)cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b - 2a b - 2a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 5 4 4 2 3 +--R (2b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 4 5 +--R (- 2a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 5 4 +--R (- 2b - a b - 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2a b + 2a b + 2a b)cos(x) + 2b + 2a b - 2a b - 2a b ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 5 6 4 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (- 2b - a b + 3a b + a b - 3a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- b - a b + 5a b + 5a b - 4a b - 4a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (- 4b - 4a b + 4a b + 4a b )cos(x) - 4b - 4a b + 4a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (a b + a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b + 3a b + a b - 3a b - 2a b )cos(x) +--R + +--R 6 5 3 3 4 2 4 +--R (2b + 4a b - 4a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 2a b - 2a b - 2a b - 4a b + 4a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 2b - 4a b - 4a b - 2a b + 2a b + 6a b + 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 4 +--R (- 2b - 2a b - 2a b + 2a b + 8a b - 4a )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 3 +--R (- 2a b - 2a b + 2a b + 6a b - 4a )cos(x) +--R + +--R 2 4 3 3 4 2 5 2 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (4b + 4a b - 4a b - 4a b )cos(x) + 2b + 2a b - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - 3a b - a b + 3a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b - 3a b + a b + 3a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- a b - a b - a b - a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- b - a b - a b - a b + 4a b + 2a b - 2a )cos(x) +--R + +--R 5 2 4 4 2 5 6 5 +--R (2a b + 2a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b + 4a b + 2a b - 2a b - 6a b - 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (2b + 3a b - a b - 3a b - 3a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R sin(x) +--R / +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b + 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 2a b + 2a b + 4a b )cos(x) +--R + +--R 6 3 3 4 5 2 4 3 +--R (- 4b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 3 5 6 5 2 4 3 3 4 +--R (4b - 4a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b + 2a b )cos(x) + (2b + 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 10a b - 10a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (2b + 6a b + 6a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 2 5 3 4 4 3 4 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (- 2b - 2a b + 6a b + 2a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (- 4b + 4a b + 4a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (2b + 2a b - 6a b - 2a b + 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b - 2a b - 6a b + 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 3 4 4 3 4 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (- 2b - 6a b - 2a b + 6a b + 4a b )cos(x) +--R + +--R 7 6 3 4 4 3 4 +--R (- 4b - 8a b + 8a b + 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (- 4b - 4a b + 4a b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (2b + 6a b + 2a b - 6a b - 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b + 6a b - 2a b - 6a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R sin(x) +--R Type: Expression Integer +--E 140 + +--S 141 of 586 +m0523b:= a0523.2-r0523 +--R +--R +--R (126) +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 +--R (- b - 2a )cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R - 4a cos(x) \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 sin(x)\|b - a +--R - 4a cos(x) \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 2 2 2 2 +--R ((- b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + b )sin(x)) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R 2b cos(x) \|- b + a \|b - a +--R Type: Expression Integer +--E 141 + +--S 142 of 586 +d0523b:= D(m0523b,x) +--R +--R +--R (127) +--R 4 3 2 2 3 +--R (- 2b + 4a b - 2a b )cos(x) sec(x) +--R + +--R 3 2 2 3 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b - 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b + 8a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (2b - 2a b )cos(x) + (8b - 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (12b + 4a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 +--R (8b + 8a b - 16a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b + 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 12a b - 4a b + 16a b)cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b - 8a b + 16a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b - 4a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (- 2b + 2a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 4 2 2 5 4 2 2 4 +--R (- 12b + 12a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 4 2 2 3 +--R (- 2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (12a b - 12a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 3 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 3 3 6 +--R ((- 2b + 2a b )cos(x) sec(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b - 4a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b - 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b + 4a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (2b + 4a b + 2a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (12b + 28a b + 16a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (8b + 24a b + 16a b )cos(x) + (2b + 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 12a b - 28a b - 16a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (- 8a b - 24a b - 16a b)cos(x) + (- 2a b - 8a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (- 2b - 4a b - 2a b )cos(x) + (- 8b - 16a b - 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (- 12b - 24a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 8b - 16a b - 8a b )cos(x) + (- 2b - 4a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 3 2 2 3 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 3 2 2 3 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 3 2 2 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2b - 4a b + 2a b )sin(x) +--R + +--R 4 3 2 2 3 +--R (- b + 2a b - a b )cos(x) sec(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b + 4a b - 10a b + 10a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (b + 2a b - 11a b + 8a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 +--R (10a b - 16a b + 6a b)cos(x) - 2b + 8a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b - 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b + 6a b - 8a b + 6a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (- 7b + 12a b - 7a b + 10a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b + 12a b + 12a b - 18a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 13b + 8a b + 21a b - 16a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 6a b + 20a b - 6a b)cos(x) - 2b - 4a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (b - a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (6b + 2a b - 8a b )cos(x) + (4b + 4a b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b + 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 3 4 7 +--R (- 2b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 7b + 2a b - 7a b + 8a b - 12a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 6b - 2a b + 2a b + 2a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 12a b + 12a b - 4a b - 20a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 16a b + 2a b + 6a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (11b - 10a b - 9a b + 8a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R (8b - 2a b - 8a b + 2a b)cos(x) + 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (- b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 2 2 5 4 2 2 4 +--R (- 6b + 6a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 2 2 3 +--R (- b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 4 8 4 2 2 3 4 7 +--R (- b - a b + 2a )cos(x) + (- 2b - 2a b - 2a b + 10a )cos(x) +--R + +--R 4 2 2 3 4 6 4 2 2 4 5 +--R (b - a b - 4a b + 20a )cos(x) + (6b - 2a b + 20a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (7b - 5a b + 4a b + 10a )cos(x) +--R + +--R 4 2 2 3 4 3 4 2 2 2 +--R (4b - 4a b + 2a b + 2a )cos(x) + (b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 2 8 +--R ((- 2a b + 2a b)cos(x) + 2b - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 3 4 3 +--R (- b + a b )cos(x) sec(x) + (- 2b - 6a b - 6a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 +--R (b + 4a b - 5a b - 8a b)cos(x) + (10a b + 4a b - 6a b)cos(x) +--R + +--R 4 3 2 2 +--R - 2b + 4a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 2a b - 2a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b - 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 2a b - 4a b - 6a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 7b - 2a b + 3a b - 4a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b - 4a b + 20a b + 14a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 13b - 18a b + 11a b + 16a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 22a b - 8a b + 6a b)cos(x) - 2b - 8a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (b + 2a b + a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (6b + 14a b + 8a b )cos(x) + (4b + 12a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b + 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 4a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 7b - 12a b - 17a b - 16a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 6b - 14a b - 14a b - 10a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 12a b - 12a b - 4a b - 12a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 4a b - 18a b - 10a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (11b + 12a b - 7a b - 8a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (8b + 14a b + 4a b - 2a b)cos(x) + 2b + 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (- b - 2a b - a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (- 6b - 12a b - 6a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (- b - 2a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- b - 2a b - 3a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 4a b - 6a b - 10a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (b + 2a b + a b - 4a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (6b + 12a b + 10a b + 8a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (7b + 14a b + 9a b + 8a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 2 +--R (4b + 8a b + 4a b + 2a b + 2a )cos(x) + (b + 2a b + a b )cos(x) +--R / +--R 5 4 2 3 3 6 +--R (2b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 4 2 3 5 4 2 3 4 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 +--R (- 2b + 2a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 5 4 2 3 5 +--R (- 12b - 4a b + 16a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 2 3 3 +--R (- 8b - 8a b + 16a b )cos(x) + (- 2b - 4a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 5 2 3 5 +--R (2b - 2a b )cos(x) + (8b - 8a b )cos(x) + (12b - 12a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 3 +--R (8b - 8a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 3 6 +--R (2b - 2a b )cos(x) sin(x) +--R + +--R 4 2 3 5 4 2 3 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b + 4a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 7 5 4 2 3 6 +--R (- 2b - 4a b - 2a b )cos(x) + (- 8b - 16a b - 8a b )cos(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (- 12b - 28a b - 16a b )cos(x) + (- 8b - 24a b - 16a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b - 8a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 7 5 4 2 3 6 +--R (2b + 4a b + 2a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (12b + 24a b + 12a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (2b + 4a b + 2a b )cos(x) +--R Type: Expression Integer +--E 142 + +--S 143 of 586 +t0524:= sin(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R sin(x) +--R (128) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 143 + +--S 144 of 586 +r0524:= -1/2*(x-2*sin(x)+cos(x)*sin(x))/a +--R +--R +--R (- cos(x) + 2)sin(x) - x +--R (129) ------------------------ +--R 2a +--R Type: Expression Integer +--E 144 + +--S 145 of 586 +a0524:= integrate(t0524,x) +--R +--R +--R (- cos(x) + 2)sin(x) - x +--R (130) ------------------------ +--R 2a +--R Type: Union(Expression Integer,...) +--E 145 + +--S 146 of 586 +m0524:= a0524-r0524 +--R +--R +--R (131) 0 +--R Type: Expression Integer +--E 146 + +--S 147 of 586 +d0524:= D(m0524,x) +--R +--R +--R (132) 0 +--R Type: Expression Integer +--E 147 + +--S 148 of 586 +t0525:= cos(x)/(a+a*sec(x)) +--R +--R +--R cos(x) +--R (133) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 148 + +--S 149 of 586 +r0525:= -x/a+sin(x)/a+sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 2)sin(x) - x cos(x) - x +--R (134) --------------------------------- +--R a cos(x) + a +--R Type: Expression Integer +--E 149 + +--S 150 of 586 +a0525:= integrate(t0525,x) +--R +--R +--R (cos(x) + 2)sin(x) - x cos(x) - x +--R (135) --------------------------------- +--R a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 150 + +--S 151 of 586 +m0525:= a0525-r0525 +--R +--R +--R (136) 0 +--R Type: Expression Integer +--E 151 + +--S 152 of 586 +d0525:= D(m0525,x) +--R +--R +--R (137) 0 +--R Type: Expression Integer +--E 152 + +--S 153 of 586 +t0526:= tan(x)/(a+a*sec(x)) +--R +--R +--R tan(x) +--R (138) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 153 + +--S 154 of 586 +r0526:= -log(cos(x)+1)/a +--R +--R +--R log(cos(x) + 1) +--R (139) - --------------- +--R a +--R Type: Expression Integer +--E 154 + +--S 155 of 586 +a0526:= integrate(t0526,x) +--R +--R +--R 2 +--R log(----------) +--R cos(x) + 1 +--R (140) --------------- +--R a +--R Type: Union(Expression Integer,...) +--E 155 + +--S 156 of 586 +m0526:= a0526-r0526 +--R +--R +--R 2 +--R log(cos(x) + 1) + log(----------) +--R cos(x) + 1 +--R (141) --------------------------------- +--R a +--R Type: Expression Integer +--E 156 + +--S 157 of 586 +d0526:= D(m0526,x) +--R +--R +--R (142) 0 +--R Type: Expression Integer +--E 157 + +--S 158 of 586 +t0527:= tan(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R tan(x) +--R (143) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 158 + +--S 159 of 586 +r0527:= (-x+atanh(sin(x)))/a +--R +--R +--R atanh(sin(x)) - x +--R (144) ----------------- +--R a +--R Type: Expression Integer +--E 159 + +--S 160 of 586 +a0527:= integrate(t0527,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - x +--R cos(x) + 1 cos(x) + 1 +--R (145) ------------------------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 160 + +--S 161 of 586 +m0527:= a0527-r0527 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (146) ------------------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 161 + +--S 162 of 586 +d0527:= D(m0527,x) +--R +--R +--R (147) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression Integer +--E 162 + +--S 163 of 586 +t0528:= tan(x)^4/(a+a*sec(x)) +--R +--R +--R 4 +--R tan(x) +--R (148) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 163 + +--S 164 of 586 +r0528:= x/a-1/2*atanh(sin(x))/a-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R - atanh(sin(x)) + (sec(x) - 2)tan(x) + 2x +--R (149) ----------------------------------------- +--R 2a +--R Type: Expression Integer +--E 164 + +--S 165 of 586 +a0528:= integrate(t0528,x) +--R +--R +--R (150) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R - cos(x) log(-------------------) + cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 +--R (- 2cos(x) + 1)sin(x) + 2x cos(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Union(Expression Integer,...) +--E 165 + +--S 166 of 586 +m0528:= a0528-r0528 +--R +--R +--R (151) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R - cos(x) log(-------------------) + cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression Integer +--E 166 + +--S 167 of 586 +d0528:= D(m0528,x) +--R +--R +--R (152) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) + 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 3 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) + 2cos(x) - 6cos(x) +--R + +--R 2 +--R - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 3 2 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) + cos(x) + 2cos(x) + cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 167 + +--S 168 of 586 +t0529:= sec(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (153) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 168 + +--S 169 of 586 +r0529:= atanh(sin(x))/a-sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 1)atanh(sin(x)) - sin(x) +--R (154) ---------------------------------- +--R a cos(x) + a +--R Type: Expression Integer +--E 169 + +--S 170 of 586 +a0529:= integrate(t0529,x) +--R +--R +--R (155) +--R sin(x) + cos(x) + 1 +--R (cos(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- cos(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 170 + +--S 171 of 586 +m0529:= a0529-r0529 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (156) ------------------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 171 + +--S 172 of 586 +d0529:= D(m0529,x) +--R +--R +--R (157) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression Integer +--E 172 + +--S 173 of 586 +t0530:= sec(x)^3/(a+a*sec(x)) +--R +--R +--R 3 +--R sec(x) +--R (158) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 173 + +--S 174 of 586 +r0530:= -atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+tan(x)/a +--R +--R +--R (- cos(x) - 1)atanh(sin(x)) + (cos(x) + 1)tan(x) + sin(x) +--R (159) --------------------------------------------------------- +--R a cos(x) + a +--R Type: Expression Integer +--E 174 + +--S 175 of 586 +a0530:= integrate(t0530,x) +--R +--R +--R (160) +--R 2 sin(x) + cos(x) + 1 +--R (- cos(x) - cos(x))log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (cos(x) + cos(x))log(-------------------) + (2cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R 2 +--R a cos(x) + a cos(x) +--R Type: Union(Expression Integer,...) +--E 175 + +--S 176 of 586 +m0530:= a0530-r0530 +--R +--R +--R (161) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression Integer +--E 176 + +--S 177 of 586 +d0530:= D(m0530,x) +--R +--R +--R (162) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 177 + +--S 178 of 586 +t0531:= sec(x)^4/(a+a*sec(x)) +--R +--R +--R 4 +--R sec(x) +--R (163) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 178 + +--S 179 of 586 +r0531:= 3/2*atanh(sin(x))/a-sin(x)/a/(cos(x)+1)-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R (164) +--R (3cos(x) + 3)atanh(sin(x)) + ((cos(x) + 1)sec(x) - 2cos(x) - 2)tan(x) +--R + +--R - 2sin(x) +--R / +--R 2a cos(x) + 2a +--R Type: Expression Integer +--E 179 + +--S 180 of 586 +a0531:= integrate(t0531,x) +--R +--R +--R (165) +--R 3 2 sin(x) + cos(x) + 1 +--R (3cos(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 4cos(x) - cos(x) + 1)sin(x) +--R / +--R 3 2 +--R 2a cos(x) + 2a cos(x) +--R Type: Union(Expression Integer,...) +--E 180 + +--S 181 of 586 +m0531:= a0531-r0531 +--R +--R +--R (166) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R - 3cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression Integer +--E 181 + +--S 182 of 586 +d0531:= D(m0531,x) +--R +--R +--R (167) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) - 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 4 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) - 6cos(x) - 4cos(x) +--R + +--R 3 2 +--R 2cos(x) - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) - 3cos(x) + 4cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 182 + +--S 183 of 586 +t0532:= csc(x)/(a+a*sec(x)) +--R +--R +--R csc(x) +--R (168) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 183 + +--S 184 of 586 +r0532:= -1/2*atanh(cos(x))/a-1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) - 1 +--R (169) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression Integer +--E 184 + +--S 185 of 586 +a0532:= integrate(t0532,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) + cos(x) - 1 +--R cos(x) + 1 +--R (170) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression Integer,...) +--E 185 + +--S 186 of 586 +m0532:= a0532-r0532 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) + 1 +--R cos(x) + 1 +--R (171) ------------------------------------- +--R 4a +--R Type: Expression Integer +--E 186 + +--S 187 of 586 +d0532:= D(m0532,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (172) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression Integer +--E 187 + +--S 188 of 586 +t0533:= csc(x)^3/(a+a*sec(x)) +--R +--R +--R 3 +--R csc(x) +--R (173) ------------ +--R a sec(x) + a +--R Type: Expression Integer +--E 188 + +--S 189 of 586 +r0533:= -1/8*atanh(cos(x))/a-1/8/a/(1-cos(x))-1/8/a/(cos(x)+1)^2 +--R +--R +--R (174) +--R 3 2 2 +--R (- cos(x) - cos(x) + cos(x) + 1)atanh(cos(x)) + cos(x) + cos(x) + 2 +--R ---------------------------------------------------------------------- +--R 3 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R Type: Expression Integer +--E 189 + +--S 190 of 586 +a0533:= integrate(t0533,x) +--R +--R +--R (175) +--R 3 2 sin(x) 3 2 +--R (4cos(x) + 4cos(x) - 4cos(x) - 4)log(----------) + 3cos(x) + 7cos(x) +--R cos(x) + 1 +--R + +--R cos(x) + 5 +--R / +--R 3 2 +--R 32a cos(x) + 32a cos(x) - 32a cos(x) - 32a +--R Type: Union(Expression Integer,...) +--E 190 + +--S 191 of 586 +m0533:= a0533-r0533 +--R +--R +--R sin(x) +--R 4log(----------) + 4atanh(cos(x)) + 3 +--R cos(x) + 1 +--R (176) ------------------------------------- +--R 32a +--R Type: Expression Integer +--E 191 + +--S 192 of 586 +d0533:= D(m0533,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (177) -------------------------------- +--R 2 +--R (8a cos(x) - 8a)sin(x) +--R Type: Expression Integer +--E 192 + +--S 193 of 586 +t0534:= sin(x)/(a+b*csc(x)) +--R +--R +--R sin(x) +--R (178) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 193 + +--S 194 of 586 +r0534:= -b*x/a^2-2*b^2*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)-cos(x)/a +--R +--R +--R x +--R b tan(-) + a +---------+ +--R 2 2 | 2 2 +--R - 2b atanh(------------) + (- a cos(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (179) --------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 194 + +--S 195 of 586 +a0534:= integrate(t0534,x) +--R +--R +--R (180) +--R [ +--R 2 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (- a cos(x) - b x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R 2 (b sin(x) + a cos(x) + a)\|b - a | 2 2 +--R 2b atan(-----------------------------------) + (- a cos(x) - b x)\|b - a +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R ---------------------------------------------------------------------------] +--R +-------+ +--R 2 | 2 2 +--R a \|b - a +--R Type: Union(List Expression Integer,...) +--E 195 + +--S 196 of 586 +m0534a:= a0534.1-r0534 +--R +--R +--R (181) +--R 2 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 2 2 +--R 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 196 + +--S 197 of 586 +d0534a:= D(m0534a,x) +--R +--R +--R (182) +--R 4 2 2 2 2 3 2 3 x 2 +--R (((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 2 2 2 3 2 2 2 4 2 2 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (- 2b + 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 2 3 2 3 +--R ((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 4 3 2 5 2 3 2 5 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 5 2 3 4 3 2 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 3 2 5 2 3 2 5 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 3 +--R a b +--R / +--R 3 2 2 2 3 4 2 3 4 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 4 3 2 3 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 5 3 2 5 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 2 3 4 4 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 4 2 3 4 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 4 3 2 3 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 2 3 3 5 5 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 4 2 6 2 4 6 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 5 3 3 5 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 3 3 5 5 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression Integer +--E 197 + +--S 198 of 586 +m0534b:= a0534.2-r0534 +--R +--R +--R (183) +--R x +--R +-------+ b tan(-) + a +--R 2 | 2 2 2 +--R 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression Integer +--E 198 + +--S 199 of 586 +d0534b:= D(m0534b,x) +--R +--R +--R (184) +--R 3 2 2 2 3 2 3 x 2 +--R (b sin(x) + (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 3 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + b sin(x) +--R 2 +--R + +--R 2 2 3 2 3 +--R (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression Integer +--E 199 + +--S 200 of 586 +t0535:= sin(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R sin(x) +--R (185) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 200 + +--S 201 of 586 +r0535:= 1/2*x/a+b^2*x/a^3+2*b^3*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+b*cos(x)/a^2-1/2*cos(x)*sin(x)/a +--R +--R +--R (186) +--R x +--R b tan(-) + a +--R 3 2 +--R 4b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression Integer +--E 201 + +--S 202 of 586 +a0535:= integrate(t0535,x) +--R +--R +--R (187) +--R [ +--R 3 +--R 2b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 4b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 202 + +--S 203 of 586 +m0535a:= a0535.1-r0535 +--R +--R +--R (188) +--R 3 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 3 2 +--R - 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 203 + +--S 204 of 586 +d0535a:= D(m0535a,x) +--R +--R +--R (189) +--R 5 2 3 2 3 4 2 4 x 2 +--R (((- b + a b )cos(x) + a b )sin(x) - a b cos(x) + a b )tan(-) +--R 2 +--R + +--R 2 3 2 4 2 3 2 5 2 3 +--R (- 2a b sin(x) - 2a b sin(x) - 2a b cos(x) + (2b - 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 3 4 2 4 +--R ((- b + a b )cos(x) + a b )sin(x) - a b cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 3 5 3 3 6 2 4 2 6 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 6 2 4 5 3 3 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 3 3 6 2 4 2 6 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R / +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 4 2 6 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 5 2 2 4 3 6 2 5 6 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 5 2 7 3 4 7 +--R (- 2a b + 2a b)sin(x) + ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 4 3 6 2 5 6 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression Integer +--E 204 + +--S 205 of 586 +m0535b:= a0535.2-r0535 +--R +--R +--R (190) +--R x +--R +-------+ b tan(-) + a +--R 3 | 2 2 2 +--R - 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R - 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression Integer +--E 205 + +--S 206 of 586 +d0535b:= D(m0535b,x) +--R +--R +--R (191) +--R 4 2 3 3 4 2 4 x 2 +--R (- b sin(x) + (2a b cos(x) + 2a b )sin(x) - b cos(x) + b )tan(-) +--R 2 +--R + +--R 3 2 3 2 3 x 4 2 +--R (- 4a b sin(x) - 4a b cos(x) - 4a b cos(x))tan(-) - b sin(x) +--R 2 +--R + +--R 3 3 4 2 4 +--R (2a b cos(x) + 2a b )sin(x) - b cos(x) + b +--R / +--R 3 2 2 4 4 3 2 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 3 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression Integer +--E 206 + +--S 207 of 586 +t0536:= sin(x)^3/(a+b*csc(x)) +--R +--R +--R 3 +--R sin(x) +--R (192) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 207 + +--S 208 of 586 +r0536:= -1/2*b*x/a^2-b^3*x/a^4-2*b^4*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)-cos(x)/a-b^2*cos(x)/a^3+1/3*cos(x)^3/a+1/2*b*cos(x)*sin(x)/a^2 +--R +--R +--R (193) +--R x +--R b tan(-) + a +--R 4 2 +--R - 12b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression Integer +--E 208 + +--S 209 of 586 +a0536:= integrate(t0536,x) +--R +--R +--R (194) +--R [ +--R 4 +--R 6b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 4 (b sin(x) + a cos(x) + a)\|b - a +--R 12b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 209 + +--S 210 of 586 +m0536a:= a0536.1-r0536 +--R +--R +--R (195) +--R 4 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 4 2 +--R 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R a \|- b + a +--R Type: Expression Integer +--E 210 + +--S 211 of 586 +d0536a:= D(m0536a,x) +--R +--R +--R (196) +--R 6 2 4 2 4 5 2 5 x 2 +--R (((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 2 4 2 5 2 4 2 6 2 4 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (- 2b + 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 4 5 2 5 +--R ((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 6 3 4 7 2 5 2 7 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 6 3 4 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 6 3 4 7 2 5 2 7 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 5 +--R a b +--R / +--R 5 2 2 4 3 6 4 3 6 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 5 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 2 7 5 2 7 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 4 3 6 6 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 4 3 6 4 3 6 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 5 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 2 5 3 7 3 5 7 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 7 2 6 2 8 4 4 8 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 2 5 3 7 3 5 7 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression Integer +--E 211 + +--S 212 of 586 +m0536b:= a0536.2-r0536 +--R +--R +--R (197) +--R x +--R +-------+ b tan(-) + a +--R 4 | 2 2 2 +--R 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 4 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression Integer +--E 212 + +--S 213 of 586 +d0536b:= D(m0536b,x) +--R +--R +--R (198) +--R 5 2 4 4 5 2 5 x 2 +--R (b sin(x) + (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b )tan(-) +--R 2 +--R + +--R 4 2 4 2 4 x 5 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + b sin(x) +--R 2 +--R + +--R 4 4 5 2 5 +--R (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b +--R / +--R 4 2 2 5 5 4 2 2 4 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 4 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 5 5 4 2 2 4 2 4 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression Integer +--E 213 + +--S 214 of 586 +t0537:= sin(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R sin(x) +--R (199) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 214 + +--S 215 of 586 +r0537:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5+2*b^5*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)+b*cos(x)/a^2+b^3*cos(x)/a^4-1/3*b*cos(x)^3/a^2-3/8*cos(x)*sin(x)/a-1/2*b^2*cos(x)*sin(x)/a^3-1/4*cos(x)*sin(x)^3/a +--R +--R +--R (200) +--R x +--R b tan(-) + a +--R 5 2 +--R 48b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R - 6a cos(x)sin(x) + (- 12a b - 9a )cos(x)sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression Integer +--E 215 + +--S 216 of 586 +a0537:= integrate(t0537,x) +--R +--R +--R (201) +--R [ +--R 5 +--R 24b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b - 15a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 (b sin(x) + a cos(x) + a)\|b - a +--R - 48b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b - 15a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 216 + +--S 217 of 586 +m0537a:= a0537.1-r0537 +--R +--R +--R (202) +--R 5 +--R 4b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 5 2 +--R - 8b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 4 3 4 3 4 | 2 2 +--R (a cos(x)sin(x) + (a cos(x) - a cos(x))sin(x))\|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 4a \|- b + a +--R Type: Expression Integer +--E 217 + +--S 218 of 586 +d0537a:= D(m0537a,x) +--R +--R +--R (203) +--R 5 2 6 4 3 6 4 3 6 5 +--R - a b sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (a b cos(x) - a b cos(x) + (- a b + a b )cos(x) + a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 7 2 5 2 5 +--R (- 4b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (- a b + a b )cos(x) + a b cos(x) + (a b - a b )cos(x) +--R + +--R 6 5 2 2 6 +--R (- 4a b - a b )cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 6 5 2 7 5 2 7 5 +--R - 2a b sin(x) + ((2a b - 2a )cos(x) - 2a b - 2a )sin(x) +--R + +--R 4 3 6 4 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 5 2 7 5 2 7 3 +--R ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 6 4 6 2 4 3 6 2 5 +--R 2a b cos(x) - 2a b cos(x) + (- 2a b + 2a b)cos(x) - 8a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 7 4 +--R (- 2a b + 2a )cos(x) + (2a b + 2a )cos(x) +--R + +--R 5 2 7 3 5 2 7 2 6 +--R (2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) - 8a b +--R * +--R sin(x) +--R + +--R 4 3 6 5 6 4 4 3 6 3 +--R (- 2a b + 2a b)cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 6 2 7 2 5 +--R (- 8a b - 2a b)cos(x) + (8b - 8a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R - a b sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (a b cos(x) - a b cos(x) + (- a b + a b )cos(x) + a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 4 3 6 3 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 3 6 2 7 2 5 2 5 +--R (- a b - a b)cos(x) + (- 4b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (- a b + a b )cos(x) + a b cos(x) + (a b - a b )cos(x) +--R + +--R 6 5 2 2 6 +--R (- 4a b - a b )cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 6 5 3 7 3 5 7 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 5 3 7 3 5 7 3 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (- a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 3 7 3 3 5 7 2 +--R (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 3 8 2 6 4 4 6 2 2 8 2 6 +--R (a b - a b )cos(x) + (4b - 4a b + a b - a b )cos(x) - 4b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 7 6 6 2 8 4 4 8 5 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 5 3 7 4 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 6 2 8 4 4 8 3 +--R ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 5 3 7 4 5 3 7 2 +--R (- 2a b + 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 7 3 5 5 3 7 +--R (- 2a b + 2a b)cos(x) + 8a b - 8a b - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 8 5 4 4 8 4 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 6 2 8 3 4 4 8 2 8 2 6 +--R (2a b - 2a )cos(x) + (2a b - 2a )cos(x) + 8b - 8a b +--R * +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 5 3 7 3 7 3 5 5 3 7 2 +--R (2a b - 2a b)cos(x) + (8a b - 8a b + 2a b - 2a b)cos(x) +--R + +--R 7 3 5 +--R (8a b - 8a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 6 5 3 7 3 5 7 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 5 3 7 3 5 7 3 +--R (a b - a b )cos(x)sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- a b + a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 +--R - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 5 3 7 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 5 7 2 7 3 5 7 3 5 +--R (a b - a b)cos(x) + (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 +--R (4b - 4a b + a b - a b )cos(x) - 4b + 4a b +--R / +--R 6 2 2 5 3 7 5 3 7 +--R 4a b sin(x) + ((- 4a b + 4a b)cos(x) + 4a b + 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 2 6 2 8 6 2 8 +--R 8a b sin(x) + ((- 8a b + 8a )cos(x) + 8a b + 8a )sin(x) +--R + +--R 5 3 7 7 +--R (- 8a b + 8a b)cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 2 5 3 7 5 3 7 +--R 4a b sin(x) + ((- 4a b + 4a b)cos(x) + 4a b + 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 4 7 2 2 +--R (- 4a b + 4a b )sin(x) +--R + +--R 6 3 8 4 5 8 +--R ((- 4a b + 4a b)cos(x) - 4a b + 4a b)sin(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 8 2 7 2 9 5 4 9 +--R (- 8a b + 8a b)sin(x) + ((- 8a b + 8a )cos(x) - 8a b + 8a )sin(x) +--R + +--R 6 3 8 6 3 8 +--R (- 8a b + 8a b)cos(x) - 8a b + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 7 2 2 6 3 8 4 5 8 +--R (- 4a b + 4a b )sin(x) + ((- 4a b + 4a b)cos(x) - 4a b + 4a b)sin(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R Type: Expression Integer +--E 218 + +--S 219 of 586 +m0537b:= a0537.2-r0537 +--R +--R +--R (204) +--R x +--R +-------+ b tan(-) + a +--R 5 | 2 2 2 +--R - 8b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R - 8b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +-------+ +--R 4 3 4 3 4 | 2 2 | 2 2 +--R (a cos(x)sin(x) + (a cos(x) - a cos(x))sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 | 2 2 | 2 2 +--R 4a \|- b + a \|b - a +--R Type: Expression Integer +--E 219 + +--S 220 of 586 +d0537b:= D(m0537b,x) +--R +--R +--R (205) +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 5 +--R 8a b cos(x) + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 6 4 2 2 6 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) + (- 4b - a b )cos(x) + 4b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 5 +--R - 2a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 5 2 5 4 6 6 3 +--R (- 2a b cos(x) - 4a b cos(x))sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 5 4 5 5 5 2 +--R (2a b cos(x) + 4a b cos(x) - 16a b + 2a b)sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 6 5 5 5 3 5 5 2 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) + (- 16a b - 2a b)cos(x) +--R + +--R 5 +--R - 16a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 5 +--R 8a b cos(x) + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 6 4 2 2 6 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) + (- 4b - a b )cos(x) + 4b +--R / +--R 5 2 2 6 6 5 2 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 5 2 +--R 8a b cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 7 6 2 +--R 8a b sin(x) + (16a cos(x) + 16a )sin(x) + 8a b cos(x) +--R + +--R 6 6 +--R 16a b cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 6 5 2 2 5 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) + 8a b cos(x) +--R + +--R 5 2 +--R 4a b +--R Type: Expression Integer +--E 220 + +--S 221 of 586 +t0538:= cos(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R cos(x) +--R (206) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 221 + +--S 222 of 586 +r0538:= 1/2*x/a-b^2*x/a^3+2*b*(a^2-b^2)^(1/2)*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3-b*cos(x)/a^2+1/2*cos(x)*sin(x)/a +--R +--R +--R (207) +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 2 +--R 4b\|- b + a atanh(------------) + a cos(x)sin(x) - 2a b cos(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression Integer +--E 222 + +--S 223 of 586 +a0538:= integrate(t0538,x) +--R +--R +--R (208) +--R [ +--R +---------+ +--R | 2 2 +--R 2b\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 2 2 +--R a cos(x)sin(x) - 2a b cos(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a 2 +--R - 4b\|b - a atan(-----------------------) + a cos(x)sin(x) +--R b sin(x) + a cos(x) + a +--R + +--R 2 2 +--R - 2a b cos(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R ] +--R Type: Union(List Expression Integer,...) +--E 223 + +--S 224 of 586 +m0538a:= a0538.1-r0538 +--R +--R +--R (209) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - 2b\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 +--R a +--R Type: Expression Integer +--E 224 + +--S 225 of 586 +d0538a:= D(m0538a,x) +--R +--R +--R (210) +--R 3 3 3 3 4 2 2 2 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) + (b - a b )cos(x) +--R + +--R 4 2 2 +--R - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 4 2 2 +--R (2a b - 2a b)sin(x) + (2b - 2a b )sin(x) +--R + +--R 3 3 2 3 3 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 3 4 2 2 2 4 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) + (b - a b )cos(x) - b +--R + +--R 2 2 +--R a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 4 2 3 4 4 3 2 2 +--R ((b - 2a b + a b)cos(x) - a b + a b)sin(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 4 3 2 2 3 4 2 +--R (2a b - 2a b)sin(x) + (2a b - 2a b )sin(x) + (2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 +--R (- 2b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 3 4 4 3 2 2 +--R ((b - 2a b + a b)cos(x) - a b + a b)sin(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b + a b +--R / +--R 3 2 2 4 2 3 4 3 2 3 2 +--R (a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 3 2 5 4 +--R 2a b sin(x) + (2a cos(x) + 2a b + 2a )sin(x) + 2a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 2 3 4 3 2 3 2 +--R a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 4 2 6 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R Type: Expression Integer +--E 225 + +--S 226 of 586 +m0538b:= a0538.2-r0538 +--R +--R +--R (211) +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - 2b\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2b\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R / +--R 3 +--R a +--R Type: Expression Integer +--E 226 + +--S 227 of 586 +d0538b:= D(m0538b,x) +--R +--R +--R (212) +--R 4 2 2 2 3 3 3 3 +--R (b - a b )sin(x) + ((- 2a b + 2a b)cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 2 3 3 +--R ((4a b - 4a b)sin(x) + (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 3 3 +--R (b - a b )sin(x) + ((- 2a b + 2a b)cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(x) - b + a b +--R / +--R 3 2 2 4 4 3 2 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 3 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression Integer +--E 227 + +--S 228 of 586 +t0539:= cos(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R cos(x) +--R (213) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 228 + +--S 229 of 586 +r0539:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5+2*b*(a^2-b^2)^(3/2)*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^5-b*cos(x)/a^2+b^3*cos(x)/a^4-1/3*b*cos(x)^3/a^2+5/8*cos(x)*sin(x)/a-1/2*b^2*cos(x)*sin(x)/a^3-1/4*cos(x)*sin(x)^3/a +--R +--R +--R (214) +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 4 3 +--R (- 48b + 48a b)\|- b + a atanh(------------) - 6a cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 3 3 3 3 +--R (- 12a b + 15a )cos(x)sin(x) - 8a b cos(x) + (24a b - 24a b)cos(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression Integer +--E 229 + +--S 230 of 586 +a0539:= integrate(t0539,x) +--R +--R +--R (215) +--R [ +--R +---------+ +--R 3 2 | 2 2 +--R (24b - 24a b)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b + 9a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b - 24a b)cos(x) + (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a +--R (48b - 48a b)\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b + 9a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b - 24a b)cos(x) + (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R ] +--R Type: Union(List Expression Integer,...) +--E 230 + +--S 231 of 586 +m0539a:= a0539.1-r0539 +--R +--R +--R (216) +--R +---------+ +--R 3 2 | 2 2 +--R (4b - 4a b)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 4 3 +--R (8b - 8a b)\|- b + a atanh(------------) + a cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 4 +--R (a cos(x) - a cos(x))sin(x) +--R / +--R 5 +--R 4a +--R Type: Expression Integer +--E 231 + +--S 232 of 586 +d0539a:= D(m0539a,x) +--R +--R +--R (217) +--R 4 2 6 5 3 3 5 5 +--R - a b sin(x) + (- a b cos(x) - a b - a b)sin(x) +--R + +--R 4 2 4 5 3 3 5 3 +--R - a b cos(x)sin(x) + (a b cos(x) + a b + a b)sin(x) +--R + +--R 4 2 4 4 2 2 4 2 4 2 2 +--R (a b cos(x) - a b cos(x) + a b cos(x) + a b )sin(x) +--R + +--R 5 5 3 3 5 4 5 3 +--R a b cos(x) + (a b + a b)cos(x) - a b cos(x) +--R + +--R 3 3 5 2 5 3 3 5 5 +--R (- a b - a b)cos(x) + (4a b - 8a b + 4a b)cos(x) + 4a b +--R + +--R 3 3 5 +--R - 8a b + 4a b +--R * +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R a b cos(x) + a b cos(x) - a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 2a b sin(x) + (- 2a cos(x) - 2a b - 2a )sin(x) +--R + +--R 5 4 6 4 2 6 3 +--R - 2a b cos(x)sin(x) + (2a cos(x) + 2a b + 2a )sin(x) +--R + +--R 5 4 5 2 5 5 3 3 +--R 2a b cos(x) - 2a b cos(x) + 2a b cos(x) - 8a b + 16a b +--R + +--R 5 +--R - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 2 6 4 6 3 +--R 2a cos(x) + (2a b + 2a )cos(x) - 2a cos(x) +--R + +--R 4 2 6 2 6 2 4 4 2 +--R (- 2a b - 2a )cos(x) - 8b + 16a b - 8a b +--R * +--R sin(x) +--R + +--R 5 5 5 4 5 3 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 8a b + 16a b - 10a b)cos(x) + (- 8a b + 16a b - 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - a b sin(x) + (- a b cos(x) - a b - a b)sin(x) +--R + +--R 4 2 4 5 3 3 5 3 +--R - a b cos(x)sin(x) + (a b cos(x) + a b + a b)sin(x) +--R + +--R 4 2 4 4 2 2 4 2 4 2 2 +--R (a b cos(x) - a b cos(x) + a b cos(x) + a b )sin(x) +--R + +--R 5 5 3 3 5 4 5 3 +--R a b cos(x) + (a b + a b)cos(x) - a b cos(x) +--R + +--R 3 3 5 2 5 3 3 5 5 +--R (- a b - a b)cos(x) + (4a b - 8a b + 4a b)cos(x) + 4a b +--R + +--R 3 3 5 +--R - 8a b + 4a b +--R * +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R a b cos(x) + a b cos(x) - a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (- a b cos(x) + a b cos(x) + (a b - a b )cos(x) - a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (4b - 12a b + 12a b - 4a b)cos(x) - 4a b + 8a b - 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (a b - a b )cos(x) - a b cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 8a b + 5a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 6 5 2 7 5 2 7 5 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 4 3 6 4 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 7 5 2 7 3 +--R ((2a b - 2a )cos(x) - 2a b - 2a )sin(x) +--R + +--R 6 4 6 2 4 3 6 2 5 +--R - 2a b cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) + 8a b +--R + +--R 4 3 6 +--R - 16a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 7 4 +--R (2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) +--R + +--R 5 2 7 3 5 2 7 2 6 3 4 +--R (- 2a b + 2a )cos(x) + (2a b + 2a )cos(x) + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R sin(x) +--R + +--R 4 3 6 5 6 4 4 3 6 3 +--R (2a b - 2a b)cos(x) - 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (8a b - 16a b + 10a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 8b + 24a b - 24a b + 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 4 4 3 6 4 3 6 3 +--R (- a b + a b )cos(x)sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (- a b cos(x) + a b cos(x) + (a b - a b )cos(x) - a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 4 3 6 3 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 2 7 2 5 4 3 6 2 5 +--R (a b + a b)cos(x) + (4b - 12a b + 12a b - 4a b)cos(x) - 4a b +--R + +--R 4 3 6 +--R 8a b - 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (a b - a b )cos(x) - a b cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 8a b + 5a b )cos(x) - 4a b + 8a b - 4a b +--R / +--R 5 2 2 6 4 3 6 5 2 +--R 4a b sin(x) + (4a b cos(x) + 4a b + 4a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 +--R 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 5 2 7 6 +--R 8a b sin(x) + (8a cos(x) + 8a b + 8a )sin(x) + 8a b cos(x) +--R + +--R 6 +--R 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 4 3 6 5 2 5 2 +--R 4a b sin(x) + (4a b cos(x) + 4a b + 4a b)sin(x) + 4a b cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 2 2 5 3 7 5 3 7 +--R - 4a b sin(x) + ((4a b - 4a b)cos(x) - 4a b - 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (4a b - 4a b )cos(x) - 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 2 6 2 8 6 2 8 +--R - 8a b sin(x) + ((8a b - 8a )cos(x) - 8a b - 8a )sin(x) +--R + +--R 5 3 7 7 +--R (8a b - 8a b)cos(x) - 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 2 5 3 7 5 3 7 +--R - 4a b sin(x) + ((4a b - 4a b)cos(x) - 4a b - 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (4a b - 4a b )cos(x) - 4a b +--R Type: Expression Integer +--E 232 + +--S 233 of 586 +m0539b:= a0539.2-r0539 +--R +--R +--R (218) +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 +--R (8b - 8a b)\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a 4 3 +--R (8b - 8a b)\|b - a atan(-----------------------) + a cos(x)sin(x) +--R b sin(x) + a cos(x) + a +--R + +--R 4 3 4 +--R (a cos(x) - a cos(x))sin(x) +--R / +--R 5 +--R 4a +--R Type: Expression Integer +--E 233 + +--S 234 of 586 +d0539b:= D(m0539b,x) +--R +--R +--R (219) +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 2 4 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + 8a b - 3a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a b - 16a b + 8a b)cos(x) + 8a b - 16a b + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 5 +--R - 2a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 5 2 5 4 6 6 3 +--R (- 2a b cos(x) - 4a b cos(x))sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 5 4 5 5 3 3 5 2 +--R (2a b cos(x) + 4a b cos(x) - 16a b + 32a b - 14a b)sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 6 5 5 5 3 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 16a b + 32a b - 18a b)cos(x) + (- 16a b + 32a b - 16a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 2 4 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + 8a b - 3a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a b - 16a b + 8a b)cos(x) + 8a b - 16a b + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R / +--R 5 2 2 6 6 5 2 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 5 2 +--R 8a b cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 7 6 2 +--R 8a b sin(x) + (16a cos(x) + 16a )sin(x) + 8a b cos(x) +--R + +--R 6 6 +--R 16a b cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 6 5 2 2 5 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) + 8a b cos(x) +--R + +--R 5 2 +--R 4a b +--R Type: Expression Integer +--E 234 + +--S 235 of 586 +t0540:= tan(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R tan(x) +--R (220) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 235 + +--S 236 of 586 +r0540:= -x/a+2*b^3*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(3/2)+1/2*cos(x)/(a+b)/(1-sin(x))-1/2*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (221) +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (- 2b sin(x) + 2b )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 2 2 +--R ((- b + a )x sin(x) + a cos(x)sin(x) - a b cos(x) + (b - a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )sin(x) - a b + a )\|- b + a +--R Type: Expression Integer +--E 236 + +--S 237 of 586 +a0540:= integrate(t0540,x) +--R +--R +--R (222) +--R [ +--R 3 +--R b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a sin(x) + ((- b + a )x + a b)cos(x) + a b)\|- b + a +--R / +--R +---------+ +--R 2 3 | 2 2 +--R (a b - a )cos(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 (b sin(x) + a cos(x) + a)\|b - a +--R 2b cos(x)atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a sin(x) + ((- b + a )x + a b)cos(x) + a b)\|b - a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b - a )cos(x)\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 237 + +--S 238 of 586 +m0540a:= a0540.1-r0540 +--R +--R +--R (223) +--R 3 2 3 +--R (b cos(x)sin(x) - b cos(x)) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (2b cos(x)sin(x) - 2b cos(x))atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 2 +--R - a sin(x) + (a b cos(x) + a b)sin(x) + (- a cos(x) + a )sin(x) +--R + +--R 2 +--R a b cos(x) - a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )cos(x)sin(x) + (- a b + a )cos(x))\|- b + a +--R Type: Expression Integer +--E 238 + +--S 239 of 586 +d0540a:= D(m0540a,x) +--R +--R +--R (224) +--R 3 2 8 2 3 4 4 7 +--R - a b sin(x) + ((a b - a b)cos(x) - a b)sin(x) +--R + +--R 4 3 2 6 +--R (a b + 2a b )sin(x) +--R + +--R 5 2 3 3 2 3 2 +--R (b - a b )cos(x) - 2a b cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (- b - a b + 2a b)cos(x) + a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 2 +--R (a b + a b )cos(x) + (a b - a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- b + a b)cos(x) + (3a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (2b - a b - a b)cos(x) - 2a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 4 4 +--R (a b - a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 3 4 3 2 2 4 +--R (- 2a b + 2a b )cos(x) + (3a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 3a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 2 3 +--R (- b + a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 8 3 2 5 5 7 +--R - 2a b sin(x) + ((2a b - 2a )cos(x) - 2a )sin(x) +--R + +--R 2 3 2 2 3 4 6 +--R (2a b cos(x) + 2a b + 4a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b + 4a )cos(x) +--R + +--R 3 2 5 +--R 2a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (2a b + 2a b)cos(x) + (- 2b + 4a b - 2a b)cos(x) +--R + +--R 2 3 2 2 3 4 +--R - 6a b cos(x) - 4a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (2a b - 4a b + 2a )cos(x) + (- 4a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 2 5 +--R (4a b - 2a b - 2a )cos(x) - 4a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R (2a b - 2a b)cos(x) - 8a b cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 2 3 +--R (4b - 8a b + 4a b)cos(x) + (4a b + 2a b)cos(x) + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (4a b - 6a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 4 5 2 +--R (- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 2a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 5 2 3 4 3 4 2 +--R (- 2b + 4a b - 2a b)cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 8 2 3 4 4 7 +--R - a b sin(x) + ((a b - a b)cos(x) - a b)sin(x) +--R + +--R 4 3 2 6 +--R (a b + 2a b )sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 4 +--R (b - a b )cos(x) - 2a b cos(x) + (- b - a b + 2a b)cos(x) +--R + +--R 2 3 4 +--R a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 2 +--R (a b + a b )cos(x) + (a b - a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- b + a b)cos(x) + (3a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (2b - a b - a b)cos(x) - 2a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (a b - a b )cos(x) - 4a b cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 +--R (3a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 3a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 5 2 3 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) + (- b + a b )cos(x) +--R + +--R 2 3 +--R a b +--R * +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 4 3 2 3 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 8 3 3 5 3 3 5 7 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 2 4 4 2 6 +--R (b + a b - 2a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (a b + a b - 2a b)cos(x) + a b + a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 4 2 4 2 4 4 2 3 +--R (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R (- 2b + 2a b )cos(x) - 2b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 5 4 +--R (a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 3 5 3 3 5 2 +--R (a b - a b)cos(x) + (3a b - 2a b - a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 2a b + a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (- a b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 4 2 2 6 2 4 +--R (2a b - 2a b )cos(x) + (3b - 2a b - a b )cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 2a b + 3a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 3 3 5 3 5 5 2 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 6 4 2 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 4 2 2 +--R (- b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 8 +--R (- 2a b + 2a b)sin(x) +--R + +--R 4 2 6 4 2 6 7 +--R ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 6 +--R ((2a b - 2a b )cos(x) + 2a b + 2a b - 4a b)sin(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (2b - 4a b + 2a b )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 2 4 4 2 6 +--R 2a b + 2a b - 4a +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 4 5 3 3 5 3 +--R (2a b - 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 2 5 3 3 5 +--R (- 6a b + 6a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (2a b - 2a )cos(x) + (- 2a b + 4a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 3 6 2 4 6 2 +--R (- 2a b + 4a b - 2a )cos(x) + (- 4b + 6a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 4a b + 2a b + 2a )cos(x) - 4a b + 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 4a b + 8a b - 4a b)cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 +--R 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b + 6a b - 2a )cos(x) + (- 2a b + 4a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 3 6 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )cos(x) + (2b - 2a b - 2a b + 2a )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 3 5 5 5 5 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 8 3 3 5 3 3 5 7 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 2 4 4 2 6 +--R (b + a b - 2a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (a b + a b - 2a b)cos(x) + a b + a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 4 2 4 2 4 4 2 3 6 2 4 2 +--R (b - a b )cos(x) + (- a b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 +--R - 2b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 5 4 +--R (a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 3 5 3 3 5 2 +--R (a b - a b)cos(x) + (3a b - 2a b - a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 2a b + a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (- a b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 4 2 2 6 2 4 +--R (2a b - 2a b )cos(x) + (3b - 2a b - a b )cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 2a b + 3a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 3 3 5 3 5 5 2 5 3 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b )cos(x) +--R + +--R 5 3 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 6 4 2 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 4 2 2 +--R (- b + a b )cos(x) +--R / +--R 2 4 4 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 5 3 3 5 3 5 5 2 5 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 4 +--R ((- b + 2a b - a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 3 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 2 +--R ((2b - 4a b + 2a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 +--R (- b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 6 +--R (2a b - 2a b)cos(x) sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 5 +--R ((- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R ((- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 2a b)cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 3 +--R ((4a b - 8a b + 4a )cos(x) + (- 4a b + 4a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 2 +--R ((4a b - 8a b + 4a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 +--R ((- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 5 3 3 5 3 5 5 2 5 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 4 +--R ((- b + 2a b - a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 3 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 2 +--R ((2b - 4a b + 2a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 +--R (- b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 5 2 2 6 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) ) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((a b - 2a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 2b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 6 +--R (2a b - 4a b + 2a b)cos(x) sin(x) +--R + +--R 3 4 5 2 7 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 3 +--R (- 4a b + 8a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R ((- 4a b + 8a b - 4a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 2 6 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 5 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 4 +--R ((a b - 2a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 2b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R Type: Expression Integer +--E 239 + +--S 240 of 586 +m0540b:= a0540.2-r0540 +--R +--R +--R (225) +--R x +--R +-------+ b tan(-) + a +--R 3 2 3 | 2 2 2 +--R (2b cos(x)sin(x) - 2b cos(x))\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x)sin(x) - 2b cos(x))\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 2 2 +--R - a sin(x) + (a b cos(x) + a b)sin(x) + (- a cos(x) + a )sin(x) +--R + +--R 2 +--R a b cos(x) - a b cos(x) - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 3 2 2 3 | 2 2 | 2 2 +--R ((a b - a )cos(x)sin(x) + (- a b + a )cos(x))\|- b + a \|b - a +--R Type: Expression Integer +--E 240 + +--S 241 of 586 +d0540b:= D(m0540b,x) +--R +--R +--R (226) +--R 2 2 8 3 3 3 7 +--R - a b sin(x) + (- 2a b cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 2 2 2 6 +--R ((b - a b )cos(x) + 3a b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R - 2a b cos(x) - 2a b cos(x) + (2a b + 4a b)cos(x) - a b +--R + +--R 3 +--R 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R ((b + a b )cos(x) - 2a b cos(x) + (- 3b + a b )cos(x) - 3a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 3 3 4 3 3 3 +--R 2a b cos(x) + (- 3a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b + 2a b)cos(x) + (- 4a b - 2a b)cos(x) - a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 2 2 4 2 2 3 +--R a b cos(x) - 2a b cos(x) + (- 2b - a b )cos(x) + 4a b cos(x) +--R + +--R 4 2 2 2 2 2 +--R (3b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 3 5 3 3 4 +--R - 2a b cos(x) + (- 4a b + 2a b)cos(x) + (- a b + 2a b)cos(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 4 2 2 3 +--R a b cos(x) + 2a b cos(x) + b cos(x) - 2a b cos(x) +--R + +--R 4 2 2 2 +--R (- b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 8 4 2 2 4 7 +--R - 2a b sin(x) + (- 4a cos(x) + 2a b - 4a )sin(x) +--R + +--R 3 3 2 3 6 +--R ((4a b - 2a b)cos(x) + 6a b)sin(x) +--R + +--R 2 2 4 2 2 4 5 +--R ((4a b + 8a )cos(x) - 2a b + 8a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (4a b + 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 2 3 +--R (- 8a b + 2a b)cos(x) - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 2 2 4 4 2 2 4 3 +--R 4a cos(x) + (- 6a b + 4a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (- 4a b + 4a )cos(x) + (- 8a b - 4a )cos(x) - 2a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 3 5 3 3 4 +--R 2a b cos(x) - 4a b cos(x) + (- 8a b - 2a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 +--R (- 8a b + 8a b)cos(x) + (4a b + 2a b)cos(x) + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 6 2 2 4 5 2 2 4 4 +--R - 4a b cos(x) + (- 8a b + 4a )cos(x) + (- 2a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 2 2 2 2 +--R (4a b - 4a )cos(x) + (4a b - 4a )cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 3 6 3 5 3 4 3 3 3 +--R 2a b cos(x) + 4a b cos(x) + 4a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 8 3 3 3 7 +--R - a b sin(x) + (- 2a b cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 2 2 2 6 +--R ((b - a b )cos(x) + 3a b )sin(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R (- 2a b cos(x) - 2a b cos(x) + (2a b + 4a b)cos(x) - a b + 4a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R ((b + a b )cos(x) - 2a b cos(x) + (- 3b + a b )cos(x) - 3a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 3 3 4 3 3 3 +--R 2a b cos(x) + (- 3a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b + 2a b)cos(x) + (- 4a b - 2a b)cos(x) - a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 2 2 4 2 2 3 +--R a b cos(x) - 2a b cos(x) + (- 2b - a b )cos(x) + 4a b cos(x) +--R + +--R 4 2 2 2 2 2 +--R (3b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 3 5 3 3 4 +--R - 2a b cos(x) + (- 4a b + 2a b)cos(x) + (- a b + 2a b)cos(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 4 2 2 3 +--R a b cos(x) + 2a b cos(x) + b cos(x) - 2a b cos(x) +--R + +--R 4 2 2 2 +--R (- b - a b )cos(x) +--R / +--R 4 3 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 4 2 5 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 3 +--R ((- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 6 +--R (2a b - 2a b)cos(x) sin(x) +--R + +--R 3 2 5 3 3 2 5 2 5 +--R ((4a b - 4a )cos(x) + (4a b - 4a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 3 2 5 2 3 +--R ((- 8a b + 8a )cos(x) + (- 8a b + 8a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R ((4a b - 4a )cos(x) + (4a b - 4a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 2 3 4 2 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 4 2 5 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 3 +--R ((- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + (a b - a b )cos(x) +--R Type: Expression Integer +--E 241 + +--S 242 of 586 +t0541:= tan(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R tan(x) +--R (227) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 242 + +--S 243 of 586 +r0541:= x/a+2*b^5*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(5/2)+1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))-1/4*(3*a+4*b)*cos(x)/(a+b)^2/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2+1/4*(3*a-4*b)*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (228) +--R x +--R b tan(-) + a +--R 5 4 5 2 5 2 +--R (6b sin(x) - 12b sin(x) + 6b )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 4 4 2 2 4 3 +--R (3b - 6a b + 3a )x sin(x) + (- 7a b + 4a )cos(x)sin(x) +--R + +--R 3 3 4 2 2 4 2 +--R ((6a b - 3a b)cos(x) + (- 6b + 12a b - 6a )x)sin(x) +--R + +--R 2 2 4 3 3 +--R (6a b - 3a )cos(x)sin(x) + (- 5a b + 2a b)cos(x) +--R + +--R 4 2 2 4 +--R (3b - 6a b + 3a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (3a b - 6a b + 3a )sin(x) + (- 6a b + 12a b - 6a )sin(x) + 3a b +--R + +--R 3 2 5 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 243 + +--S 244 of 586 +a0541:= integrate(t0541,x) +--R +--R +--R (229) +--R [ +--R 5 3 +--R 3b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 2 2 4 2 2 2 4 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((3b - 6a b + 3a )x - 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 3 2 5 3 | 2 2 +--R (3a b - 6a b + 3a )cos(x) \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 6b cos(x) atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 4 2 2 2 4 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((3b - 6a b + 3a )x - 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 3 2 5 3 | 2 2 +--R (3a b - 6a b + 3a )cos(x) \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 244 + +--S 245 of 586 +m0541a:= a0541.1-r0541 +--R +--R +--R (230) +--R 5 3 4 5 3 2 5 3 +--R (3b cos(x) sin(x) - 6b cos(x) sin(x) + 3b cos(x) ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 5 3 4 5 3 2 5 3 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) ) +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 2 2 2 4 5 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R ((- 5a b + 2a b)cos(x) + (- 6a b + 3a b)cos(x) + a b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 3 +--R ((7a b - 4a )cos(x) + (- 14a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b + 3a b)cos(x) + (10a b - 4a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (12a b - 6a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R ((- 6a b + 3a )cos(x) + (7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (5a b - 2a b)cos(x) + (- 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 2 5 3 4 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 3 2 5 3 2 4 3 2 5 3 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 245 + +--S 246 of 586 +d0541a:= D(m0541a,x) +--R +--R +--R (231) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (a b + 6a b - 4a b)cos(x) + (3a b - 6a b + 3a b)cos(x) +--R + +--R 4 3 6 +--R - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b - 18a b + 12a b )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 3 4 +--R (- 3b + 3a b )cos(x) + (9a b - 3a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b - 15a b + 13a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (9a b - 5a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 5 2 +--R (18a b + 11a b - 11a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 22a b - a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (24a b + 9a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (21a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (19a b - 29a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 20a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 18a b + 5a b + a b )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 12b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (2b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (18a b + 9a b - 9a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 22a b + 3a b + 7a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 17a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (14a b + 11a b - 7a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (6a b - 6a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (8b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 2b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 5a b - 5a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 6b + 8a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 +--R (7a b - 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (3a b + 6a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (7a b - 11a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- 3a b - 7a b + 4a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 3 4 5 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 10 +--R ((14a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 3 4 5 2 7 3 +--R (- 14a b + 22a b - 8a )cos(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (2a b + 12a b - 8a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 5 2 7 +--R - 6a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 2 5 4 2 5 4 3 6 3 +--R - 6a b cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 12a b - 36a b + 24a b)cos(x) + 6a b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 26a b - 64a b + 26a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 20a b - 30a b + 26a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) + 6a b + 12a b - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (- 6a b - 14a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (30a b - 10a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 6 +--R (36a b + 22a b - 22a b)cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 5 2 7 7 +--R (14a b - 22a b + 8a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (10a b - 18a b + 8a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 12a b + 34a b - 32a b + 10a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (18a b - 26a b - 2a b + 10a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 36a b + 6a b + 60a b - 30a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (48a b + 18a b - 30a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (18a b - 18a b - 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 10a b + 14a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (42a b - 8a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 18b + 56a b - 58a b + 20a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 40a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 36a b + 10a b + 2a b)cos(x) + 18a b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 24a b + 42a b - 24a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (2a b - 8a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (22a b - 62a b + 58a b - 18a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (36a b - 34a b - 16a b + 14a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 44a b + 6a b + 14a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 18a b + 30a b - 6a b - 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6a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 6b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 4 3 6 4 2 5 4 3 6 3 +--R (- 14a b + 8a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 3 6 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 7a b + 11a b - 4a b)cos(x) + (a b + 6a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b - 18a b + 12a b )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 3 4 +--R (- 3b + 3a b )cos(x) + (9a b - 3a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b - 15a b + 13a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (- 6a b + 9a b - 3a b )cos(x) + (9a b - 5a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 5 2 +--R (18a b + 11a b - 11a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (7a b - 11a b + 4a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 22a b - a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (24a b + 9a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 5a b + 7a b - 2a b )cos(x) + (21a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (19a b - 29a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 20a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 6a b + 12a b - 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16a b + 11a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 2b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 5a b - 5a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 6b + 8a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 +--R (7a b - 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (3a b + 6a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (7a b - 11a b + 4a b )cos(x) + (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 7a b + 11a b - 4a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b - 5a b + 10a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (6b + 12a b - 30a b + 12a b )cos(x) - 3b - 3a b + 15a b +--R + +--R 6 2 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 3a b + 3a b )cos(x) + (- 9a b + 12a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b + 5a b - 28a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 9b + 14a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 18b + 7a b + 22a b - 11a b )cos(x) + 9b - 9a b - 9a b +--R + +--R 6 2 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 5a b + 14a b - 13a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (22a b - 21a b - 6a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 18a b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b + 15a b + 24a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 21b + 25a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 6 2 4 +--R (19a b - 29a b + 10a b )cos(x) + (20b - 21a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (18b - 23a b + 4a b + a b )cos(x) - 9b + 15a b - 3a b +--R + +--R 6 2 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 12a b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (2a b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 18a b + 9a b + 18a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (18a b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (22a b - 25a b - 4a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (17b - 14a b - 5a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 14b + 3a b + 18a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 6b + 12a b - 9a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (8a b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 7a b + 8a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 6a b + 8a b - a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 7a b + 10a b - 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 3b - 3a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (7a b - 11a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- 14a b + 22a b - 8a b)cos(x) + 6a b - 12a b + 6a b)sin(x) +--R + +--R 4 4 6 2 8 3 +--R (- 14a b + 22a b - 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b - 10a b + 20a b - 8a )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 8 +--R (6a b - 12a b + 6a )cos(x) + 6a b - 12a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 4 3 5 5 3 7 3 +--R (6a b - 6a b )cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 +--R (12a b + 24a b - 60a b + 24a b)cos(x) - 6a b - 6a b +--R + +--R 5 3 7 +--R 30a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (12a b + 26a b - 64a b + 26a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (20a b + 10a b - 56a b + 26a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) - 6a b - 6a b + 30a b +--R + +--R 8 +--R - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 +--R (6a b + 8a b - 22a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 30a b + 40a b - 14a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 +--R (- 36a b + 14a b + 44a b - 22a b)cos(x) + 18a b - 18a b +--R + +--R 5 3 7 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 6 2 8 7 +--R (14a b - 22a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 10a b + 28a b - 26a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 12a b + 34a b - 32a b + 10a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 18b + 44a b - 24a b - 12a b + 10a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 36a b + 6a b + 60a b - 30a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 48a b + 30a b + 48a b - 30a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) + 18a b - 18a b +--R + +--R 6 2 8 +--R - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 10a b + 14a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 42a b + 50a b - 10a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 56a b - 58a b + 20a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (40a b - 42a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (36a b - 46a b + 8a b + 2a b)cos(x) - 18a b + 30a b - 6a b +--R + +--R 7 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (- 24a b + 42a b - 24a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (22a b - 62a b + 58a b - 18a )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (18b - 36a b + 36a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (36a b - 34a b - 16a b + 14a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (44a b - 50a b - 8a b + 14a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) - 18a b + 30a b - 6a b +--R + +--R 8 +--R - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (22a b - 32a b + 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (34a b - 28a b - 10a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 58a b + 62a b - 22a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 16a b - 6a b + 36a b - 14a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (- 12a b + 24a b - 18a b + 6a b)cos(x) + 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (16a b - 32a b + 22a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (4a b - 14a b + 16a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 10a b + 28a b - 26a b + 8a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 6b + 10a b + 6a b - 18a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 16a b - 2a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 14a b + 20a b - 4a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 12a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b - 6a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (14a b - 22a b + 8a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 7a b + 11a b - 4a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b - 5a b + 10a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (6b + 12a b - 30a b + 12a b )cos(x) - 3b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 3a b + 3a b )cos(x) + (- 9a b + 12a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b + 5a b - 28a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 9b + 14a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 18b + 7a b + 22a b - 11a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 5a b + 14a b - 13a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (22a b - 21a b - 6a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 18a b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b + 15a b + 24a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 21b + 25a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 6 2 4 +--R (19a b - 29a b + 10a b )cos(x) + (20b - 21a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (18b - 23a b + 4a b + a b )cos(x) - 9b + 15a b - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 12a b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (2a b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 18a b + 9a b + 18a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (18a b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (22a b - 25a b - 4a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (17b - 14a b - 5a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 14b + 3a b + 18a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 6b + 12a b - 9a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (8a b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 7a b + 8a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 7 5 3 7 4 7 3 5 5 3 7 3 +--R (5a b - 9a b + 4a b)cos(x) + (- 6a b + 8a b - a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 7a b + 10a b - 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 8 2 6 4 4 6 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (- 3b - 3a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 4 4 6 2 4 +--R (7a b - 11a b + 4a b )cos(x) + (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (3b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 6a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3b - 9a b + 9a b - 3a b )cos(x) + (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 6a b + 12a b - 12a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (12a b - 36a b + 36a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (18a b - 36a b + 36a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 18a b + 36a b - 36a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 12a b + 36a b - 36a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (6a b - 12a b + 12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R Type: Expression Integer +--E 246 + +--S 247 of 586 +m0541b:= a0541.2-r0541 +--R +--R +--R (232) +--R +-------+ +--R 5 3 4 5 3 2 5 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|b - a +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 5 3 4 5 3 2 5 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 4 2 2 2 4 5 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R ((- 5a b + 2a b)cos(x) + (- 6a b + 3a b)cos(x) + a b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 3 +--R ((7a b - 4a )cos(x) + (- 14a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b + 3a b)cos(x) + (10a b - 4a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (12a b - 6a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R ((- 6a b + 3a )cos(x) + (7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (5a b - 2a b)cos(x) + (- 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 2 5 3 4 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 3 2 5 3 2 4 3 2 5 3 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 247 + +--S 248 of 586 +d0541b:= D(m0541b,x) +--R +--R +--R (233) +--R 2 4 4 2 2 2 4 4 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (14a b - 8a b)cos(x) + (- 6a b + 17a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 +--R (- 6a b + 6a b)cos(x) + 3a b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b + 7a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 30a b + 18a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 6a b cos(x) + 6a b cos(x) + (- 12a b - 38a b + 26a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (15a b - 53a b + 26a b)cos(x) + (6a b + 12a b - 18a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b - 7a b + 4a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b - 18a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (47a b - 29a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 7 5 3 3 5 6 +--R (- 14a b + 8a b)cos(x) + (18a b - 23a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b - 22a b + 10a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 5a b - 23a b + 10a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (36a b + 30a b - 30a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 +--R (- 9a b + 57a b - 30a b)cos(x) + (- 18a b + 18a b)cos(x) +--R + +--R 3 3 5 +--R - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 7a b + 4a b )cos(x) + (10a b - 4a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (9b + 6a b )cos(x) + (- 38a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 18b + 9a b - 9a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 31a b + 19a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (12a b - 6a b )cos(x) + (24a b - 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 6 +--R (- 7a b - 5a b + 6a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 4a b + 40a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 42a b - 18a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 36a b - 2a b + 14a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 3a b - 23a b + 14a b)cos(x) +--R + +--R 5 3 3 5 5 5 +--R (18a b - 12a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 3a b + 3a b )cos(x) + (- 22a b + 10a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 9b + 2a b - 5a b )cos(x) + (40a b - 22a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b + 8a b - 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b - 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (- 8a b + 2a b )cos(x) + (- 16a b + 16a b - 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 3a b + 12a b - 6a b)cos(x) + (4a b - 18a b + 8a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b - 19a b + 8a b)cos(x) + (12a b - 4a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (3a b + 2a b - 2a b)cos(x) + (- 6a b + 6a b )cos(x) - 3a b +--R + +--R 3 3 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (6a b - 3a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (3b - a b + a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b - 6a b + 3a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 3 3 5 10 +--R ((14a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 2 6 3 2 4 4 2 6 2 +--R (28a b - 16a )cos(x) + (- 12a b + 34a b - 16a )cos(x) +--R + +--R 4 2 6 2 4 4 2 6 +--R (- 12a b + 12a )cos(x) + 6a b - 18a b + 12a +--R * +--R 9 +--R sin(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (- 12a b + 14a b - 8a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 60a b + 36a b)cos(x) + 24a b - 24a b +--R * +--R 8 +--R sin(x) +--R + +--R 2 4 4 2 6 3 +--R (- 24a b - 76a b + 52a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (30a b - 106a b + 52a )cos(x) + (12a b + 24a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 +--R - 12a b + 48a b - 36a +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 12a b - 14a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (36a b - 36a b + 24a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (94a b - 58a b)cos(x) - 36a b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 6 7 2 4 4 2 6 6 +--R (- 28a b + 16a )cos(x) + (36a b - 46a b + 16a )cos(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (24a b - 44a b + 20a )cos(x) + (26a b - 46a b + 20a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (72a b + 60a b - 60a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 6 +--R (- 18a b + 114a b - 60a )cos(x) + (- 36a b + 36a )cos(x) +--R + +--R 4 2 6 +--R - 36a b + 36a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (- 14a b + 8a b)cos(x) + (20a b - 8a b)cos(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (36a b + 12a b )cos(x) + (36a b - 76a b + 40a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (- 36a b + 18a b - 18a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 62a b + 38a b)cos(x) + 24a b - 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 6 7 +--R (24a b - 12a b )cos(x) + (48a b - 36a b + 12a )cos(x) +--R + +--R 2 4 4 2 6 6 +--R (- 14a b - 10a b + 12a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 44a b + 80a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 48a b + 84a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (- 72a b - 4a b + 28a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 6a b - 46a b + 28a )cos(x) + (36a b - 24a b - 12a )cos(x) +--R + +--R 2 4 6 +--R 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (- 6a b + 6a b)cos(x) + (- 44a b + 20a b)cos(x) +--R + +--R 5 3 3 5 6 +--R (- 36a b + 4a b - 10a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 80a b - 44a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (12a b + 16a b - 4a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (12a b - 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 6 7 +--R (- 16a b + 4a b )cos(x) + (- 32a b + 32a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 6 +--R (- 6a b + 24a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (20a b - 36a b + 16a )cos(x) + (22a b - 38a b + 16a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (24a b - 8a b - 4a )cos(x) + (6a b + 4a b - 4a )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (12a b - 6a b)cos(x) + (24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (12a b - 2a b + 2a b)cos(x) + (12a b - 28a b + 16a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (- 12a b + 6a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 4 4 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (14a b - 8a b)cos(x) + (- 6a b + 17a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 +--R (- 6a b + 6a b)cos(x) + 3a b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b + 7a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 30a b + 18a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 6a b cos(x) + 6a b cos(x) + (- 12a b - 38a b + 26a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (15a b - 53a b + 26a b)cos(x) + (6a b + 12a b - 18a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b - 7a b + 4a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b - 18a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (47a b - 29a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 7 5 3 3 5 6 +--R (- 14a b + 8a b)cos(x) + (18a b - 23a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 6a b - 22a b + 10a b)cos(x) + (- 5a b - 23a b + 10a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (36a b + 30a b - 30a b)cos(x) + (- 9a b + 57a b - 30a b)cos(x) +--R + +--R 5 5 3 3 5 +--R (- 18a b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 7a b + 4a b )cos(x) + (10a b - 4a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (9b + 6a b )cos(x) + (- 38a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 18b + 9a b - 9a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 31a b + 19a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (12a b - 6a b )cos(x) + (24a b - 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 7a b - 5a b + 6a b)cos(x) + (- 4a b + 40a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 42a b - 18a b)cos(x) + (- 36a b - 2a b + 14a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 3a b - 23a b + 14a b)cos(x) + (18a b - 12a b - 6a b)cos(x) +--R + +--R 5 5 +--R 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 3a b + 3a b )cos(x) + (- 22a b + 10a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 9b + 2a b - 5a b )cos(x) + (40a b - 22a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b + 8a b - 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b - 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (- 8a b + 2a b )cos(x) + (- 16a b + 16a b - 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 3a b + 12a b - 6a b)cos(x) + (4a b - 18a b + 8a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b - 19a b + 8a b)cos(x) + (12a b - 4a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (3a b + 2a b - 2a b)cos(x) + (- 6a b + 6a b )cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (6a b - 3a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (3b - a b + a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b - 6a b + 3a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (a b - a b )cos(x) +--R / +--R 6 3 4 5 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (3a b - 6a b + 3a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 9a b + 18a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 18a b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (9a b - 18a b + 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (18a b - 36a b + 18a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R ((12a b - 24a b + 12a )cos(x) + (12a b - 24a b + 12a )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 5 2 7 5 +--R (- 36a b + 72a b - 36a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 36a b + 72a b - 36a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R ((36a b - 72a b + 36a )cos(x) + (36a b - 72a b + 36a )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 12a b + 24a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (3a b - 6a b + 3a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 9a b + 18a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 18a b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (9a b - 18a b + 9a b )cos(x) + (18a b - 36a b + 18a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R Type: Expression Integer +--E 248 + +--S 249 of 586 +t0542:= cot(x)/(a+b*csc(x)) +--R +--R +--R cot(x) +--R (234) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 249 + +--S 250 of 586 +r0542:= log(b+a*sin(x))/a +--R +--R +--R log(a sin(x) + b) +--R (235) ----------------- +--R a +--R Type: Expression Integer +--E 250 + +--S 251 of 586 +a0542:= integrate(t0542,x) +--R +--R +--R 2a sin(x) + 2b 2 +--R log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (236) ------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 251 + +--S 252 of 586 +m0542:= a0542-r0542 +--R +--R +--R 2a sin(x) + 2b 2 +--R - log(a sin(x) + b) + log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (237) ----------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 252 + +--S 253 of 586 +d0542:= D(m0542,x) +--R +--R +--R (238) 0 +--R Type: Expression Integer +--E 253 + +--S 254 of 586 +t0543:= cot(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R cot(x) +--R (239) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 254 + +--S 255 of 586 +r0543:= -x/a-atanh(cos(x))/b+2*(a^2-b^2)^(1/2)*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/b +--R +--R +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - a atanh(cos(x)) + 2\|- b + a atanh(------------) - b x +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (240) ---------------------------------------------------------- +--R a b +--R Type: Expression Integer +--E 255 + +--S 256 of 586 +a0543:= integrate(t0543,x) +--R +--R +--R (241) +--R [ +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R sin(x) +--R a log(----------) - b x +--R cos(x) + 1 +--R / +--R a b +--R , +--R +-------+ +--R +-------+ | 2 2 +--R sin(x) | 2 2 (cos(x) + 1)\|b - a +--R a log(----------) - 2\|b - a atan(-----------------------) - b x +--R cos(x) + 1 b sin(x) + a cos(x) + a +--R ------------------------------------------------------------------] +--R a b +--R Type: Union(List Expression Integer,...) +--E 256 + +--S 257 of 586 +m0543a:= a0543.1-r0543 +--R +--R +--R (242) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R sin(x) | 2 2 2 +--R a log(----------) + a atanh(cos(x)) - 2\|- b + a atanh(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R a b +--R Type: Expression Integer +--E 257 + +--S 258 of 586 +d0543a:= D(m0543a,x) +--R +--R +--R (243) +--R 2 4 2 2 3 2 3 +--R a b cos(x)sin(x) + (a b cos(x) + (b + a b)cos(x))sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (a cos(x) + a cos(x) + (a b - a )cos(x) + a b - a )sin(x) +--R + +--R 3 4 3 2 3 3 2 2 +--R b cos(x) + (b + a b)cos(x) + (- 2b + a b)cos(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) + b - a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 3 2 3 3 +--R (2a b cos(x) + (2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 2 3 3 2 3 2 2 +--R (2a b cos(x) + 2b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 4a b cos(x))sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 3 2 3 +--R a b cos(x)sin(x) + (a b cos(x) + (b + a b)cos(x))sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (a cos(x) + a cos(x) + (a b - a )cos(x) + a b - a )sin(x) +--R + +--R 3 4 3 2 3 3 2 2 +--R b cos(x) + (b + a b)cos(x) + (- 2b + a b)cos(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) + b - a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 3 +--R ((- a b + a b)cos(x) + (a b + a b)cos(x))sin(x) +--R + +--R 4 2 2 4 3 4 4 2 +--R (b - a b + a )cos(x) + (- b + a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- b + 2a b - a )cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 3 2 +--R (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (- a b - a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 2 2 4 2 2 4 3 +--R 2a b cos(x)sin(x) + ((2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 3 3 3 3 2 +--R (2a b cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((- 2b + 6a b )cos(x) + (2b - 6a b )cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 2 +--R (- 2a b + 2a b)cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 3 2 3 3 3 +--R a b cos(x)sin(x) + ((- a b + a b)cos(x) + (a b + a b)cos(x))sin(x) +--R + +--R 4 2 2 4 3 4 4 2 +--R (b - a b + a )cos(x) + (- b + a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- b + 2a b - a )cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (a b + a b)cos(x) + (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R / +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 4 2 2 2 2 2 4 2 2 +--R (a b cos(x) + (b + a b )cos(x) - a b cos(x) - b - a b ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 2 3 3 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 3 3 3 3 2 3 3 +--R 2a b cos(x) + (2a b + 2a b)cos(x) - 2a b cos(x) - 2a b +--R + +--R 3 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 4 2 2 2 2 2 4 2 2 2 +--R (a b cos(x) + (b + a b )cos(x) - a b cos(x) - b - a b )sin(x) +--R + +--R 3 3 3 2 3 3 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 2a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (2a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 2 +--R - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 4 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R Type: Expression Integer +--E 258 + +--S 259 of 586 +m0543b:= a0543.2-r0543 +--R +--R +--R (244) +--R x +--R +---------+ b tan(-) + a +--R sin(x) | 2 2 2 +--R a log(----------) + a atanh(cos(x)) - 2\|- b + a atanh(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R / +--R a b +--R Type: Expression Integer +--E 259 + +--S 260 of 586 +d0543b:= D(m0543b,x) +--R +--R +--R (245) +--R 2 4 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 2 3 2 3 +--R ((b + a b)cos(x) + 2a b cos(x) - b + a b)sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (2a cos(x) + 2a cos(x) + (2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 2 3 3 2 2 3 +--R (b + a b)cos(x) + 2a b cos(x) - 2b cos(x) - 2a b cos(x) + b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 3 2 3 3 +--R 2a b cos(x)sin(x) + (4a b cos(x) + 4a cos(x) - 4a b + 4a )sin(x) +--R + +--R 2 3 2 2 2 +--R (4a b cos(x) + 4a b cos(x) )sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b cos(x))sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 3 2 2 2 3 2 3 +--R a b cos(x)sin(x) + ((b + a b)cos(x) + 2a b cos(x) - b + a b)sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (2a cos(x) + 2a cos(x) + (2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 2 3 3 2 2 3 +--R (b + a b)cos(x) + 2a b cos(x) - 2b cos(x) - 2a b cos(x) + b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b cos(x) +--R / +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 3 4 3 3 3 3 +--R (a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 2 2 4 2 2 3 2 2 2 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 3 4 3 3 3 3 +--R (a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b )sin(x) +--R Type: Expression Integer +--E 260 + +--S 261 of 586 +t0544:= cot(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R cot(x) +--R (246) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 261 + +--S 262 of 586 +r0544:= x/a-a^2*atanh(cos(x))/b^3+3/2*atanh(cos(x))/b+2*(a^2-b^2)^(3/2)*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/b^3+a*cot(x)/b^2-1/2*cot(x)*csc(x)/b +--R +--R +--R (247) +--R x +--R +---------+ b tan(-) + a +--R 2 3 2 2 | 2 2 2 +--R (3a b - 2a )atanh(cos(x)) + (- 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R - a b cot(x)csc(x) + 2a b cot(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression Integer +--E 262 + +--S 263 of 586 +a0544:= integrate(t0544,x) +--R +--R +--R (248) +--R [ +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b - 2a )cos(x) - 2b + 2a )\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 +--R - 2a b cos(x)sin(x) + 2b x cos(x) + a b cos(x) - 2b x +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R , +--R +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R ((4b - 4a )cos(x) - 4b + 4a )\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 2 3 2 2 3 +--R - 2a b cos(x)sin(x) + 2b x cos(x) + a b cos(x) - 2b x +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 263 + +--S 264 of 586 +m0544a:= a0544.1-r0544 +--R +--R +--R (249) +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b - 2a )cos(x) - 2b + 2a )\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )atanh(cos(x)) +--R + +--R x +--R +---------+ b tan(-) + a +--R 2 2 2 2 2 | 2 2 2 +--R ((4b - 4a )cos(x) - 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R - 2a b cos(x)sin(x) + (a b cos(x) - a b )cot(x)csc(x) +--R + +--R 2 2 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a b cos(x) +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R Type: Expression Integer +--E 264 + +--S 265 of 586 +d0544a:= D(m0544a,x) +--R +--R +--R (250) +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 3a b cos(x) + (- a b - 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 4a b )cos(x) - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 4 4 4 2 4 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 3a b + 2a b)cos(x) + (- 3b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 5 4 5 2 3 +--R (b - 2a b)cos(x) + (3b - 2a b)cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 5 2 3 4 +--R - 2a b cos(x) + (- 2b - 2a b )cos(x) +--R + +--R 2 3 3 5 2 3 2 2 3 +--R 4a b cos(x) + (4b + 4a b )cos(x) - 2a b cos(x) +--R + +--R 5 2 3 +--R - 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - a b cos(x) + (- b - a b )cos(x) + 2a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (2b + 2a b )cos(x) - a b cos(x) - b - a b +--R * +--R csc(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R 2a b cos(x) + (2a b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (- 4a b - 4a b )cos(x) + 2a b cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- a b - 2a b + 2a )cos(x) + (- a b - 2a b + 2a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (4a b - 4a )cos(x) + (- 2a b + 4a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (3a b - 2a b + 2a )cos(x) + 5a b - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - a b cos(x) - a b cos(x) + 2a b cos(x) + 2a b cos(x) +--R + +--R 4 4 +--R - a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 2 3 2 3 +--R 2a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 2b + a b )cos(x) + (- 3b - a b + 2a b)cos(x) +--R + +--R 5 2 3 4 4 5 4 3 +--R (6b - 6a b + 2a b)cos(x) + (6b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 6b + 7a b - 4a b)cos(x) + (- 3b + a b + 2a b)cos(x) +--R + +--R 5 2 3 4 +--R 2b - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 4a b )cos(x) + (6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 2 3 3 2 3 4 2 +--R - 6a b cos(x) + (- 2a b - 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (6a b - 8a b)cos(x) - 2a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R - 2a b cos(x) + 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (- 4a b + 2a b )cos(x) + (- 6a b - 4a b + 4a )cos(x) +--R + +--R 4 3 2 5 2 4 5 4 +--R (10a b - 16a b + 4a )cos(x) + (6a b - 4a )cos(x) - 2a b +--R + +--R 3 2 5 +--R 10a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 4 3 2 4 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 3 2 3 4 3 2 2 3 2 +--R 8a b cos(x) + (8a b + 8a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 +--R - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R - 2a b cos(x) + (- 2a b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (4a b + 4a b )cos(x) - 2a b cos(x) - 2a b - 2a b +--R * +--R csc(x) +--R + +--R 4 5 2 3 4 4 4 3 +--R 4a b cos(x) + (4a b + 4a b)cos(x) - 8a b cos(x) +--R + +--R 2 3 4 2 4 2 3 4 +--R (- 8a b - 8a b)cos(x) + 4a b cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 5 5 2 3 4 +--R (- 6a b + 4a b)cos(x) + (- 4b + 2a b )cos(x) +--R + +--R 2 3 4 3 5 2 3 2 +--R (8a b - 8a b)cos(x) + (8b - 12a b )cos(x) +--R + +--R 2 3 4 5 2 3 +--R (2a b + 4a b)cos(x) - 4b + 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 4a b + 2a b )cos(x) + (- 10a b + 6a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (8a b - 4a b )cos(x) + (20a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (- 4a b - 2a b )cos(x) + (- 10a b + 10a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 6a b + 4a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (12a b - 8a b)cos(x) + (12a b - 8a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 6a b + 4a b)cos(x) + (- 6a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 4 3 2 2 4 3 2 +--R - 3a b cos(x) + (- a b - 2a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 +--R - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 3a b + 2a b)cos(x) + (- 3b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 5 4 5 2 3 +--R (b - 2a b)cos(x) + (3b - 2a b)cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - 2a b cos(x) + (- 2b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (4b + 4a b )cos(x) - 2a b cos(x) - 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - a b cos(x) + (- b - a b )cos(x) + 2a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (2b + 2a b )cos(x) - a b cos(x) - b - a b +--R * +--R csc(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R 2a b cos(x) + (2a b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (- 4a b - 4a b )cos(x) + 2a b cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- a b - 2a b + 2a )cos(x) + (- a b - 2a b + 2a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (4a b - 4a )cos(x) + (- 2a b + 4a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (3a b - 2a b + 2a )cos(x) + 5a b - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - a b cos(x) - a b cos(x) + 2a b cos(x) + 2a b cos(x) +--R + +--R 4 4 +--R - a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 2 3 2 3 +--R 2a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 2b + a b )cos(x) + (- 3b - a b + 2a b)cos(x) +--R + +--R 5 2 3 4 4 5 4 3 +--R (6b - 6a b + 2a b)cos(x) + (6b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (- 6b + 7a b - 4a b)cos(x) + (- 3b + a b + 2a b)cos(x) + 2b +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 4a b )cos(x) + (6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 3 3 5 +--R (2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 +--R a b cos(x) + (a b + 2a b )cos(x) + (- 5a b + 4a b )cos(x) +--R + +--R 2 4 4 2 +--R a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 2 4 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + a b cos(x) +--R + +--R 2 4 2 2 4 +--R - 2a b cos(x) + a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 3a b + 5a b - 2a b)cos(x) + (2a b + 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 5 +--R (2a b - 2a b + 2a b)cos(x) + (- 4a b + 2a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 6 5 +--R (2b - 3a b + 4a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 3b + 3a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 3 6 4 2 6 2 +--R (- 3b + 6a b - 8a b + 4a )cos(x) + (3b - 4a b + 4a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (3b - 5a b + 4a b - 2a )cos(x) - 5a b + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 6 2 4 3 2 4 2 +--R (4b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 4 +--R (- 2b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- b + a b )cos(x) + a b cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 2a b cos(x) + (- b + a b )cos(x) + a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 +--R (2a b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b + a b )cos(x) + (3a b + a b - 2a b)cos(x) +--R + +--R 3 3 5 4 5 5 3 +--R (2a b - 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (3a b - 5a b + 4a b)cos(x) + (5a b - a b - 2a b)cos(x) +--R + +--R 5 3 3 5 +--R - 2a b + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 10a b + 4a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 5 +--R (4a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 3 3 3 5 2 3 3 5 +--R 2a b cos(x) + (2a b + 4a b)cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 3 3 5 +--R 2a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 3 3 4 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 2 3 3 +--R - 4a b cos(x) + 2a b +--R * +--R csc(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (- 2a b + 2a b )cos(x) + (4a b + 4a b - 4a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 6 2 4 +--R (- 4a b + 12a b - 4a )cos(x) + (- 8a b + 4a )cos(x) + 2a b +--R + +--R 4 2 6 +--R - 10a b + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (8a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (4a b - 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (4a b - 4a b)cos(x) - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (6a b - 4a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 3 5 3 3 2 +--R (2a b - 12a b + 8a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b + 2a b - 4a b)cos(x) + 4a b - 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (8a b - 8a b )cos(x) - 8a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 4 2 4 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 8a b + 8a b )cos(x) + 8a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (4a b - 4a b )cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (- 2a b + 2a b )cos(x) + (- 4b + 18a b - 10a b )cos(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (4a b - 4a b )cos(x) + (8b - 40a b + 24a b )cos(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 4 2 +--R (- 2a b + 6a b )cos(x) + (- 4b + 22a b - 14a b )cos(x) - 4a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 3 3 5 5 +--R (- 6a b + 10a b - 4a b)cos(x) + (6a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (12a b - 20a b + 8a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 6a b + 10a b - 4a b)cos(x) + (6a b - 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 5 +--R (2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 2 4 +--R a b cos(x) + (a b + 2a b )cos(x) + (- 5a b + 4a b )cos(x) + a b +--R + +--R 4 2 +--R 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 2 4 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + a b cos(x) +--R + +--R 2 4 2 2 4 +--R - 2a b cos(x) + a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 3a b + 5a b - 2a b)cos(x) + (2a b + 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 5 3 3 +--R (2a b - 2a b + 2a b)cos(x) + (- 4a b + 2a b)cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 6 5 +--R (2b - 3a b + 4a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 3b + 3a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 3 6 4 2 6 2 +--R (- 3b + 6a b - 8a b + 4a )cos(x) + (3b - 4a b + 4a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (3b - 5a b + 4a b - 2a )cos(x) - 5a b + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- b + a b )cos(x) + a b cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 2a b cos(x) + (- b + a b )cos(x) + a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 5 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 3 2 5 3 3 3 3 +--R 4a b cos(x) + (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b + a b )cos(x) + (3a b + a b - 2a b)cos(x) +--R + +--R 3 3 5 4 5 5 3 +--R (2a b - 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (3a b - 5a b + 4a b)cos(x) + (5a b - a b - 2a b)cos(x) - 2a b +--R + +--R 3 3 5 +--R 2a b - 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 10a b + 4a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 6 2 4 4 2 4 3 +--R 2a b cos(x) + (2b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 2 4 6 2 4 +--R (- 4b - 4a b )cos(x) + 2a b cos(x) + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 5 5 +--R 2a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 4 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 5 5 3 3 4 3 3 3 +--R 4a b cos(x) + (4a b + 4a b )cos(x) - 8a b cos(x) +--R + +--R 5 3 3 2 3 3 5 3 3 +--R (- 8a b - 8a b )cos(x) + 4a b cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 6 2 4 4 2 4 3 +--R 2a b cos(x) + (2b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 2 4 6 2 4 +--R (- 4b - 4a b )cos(x) + 2a b cos(x) + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 5 5 +--R 2a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (2b - 2a b )cos(x) - 2a b cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R 4a b cos(x) + (2b - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 4 2 3 4 3 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 3 4 4 6 3 4 3 +--R (4a b - 4a b )cos(x) - 4a b cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 4 2 6 3 4 3 4 +--R 8a b cos(x) + (4a b - 4a b )cos(x) - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (2b - 2a b )cos(x) - 2a b cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R 4a b cos(x) + (2b - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R Type: Expression Integer +--E 265 + +--S 266 of 586 +m0544b:= a0544.2-r0544 +--R +--R +--R (251) +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 2 3 +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )atanh(cos(x)) +--R + +--R x +--R +---------+ b tan(-) + a +--R 2 2 2 2 2 | 2 2 2 +--R ((4b - 4a )cos(x) - 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R ((4b - 4a )cos(x) - 4b + 4a )\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 2 2 2 2 +--R - 2a b cos(x)sin(x) + (a b cos(x) - a b )cot(x)csc(x) +--R + +--R 2 2 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a b cos(x) +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R Type: Expression Integer +--E 266 + +--S 267 of 586 +d0544b:= D(m0544b,x) +--R +--R +--R (252) +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 3a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 6a b )cos(x) + a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- 2b - 4a b + 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 2 3 2 2 3 4 5 2 3 4 +--R (4b - 6a b )cos(x) + (4a b - 4a b)cos(x) - 2b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 2a b - 4a b + 4a )cos(x) + (- a b - 4a b + 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (8a b - 8a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (6a b - 4a b + 4a )cos(x) + 5a b - 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 8a b cos(x) + 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - a b cos(x) - 2a b cos(x) + a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R a b cos(x) - 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 6 2 3 4 5 +--R (- 2b - 2a b + 2a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b - 2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 +--R (- 6b + 6a b - 2a b)cos(x) + (- 2a b + 4a b)cos(x) + 2b +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 3a b + 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (3a b - 2a b )cos(x) + (12a b - 8a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (3a b - 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 +--R (- 3a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 6a b - 4a b)cos(x) + (2a b - 8a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (6a b - 12a b)cos(x) + 2a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 2 2 3 2 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) - 2a b cos(x) +--R + +--R 2 3 2 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 4 3 2 2 3 2 2 4 4 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) - 8a b cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 16a b + 8a )cos(x) + (16a b - 28a b + 8a )cos(x) +--R + +--R 3 2 5 4 3 2 5 +--R (8a b - 8a )cos(x) - 8a b + 20a b - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 4 4 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b + 8a b)cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (16a b - 16a b)cos(x) + (16a b - 16a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (4a b + 8a b)cos(x) + 2a b + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 8a b + 4a b )cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (16a b - 12a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (- 8a b + 4a b )cos(x) + (- 8a b + 12a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 6a b + 4a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (6a b - 4a b)cos(x) + (24a b - 16a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (6a b - 4a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 3a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 6a b )cos(x) + a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- 2b - 4a b + 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 2 3 2 2 3 4 5 2 3 4 +--R (4b - 6a b )cos(x) + (4a b - 4a b)cos(x) - 2b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 2a b - 4a b + 4a )cos(x) + (- a b - 4a b + 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (8a b - 8a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (6a b - 4a b + 4a )cos(x) + 5a b - 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 4 2 4 4 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - a b cos(x) - 2a b cos(x) + a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R a b cos(x) - 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 6 2 3 4 5 +--R (- 2b - 2a b + 2a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b - 2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 6b + 6a b - 2a b)cos(x) + (- 2a b + 4a b)cos(x) + 2b - 2a b +--R + +--R 4 +--R 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 3a b + 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 4 3 2 3 +--R (3a b - 2a b )cos(x) + (12a b - 8a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b + 4a b )cos(x) + (- 3a b + 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 5 2 5 5 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 4 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 5 3 3 4 3 3 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 4 2 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 4 2 2 4 2 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 5 2 5 5 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R Type: Expression Integer +--E 267 + +--S 268 of 586 +t0545:= sec(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R sec(x) +--R (253) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 268 + +--S 269 of 586 +r0545:= 2*a^3*b*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+1/12*cos(x)/(a+b)/(1-sin(x))^2+1/4*a*cos(x)/(a+b)^2/(1-sin(x))+1/12*cos(x)/(a+b)/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2-1/4*a*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (254) +--R x +--R b tan(-) + a +--R 3 4 3 2 3 2 +--R (6a b sin(x) - 12a b sin(x) + 6a b)atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 3 +--R (- a b - 2a )cos(x)sin(x) + 3a b cos(x)sin(x) + 3a cos(x)sin(x) +--R + +--R 3 2 +--R (b - 4a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 269 + +--S 270 of 586 +a0545:= integrate(t0545,x) +--R +--R +--R (255) +--R [ +--R 3 3 +--R 3a b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b + 2a )cos(x) - a b + a )sin(x) + (b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 6a b cos(x) atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b + 2a )cos(x) - a b + a )sin(x) + (b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 270 + +--S 271 of 586 +m0545a:= a0545.1-r0545 +--R +--R +--R (256) +--R 3 3 4 3 3 2 3 3 +--R (3a b cos(x) sin(x) - 6a b cos(x) sin(x) + 3a b cos(x) ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) ) +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 2 2 3 2 4 +--R ((b - 4a b)cos(x) - 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b + 2a )cos(x) + (- 2a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 2 4 3 2 3 2 2 3 +--R - 3a b cos(x) + (- 2b + 8a b)cos(x) + 6a b cos(x) - 2b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (- 3a cos(x) + (a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 2 2 3 2 +--R (- b + 4a b)cos(x) + (b - 4a b)cos(x) - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 271 + +--S 272 of 586 +d0545a:= D(m0545a,x) +--R +--R +--R (257) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- a b - a b + 2a b)cos(x) + (a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 3a b + 3a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (7a b - 2a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 3a b - 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 3 4 5 2 5 +--R (- a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 4 5 2 2 6 5 2 +--R (11a b + 7a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (a b + a b - 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- a b - 7a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (6a b + 9a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (a b - 5a b + 4a b )cos(x) + (2a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (a b + 7a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (a b - 5a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 7a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 6 7 2 5 4 3 6 6 +--R (- 3a b + 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (3a b + 3a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (13a b - 14a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 9a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- a b + 8a b - 7a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (4a b - 9a b - 13a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- a b + 5a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 5 2 2 6 3 4 +--R (4a b - 8a b + 4a b )cos(x) + 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 2a b + a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 4a b + 5a b - a b)cos(x) + (a b + 3a b - a b)cos(x) +--R + +--R 7 2 5 4 3 2 5 4 3 +--R (3b - 6a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 5 2 6 +--R (- 3a b + 3a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (a b + a b - 2a b )cos(x) + (- a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 10 +--R ((2a b + 4a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 3 4 5 2 7 3 3 4 7 2 +--R (- 2a b - 2a b + 4a )cos(x) + (2a b + 4a )cos(x) +--R + +--R 3 4 5 2 7 5 2 7 +--R (6a b - 12a b + 6a )cos(x) - 6a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 6 4 2 5 4 3 6 3 +--R - 6a b cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 3 6 2 2 5 4 3 6 +--R (- 12a b - 12a b)cos(x) + 6a b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 3 4 5 2 7 3 +--R (14a b - 4a b - 10a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 8a b - 6a b - 10a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) + 6a b + 12a b - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 4 +--R (- 2a b - 10a b)cos(x) + (2a b + 22a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (8a b - 16a b + 8a b)cos(x) + (22a b + 14a b)cos(x) +--R + +--R 2 5 6 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 7 6 +--R (2a b + 2a b - 4a )cos(x) + (- 2a b + 6a b - 4a )cos(x) +--R + +--R 3 4 5 2 7 5 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 4 5 2 7 3 +--R (- 30a b + 24a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (12a b + 18a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (18a b - 18a b - 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (2a b - 10a b + 8a b)cos(x) + (4a b + 32a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (2a b - 10a b - 28a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 4 3 6 2 2 5 4 3 6 +--R (- 14a b - 10a b)cos(x) + 18a b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 7 7 3 4 5 2 7 6 +--R (- 6a b + 6a )cos(x) + (2a b - 8a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (6a b - 12a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 3 +--R (26a b - 28a b + 2a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 8a b - 18a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) + 18a b - 12a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 2a b + 16a b - 14a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (8a b - 18a b - 26a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 2a b + 10a b + 16a b)cos(x) +--R + +--R 2 5 4 3 6 3 6 2 2 5 4 3 +--R (8a b - 16a b + 8a b)cos(x) + 6a b cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 8a b + 28a b - 26a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (8a b - 14a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b - 8a b + 10a b - 4a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 4a b + 8a b - 4a )cos(x) +--R + +--R 3 4 5 2 7 3 +--R (- 8a b + 10a b - 2a )cos(x) +--R + +--R 3 4 5 2 7 2 6 3 4 5 2 +--R (2a b + 6a b - 2a )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 4 5 2 +--R - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 3 6 7 6 6 +--R (- 6a b + 6a b)cos(x) + 12a b cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (- 2a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- a b - a b + 2a b)cos(x) + (a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 6 +--R (- a b + 2a b - a b )cos(x) + (- 6a b - 6a b )cos(x) + 3a b +--R + +--R 3 4 5 2 +--R 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 3a b + 3a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (7a b - 2a b - 5a b)cos(x) + (- 4a b - 3a b - 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 3 4 5 2 5 +--R (- a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 4 5 2 2 6 5 2 +--R (11a b + 7a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (a b + a b - 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- a b - 7a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 15a b + 12a b + 3a b)cos(x) + (6a b + 9a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (a b - 5a b + 4a b )cos(x) + (2a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (a b + 7a b - 8a b )cos(x) + (a b - 5a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 7a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 6 7 2 5 4 3 6 6 +--R (- 3a b + 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b + 3a b + 12a b)cos(x) + (13a b - 14a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 9a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- a b + 8a b - 7a b )cos(x) + (4a b - 9a b - 13a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- a b + 5a b + 14a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 5 2 2 6 3 4 +--R 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 2a b + a b - 5a b)cos(x) + (- 4a b + 5a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 2 5 +--R (a b + 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) - 3a b +--R + +--R 4 3 +--R 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 5 2 6 +--R (- 3a b + 3a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (a b + a b - 2a b )cos(x) + (- a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- a b - a b + 2a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- a b - a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 6 2 2 8 +--R (- a b + 2a b - a b )cos(x) + (6a b - 6a b )cos(x) - 3b +--R + +--R 2 6 4 4 6 2 +--R - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- 3a b + 3a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (7a b - 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - a b + 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 6 2 5 +--R (a b + 4a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- a b - 4a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 11a b + 4a b + 7a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (a b + a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (a b - 4a b + 5a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b + 6a b + 3a b - 10a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 3a b + 6a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 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28a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 7 +--R (14a b - 4a b - 10a b)cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 8 7 2 6 4 4 6 2 8 6 +--R (- 6a b + 6a )cos(x) + (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (26a b - 28a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (8a b + 10a b - 20a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) - 18a b + 30a b - 6a b +--R + +--R 8 +--R - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 2a b + 16a b - 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 8a b + 26a b + 8a b - 26a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 12a b - 6a b + 16a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 3 7 2 7 +--R (8a b - 16a b + 8a b)cos(x) + (- 6a b + 6a b)cos(x) + 6a b +--R + +--R 3 5 5 3 +--R - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (- 8a b + 28a b - 26a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 8a b + 22a b - 20a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (2a b - 8a b + 10a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 12a b + 12a b - 4a )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (- 8a b + 10a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b - 4a b + 8a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) + (2a b + 2a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- a b - a b + 2a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 7 3 5 5 3 7 2 +--R (- a b - a b + 2a b)cos(x) + (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 6 2 2 8 2 6 +--R (- a b + 2a b - a b )cos(x) + (6a b - 6a b )cos(x) - 3b - 3a b +--R + +--R 4 4 6 2 +--R 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- 3a b + 3a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 3 7 3 5 5 3 7 2 +--R (7a b - 2a b - 5a b)cos(x) + (4a b - a b + 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 6 2 5 +--R (a b + 4a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- a b - 4a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 11a b + 4a b + 7a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (a b + a b - 2a b)cos(x) + (a b - 4a b + 5a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b + 6a b + 3a b - 10a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 3a b + 6a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (a b - 5a b + 4a b )cos(x) + (- 2a b - 14a b + 16a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (a b + 7a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- b + 6a b + 9a b - 14a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (7a b - 2a b - 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 +--R - 9b + 15a b - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 7 7 7 3 5 5 3 7 6 +--R (- 3a b + 3a b)cos(x) + (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- a b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 7 5 3 7 4 3 5 5 3 7 3 +--R (- 3a b - 9a b + 12a b)cos(x) + (13a b - 14a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b + 5a b - 10a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- a b + 8a b - 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 4b + 13a b + 4a b - 13a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (b - 6a b - 9a b + 14a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 4 6 2 2 8 2 6 4 4 +--R (- 3a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 4a b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 4a b + 11a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (a b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 3a b + 6a b - 5a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 4a b + 5a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (- a b - 2a b + 4a b - a b)cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 7 3 5 5 3 +--R 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 2 6 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (a b + a b - 2a b )cos(x) + (a b + 4a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (3b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 6a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3b - 9a b + 9a b - 3a b )cos(x) + (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 6a b + 12a b - 12a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (12a b - 36a b + 36a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (18a b - 36a b + 36a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 18a b + 36a b - 36a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 12a b + 36a b - 36a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (6a b - 12a b + 12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R Type: Expression Integer +--E 272 + +--S 273 of 586 +m0545b:= a0545.2-r0545 +--R +--R +--R (258) +--R +-------+ +--R 3 3 4 3 3 2 3 3 | 2 2 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) )\|b - a +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) ) +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 5 +--R ((a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 2 2 3 2 4 +--R ((b - 4a b)cos(x) - 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b + 2a )cos(x) + (- 2a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 2 4 3 2 3 2 2 3 +--R - 3a b cos(x) + (- 2b + 8a b)cos(x) + 6a b cos(x) - 2b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (- 3a cos(x) + (a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 2 2 3 2 +--R (- b + 4a b)cos(x) + (b - 4a b)cos(x) - 3a b cos(x) + b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 273 + +--S 274 of 586 +d0545b:= D(m0545b,x) +--R +--R +--R (259) +--R 4 3 2 2 4 3 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b + 4a b)cos(x) + (- a b + 4a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 6a b + 6a b)cos(x) + 3b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b - 6a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 6a b cos(x) + 6a b cos(x) + (- 14a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (3b - 5a b - 10a b)cos(x) + (6b + 12a b - 18a b)cos(x) - 6b +--R + +--R 2 3 4 +--R 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 6 3 2 5 +--R (- a b - 5a b )cos(x) + 6a b cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 6a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (11a b + 7a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b - 4a b)cos(x) + (7a b - 4a b)cos(x) +--R + +--R 2 3 4 5 5 2 3 4 4 +--R (2a b - 20a b)cos(x) + (b + a b - 20a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (30a b + 6a b)cos(x) + (- 9b + 21a b + 6a b)cos(x) +--R + +--R 5 4 2 3 4 +--R (- 18b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- a b - 2a b )cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 6a b + 21a b )cos(x) + (- 2a b - 16a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (9a b - 27a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 7a b - 5a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 +--R 6a b cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (5b - 17a b + 6a b)cos(x) + (2b - 8a b + 24a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b + 24a b)cos(x) + (- 26a b + 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (9b - 23a b + 2a b)cos(x) + (18b - 12a b - 6a b)cos(x) + 6b +--R + +--R 4 +--R - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 3a b + 3a b )cos(x) + (2a b - 14a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (8a b - 20a b )cos(x) + (4a b + 14a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 4a b + 22a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 2 2 4 3 2 +--R 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 8 5 2 3 4 7 +--R (4b - 10a b )cos(x) + (8b - 20a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (3b - 6a b + 6a b)cos(x) + (- 2b + 6a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 10a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 2 3 +--R (- 3b + 8a b - 2a b)cos(x) + (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 8 3 2 7 4 3 2 6 +--R 3a b cos(x) + 6a b cos(x) + (- a b + 4a b )cos(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b - 4a b )cos(x) - 6a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((2a b + 4a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (4a b + 8a )cos(x) + (- 2a b + 8a )cos(x) +--R + +--R 3 2 5 4 3 2 5 +--R (- 12a b + 12a )cos(x) + 6a b - 18a b + 12a +--R * +--R 9 +--R sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (2a b - 8a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 12a b - 12a b)cos(x) + 24a b - 24a b +--R * +--R 8 +--R sin(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 28a b - 20a )cos(x) + (6a b - 10a b - 20a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (12a b + 24a b - 36a )cos(x) - 12a b + 48a b - 36a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 2a b - 16a b)cos(x) + (- 12a b + 36a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 2 3 +--R (- 16a b + 16a b)cos(x) + (22a b + 14a b)cos(x) - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (- 4a b - 8a )cos(x) + (14a b - 8a )cos(x) +--R + +--R 3 2 5 5 4 3 2 5 4 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (60a b + 12a )cos(x) + (- 18a b + 42a b + 12a )cos(x) +--R + +--R 4 5 3 2 5 +--R (- 36a b + 36a )cos(x) - 36a b + 36a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 2a b - 4a b)cos(x) + (- 4a b + 16a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b + 60a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (18a b - 54a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 14a b - 10a b)cos(x) + 24a b - 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 8 3 2 5 7 +--R 12a b cos(x) + (12a b + 12a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (10a b - 34a b + 12a )cos(x) + (4a b - 16a b + 12a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 12a b + 12a )cos(x) + (- 52a b + 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 46a b + 4a )cos(x) + (36a b - 24a b - 12a )cos(x) +--R + +--R 4 5 +--R 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (4a b - 28a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (16a b - 58a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 8a b + 32a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 4 2 2 3 4 +--R 6a b cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 5 7 +--R (8a b - 20a b )cos(x) + (16a b - 40a b + 12a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (6a b - 12a b + 12a )cos(x) + (- 4a b + 12a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 +--R (- 2a b + 10a b - 8a )cos(x) + (16a b - 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 +--R (- 6a b + 16a b - 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 3 2 +--R - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 8 4 7 2 3 4 6 +--R 6a b cos(x) + 12a b cos(x) + (- 2a b + 14a b)cos(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) - 6a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 4 3 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b + 4a b)cos(x) + (- a b + 4a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 6a b + 6a b)cos(x) + 3b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b - 6a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 6a b cos(x) + 6a b cos(x) + (- 14a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (3b - 5a b - 10a b)cos(x) + (6b + 12a b - 18a b)cos(x) - 6b +--R + +--R 2 3 4 +--R 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 6 3 2 5 4 3 2 4 +--R (- a b - 5a b )cos(x) + 6a b cos(x) + (- 6a b + 12a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + (11a b + 7a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b - 4a b)cos(x) + (7a b - 4a b)cos(x) +--R + +--R 2 3 4 5 5 2 3 4 4 +--R (2a b - 20a b)cos(x) + (b + a b - 20a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (30a b + 6a b)cos(x) + (- 9b + 21a b + 6a b)cos(x) +--R + +--R 5 4 2 3 4 +--R (- 18b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- a b - 2a b )cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 6a b + 21a b )cos(x) + (- 2a b - 16a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (9a b - 27a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 7a b - 5a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 5 2 3 4 6 +--R 6a b cos(x) + (6a b + 6a b)cos(x) + (5b - 17a b + 6a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 8a b + 24a b)cos(x) + (- 6a b + 24a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (- 26a b + 2a b)cos(x) + (9b - 23a b + 2a b)cos(x) +--R + +--R 5 2 3 4 5 4 +--R (18b - 12a b - 6a b)cos(x) + 6b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 3a b + 3a b )cos(x) + (2a b - 14a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (8a b - 20a b )cos(x) + (4a b + 14a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 3 2 2 +--R (- 4a b + 22a b )cos(x) + (- 8a b + 8a b )cos(x) + 3a b cos(x) +--R + +--R 4 3 2 +--R - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 8 5 2 3 4 7 +--R (4b - 10a b )cos(x) + (8b - 20a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (3b - 6a b + 6a b)cos(x) + (- 2b + 6a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 10a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 2 3 +--R (- 3b + 8a b - 2a b)cos(x) + (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 8 3 2 7 4 3 2 6 +--R 3a b cos(x) + 6a b cos(x) + (- a b + 4a b )cos(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b - 4a b )cos(x) - 6a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R / +--R 6 2 4 4 2 4 8 +--R (3b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (3b - 6a b + 3a b )cos(x) + (6b - 12a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 6b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 6 +--R (- 9b + 18a b - 9a b )cos(x) +--R + +--R 6 2 4 4 2 5 +--R (- 18b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (9b - 18a b + 9a b )cos(x) + (18b - 36a b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (6b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (- 3b + 6a b - 3a b )cos(x) + (- 6b + 12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 3b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R ((12a b - 24a b + 12a )cos(x) + (12a b - 24a b + 12a )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 5 +--R (- 36a b + 72a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 36a b + 72a b - 36a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R ((36a b - 72a b + 36a )cos(x) + (36a b - 72a b + 36a )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 12a b + 24a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 4 8 +--R (3b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (3b - 6a b + 3a b )cos(x) + (6b - 12a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 6b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R ((- 9b + 18a b - 9a b )cos(x) + (- 18b + 36a b - 18a b )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (9b - 18a b + 9a b )cos(x) + (18b - 36a b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (6b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (- 3b + 6a b - 3a b )cos(x) + (- 6b + 12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 3b + 6a b - 3a b )cos(x) +--R Type: Expression Integer +--E 274 + +--S 275 of 586 +t0546:= csc(x)^3/(a+b*csc(x)) +--R +--R +--R 3 +--R csc(x) +--R (260) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 275 + +--S 276 of 586 +r0546:= a*atanh(cos(x))/b^2-2*a^2*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)-cot(x)/b +--R +--R +--R (261) +--R x +--R +---------+ b tan(-) + a +---------+ +--R | 2 2 2 2 | 2 2 +--R a\|- b + a atanh(cos(x)) - 2a atanh(------------) - b cot(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R -------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression Integer +--E 276 + +--S 277 of 586 +a0546:= integrate(t0546,x) +--R +--R +--R (262) +--R [ +--R 2 +--R a sin(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - a sin(x)\|- b + a log(----------) - b cos(x)\|- b + a +--R cos(x) + 1 +--R / +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 sin(x) +--R - a sin(x)\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +-------+ +--R 2 (b sin(x) + a cos(x) + a)\|b - a | 2 2 +--R 2a sin(x)atan(-----------------------------------) - b cos(x)\|b - a +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b sin(x)\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 277 + +--S 278 of 586 +m0546a:= a0546.1-r0546 +--R +--R +--R (263) +--R 2 +--R a sin(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - a sin(x)\|- b + a log(----------) - a sin(x)\|- b + a atanh(cos(x)) +--R cos(x) + 1 +--R + +--R x +--R b tan(-) + a +---------+ +--R 2 2 | 2 2 +--R 2a sin(x)atanh(------------) + (b cot(x)sin(x) - b cos(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R Type: Expression Integer +--E 278 + +--S 279 of 586 +d0546a:= D(m0546a,x) +--R +--R +--R (264) +--R 3 2 5 +--R - a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 4 2 +--R (- a b cos(x) + a b )cot(x) + (a b - a b)cos(x) +--R + +--R 2 3 4 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 4 3 2 5 2 3 2 5 +--R - a cos(x) + (a b - a b - a )cos(x) + (- a b + a )cos(x) +--R + +--R 5 +--R a +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 +--R (b - a b )cos(x) - a b cos(x) + (- b + a b )cos(x) +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 4 2 +--R 2a b cos(x) + (- a b - a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 3 4 4 +--R (a b + a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (- a b + a b )cos(x) + 2a b cos(x) + (a b - 2a b )cos(x) +--R + +--R 4 2 3 2 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 5 2 3 5 2 3 4 5 2 3 3 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) +--R + +--R 2 3 2 +--R - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R - 2a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 3 2 2 +--R (- 2a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 2 5 5 +--R (- 2a b - 2a )cos(x) - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 2a b + 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 3 2 4 +--R - 2a b cos(x) + 2a b cos(x) - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 2 +--R (2a b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 3 2 3 3 2 2 3 2 +--R 4a b cos(x) - 4a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 2a b + 2a b)cos(x) + 4a b cos(x) +--R + +--R 2 3 4 3 2 3 2 4 +--R (2a b - 4a b)cos(x) - 4a b cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 2 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 +--R - a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 4 2 +--R (- a b cos(x) + a b )cot(x) + (a b - a b)cos(x) +--R + +--R 2 3 4 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 4 3 2 5 2 3 2 5 5 +--R - a cos(x) + (a b - a b - a )cos(x) + (- a b + a )cos(x) + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((b - a b )cos(x) - a b cos(x) + (- b + a b )cos(x) + a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 4 2 +--R 2a b cos(x) + (- a b - a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 3 4 4 +--R (a b + a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (- a b + a b )cos(x) + 2a b cos(x) + (a b - 2a b )cos(x) +--R + +--R 4 2 3 2 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 5 2 3 5 2 3 4 5 2 3 3 2 3 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 5 3 3 2 5 3 3 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) +--R + +--R 3 3 5 2 5 5 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 6 4 2 2 +--R (- a b + a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 +--R (a b - a b )cos(x) + b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 3 2 4 6 2 4 2 6 +--R (- a b + a )cos(x) + (- a b + a )cos(x) + (a b - a )cos(x) +--R + +--R 4 2 6 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b - a b )cos(x) + (- a b + a b)cos(x) +--R + +--R 5 5 2 5 5 3 3 5 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (a b - a b )cos(x) + (b - a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 2 +--R (- 2a b + 2a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 +--R (a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 5 3 3 3 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 2 +--R (- a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )cot(x) +--R + +--R 2 4 6 4 2 6 +--R (- 2a b + 2a )cos(x) - 2a b + 2a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 5 5 2 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 5 5 5 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 3 5 3 5 3 3 2 +--R (- 4a b + 4a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 3 5 +--R (2a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 5 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 5 3 3 2 5 3 3 2 3 3 5 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) + (- a b + a b)cos(x) +--R + +--R 5 5 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 6 4 2 2 +--R (- a b + a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 +--R (a b - a b )cos(x) + b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 3 2 4 6 2 4 2 6 +--R (- a b + a )cos(x) + (- a b + a )cos(x) + (a b - a )cos(x) +--R + +--R 4 2 6 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 4 5 5 3 5 5 2 +--R (a b - a b )cos(x) + (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 5 3 3 5 +--R (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 6 2 4 2 2 4 4 2 +--R (- b + a b )cos(x) + (a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 5 3 3 3 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 2 +--R (- a b + a b )cos(x) +--R / +--R 2 4 2 2 4 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 3 2 4 2 6 2 4 2 4 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b ) +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 3 2 4 2 6 2 4 2 4 2 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 2 6 3 4 4 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 5 4 3 3 7 4 3 2 2 5 4 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 4 3 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 4 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 6 3 4 4 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 5 4 3 3 7 4 3 2 2 5 4 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 4 3 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 3 6 3 4 2 6 3 4 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 +--R - a b + a b +--R * +--R 2 +--R sin(x) +--R Type: Expression Integer +--E 279 + +--S 280 of 586 +m0546b:= a0546.2-r0546 +--R +--R +--R (265) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R - a sin(x)\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - a sin(x)\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ b tan(-) + a +--R 2 | 2 2 2 +--R 2a sin(x)\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2a sin(x)\|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (b cot(x)sin(x) - b cos(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b sin(x)\|- b + a \|b - a +--R Type: Expression Integer +--E 280 + +--S 281 of 586 +d0546b:= D(m0546b,x) +--R +--R +--R (266) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- b cos(x) + b )cot(x) - a b cos(x) - 2a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 3 2 3 2 3 3 +--R (- 2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) + 2a cos(x) + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b cos(x) - 2b cos(x) + 2b cos(x) + b )cot(x) +--R + +--R 3 2 4 2 3 3 2 2 2 +--R (b - a b)cos(x) - 2a b cos(x) - b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + b cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2b cos(x) - 2b cos(x) - b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 3 3 4 +--R ((- 2a b cos(x) + 2a b )cot(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b)cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 4 2 2 +--R 2a b cos(x) - 2a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- b cos(x) + b )cot(x) - a b cos(x) - 2a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 3 2 3 2 3 3 +--R (- 2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) + 2a cos(x) + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b cos(x) - 2b cos(x) + 2b cos(x) + b )cot(x) +--R + +--R 3 2 4 2 3 3 2 2 2 +--R (b - a b)cos(x) - 2a b cos(x) - b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + b cos(x) + 2b cos(x) +--R + +--R 3 3 3 2 +--R - 2b cos(x) - b cos(x) +--R / +--R 4 2 4 4 +--R (b cos(x) - b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (b cos(x) + 2b cos(x) - 2b cos(x) - b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (b cos(x) - b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (b cos(x) + 2b cos(x) - 2b cos(x) - b )sin(x) +--R Type: Expression Integer +--E 281 + +--S 282 of 586 +t0547:= csc(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R csc(x) +--R (267) ------------ +--R b csc(x) + a +--R Type: Expression Integer +--E 282 + +--S 283 of 586 +r0547:= -a^2*atanh(cos(x))/b^3-1/2*atanh(cos(x))/b+2*a^3*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)+a*cot(x)/b^2-1/2*cot(x)*csc(x)/b +--R +--R +--R (268) +--R x +--R +---------+ b tan(-) + a +--R 2 2 | 2 2 3 2 +--R (- b - 2a )\|- b + a atanh(cos(x)) + 4a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- b cot(x)csc(x) + 2a b cot(x))\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression Integer +--E 283 + +--S 284 of 586 +a0547:= integrate(t0547,x) +--R +--R +--R (269) +--R [ +--R 3 2 3 +--R (2a cos(x) - 2a ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + b cos(x))\|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R , +--R +--R +-------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R 3 2 3 (b sin(x) + a cos(x) + a)\|b - a +--R (- 4a cos(x) + 4a )atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + b cos(x))\|b - a +--R / +--R +-------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 284 + +--S 285 of 586 +m0547a:= a0547.1-r0547 +--R +--R +--R (270) +--R 3 2 3 +--R (2a cos(x) - 2a ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((b + 2a )cos(x) - b - 2a )\|- b + a atanh(cos(x)) +--R + +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (- 4a cos(x) + 4a )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (b cos(x) - b )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R Type: Expression Integer +--E 285 + +--S 286 of 586 +d0547a:= D(m0547a,x) +--R +--R +--R (271) +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 +--R 3a b cos(x) + (- a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 2 4 4 2 +--R - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 2 4 4 2 4 2 2 4 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- a b - a b + 2a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 5 +--R (2a b - 2a b - 2a b)cos(x) + (- 4a b - 2a b)cos(x) + a b +--R + +--R 3 3 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 5 6 2 4 4 2 6 4 +--R (a b + 2a )cos(x) + (- b - a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 6 3 6 4 2 6 2 +--R (- b + 2a b - 4a )cos(x) + (b - 4a b - 4a )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 6 +--R (- b - a b + 2a )cos(x) + 3a b + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 +--R (2b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 6 2 4 3 2 4 2 +--R (- 4b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 6 2 4 2 4 +--R (2b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (b - a b )cos(x) - a b cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R 2a b cos(x) + (b - a b )cos(x) - a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b - a b )cos(x) + (a b + 3a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 8a b - 4a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- a b - 3a b - 4a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- a b + 5a b + 2a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- b - a b + 2a b )cos(x) + (a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (2b + 2a b - 4a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- b - a b + 2a b )cos(x) + (a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 3 3 5 2 3 3 5 +--R 6a b cos(x) + (- 2a b - 4a b)cos(x) + (2a b - 8a b)cos(x) +--R + +--R 3 3 5 +--R - 2a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (- 2a b - 2a b )cos(x) + (4a b + 4a b + 4a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 2 4 +--R (4a b - 4a b + 4a )cos(x) + (- 8a b - 4a )cos(x) + 2a b +--R + +--R 4 2 6 +--R 2a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 8a b + 8a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (4a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 4a b + 4a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (8a b - 8a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (2a b + 4a b)cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 5 2 +--R (- 2a b + 4a b - 8a b)cos(x) + 2a b cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 2a b - 2a b + 4a b)cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 4 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 8a b + 8a b )cos(x) + 8a b cos(x) +--R + +--R 5 3 3 3 3 +--R (4a b - 4a b )cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 4 +--R (2a b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 4 2 4 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (8a b - 8a b )cos(x) - 8a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 2a b - 2a b )cos(x) + (2a b + 10a b )cos(x) +--R + +--R 2 4 4 2 4 4 2 3 +--R (4a b + 4a b )cos(x) - 24a b cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 4 2 +--R (- 2a b - 6a b )cos(x) + (- 2a b + 14a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 3 3 5 5 +--R (- 2a b - 2a b + 4a b)cos(x) + (2a b + 4a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (4a b + 4a b - 8a b)cos(x) + (- 4a b - 8a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 2a b - 2a b + 4a b)cos(x) + (2a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 +--R 3a b cos(x) + (- a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 2 4 4 2 +--R - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 2 4 2 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- a b - a b + 2a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 5 +--R (2a b - 2a b - 2a b)cos(x) + (- 4a b - 2a b)cos(x) + a b +--R + +--R 3 3 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 5 6 2 4 4 2 6 4 +--R (a b + 2a )cos(x) + (- b - a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 6 3 6 4 2 6 2 +--R (- b + 2a b - 4a )cos(x) + (b - 4a b - 4a )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 6 +--R (- b - a b + 2a )cos(x) + 3a b + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 +--R (2b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 6 2 4 3 2 4 2 +--R (- 4b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 6 2 4 2 4 +--R (2b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (b - a b )cos(x) - a b cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R 2a b cos(x) + (b - a b )cos(x) - a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b - a b )cos(x) + (a b + 3a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 8a b - 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b - 3a b - 4a b)cos(x) + (- a b + 5a b + 2a b)cos(x) +--R + +--R 3 3 5 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- b - a b + 2a b )cos(x) + (a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (2b + 2a b - 4a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- b - a b + 2a b )cos(x) + (a b + 2a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 5 4 3 2 2 5 4 3 5 +--R ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 6 3 4 3 6 3 4 5 2 2 +--R (- a b + a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (a b + 3a b - 4a b )cos(x) + a b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 4 6 3 4 2 6 +--R (2a b - 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4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (4a b - 4a b )cos(x) + (4a b + 12a b - 16a b )cos(x) +--R + +--R 3 4 5 2 2 6 3 4 5 2 3 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 8a b + 10a b )cos(x) - 4a b +--R + +--R 5 2 +--R 4a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 2a b - 2a b + 4a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (4a b + 4a b - 8a b)cos(x) + (4a b + 4a b - 8a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 2a b - 2a b + 4a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 5 +--R ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 6 3 4 3 6 3 4 5 2 2 +--R (- a b + a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (a b + 3a b - 4a b )cos(x) + a b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 4 6 3 4 2 6 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 3 4 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 4 6 3 4 2 6 3 4 +--R (a b - a b )cos(x) + (- 2a b + 2a b )cos(x) + a b - a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 4 3 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 4 7 2 5 6 3 +--R (- a b - a b + 2a b)cos(x) + (- b - a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- b + 5a b - 2a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (b + 3a b - 2a b - 2a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 5 7 4 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 5 4 3 3 7 4 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 4 3 7 4 3 +--R (2a b - 2a b )cos(x) + 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 7 4 3 4 +--R (a b - a b )cos(x) + (b - a b )cos(x) +--R + +--R 2 5 4 3 3 7 4 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 5 4 3 7 4 3 +--R (a b - a b )cos(x) + b - a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 6 5 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 7 5 6 3 4 7 4 +--R (- a b - a b + 2a )cos(x) + (- a b - a b + 2a )cos(x) +--R + +--R 3 4 7 3 6 3 4 7 2 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 6 3 4 7 6 3 4 7 +--R (- a b - a b + 2a )cos(x) - 3a b + a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (a b - a b )cos(x) + a b - a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 5 +--R (- a b + a b )cos(x) + (- b - 2a b + a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 7 2 5 4 3 6 3 +--R (2a b - 4a b + 2a b)cos(x) + (2b + 6a b - 4a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (a b + 3a b - 4a b)cos(x) + (- b - 4a b + 3a b + 2a b)cos(x) +--R + +--R 2 5 6 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (2a b + 2a b - 4a b )cos(x) + (2a b + 2a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R / +--R 2 5 4 2 5 2 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 4 2 3 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (8a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 4a b + 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 3 4 4 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 6 3 4 3 3 4 2 +--R (8a b - 8a b )cos(x) - 8a b cos(x) +--R + +--R 6 3 4 3 4 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 3 5 4 7 3 5 2 7 3 5 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 5 8 4 4 4 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 8 4 4 2 +--R (4a b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 6 4 4 8 4 4 +--R (- 2a b + 2a b )cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 4 2 6 4 4 2 2 6 4 4 +--R ((- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b + 4a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 7 5 3 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 5 5 3 3 7 5 3 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 5 5 3 7 5 3 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 5 2 6 4 4 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 3 5 4 7 3 5 2 7 3 5 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 5 8 4 4 4 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 8 4 4 2 +--R (4a b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 6 4 4 8 4 4 +--R (- 2a b + 2a b )cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R Type: Expression Integer +--E 286 + +--S 287 of 586 +m0547b:= a0547.2-r0547 +--R +--R +--R (272) +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 +--R ((b + 2a )cos(x) - b - 2a )\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ b tan(-) + a +--R 3 2 3 | 2 2 2 +--R (- 4a cos(x) + 4a )\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 3 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R (- 4a cos(x) + 4a )\|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (b cos(x) - b )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + b cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (2b cos(x) - 2b )\|- b + a \|b - a +--R Type: Expression Integer +--E 287 + +--S 288 of 586 +d0547b:= D(m0547b,x) +--R +--R +--R (273) +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 2 4 2 2 +--R (b - 2a b )cos(x) + (b - 4a b )cos(x) + (- b - 6a b )cos(x) +--R + +--R 4 2 2 +--R b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2b cos(x) + 4b cos(x) - 2b )cot(x) - b cos(x) +--R + +--R 4 2 4 +--R 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (2b + 4a b + 4a )cos(x) + (3b + 4a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 8a b - 8a )cos(x) + (- 8a b - 8a )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (2b + 4a b + 4a )cos(x) + b + 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2b cos(x) - 4b cos(x) + 2b cos(x) + 8b cos(x) +--R + +--R 4 2 4 4 +--R 2b cos(x) - 4b cos(x) - 2b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - b cos(x) - 2b cos(x) + b cos(x) + 4b cos(x) + b cos(x) +--R + +--R 4 4 +--R - 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b - 2a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (6a b + 4a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 4 2 2 5 +--R (b + 2a b )cos(x) + (2b + 4a b )cos(x) + (- b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 3 4 2 2 2 +--R (- 4b - 8a b )cos(x) + (- b - 2a b )cos(x) + (2b + 4a b )cos(x) +--R + +--R 4 2 2 +--R (b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 3 3 2 +--R (2a b - 4a b)cos(x) + (2a b - 8a b)cos(x) +--R + +--R 3 3 3 3 +--R (- 2a b - 12a b)cos(x) + 2a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) - 2a b cos(x) +--R + +--R 3 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 4 2 2 2 2 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 8a cos(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (- 12a b + 8a )cos(x) + (- 8a b - 8a )cos(x) + 4a b - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 2 2 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 +--R (4a b + 8a b)cos(x) + (6a b + 8a b)cos(x) - 16a b cos(x) +--R + +--R 3 2 3 3 3 3 +--R - 16a b cos(x) + (4a b + 8a b)cos(x) + 2a b + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 5 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 3 3 3 2 3 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 4a b cos(x) - 12a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 4a b cos(x) + 12a b cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b + 4a b)cos(x) + (4a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 2a b - 4a b)cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 2a b - 4a b)cos(x) + (4a b + 8a b)cos(x) + (2a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 2 4 2 2 4 +--R (b - 2a b )cos(x) + (b - 4a b )cos(x) + (- b - 6a b )cos(x) + b +--R + +--R 2 2 +--R - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 4 2 +--R (- 2b cos(x) + 4b cos(x) - 2b )cot(x) - b cos(x) + 2b cos(x) +--R + +--R 4 +--R - b +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (2b + 4a b + 4a )cos(x) + (3b + 4a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 8a b - 8a )cos(x) + (- 8a b - 8a )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (2b + 4a b + 4a )cos(x) + b + 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2b cos(x) - 4b cos(x) + 2b cos(x) + 8b cos(x) +--R + +--R 4 2 4 4 +--R 2b cos(x) - 4b cos(x) - 2b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - b cos(x) - 2b cos(x) + b cos(x) + 4b cos(x) + b cos(x) +--R + +--R 4 4 +--R - 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b - 2a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (6a b + 4a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 4 2 2 5 +--R (b + 2a b )cos(x) + (2b + 4a b )cos(x) + (- b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 3 4 2 2 2 +--R (- 4b - 8a b )cos(x) + (- b - 2a b )cos(x) + (2b + 4a b )cos(x) +--R + +--R 4 2 2 +--R (b + 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2b cos(x) - 4b cos(x) + 2b )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2b cos(x) + 4b cos(x) - 2b cos(x) - 8b cos(x) - 2b cos(x) +--R + +--R 5 5 +--R 4b cos(x) + 2b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 4 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 2 3 2 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 4 2 4 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2b cos(x) - 4b cos(x) + 2b )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2b cos(x) + 4b cos(x) - 2b cos(x) - 8b cos(x) - 2b cos(x) +--R + +--R 5 5 +--R 4b cos(x) + 2b +--R * +--R sin(x) +--R Type: Expression Integer +--E 288 + +--S 289 of 586 +t0548:= sin(x)/(a+a*csc(x)) +--R +--R +--R sin(x) +--R (274) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 289 + +--S 290 of 586 +r0548:= -(cos(x)^2+x*cos(x)-sin(x)+1)/a/cos(x) +--R +--R +--R 2 +--R sin(x) - cos(x) - x cos(x) - 1 +--R (275) ------------------------------- +--R a cos(x) +--R Type: Expression Integer +--E 290 + +--S 291 of 586 +a0548:= integrate(t0548,x) +--R +--R +--R 2 +--R (- cos(x) - x - 1)sin(x) - cos(x) + (- x - 4)cos(x) - x - 3 +--R (276) ------------------------------------------------------------ +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 291 + +--S 292 of 586 +m0548:= a0548-r0548 +--R +--R +--R 2 2 +--R - sin(x) - 2cos(x)sin(x) - 3cos(x) - 2cos(x) + 1 +--R (277) -------------------------------------------------- +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression Integer +--E 292 + +--S 293 of 586 +d0548:= D(m0548,x) +--R +--R +--R (278) +--R 4 3 2 +--R - sin(x) + (- 2cos(x) - 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (- 2cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 3 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 293 + +--S 294 of 586 +t0549:= sin(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R sin(x) +--R (279) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 294 + +--S 295 of 586 +r0549:= -1/2*(sin(x)*cos(x)^2-2*cos(x)^2-3*x*cos(x)-2+2*sin(x))/a/cos(x) +--R +--R +--R 2 2 +--R (- cos(x) - 2)sin(x) + 2cos(x) + 3x cos(x) + 2 +--R (280) ------------------------------------------------ +--R 2a cos(x) +--R Type: Expression Integer +--E 295 + +--S 296 of 586 +a0549:= integrate(t0549,x) +--R +--R +--R (281) +--R 2 3 2 +--R (- cos(x) + cos(x) + 3x + 2)sin(x) + cos(x) + 2cos(x) + (3x + 7)cos(x) +--R + +--R 3x + 6 +--R / +--R 2a sin(x) + 2a cos(x) + 2a +--R Type: Union(Expression Integer,...) +--E 296 + +--S 297 of 586 +m0549:= a0549-r0549 +--R +--R +--R (282) +--R 2 2 4 2 +--R (cos(x) + 2)sin(x) + 4cos(x)sin(x) + cos(x) + 5cos(x) + 4cos(x) - 2 +--R ----------------------------------------------------------------------- +--R 2 +--R 2a cos(x)sin(x) + 2a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 297 + +--S 298 of 586 +d0549:= D(m0549,x) +--R +--R +--R (283) +--R 2 4 2 3 +--R (- cos(x) + 2)sin(x) + (- cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 4 2 2 +--R (- 2cos(x) + cos(x) - 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (- cos(x) + 4cos(x) + 3cos(x) - 4cos(x) - 2)sin(x) - cos(x) - cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 298 + +--S 299 of 586 +t0550:= sin(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R sin(x) +--R (284) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 299 + +--S 300 of 586 +r0550:= 1/6*(2*cos(x)^4+3*sin(x)*cos(x)^2-12*cos(x)^2-9*x*cos(x)-6+6*sin(x))/a/cos(x) +--R +--R +--R 2 4 2 +--R (3cos(x) + 6)sin(x) + 2cos(x) - 12cos(x) - 9x cos(x) - 6 +--R (285) ----------------------------------------------------------- +--R 6a cos(x) +--R Type: Expression Integer +--E 300 + +--S 301 of 586 +a0550:= integrate(t0550,x) +--R +--R +--R (286) +--R 3 2 4 3 +--R (2cos(x) + 3cos(x) - 9cos(x) - 9x - 10)sin(x) + 2cos(x) - cos(x) +--R + +--R 2 +--R - 12cos(x) + (- 9x - 31)cos(x) - 9x - 22 +--R / +--R 6a sin(x) + 6a cos(x) + 6a +--R Type: Union(Expression Integer,...) +--E 301 + +--S 302 of 586 +m0550:= a0550-r0550 +--R +--R +--R (287) +--R 2 2 4 2 +--R (- 3cos(x) - 6)sin(x) - 16cos(x)sin(x) - 3cos(x) - 19cos(x) +--R + +--R - 16cos(x) + 6 +--R / +--R 2 +--R 6a cos(x)sin(x) + 6a cos(x) + 6a cos(x) +--R Type: Expression Integer +--E 302 + +--S 303 of 586 +d0550:= D(m0550,x) +--R +--R +--R (288) +--R 2 4 2 3 +--R (cos(x) - 2)sin(x) + (cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 4 2 2 +--R (2cos(x) - cos(x) + 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (cos(x) - 4cos(x) - 3cos(x) + 4cos(x) + 2)sin(x) + cos(x) + cos(x) +--R + +--R 2 +--R - 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression Integer +--E 303 + +--S 304 of 586 +t0551:= cos(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R cos(x) +--R (289) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 304 + +--S 305 of 586 +r0551:= 1/2*(-x-2*cos(x)+cos(x)*sin(x))/a +--R +--R +--R cos(x)sin(x) - 2cos(x) - x +--R (290) -------------------------- +--R 2a +--R Type: Expression Integer +--E 305 + +--S 306 of 586 +a0551:= integrate(t0551,x) +--R +--R +--R cos(x)sin(x) - 2cos(x) - x +--R (291) -------------------------- +--R 2a +--R Type: Union(Expression Integer,...) +--E 306 + +--S 307 of 586 +m0551:= a0551-r0551 +--R +--R +--R (292) 0 +--R Type: Expression Integer +--E 307 + +--S 308 of 586 +d0551:= D(m0551,x) +--R +--R +--R (293) 0 +--R Type: Expression Integer +--E 308 + +--S 309 of 586 +t0552:= cos(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R cos(x) +--R (294) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 309 + +--S 310 of 586 +r0552:= 1/24/a*(-3*cos(x)*sin(x)+6*cos(x)^3*sin(x)-3*x-8*cos(x)^3) +--R +--R +--R 3 3 +--R (6cos(x) - 3cos(x))sin(x) - 8cos(x) - 3x +--R (295) ------------------------------------------ +--R 24a +--R Type: Expression Integer +--E 310 + +--S 311 of 586 +a0552:= integrate(t0552,x) +--R +--R +--R 3 3 +--R (6cos(x) - 3cos(x))sin(x) - 8cos(x) - 3x +--R (296) ------------------------------------------ +--R 24a +--R Type: Union(Expression Integer,...) +--E 311 + +--S 312 of 586 +m0552:= a0552-r0552 +--R +--R +--R (297) 0 +--R Type: Expression Integer +--E 312 + +--S 313 of 586 +d0552:= D(m0552,x) +--R +--R +--R (298) 0 +--R Type: Expression Integer +--E 313 + +--S 314 of 586 +t0553:= tan(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R tan(x) +--R (299) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 314 + +--S 315 of 586 +r0553:= -1/3*(-4*sin(x)*cos(x)^2+3*cos(x)^2-1+sin(x)+3*x*cos(x)^3)/a/cos(x)^3 +--R +--R +--R 2 3 2 +--R (4cos(x) - 1)sin(x) - 3x cos(x) - 3cos(x) + 1 +--R (300) ------------------------------------------------ +--R 3 +--R 3a cos(x) +--R Type: Expression Integer +--E 315 + +--S 316 of 586 +a0553:= integrate(t0553,x) +--R +--R +--R 2 +--R ((- 3x - 2)cos(x) + 1)sin(x) - 4cos(x) + (- 3x - 2)cos(x) + 2 +--R (301) -------------------------------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression Integer,...) +--E 316 + +--S 317 of 586 +m0553:= a0553-r0553 +--R +--R +--R (302) +--R 2 2 3 4 3 2 +--R (- 4cos(x) + 1)sin(x) - 2cos(x) sin(x) - 4cos(x) - 2cos(x) + 5cos(x) - 1 +--R ----------------------------------------------------------------------------- +--R 3 3 +--R 3a cos(x) sin(x) + 3a cos(x) +--R Type: Expression Integer +--E 317 + +--S 318 of 586 +d0553:= D(m0553,x) +--R +--R +--R (303) +--R 2 4 2 3 2 2 +--R (- 4cos(x) + 3)sin(x) + (- 4cos(x) + 3)sin(x) + (6cos(x) - 3)sin(x) +--R + +--R 4 2 6 4 2 +--R (- 4cos(x) + 7cos(x) - 3)sin(x) + 4cos(x) - 5cos(x) + cos(x) +--R / +--R 4 2 4 4 +--R 3a cos(x) sin(x) + 6a cos(x) sin(x) + 3a cos(x) +--R Type: Expression Integer +--E 318 + +--S 319 of 586 +t0554:= cot(x)/(a+a*csc(x)) +--R +--R +--R cot(x) +--R (304) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 319 + +--S 320 of 586 +r0554:= log(1+sin(x))/a +--R +--R +--R log(sin(x) + 1) +--R (305) --------------- +--R a +--R Type: Expression Integer +--E 320 + +--S 321 of 586 +a0554:= integrate(t0554,x) +--R +--R +--R sin(x) + cos(x) + 1 2 +--R 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (306) ------------------------------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 321 + +--S 322 of 586 +m0554:= a0554-r0554 +--R +--R +--R sin(x) + cos(x) + 1 2 +--R - log(sin(x) + 1) + 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (307) --------------------------------------------------------------- +--R a +--R Type: Expression Integer +--E 322 + +--S 323 of 586 +d0554:= D(m0554,x) +--R +--R +--R (308) +--R 3 2 2 3 +--R sin(x) - cos(x)sin(x) + (cos(x) - 1)sin(x) - cos(x) + cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (a cos(x) + 3a cos(x) + 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R Type: Expression Integer +--E 323 + +--S 324 of 586 +t0555:= cot(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R cot(x) +--R (309) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 324 + +--S 325 of 586 +r0555:= -(x+atanh(cos(x)))/a +--R +--R +--R - atanh(cos(x)) - x +--R (310) ------------------- +--R a +--R Type: Expression Integer +--E 325 + +--S 326 of 586 +a0555:= integrate(t0555,x) +--R +--R +--R sin(x) +--R log(----------) - x +--R cos(x) + 1 +--R (311) ------------------- +--R a +--R Type: Union(Expression Integer,...) +--E 326 + +--S 327 of 586 +m0555:= a0555-r0555 +--R +--R +--R sin(x) +--R log(----------) + atanh(cos(x)) +--R cos(x) + 1 +--R (312) ------------------------------- +--R a +--R Type: Expression Integer +--E 327 + +--S 328 of 586 +d0555:= D(m0555,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (313) -------------------------------- +--R 2 +--R (a cos(x) - a)sin(x) +--R Type: Expression Integer +--E 328 + +--S 329 of 586 +t0556:= cot(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R cot(x) +--R (314) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 329 + +--S 330 of 586 +r0556:= x/a+1/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a +--R +--R +--R atanh(cos(x)) - cot(x)csc(x) + 2cot(x) + 2x +--R (315) ------------------------------------------- +--R 2a +--R Type: Expression Integer +--E 330 + +--S 331 of 586 +a0556:= integrate(t0556,x) +--R +--R +--R (316) +--R 2 sin(x) 2 +--R (- cos(x) + 1)log(----------) - 2cos(x)sin(x) + 2x cos(x) + cos(x) - 2x +--R cos(x) + 1 +--R ------------------------------------------------------------------------- +--R 2 +--R 2a cos(x) - 2a +--R Type: Union(Expression Integer,...) +--E 331 + +--S 332 of 586 +m0556:= a0556-r0556 +--R +--R +--R (317) +--R 2 sin(x) 2 +--R (- cos(x) + 1)log(----------) + (- cos(x) + 1)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R 2 2 +--R - 2cos(x)sin(x) + (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) +--R + +--R cos(x) +--R / +--R 2 +--R 2a cos(x) - 2a +--R Type: Expression Integer +--E 332 + +--S 333 of 586 +d0556:= D(m0556,x) +--R +--R +--R (318) +--R 2 3 3 2 2 +--R (- 2cos(x) - 2)sin(x) + (- cos(x) + cos(x) + cos(x) + 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) - 2cos(x) + 2 +--R * +--R sin(x) +--R + +--R 5 3 +--R - cos(x) + 2cos(x) - cos(x) +--R / +--R 4 2 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R Type: Expression Integer +--E 333 + +--S 334 of 586 +t0557:= sec(x)/(a+a*csc(x)) +--R +--R +--R sec(x) +--R (319) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 334 + +--S 335 of 586 +r0557:= 1/2*atanh(sin(x))/a+1/2/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(sin(x)) + 1 +--R (320) ----------------------------- +--R 2a sin(x) + 2a +--R Type: Expression Integer +--E 335 + +--S 336 of 586 +a0557:= integrate(t0557,x) +--R +--R +--R (321) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression Integer,...) +--E 336 + +--S 337 of 586 +m0557:= a0557-r0557 +--R +--R +--R (322) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) - 1 +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 2a +--R Type: Expression Integer +--E 337 + +--S 338 of 586 +d0557:= D(m0557,x) +--R +--R +--R (323) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R / +--R 4 2 2 2 +--R 2a sin(x) + (- 2a cos(x) - 4a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R Type: Expression Integer +--E 338 + +--S 339 of 586 +t0558:= sec(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R sec(x) +--R (324) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 339 + +--S 340 of 586 +r0558:= 1/3/a/cos(x)^3*(-sin(x)+sin(x)*cos(x)^2+1) +--R +--R +--R 2 +--R (cos(x) - 1)sin(x) + 1 +--R (325) ----------------------- +--R 3 +--R 3a cos(x) +--R Type: Expression Integer +--E 340 + +--S 341 of 586 +a0558:= integrate(t0558,x) +--R +--R +--R 2 +--R (cos(x) + 1)sin(x) - cos(x) + cos(x) + 2 +--R (326) ----------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression Integer,...) +--E 341 + +--S 342 of 586 +m0558:= a0558-r0558 +--R +--R +--R (327) +--R 2 2 3 4 3 2 +--R (- cos(x) + 1)sin(x) + cos(x) sin(x) - cos(x) + cos(x) + 2cos(x) - 1 +--R ------------------------------------------------------------------------- +--R 3 3 +--R 3a cos(x) sin(x) + 3a cos(x) +--R Type: Expression Integer +--E 342 + +--S 343 of 586 +d0558:= D(m0558,x) +--R +--R +--R (328) +--R 2 4 2 3 2 2 +--R (- cos(x) + 3)sin(x) + (- cos(x) + 3)sin(x) + (3cos(x) - 3)sin(x) +--R + +--R 4 2 6 4 2 +--R (- cos(x) + 4cos(x) - 3)sin(x) + cos(x) - 2cos(x) + cos(x) +--R / +--R 4 2 4 4 +--R 3a cos(x) sin(x) + 6a cos(x) sin(x) + 3a cos(x) +--R Type: Expression Integer +--E 343 + +--S 344 of 586 +t0559:= sec(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R sec(x) +--R (329) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 344 + +--S 345 of 586 +r0559:= 1/8/cos(x)^4*(atanh(sin(x))*cos(x)^4-2*sin(x)+2+sin(x)*cos(x)^2)/a +--R +--R +--R 4 2 +--R cos(x) atanh(sin(x)) + (cos(x) - 2)sin(x) + 2 +--R (330) ---------------------------------------------- +--R 4 +--R 8a cos(x) +--R Type: Expression Integer +--E 345 + +--S 346 of 586 +a0559:= integrate(t0559,x) +--R +--R +--R (331) +--R 2 2 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (- 2cos(x) + 1)sin(x) - 3cos(x) + 3 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression Integer,...) +--E 346 + +--S 347 of 586 +m0559:= a0559-r0559 +--R +--R +--R (332) +--R 4 4 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (- cos(x) sin(x) - cos(x) )atanh(sin(x)) + (- cos(x) + 2)sin(x) +--R + +--R 4 4 2 +--R - 2cos(x) sin(x) - 3cos(x) + 3cos(x) - 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression Integer +--E 347 + +--S 348 of 586 +d0559:= D(m0559,x) +--R +--R +--R (333) +--R 2 7 +--R (- 2cos(x) + 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (- 2cos(x) + cos(x) + 4cos(x) + 4cos(x) - 16cos(x) - 24)sin(x) +--R + +--R 5 4 2 4 +--R (- 2cos(x) - cos(x) + 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 2cos(x) + cos(x) + 4cos(x) - 10cos(x) - 20cos(x) - 2cos(x) +--R + +--R 32cos(x) + 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 2 +--R (- 2cos(x) - cos(x) + 4cos(x) + 2cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 2cos(x) - 2cos(x) + cos(x) + 2cos(x) + 9cos(x) + 16cos(x) +--R + +--R - 16cos(x) - 8 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 2cos(x) - cos(x) - 6cos(x) - cos(x) + 4cos(x) + 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression Integer +--E 348 + +--S 349 of 586 +t0560:= sec(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R sec(x) +--R (334) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 349 + +--S 350 of 586 +r0560:= 1/15/a/cos(x)^5*(2*sin(x)*cos(x)^4+sin(x)*cos(x)^2-3*sin(x)+3) +--R +--R +--R 4 2 +--R (2cos(x) + cos(x) - 3)sin(x) + 3 +--R (335) ---------------------------------- +--R 5 +--R 15a cos(x) +--R Type: Expression Integer +--E 350 + +--S 351 of 586 +a0560:= integrate(t0560,x) +--R +--R +--R 3 2 4 3 2 +--R (3cos(x) + 2cos(x) + 1)sin(x) - 2cos(x) + 3cos(x) + cos(x) + 4 +--R (336) ------------------------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Union(Expression Integer,...) +--E 351 + +--S 352 of 586 +m0560:= a0560-r0560 +--R +--R +--R (337) +--R 4 2 2 5 6 5 +--R (- 2cos(x) - cos(x) + 3)sin(x) + 3cos(x) sin(x) - 2cos(x) + 3cos(x) +--R + +--R 4 2 +--R cos(x) + 4cos(x) - 3 +--R / +--R 5 5 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Expression Integer +--E 352 + +--S 353 of 586 +d0560:= D(m0560,x) +--R +--R +--R (338) +--R 4 2 4 4 2 3 +--R (- 2cos(x) - 3cos(x) + 15)sin(x) + (- 2cos(x) - 3cos(x) + 15)sin(x) +--R + +--R 2 2 6 4 2 +--R (15cos(x) - 15)sin(x) + (- 2cos(x) - cos(x) + 18cos(x) - 15)sin(x) +--R + +--R 8 6 4 2 +--R 2cos(x) - cos(x) - 4cos(x) + 3cos(x) +--R / +--R 6 2 6 6 +--R 15a cos(x) sin(x) + 30a cos(x) sin(x) + 15a cos(x) +--R Type: Expression Integer +--E 353 + +--S 354 of 586 +t0561:= csc(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R csc(x) +--R (339) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 354 + +--S 355 of 586 +r0561:= -1/a/cos(x)*(atanh(cos(x))*cos(x)+sin(x)-1) +--R +--R +--R - cos(x)atanh(cos(x)) - sin(x) + 1 +--R (340) ---------------------------------- +--R a cos(x) +--R Type: Expression Integer +--E 355 + +--S 356 of 586 +a0561:= integrate(t0561,x) +--R +--R +--R sin(x) +--R (sin(x) + cos(x) + 1)log(----------) + 2cos(x) + 2 +--R cos(x) + 1 +--R (341) -------------------------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 356 + +--S 357 of 586 +m0561:= a0561-r0561 +--R +--R +--R (342) +--R 2 sin(x) +--R (cos(x)sin(x) + cos(x) + cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (cos(x)sin(x) + cos(x) + cos(x))atanh(cos(x)) + sin(x) + cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) + cos(x) - 1 +--R / +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression Integer +--E 357 + +--S 358 of 586 +d0561:= D(m0561,x) +--R +--R +--R (343) +--R 2 5 3 2 4 +--R (cos(x) - 1)sin(x) + (3cos(x) + cos(x) - 2cos(x) - 1)sin(x) +--R + +--R 4 3 2 3 +--R (2cos(x) + 2cos(x) - cos(x) + 1)sin(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 3cos(x) - 4cos(x) - 2cos(x) + 2cos(x) + 1)sin(x) +--R + +--R 6 5 3 2 7 6 +--R (cos(x) + 2cos(x) - 2cos(x) - cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 4 3 +--R - 2cos(x) - cos(x) +--R / +--R 4 2 3 +--R (a cos(x) - a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (2a cos(x) + 2a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 6 5 3 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a cos(x) )sin(x) +--R Type: Expression Integer +--E 358 + +--S 359 of 586 +t0562:= csc(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R csc(x) +--R (344) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 359 + +--S 360 of 586 +r0562:= atanh(cos(x))/a-cot(x)/a-cos(x)/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(cos(x)) - cot(x)sin(x) - cot(x) - cos(x) +--R (345) ---------------------------------------------------------- +--R a sin(x) + a +--R Type: Expression Integer +--E 360 + +--S 361 of 586 +a0562:= integrate(t0562,x) +--R +--R +--R (346) +--R 2 sin(x) +--R ((- cos(x) - 1)sin(x) + cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 3cos(x) - 2)sin(x) - cos(x) - cos(x) +--R / +--R 2 +--R (a cos(x) + a)sin(x) - a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 361 + +--S 362 of 586 +m0562:= a0562-r0562 +--R +--R +--R (347) +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R atanh(cos(x)) +--R + +--R 2 +--R ((cos(x) + 1)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 +--R ((- cos(x) + cos(x) + 2)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 3 2 +--R (- cos(x) + 1)cot(x) - cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (- a cos(x) + a cos(x) + 2a)sin(x) - a cos(x) + a +--R Type: Expression Integer +--E 362 + +--S 363 of 586 +d0562:= D(m0562,x) +--R +--R +--R (348) +--R 2 6 +--R (- cos(x) - 1)sin(x) +--R + +--R 3 2 2 3 2 +--R (- cos(x) - cos(x) + cos(x) + 1)cot(x) + 4cos(x) - 2cos(x) +--R + +--R - 2cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (2cos(x) - 2cos(x) - 6cos(x) + 2cos(x) + 4)cot(x) + 2cos(x) +--R + +--R 3 2 +--R 10cos(x) - 5cos(x) - 6cos(x) - 3 +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- cos(x) + 5cos(x) + cos(x) - 11cos(x) + 6)cot(x) + 3cos(x) +--R + +--R 4 3 2 +--R 3cos(x) + 2cos(x) - 8cos(x) - 3cos(x) + 3 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) + 4cos(x) + 4cos(x) - 8cos(x) - 2cos(x) + 4)cot(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 10cos(x) + cos(x) - 15cos(x) - 6cos(x) + 5cos(x) + 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + 1)cot(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) - cos(x) + 9cos(x) + 3cos(x) - 13cos(x) - 3cos(x) +--R + +--R 5cos(x) + 1 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + cos(x) +--R / +--R 3 2 5 +--R (a cos(x) + a cos(x) - a cos(x) - a)sin(x) +--R + +--R 4 3 2 4 +--R (- 2a cos(x) + 2a cos(x) + 6a cos(x) - 2a cos(x) - 4a)sin(x) +--R + +--R 5 4 3 2 3 +--R (a cos(x) - 5a cos(x) - a cos(x) + 11a cos(x) - 6a)sin(x) +--R + +--R 5 4 3 2 +--R (2a cos(x) - 4a cos(x) - 4a cos(x) + 8a cos(x) + 2a cos(x) - 4a) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (a cos(x) - a cos(x) - 2a cos(x) + 2a cos(x) + a cos(x) - a)sin(x) +--R Type: Expression Integer +--E 363 + +--S 364 of 586 +t0563:= csc(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R csc(x) +--R (349) ------------ +--R a csc(x) + a +--R Type: Expression Integer +--E 364 + +--S 365 of 586 +r0563:= -3/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a+cos(x)/a/(1+sin(x)) +--R +--R +--R (350) +--R (- 3sin(x) - 3)atanh(cos(x)) + (- cot(x)csc(x) + 2cot(x))sin(x) +--R + +--R - cot(x)csc(x) + 2cot(x) + 2cos(x) +--R / +--R 2a sin(x) + 2a +--R Type: Expression Integer +--E 365 + +--S 366 of 586 +a0563:= integrate(t0563,x) +--R +--R +--R (351) +--R 2 3 2 sin(x) +--R ((3cos(x) - 3)sin(x) + 3cos(x) + 3cos(x) - 3cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (- 2cos(x) - cos(x))sin(x) + 6cos(x) + 5cos(x) - 5cos(x) - 4 +--R / +--R 2 3 2 +--R (2a cos(x) - 2a)sin(x) + 2a cos(x) + 2a cos(x) - 2a cos(x) - 2a +--R Type: Union(Expression Integer,...) +--E 366 + +--S 367 of 586 +m0563:= a0563-r0563 +--R +--R +--R (352) +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 +--R (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) - 2cos(x) +--R + +--R - cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) - cos(x) - 2)cot(x)csc(x) +--R + +--R 3 2 3 2 +--R (- 2cos(x) - 4cos(x) + 2cos(x) + 4)cot(x) + 4cos(x) + 3cos(x) +--R + +--R - 4cos(x) - 4 +--R * +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) - cos(x) - 1)cot(x)csc(x) +--R + +--R 3 2 4 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R 7cos(x) - 3cos(x) - 4 +--R / +--R 2 2 +--R (2a cos(x) - 2a)sin(x) +--R + +--R 3 2 3 +--R (2a cos(x) + 4a cos(x) - 2a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 2 +--R 2a cos(x) - 2a cos(x) - 2a +--R Type: Expression Integer +--E 367 + +--S 368 of 586 +d0563:= D(m0563,x) +--R +--R +--R (353) +--R 3 2 6 +--R (3cos(x) - cos(x) - 7cos(x) - 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 4 3 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) + 2cos(x) + 10cos(x) - 6cos(x) +--R + +--R - 22cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 3 2 +--R (- 4cos(x) - 8cos(x) + 8cos(x) + 16cos(x) - 4cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 4cos(x) + 8cos(x) - 2cos(x) - 4 +--R * +--R csc(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 8cos(x) - 8cos(x) - 16cos(x) + 4cos(x) + 8)cot(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 15cos(x) - 9cos(x) - 21cos(x) - 13cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 12cos(x) - 8cos(x) + 24cos(x) + 22cos(x) +--R + +--R - 12cos(x) - 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 6cos(x) - 4cos(x) + 12cos(x) + 11cos(x) - 6cos(x) +--R + +--R - 6 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 12cos(x) + 8cos(x) - 24cos(x) - 22cos(x) +--R + +--R 12cos(x) + 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) + 30cos(x) + 14cos(x) - 44cos(x) - 24cos(x) + 18cos(x) +--R + +--R 10 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R (- 4cos(x) - 12cos(x) + 24cos(x) + 12cos(x) - 12cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 3 2 +--R - 2cos(x) - 6cos(x) + 12cos(x) + 6cos(x) - 6cos(x) - 4 +--R * +--R csc(x) +--R + +--R 6 5 3 2 2 +--R (4cos(x) + 12cos(x) - 24cos(x) - 12cos(x) + 12cos(x) + 8)cot(x) +--R + +--R 7 6 5 4 3 +--R 7cos(x) + 12cos(x) + 7cos(x) - 17cos(x) - 35cos(x) + 25cos(x) + 9 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 2cos(x) + 8cos(x) + 2cos(x) +--R + +--R - 4cos(x) - 2 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 2cos(x) + cos(x) + 4cos(x) + cos(x) - 2cos(x) - 1 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 3 +--R 2cos(x) + 10cos(x) + 10cos(x) - 12cos(x) - 28cos(x) - 10cos(x) +--R + +--R 2 +--R 14cos(x) + 12cos(x) + 2 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) + 6cos(x) - 3cos(x) - 12cos(x) - 3cos(x) + 6cos(x) + 3cos(x) +--R / +--R 4 2 5 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R + +--R 5 4 3 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 16a cos(x) + 4a cos(x) + 8a) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 12a cos(x) + 8a cos(x) - 24a cos(x) - 22a cos(x) +--R + +--R 12a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R 4a cos(x) + 12a cos(x) - 24a cos(x) - 12a cos(x) + 12a cos(x) +--R + +--R 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression Integer +--E 368 + +--S 369 of 586 +t0564:= sin(x)/(a+b*sin(x))^2 +--R +--R +--R sin(x) +--R (354) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 369 + +--S 370 of 586 +r0564:= -2*b*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-a*cos(x)/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R (2b sin(x) + 2a b)atan(------------) + a cos(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (355) ----------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|- b + a +--R Type: Expression Integer +--E 370 + +--S 371 of 586 +a0564:= integrate(t0564,x) +--R +--R +--R (356) +--R [ +--R 2 +--R (b sin(x) + a b) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R / +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2b sin(x) - 2a b)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a +--R / +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 371 + +--S 372 of 586 +m0564a:= a0564.1-r0564 +--R +--R +--R (357) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R | 2 2 2 | 2 2 | 2 2 +--R - 2b\|b - a atan(------------) + \|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (b - a )\|- b + a \|b - a +--R Type: Expression Integer +--E 372 + +--S 373 of 586 +d0564a:= D(m0564a,x) +--R +--R +--R (358) +--R 4 2 2 4 3 2 3 x 2 +--R (((- b + a b )cos(x) - b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 4 2 3 4 2 4 2 2 x +--R (2b sin(x) + 2a b sin(x) + 2b cos(x) + (2b - 2a b )cos(x))tan(-) +--R 2 +--R + +--R 4 2 2 4 3 2 3 +--R ((- b + a b )cos(x) - b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 3 5 2 3 4 3 2 2 4 +--R ((b - a b )cos(x) + b - a b )sin(x) + (- a b + a b )cos(x) + a b +--R + +--R 3 2 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 4 3 2 +--R (- 2b + 2a b )sin(x) + (- 2a b + 2a b )sin(x) +--R + +--R 5 2 3 2 5 2 3 +--R (- 2b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 5 2 3 4 3 2 2 4 +--R ((b - a b )cos(x) + b - a b )sin(x) + (- a b + a b )cos(x) + a b +--R + +--R 3 2 +--R - a b +--R / +--R 2 4 4 2 2 +--R (a b - a b )sin(x) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (2a b - 2a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 4a b + 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 +--R (a b - a b )sin(x) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 2 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 2 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 6 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R Type: Expression Integer +--E 373 + +--S 374 of 586 +m0564b:= a0564.2-r0564 +--R +--R +--R (359) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R (a sin(x) + b cos(x) + b)\|- b + a 2 +--R - 2b atan(-------------------------------------) - 2b atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression Integer +--E 374 + +--S 375 of 586 +d0564b:= D(m0564b,x) +--R +--R +--R (360) +--R 2 2 2 2 x 2 +--R (a b sin(x) + (- 2b cos(x) - 2b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 2 +--R (4b sin(x) + 4b cos(x) + 4b cos(x))tan(-) + a b sin(x) +--R 2 +--R + +--R 2 2 2 +--R (- 2b cos(x) - 2b )sin(x) + a b cos(x) - a b +--R / +--R 2 2 4 2 3 3 3 3 +--R (a b - a )sin(x) + ((2a b - 2a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 4 2 2 4 2 2 +--R (2a b - 2a b)sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 3 3 3 3 +--R (a b - a )sin(x) + ((2a b - 2a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + a b - a +--R Type: Expression Integer +--E 375 + +--S 376 of 586 +t0565:= sin(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (361) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 376 + +--S 377 of 586 +r0565:= x/b^2+2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(3/2)-4*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+a^2*cos(x)/b/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (362) +--R x +--R a tan(-) + b +--R 3 3 2 2 4 2 +--R ((- 4a b + 2a b)sin(x) - 4a b + 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 2 2 3 | 2 2 +--R ((b - a b)x sin(x) - a b cos(x) + (a b - a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R Type: Expression Integer +--E 377 + +--S 378 of 586 +a0565:= integrate(t0565,x) +--R +--R +--R (363) +--R [ +--R 3 3 2 2 4 +--R ((2a b - a b)sin(x) + 2a b - a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 3 2 2 2 2 3 2 | 2 2 +--R (((b - a b)x - a b )sin(x) - a b cos(x) + (a b - a )x - a b)\|b - a +--R / +--R +-------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|b - a +--R , +--R +--R 3 3 2 2 4 +--R ((4a b - 2a b)sin(x) + 4a b - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 2 2 2 2 3 2 +--R (((b - a b)x - a b )sin(x) - a b cos(x) + (a b - a )x - a b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 378 + +--S 379 of 586 +m0565a:= a0565.1-r0565 +--R +--R +--R (364) +--R +---------+ +--R 2 3 | 2 2 +--R (2a b - a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 2 3 | 2 2 2 | 2 2 | 2 2 +--R (4a b - 2a )\|b - a atan(------------) - a b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 4 2 2 | 2 2 | 2 2 +--R (b - a b )\|- b + a \|b - a +--R Type: Expression Integer +--E 379 + +--S 380 of 586 +d0565a:= D(m0565a,x) +--R +--R +--R (365) +--R 4 3 2 5 4 3 2 +--R ((2a b - 3a b + a )cos(x) + 2a b - a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + a b)cos(x) + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 3 4 +--R (- 4a b + 2a b )sin(x) + (- 4a b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (- 4a b + 2a b )cos(x) + (- 4a b + 6a b - 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 4 3 2 +--R ((2a b - 3a b + a )cos(x) + 2a b - a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + a b)cos(x) + 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((2a b - 3a b + a b)cos(x) + 2a b - 3a b + a b)sin(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 2a b + 3a b - a )cos(x) + 2a b - 3a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (- 4a b + 6a b - 2a b)sin(x) + (- 4a b + 6a b - 2a )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b + 6a b - 2a b)cos(x) + (- 4a b + 6a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((2a b - 3a b + a b)cos(x) + 2a b - 3a b + a b)sin(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 2a b + 3a b - a )cos(x) + 2a b - 3a b + a +--R / +--R 2 5 4 3 2 +--R (a b - a b )sin(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 +--R (2a b - 2a b )sin(x) +--R + +--R 7 2 5 4 3 7 4 3 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 +--R (a b - a b )sin(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 6 2 2 +--R (a b - 2a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R ((a b - 2a b + a b )cos(x) + a b - a b - a b + a b)sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (a b - 2a b + a b )cos(x) + a b - 2a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 2 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 2 6 4 4 6 2 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b - 2a b + 2a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 +--R (a b - 2a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R ((a b - 2a b + a b )cos(x) + a b - a b - a b + a b)sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (a b - 2a b + a b )cos(x) + a b - 2a b + a b +--R Type: Expression Integer +--E 380 + +--S 381 of 586 +m0565b:= a0565.2-r0565 +--R +--R +--R (366) +--R +---------+ +--R | 2 2 +--R 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4a b - 2a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 3 2 | 2 2 +--R (4a b - 2a )atan(------------) - a b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 | 2 2 +--R (b - a b )\|- b + a +--R Type: Expression Integer +--E 381 + +--S 382 of 586 +d0565b:= D(m0565b,x) +--R +--R +--R (367) +--R 2 2 4 2 3 3 3 3 +--R (- 2a b + a )sin(x) + ((4a b - 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 2 +--R (- 8a b + 4a b)sin(x) + (- 8a b + 4a b)cos(x) +--R + +--R 3 3 +--R (- 8a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 3 3 3 3 +--R (- 2a b + a )sin(x) + ((4a b - 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + 2a b - a +--R / +--R 2 4 4 2 2 5 3 3 5 3 3 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 6 2 4 6 2 4 +--R (2a b - 2a b )sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 3 3 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 3 3 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R Type: Expression Integer +--E 382 + +--S 383 of 586 +t0566:= sin(x)^3/(a+b*sin(x))^2 +--R +--R +--R 3 +--R sin(x) +--R (368) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 383 + +--S 384 of 586 +r0566:= -2*a*x/b^3-2*a^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(3/2)+6*a^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-cos(x)/b^2-a^3*cos(x)/b^2/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (369) +--R x +--R a tan(-) + b +--R 2 3 4 3 2 5 2 +--R ((6a b - 4a b)sin(x) + 6a b - 4a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R Type: Expression Integer +--E 384 + +--S 385 of 586 +a0566:= integrate(t0566,x) +--R +--R +--R (370) +--R [ +--R 2 3 4 3 2 5 +--R ((3a b - 2a b)sin(x) + 3a b - 2a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 4 2 2 3 3 4 2 2 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x - b + 2a b )sin(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x - a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|b - a +--R , +--R +--R 2 3 4 3 2 5 +--R ((- 6a b + 4a b)sin(x) - 6a b + 4a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 2 2 3 3 4 2 2 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x - b + 2a b )sin(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x - a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 385 + +--S 386 of 586 +m0566a:= a0566.1-r0566 +--R +--R +--R (371) +--R +---------+ +--R 2 2 4 | 2 2 +--R (3a b - 2a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 2 4 | 2 2 2 +--R (- 6a b + 4a )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R (- b + 2a b)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 2 3 | 2 2 | 2 2 +--R (b - a b )\|- b + a \|b - a +--R Type: Expression Integer +--E 386 + +--S 387 of 586 +d0566a:= D(m0566a,x) +--R +--R +--R (372) +--R 2 4 4 2 6 2 4 4 2 +--R ((- 3a b + 5a b - 2a )cos(x) - 3a b + 2a b )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (3a b - 2a b)cos(x) - 3a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 3 3 5 +--R (6a b - 4a b )sin(x) + (6a b - 4a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 +--R (6a b - 4a b )cos(x) + (6a b - 10a b + 4a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 2 4 4 2 +--R ((- 3a b + 5a b - 2a )cos(x) - 3a b + 2a b )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (3a b - 2a b)cos(x) - 3a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R ((3a b - 5a b + 2a b)cos(x) + 3a b - 5a b + 2a b)sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (- 3a b + 5a b - 2a )cos(x) + 3a b - 5a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 3 4 5 2 7 +--R (- 6a b + 10a b - 4a b)sin(x) + (- 6a b + 10a b - 4a )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 6a b + 10a b - 4a b)cos(x) + (- 6a b + 10a b - 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R ((3a b - 5a b + 2a b)cos(x) + 3a b - 5a b + 2a b)sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (- 3a b + 5a b - 2a )cos(x) + 3a b - 5a b + 2a +--R / +--R 2 6 4 4 2 +--R (a b - a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (a b - 2a b + a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 2 +--R (2a b - 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 4 4 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 2 +--R (a b - a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (a b - 2a b + a b )cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 2 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- a b + 2a b - a b )cos(x) - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 2 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 2 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- a b + 2a b - a b )cos(x) - a b + 2a b - a b +--R Type: Expression Integer +--E 387 + +--S 388 of 586 +m0566b:= a0566.2-r0566 +--R +--R +--R (373) +--R +---------+ +--R | 2 2 +--R 2 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 6a b + 4a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 2 4 2 3 2 | 2 2 +--R (- 6a b + 4a )atan(------------) + (- b + 2a b)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 | 2 2 +--R (b - a b )\|- b + a +--R Type: Expression Integer +--E 388 + +--S 389 of 586 +d0566b:= D(m0566b,x) +--R +--R +--R (374) +--R 3 2 5 2 2 3 4 2 3 4 +--R (3a b - 2a )sin(x) + ((- 6a b + 4a b)cos(x) - 6a b + 4a b)sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (3a b - 2a )cos(x) - 3a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 2 +--R (12a b - 8a b)sin(x) + (12a b - 8a b)cos(x) +--R + +--R 2 3 4 +--R (12a b - 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 2 3 4 2 3 4 +--R (3a b - 2a )sin(x) + ((- 6a b + 4a b)cos(x) - 6a b + 4a b)sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (3a b - 2a )cos(x) - 3a b + 2a +--R / +--R 2 5 4 3 2 6 3 4 6 3 4 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 7 2 5 +--R (2a b - 2a b )sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 6 3 4 2 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 6 3 4 6 3 4 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R Type: Expression Integer +--E 389 + +--S 390 of 586 +t0567:= sin(x)^4/(a+b*sin(x))^2 +--R +--R +--R 4 +--R sin(x) +--R (375) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 390 + +--S 391 of 586 +r0567:= 3*a^2*x/b^4+1/2*x/b^2+2*a^5*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(3/2)-8*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)+2*a*cos(x)/b^3-1/2*cos(x)*sin(x)/b^2+a^4*cos(x)/b^3/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (376) +--R x +--R a tan(-) + b +--R 3 3 5 4 2 6 2 +--R ((- 16a b + 12a b)sin(x) - 16a b + 12a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 3 2 5 2 3 4 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x)sin(x) +--R + +--R 2 3 4 4 3 2 5 +--R (4a b - 6a b)cos(x) + (a b + 5a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R Type: Expression Integer +--E 391 + +--S 392 of 586 +a0567:= integrate(t0567,x) +--R +--R +--R (377) +--R [ +--R 3 3 5 4 2 6 +--R ((8a b - 6a b)sin(x) + 8a b - 6a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 4 3 2 5 2 3 4 4 3 2 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x + 4a b - 6a b ) +--R * +--R sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R (b - a b )cos(x) + (- b + 5a b - 6a b)cos(x) +--R + +--R 4 3 2 5 2 3 4 +--R (a b + 5a b - 6a )x + 4a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|b - a +--R , +--R +--R 3 3 5 4 2 6 +--R ((16a b - 12a b)sin(x) + 16a b - 12a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 3 2 5 2 3 4 4 3 2 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x + 4a b - 6a b ) +--R * +--R sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R (b - a b )cos(x) + (- b + 5a b - 6a b)cos(x) +--R + +--R 4 3 2 5 2 3 4 +--R (a b + 5a b - 6a )x + 4a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 392 + +--S 393 of 586 +m0567a:= a0567.1-r0567 +--R +--R +--R (378) +--R +---------+ +--R 3 3 5 4 2 6 | 2 2 +--R ((8a b - 6a b)sin(x) + 8a b - 6a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 3 5 4 2 6 | 2 2 2 +--R ((16a b - 12a b)sin(x) + 16a b - 12a )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 2 3 3 +--R (b - a b )cos(x)sin(x) + (4a b - 6a b )sin(x) + (b - a b )cos(x) +--R + +--R 5 2 3 2 3 4 +--R (- b + a b )cos(x) + 4a b - 6a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 7 2 5 6 3 4 | 2 2 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a \|b - a +--R Type: Expression Integer +--E 393 + +--S 394 of 586 +d0567a:= D(m0567a,x) +--R +--R +--R (379) +--R 2 6 4 4 5 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 3 +--R ((- 2a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 8a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 4 6 2 2 +--R (- 8a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (a b + 6a b - 13a b + 6a )cos(x) + a b + 15a b - 12a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 5 7 3 5 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 5 3 7 +--R (a b - a b - 8a b + 6a b)cos(x) + 8a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 4 4 4 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 5 3 +--R (- 4a b + 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 5 5 3 +--R - 16a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 3 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 2 8 2 6 4 4 +--R (- 4b + 2a b + 2a b )cos(x) + (2b - 4a b + 2a b )cos(x) +--R + +--R 8 4 4 6 2 +--R 2b - 34a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 4 7 3 5 5 3 3 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 5 5 3 2 +--R (- 16a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (2a b - 20a b + 30a b - 12a b)cos(x) + 2a b - 2a b +--R + +--R 5 3 7 +--R - 16a b + 12a b +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 5 8 2 6 4 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 3 +--R (2b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (2b - 2a b - 16a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 +--R (- 16a b + 28a b - 12a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 5 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 3 +--R ((- 2a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 8a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 4 6 2 2 2 6 4 4 6 2 8 +--R (- 8a b + 6a b )cos(x) + (a b + 6a b - 13a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 +--R a b + 15a b - 12a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 5 7 3 5 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 7 2 +--R (a b - 2a b + a b )cos(x) + (a b - a b - 8a b + 6a b)cos(x) +--R + +--R 5 3 7 +--R 8a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 5 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 2 7 4 5 6 3 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 8 3 6 7 2 2 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (a b + 6a b - 13a b + 6a b )cos(x) + a b + 7a b - 15a b +--R + +--R 7 2 +--R 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 6 3 3 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 +--R (- 8a b + 14a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 14a b - 27a b +--R + +--R 8 +--R 12a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 5 8 3 6 5 4 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 5 4 7 2 9 +--R (a b - 2a b - 7a b + 14a b - 6a )cos(x) + 8a b - 14a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 5 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 4 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b )sin(x) +--R + +--R 8 3 6 5 4 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 3 6 5 4 7 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 16a b + 28a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 3 9 2 7 6 3 2 +--R (- 4b + 8a b - 4a b )cos(x) + (- 4b + 6a b - 2a b )cos(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 8 +--R (2b - 4a b + 2a b )cos(x) + 2b - 2a b - 34a b + 58a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 16a b + 28a b - 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (2a b - 20a b + 30a b - 12a b )cos(x) + 2a b - 4a b - 14a b +--R + +--R 7 2 9 +--R 28a b - 12a +--R * +--R sin(x) +--R + +--R 9 2 7 4 5 5 9 2 7 4 5 4 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 4a b - 2a b )cos(x) +--R + +--R 9 2 7 4 5 3 +--R (2b - 4a b + 2a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (2b - 4a b - 14a b + 28a b - 12a b)cos(x) +--R + +--R 4 5 6 3 8 +--R (- 16a b + 28a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 5 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 2 7 4 5 6 3 3 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 7 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 3a b - a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 7 2 +--R (a b + 6a b - 13a b + 6a b )cos(x) + a b + 7a b - 15a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 6 3 3 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 +--R (- 8a b + 14a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 8 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 14a b - 27a b + 12a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 5 8 3 6 5 4 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 5 4 7 2 9 +--R (a b - 2a b - 7a b + 14a b - 6a )cos(x) + 8a b - 14a b + 6a +--R / +--R 2 8 4 6 3 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b + 2a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 6 4 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 2a b - 2a b )sin(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 3 +--R (4a b - 4a b )sin(x) +--R + +--R 10 2 8 4 6 10 2 8 4 6 2 +--R ((4b - 8a b + 4a b )cos(x) + 4b + 4a b - 8a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 +--R ((8a b - 16a b + 8a b )cos(x) + 8a b - 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 3 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b + 2a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 6 4 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 2a b - 2a b )sin(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 9 4 7 6 5 3 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 10 3 8 5 6 10 5 6 7 4 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b - 6a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 8 3 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 6a b + 2a b )sin(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 10 3 8 5 6 3 +--R (4a b - 8a b + 4a b )sin(x) +--R + +--R 11 2 9 4 7 11 4 7 6 5 2 +--R ((4b - 8a b + 4a b )cos(x) + 4b - 12a b + 8a b )sin(x) +--R + +--R 10 3 8 5 6 10 3 8 7 4 +--R ((8a b - 16a b + 8a b )cos(x) + 8a b - 12a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 6 5 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 9 4 7 6 5 3 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 10 3 8 5 6 10 5 6 7 4 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b - 6a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 8 3 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 6a b + 2a b )sin(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R Type: Expression Integer +--E 394 + +--S 395 of 586 +m0567b:= a0567.2-r0567 +--R +--R +--R (380) +--R 3 3 5 4 2 6 +--R ((16a b - 12a b)sin(x) + 16a b - 12a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 3 3 5 4 2 6 2 +--R ((16a b - 12a b)sin(x) + 16a b - 12a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 2 3 3 +--R (b - a b )cos(x)sin(x) + (4a b - 6a b )sin(x) + (b - a b )cos(x) +--R + +--R 5 2 3 2 3 4 +--R (- b + a b )cos(x) + 4a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R Type: Expression Integer +--E 395 + +--S 396 of 586 +d0567b:= D(m0567b,x) +--R +--R +--R (381) +--R 2 6 4 4 6 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 7 3 5 5 3 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 2 6 +--R (- 3a b + 3a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b +--R + +--R 4 4 6 2 +--R - 6a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 12a b - 10a b )cos(x) + 2a b + 14a b - 28a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 3 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b - 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (4a b + 28a b - 24a b )cos(x) + 3a b + 37a b - 38a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 16a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 14a b - 12a b)cos(x) + a b + 31a b - 24a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 5 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 6 2 +--R (2a b - 2a b )cos(x) + (a b - a b - 8a b + 6a )cos(x) + 8a b +--R + +--R 8 +--R - 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 6 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 8 2 6 4 4 5 +--R ((- 4b + 4a b )cos(x) - 4b + 2a b + 2a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 7 +--R (- 6a b + 6a b )cos(x) + (- 8a b + 8a b )cos(x) - 4a b +--R + +--R 3 5 5 3 +--R - 28a b + 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 2 6 3 8 2 6 4 4 2 +--R (- 8b + 8a b )cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 8 2 6 4 4 6 2 +--R (4b - 8a b + 4a b )cos(x) + 4b - 4a b - 64a b + 48a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 4 7 3 5 3 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b - 28a b + 24a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (8a b - 40a b + 24a b )cos(x) + 6a b - 6a b - 32a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 5 8 2 6 4 4 4 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 3 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 4a b - 64a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (4a b - 68a b + 48a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 7 3 5 6 7 3 5 5 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 5 3 7 2 +--R (4a b - 4a b )cos(x) + (2a b - 2a b - 32a b + 24a b)cos(x) +--R + +--R 5 3 7 +--R (- 32a b + 24a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 7 3 5 5 3 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 2 6 4 4 +--R (- 3a b + 3a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b - 6a b +--R + +--R 6 2 +--R 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 12a b - 10a b )cos(x) + 2a b + 14a b - 28a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 3 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (- 2a b - 6a b + 6a b )cos(x) + (4a b + 28a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 +--R 3a b + 37a b - 38a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 16a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 14a b - 12a b)cos(x) + a b + 31a b - 24a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 5 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 6 2 8 +--R (2a b - 2a b )cos(x) + (a b - a b - 8a b + 6a )cos(x) + 8a b - 6a +--R / +--R 2 8 4 6 4 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 9 5 5 3 +--R ((4a b - 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) + 10a b - 8a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R ((4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) + 8a b - 8a b ) +--R * +--R sin(x) +--R + +--R 4 6 6 4 2 4 6 6 4 4 6 6 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 4 10 2 8 10 4 6 3 +--R (4a b - 4a b )sin(x) + ((8b - 8a b )cos(x) + 8b - 8a b )sin(x) +--R + +--R 9 3 7 2 9 3 7 9 +--R (4a b - 4a b )cos(x) + (24a b - 24a b )cos(x) + 20a b +--R + +--R 3 7 5 5 +--R - 16a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) + 16a b +--R + +--R 4 6 +--R - 16a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) + 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 4 9 3 7 9 5 5 3 +--R (2a b - 2a b )sin(x) + ((4a b - 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) + 10a b - 8a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R ((4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) + 8a b - 8a b )sin(x) +--R + +--R 4 6 6 4 2 4 6 6 4 4 6 6 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R Type: Expression Integer +--E 396 + +--S 397 of 586 +t0568:= sin(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (382) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 397 + +--S 398 of 586 +r0568:= x/a^2-1/3*cos(x)/a^2/(1+sin(x))^2+5/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R 2 +--R 3x sin(x) + (5cos(x) + 6x)sin(x) + 4cos(x) + 3x +--R (383) ------------------------------------------------ +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression Integer +--E 398 + +--S 399 of 586 +a0568:= integrate(t0568,x) +--R +--R +--R (384) +--R 2 +--R ((3x + 9)cos(x) + 6x + 9)sin(x) + (- 3x + 1)cos(x) + (3x + 8)cos(x) + 6x + 7 +--R ----------------------------------------------------------------------------- +--R 2 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Union(Expression Integer,...) +--E 399 + +--S 400 of 586 +m0568:= a0568-r0568 +--R +--R +--R (385) +--R 3 2 2 +--R (9cos(x) + 9)sin(x) + (- 4cos(x) + 16cos(x) + 25)sin(x) +--R + +--R 3 2 3 2 +--R (5cos(x) - 7cos(x) + 7cos(x) + 23)sin(x) + 4cos(x) - 3cos(x) + 7 +--R / +--R 2 2 3 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) + (- 3a cos(x) + 9a cos(x) + 18a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a cos(x) + 9a cos(x) + 18a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Expression Integer +--E 400 + +--S 401 of 586 +d0568:= D(m0568,x) +--R +--R +--R (386) +--R 6 2 5 +--R - 9sin(x) + (- 5cos(x) - 2cos(x) - 25)sin(x) +--R + +--R 3 2 4 +--R (- 10cos(x) - 40cos(x) - 8cos(x) - 14)sin(x) +--R + +--R 3 2 3 +--R (- 18cos(x) - 62cos(x) - 8cos(x) + 18)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 10cos(x) - 28cos(x) - 4cos(x) - 8cos(x) + 4cos(x) + 23)sin(x) +--R + +--R 6 5 4 3 2 +--R 5cos(x) - 16cos(x) - 47cos(x) + 6cos(x) + 35cos(x) + 10cos(x) +--R + +--R 7 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 3cos(x) - 6cos(x) - 19cos(x) + 2cos(x) + 16cos(x) + 4cos(x) +--R / +--R 2 2 2 2 5 +--R (3a cos(x) + 12a cos(x) + 12a )sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 6a cos(x) + 3a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 3 +--R (3a cos(x) - 24a cos(x) - 18a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (9a cos(x) - 36a cos(x) - 42a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (9a cos(x) - 24a cos(x) - 33a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 3a cos(x) - 6a cos(x) - 9a cos(x) + 12a cos(x) + 12a +--R Type: Expression Integer +--E 401 + +--S 402 of 586 +t0569:= sin(x)^3/(a+a*sin(x))^2 +--R +--R +--R 3 +--R sin(x) +--R (387) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 402 + +--S 403 of 586 +r0569:= -2*x/a^2-cos(x)/a^2+1/3*cos(x)/a^2/(1+sin(x))^2-8/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R 2 +--R (- 3cos(x) - 6x)sin(x) + (- 14cos(x) - 12x)sin(x) - 10cos(x) - 6x +--R (388) ------------------------------------------------------------------ +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression Integer +--E 403 + +--S 404 of 586 +a0569:= integrate(t0569,x) +--R +--R +--R (389) +--R 2 3 +--R (- 3cos(x) + (- 6x - 24)cos(x) - 12x - 21)sin(x) + 3cos(x) +--R + +--R 2 +--R (6x - 1)cos(x) + (- 6x - 23)cos(x) - 12x - 19 +--R / +--R 2 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Union(Expression Integer,...) +--E 404 + +--S 405 of 586 +m0569:= a0569-r0569 +--R +--R +--R (390) +--R 3 2 2 +--R (- 18cos(x) - 21)sin(x) + (10cos(x) - 37cos(x) - 61)sin(x) +--R + +--R 3 2 3 2 +--R (- 8cos(x) + 19cos(x) - 22cos(x) - 59)sin(x) - 7cos(x) + 9cos(x) +--R + +--R - 3cos(x) - 19 +--R / +--R 2 2 3 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) + (- 3a cos(x) + 9a cos(x) + 18a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a cos(x) + 9a cos(x) + 18a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Expression Integer +--E 405 + +--S 406 of 586 +d0569:= D(m0569,x) +--R +--R +--R (391) +--R 6 2 5 +--R 15sin(x) + (8cos(x) + 2cos(x) + 43)sin(x) +--R + +--R 3 2 4 +--R (16cos(x) + 64cos(x) + 8cos(x) + 26)sin(x) +--R + +--R 3 2 3 +--R (30cos(x) + 104cos(x) + 8cos(x) - 30)sin(x) +--R + +--R 5 4 3 2 2 +--R (16cos(x) + 43cos(x) + 4cos(x) + 20cos(x) - 4cos(x) - 41)sin(x) +--R + +--R 6 5 4 3 2 +--R - 8cos(x) + 28cos(x) + 77cos(x) - 18cos(x) - 56cos(x) - 10cos(x) +--R + +--R - 13 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) + 12cos(x) + 34cos(x) - 8cos(x) - 28cos(x) - 4cos(x) +--R / +--R 2 2 2 2 5 +--R (3a cos(x) + 12a cos(x) + 12a )sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 6a cos(x) + 3a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 3 +--R (3a cos(x) - 24a cos(x) - 18a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (9a cos(x) - 36a cos(x) - 42a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (9a cos(x) - 24a cos(x) - 33a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 3a cos(x) - 6a cos(x) - 9a cos(x) + 12a cos(x) + 12a +--R Type: Expression Integer +--E 406 + +--S 407 of 586 +t0570:= cos(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (392) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 407 + +--S 408 of 586 +r0570:= -x/b^2+2*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)-cos(x)/b/(a+b*sin(x)) +--R +--R +--R (393) +--R x +--R a tan(-) + b +--R 2 2 +--R (2a b sin(x) + 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b x sin(x) - b cos(x) - a x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (b sin(x) + a b )\|- b + a +--R Type: Expression Integer +--E 408 + +--S 409 of 586 +a0570:= integrate(t0570,x) +--R +--R +--R (394) +--R [ +--R 2 3 +--R (a b sin(x) + a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|b - a +--R / +--R +-------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2a b sin(x) - 2a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|- b + a +--R / +--R +---------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 409 + +--S 410 of 586 +m0570a:= a0570.1-r0570 +--R +--R +--R (395) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 2 | 2 2 2 | 2 2 | 2 2 +--R - 2a \|b - a atan(------------) - b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a b \|- b + a \|b - a +--R Type: Expression Integer +--E 410 + +--S 411 of 586 +d0570a:= D(m0570a,x) +--R +--R +--R (396) +--R 2 3 2 2 2 2 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 3 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 3 3 3 2 2 4 2 2 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 4 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 2 4 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 3 2 2 4 2 2 2 4 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression Integer +--E 411 + +--S 412 of 586 +m0570b:= a0570.2-r0570 +--R +--R +--R (397) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 2 (a sin(x) + b cos(x) + b)\|- b + a 2 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R - b\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a b \|- b + a +--R Type: Expression Integer +--E 412 + +--S 413 of 586 +d0570b:= D(m0570b,x) +--R +--R +--R (398) +--R 2 2 2 2 2 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 2 2 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression Integer +--E 413 + +--S 414 of 586 +t0571:= cos(x)^4/(a+b*sin(x))^2 +--R +--R +--R 4 +--R cos(x) +--R (399) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 414 + +--S 415 of 586 +r0571:= 3*a^2*x/b^4-3/2*x/b^2-6*a*(a^2-b^2)^(1/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4+2*a*cos(x)/b^3-1/2*cos(x)*sin(x)/b^2+(a^2-b^2)*cos(x)/b^3/(a+b*sin(x)) +--R +--R +--R (400) +--R x +--R +---------+ a tan(-) + b +--R 2 | 2 2 2 3 2 +--R (- 12a b sin(x) - 12a )\|- b + a atan(------------) - b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 2 +--R (3a b cos(x) + (- 3b + 6a b)x)sin(x) + (- 2b + 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b + 6a )x +--R / +--R 5 4 +--R 2b sin(x) + 2a b +--R Type: Expression Integer +--E 415 + +--S 416 of 586 +a0571:= integrate(t0571,x) +--R +--R +--R (401) +--R [ +--R +-------+ +--R 2 3 | 2 2 +--R (6a b sin(x) + 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 4 2 2 3 3 +--R (3a b cos(x) + (- 3a b + 6a b)x - 2b + 6a b )sin(x) + a b cos(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- 3a b + 6a b)cos(x) + (- 3a b + 6a )x - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (12a b sin(x) + 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 2 3 3 4 2 2 3 3 +--R (3a b cos(x) + (- 3a b + 6a b)x - 2b + 6a b )sin(x) + a b cos(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- 3a b + 6a b)cos(x) + (- 3a b + 6a )x - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 416 + +--S 417 of 586 +m0571a:= a0571.1-r0571 +--R +--R +--R (402) +--R +-------+ +--R 2 3 | 2 2 +--R (6a b sin(x) + 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 3 | 2 2 2 3 2 +--R (12a b sin(x) + 12a )\|- b + a atan(------------) + a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 3 3 3 +--R (- 2b + 6a b )sin(x) + a b cos(x) - a b cos(x) - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R Type: Expression Integer +--E 417 + +--S 418 of 586 +d0571a:= D(m0571a,x) +--R +--R +--R (403) +--R 2 3 5 4 4 3 2 4 +--R - a b sin(x) + (- a b cos(x) - a b - a b )sin(x) +--R + +--R 2 3 2 2 3 3 +--R (- 2a b cos(x) - a b cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 5a b + 6a b )cos(x) - 5a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - a b cos(x) - a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 5a b + 6a b)cos(x) - 11a b + 12a b +--R * +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - a b cos(x) - a b cos(x) + a b cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 5 5 2 3 4 +--R - 2a b sin(x) + (- 2b cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 2 4 4 3 2 3 +--R (- 4a b cos(x) - 2a b cos(x) + 12a b - 12a b )sin(x) +--R + +--R 5 3 5 2 3 2 5 5 +--R - 4b cos(x) + (- 4b - 2a b )cos(x) + 2b cos(x) + 2b +--R + +--R 2 3 4 +--R 26a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 4 3 4 3 2 2 +--R - 2a b cos(x) - 2a b cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 4 3 2 5 +--R (14a b - 12a b )cos(x) + 2a b + 12a b - 12a +--R * +--R sin(x) +--R + +--R 5 5 5 4 5 3 +--R - 2b cos(x) - 2b cos(x) + 2b cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (2b + 12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 4 4 3 2 4 +--R - a b sin(x) + (- a b cos(x) - a b - a b )sin(x) +--R + +--R 2 3 2 2 3 3 +--R (- 2a b cos(x) - a b cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 5a b + 6a b )cos(x) - 5a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - a b cos(x) - a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 5a b + 6a b)cos(x) - 11a b + 12a b +--R * +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - a b cos(x) - a b cos(x) + a b cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 5 5 3 3 5 3 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 2 2 4 4 2 3 +--R (2a b cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (5a b - 11a b + 6a b)cos(x) + 5a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 2 4 4 2 2 +--R a b cos(x) + (a b - a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (5a b - 11a b + 6a )cos(x) + 11a b - 12a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 4 5 3 3 3 +--R (a b - a b )cos(x) + a b cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- a b - 6a b + 6a b)cos(x) + 6a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 5 6 2 4 6 2 4 4 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 5 2 5 3 3 5 3 3 3 +--R (4a b cos(x) + (2a b - 2a b )cos(x) - 12a b + 12a b )sin(x) +--R + +--R 6 2 4 3 6 2 4 2 +--R (4b - 4a b )cos(x) + (4b + 2a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 +--R (- 2b + 2a b )cos(x) - 2b - 26a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 5 3 3 3 +--R 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 2 5 3 3 5 +--R (- 12a b + 12a b )cos(x) + (- 14a b + 26a b - 12a b)cos(x) +--R + +--R 5 3 3 5 +--R - 2a b - 12a b + 12a b +--R * +--R sin(x) +--R + +--R 6 2 4 5 6 4 6 2 4 3 +--R (2b - 2a b )cos(x) + 2b cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (- 2b - 12a b + 12a b )cos(x) + (- 12a b + 24a b - 12a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 5 5 3 3 5 3 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 2 2 4 4 2 3 +--R (2a b cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (5a b - 11a b + 6a b)cos(x) + 5a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 2 4 4 2 2 +--R a b cos(x) + (a b - a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (5a b - 11a b + 6a )cos(x) + 11a b - 12a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 4 5 3 3 3 +--R (a b - a b )cos(x) + a b cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- a b - 6a b + 6a b)cos(x) + 6a b - 6a b +--R / +--R 2 5 3 6 6 3 4 2 +--R 2a b sin(x) + (2a b cos(x) + 2a b + 4a b )sin(x) +--R + +--R 2 5 2 5 4 3 3 4 3 4 +--R (4a b cos(x) + 4a b + 2a b )sin(x) + 2a b cos(x) + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 7 7 2 5 2 +--R 4a b sin(x) + (4b cos(x) + 4b + 8a b )sin(x) +--R + +--R 6 6 3 4 2 5 2 5 +--R (8a b cos(x) + 8a b + 4a b )sin(x) + 4a b cos(x) + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 3 6 6 3 4 2 +--R 2a b sin(x) + (2a b cos(x) + 2a b + 4a b )sin(x) +--R + +--R 2 5 2 5 4 3 3 4 3 4 +--R (4a b cos(x) + 4a b + 2a b )sin(x) + 2a b cos(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 3 7 3 5 7 3 5 2 +--R - 2a b sin(x) + ((- 2a b + 2a b )cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R ((- 4a b + 4a b )cos(x) - 4a b - 2a b )sin(x) +--R + +--R 3 5 5 3 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 8 2 6 8 2 6 2 +--R - 4a b sin(x) + ((- 4b + 4a b )cos(x) - 4b - 8a b )sin(x) +--R + +--R 7 3 5 7 3 5 +--R ((- 8a b + 8a b )cos(x) - 8a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 +--R (- 4a b + 4a b )cos(x) - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 3 7 3 5 7 3 5 2 +--R - 2a b sin(x) + ((- 2a b + 2a b )cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 3 5 5 3 +--R ((- 4a b + 4a b )cos(x) - 4a b - 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 5 +--R - 2a b +--R Type: Expression Integer +--E 418 + +--S 419 of 586 +m0571b:= a0571.2-r0571 +--R +--R +--R (404) +--R +---------+ +--R +---------+ | 2 2 +--R 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (12a b sin(x) + 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 3 | 2 2 2 3 2 +--R (12a b sin(x) + 12a )\|- b + a atan(------------) + a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 3 3 3 +--R (- 2b + 6a b )sin(x) + a b cos(x) - a b cos(x) - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R Type: Expression Integer +--E 419 + +--S 420 of 586 +d0571b:= D(m0571b,x) +--R +--R +--R (405) +--R 2 4 6 5 5 3 3 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b - a b )sin(x) +--R + +--R 2 4 2 2 4 2 4 4 2 4 +--R (- 3a b cos(x) - 4a b cos(x) + 4a b - 6a b )sin(x) +--R + +--R 5 3 5 3 3 2 +--R - 4a b cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 10a b + 10a b )cos(x) - 10a b + 24a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R - 3a b cos(x) - 6a b cos(x) + (4a b - 6a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 6 +--R (- 20a b + 24a b )cos(x) - 27a b + 36a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 3 3 4 5 3 3 3 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (2a b + 12a b - 12a b)cos(x) + (- 10a b + 12a b)cos(x) +--R + +--R 3 3 5 +--R - 23a b + 24a b +--R * +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 3 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 2 4 5 +--R - 2a b sin(x) + (- 4b cos(x) - 4b - 2a b )sin(x) +--R + +--R 5 2 5 5 3 3 4 +--R (- 6a b cos(x) - 8a b cos(x) + 20a b - 24a b )sin(x) +--R + +--R 6 3 6 2 4 2 6 2 4 6 +--R - 8b cos(x) + (- 8b - 4a b )cos(x) + (4b - 4a b )cos(x) + 4b +--R + +--R 2 4 4 2 +--R 48a b - 48a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 5 3 5 3 3 2 +--R - 6a b cos(x) - 12a b cos(x) + (20a b - 24a b )cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (32a b - 24a b )cos(x) + 6a b + 24a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 6 2 4 4 6 2 4 3 +--R - 4b cos(x) + (- 4b - 2a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 2 4 +--R (4b + 48a b - 48a b )cos(x) + (52a b - 48a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 5 6 5 5 5 3 +--R - 2a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (2a b + 24a b - 24a b)cos(x) + (24a b - 24a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 6 5 5 3 3 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b - a b )sin(x) +--R + +--R 2 4 2 2 4 2 4 4 2 4 +--R (- 3a b cos(x) - 4a b cos(x) + 4a b - 6a b )sin(x) +--R + +--R 5 3 5 3 3 2 5 3 3 +--R - 4a b cos(x) + (- 4a b - 2a b )cos(x) + (- 10a b + 10a b )cos(x) +--R + +--R 5 3 3 5 +--R - 10a b + 24a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R - 3a b cos(x) - 6a b cos(x) + (4a b - 6a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 6 +--R (- 20a b + 24a b )cos(x) - 27a b + 36a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 3 3 4 5 3 3 3 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 +--R (2a b + 12a b - 12a b)cos(x) + (- 10a b + 12a b)cos(x) - 23a b +--R + +--R 5 +--R 24a b +--R * +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 3 2 4 4 2 6 2 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) + (a b + 6a b - 6a )cos(x) +--R + +--R 4 2 6 +--R - 6a b + 6a +--R / +--R 2 6 4 7 7 3 5 3 +--R 2a b sin(x) + (4a b cos(x) + 4a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 4 4 2 +--R (2a b cos(x) + 12a b cos(x) + 10a b + 2a b )sin(x) +--R + +--R 3 5 2 3 5 3 5 4 4 2 +--R (4a b cos(x) + 12a b cos(x) + 8a b )sin(x) + 2a b cos(x) +--R + +--R 4 4 4 4 +--R 4a b cos(x) + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 4 8 8 2 6 3 +--R 4a b sin(x) + (8b cos(x) + 8b + 8a b )sin(x) +--R + +--R 7 2 7 7 3 5 2 +--R (4a b cos(x) + 24a b cos(x) + 20a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 3 5 2 +--R (8a b cos(x) + 24a b cos(x) + 16a b )sin(x) + 4a b cos(x) +--R + +--R 3 5 3 5 +--R 8a b cos(x) + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 7 7 3 5 3 +--R 2a b sin(x) + (4a b cos(x) + 4a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 4 4 2 +--R (2a b cos(x) + 12a b cos(x) + 10a b + 2a b )sin(x) +--R + +--R 3 5 2 3 5 3 5 4 4 2 4 4 +--R (4a b cos(x) + 12a b cos(x) + 8a b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 4 +--R 2a b +--R Type: Expression Integer +--E 420 + +--S 421 of 586 +t0572:= cos(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (406) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 421 + +--S 422 of 586 +r0572:= -(x*cos(x)-2*sin(x)+2)/a^2/cos(x) +--R +--R +--R 2sin(x) - x cos(x) - 2 +--R (407) ---------------------- +--R 2 +--R a cos(x) +--R Type: Expression Integer +--E 422 + +--S 423 of 586 +a0572:= integrate(t0572,x) +--R +--R +--R - x sin(x) + (- x - 4)cos(x) - x - 4 +--R (408) ------------------------------------ +--R 2 2 2 +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression Integer,...) +--E 423 + +--S 424 of 586 +m0572:= a0572-r0572 +--R +--R +--R 2 2 +--R - 2sin(x) - 2cos(x)sin(x) - 4cos(x) - 2cos(x) + 2 +--R (409) --------------------------------------------------- +--R 2 2 2 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression Integer +--E 424 + +--S 425 of 586 +d0572:= D(m0572,x) +--R +--R +--R (410) +--R 4 3 2 +--R - 2sin(x) + (- 4cos(x) - 2)sin(x) + 2sin(x) +--R + +--R 3 2 4 2 +--R (- 4cos(x) - 2cos(x) + 4cos(x) + 2)sin(x) + 2cos(x) - 2cos(x) +--R / +--R 2 2 2 2 3 2 2 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 2 3 2 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression Integer +--E 425 + +--S 426 of 586 +t0573:= cos(x)^4/(a+a*sin(x))^2 +--R +--R +--R 4 +--R cos(x) +--R (411) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 426 + +--S 427 of 586 +r0573:= -1/2*(-3*x-4*cos(x)+cos(x)*sin(x))/a^2 +--R +--R +--R - cos(x)sin(x) + 4cos(x) + 3x +--R (412) ----------------------------- +--R 2 +--R 2a +--R Type: Expression Integer +--E 427 + +--S 428 of 586 +a0573:= integrate(t0573,x) +--R +--R +--R - cos(x)sin(x) + 4cos(x) + 3x +--R (413) ----------------------------- +--R 2 +--R 2a +--R Type: Union(Expression Integer,...) +--E 428 + +--S 429 of 586 +m0573:= a0573-r0573 +--R +--R +--R (414) 0 +--R Type: Expression Integer +--E 429 + +--S 430 of 586 +d0573:= D(m0573,x) +--R +--R +--R (415) 0 +--R Type: Expression Integer +--E 430 + +--S 431 of 586 +t0574:= tan(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R tan(x) +--R (416) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 431 + +--S 432 of 586 +r0574:= -2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-4*a*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+1/2*cos(x)/(a+b)^2/(1-sin(x))-1/2*cos(x)/(a-b)^2/(1+sin(x))-a^2*b*cos(x)/(a^2-b^2)^2/(a+b*sin(x)) +--R +--R +--R (417) +--R 3 3 3 2 2 4 2 +--R (- 4a b - 2a b)sin(x) + (- 4a b - 2a )sin(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 2a b)sin(x) + 4a b + 2a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 2 3 2 +--R ((- b - 2a b)cos(x)sin(x) + (a b - a )cos(x)sin(x) + 3a b cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)sin(x) + (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)sin(x) - a b + 2a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 432 + +--S 433 of 586 +a0574:= integrate(t0574,x) +--R +--R +--R (418) +--R [ +--R 3 3 2 2 4 +--R ((2a b + a b)cos(x)sin(x) + (2a b + a )cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 2 2 +--R (- 3a b cos(x) - a b + a )sin(x) + (- b - 2a b)cos(x) +--R + +--R 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x))\|b - a +--R , +--R +--R 3 3 2 2 4 +--R ((4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 3 3 2 2 +--R (- 3a b cos(x) - a b + a )sin(x) + (- b - 2a b)cos(x) +--R + +--R 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x))\|- b + a +--R ] +--R Type: Union(List Expression Integer,...) +--E 433 + +--S 434 of 586 +m0574a:= a0574.1-r0574 +--R +--R +--R (419) +--R 3 3 3 2 2 4 2 +--R (2a b + a b)cos(x)sin(x) + (2a b + a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 2a b - a b)cos(x)sin(x) + (- 2a b - a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 +--R (- 3a b cos(x) - a b + a )sin(x) +--R + +--R 2 3 2 2 +--R (- 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 2 2 2 3 +--R ((- a b + a )cos(x) + 3a b cos(x) + a b - a )sin(x) +--R + +--R 3 2 2 2 3 2 +--R (b - a b)cos(x) + 3a b cos(x) - b + a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression Integer +--E 434 + +--S 435 of 586 +d0574a:= D(m0574a,x) +--R +--R +--R (420) +--R 3 4 5 2 8 +--R (- a b + a b )sin(x) +--R + +--R 2 5 4 3 6 4 3 6 7 +--R ((- a b + 2a b - a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (2a b - a b - a b )cos(x) + (2a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (a b - 3a b + 3a b - a )cos(x) + a b + a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 4 2 5 4 3 3 +--R (- 2a b - a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (3a b + 3a b )cos(x) + (3a b - 6a b + 3a b)cos(x) + a b +--R + +--R 4 3 6 +--R a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 6 3 4 3 +--R - 3a b cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 6 5 2 2 +--R (- 6a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (- 2a b + 6a b - 6a b + 2a )cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b - 4a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b + 3a b )cos(x) +--R + +--R 6 3 4 7 3 6 3 4 5 2 2 +--R (5a b - 6a b + a )cos(x) + (5a b - 4a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 3 +--R (- 3a b + a b - a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (4a b + a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 2 5 4 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- a b + 2a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 8 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 3 4 2 6 3 4 5 2 +--R (- 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 4 5 2 +--R - 2a b + 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 2 7 2 5 4 3 6 +--R (- 6a b - 6a b )cos(x) + (2b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 +--R 2b + 2a b - 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 4 6 3 4 5 2 3 +--R (- 4a b - 2a b )cos(x) + (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (6a b + 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (6a b - 12a b + 6a b )cos(x) + 2a b + 2a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 7 2 5 4 3 6 3 +--R - 6a b cos(x) + (- 4b + 4a b - 2a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 4b + 16a b + 12a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (- 4b + 12a b - 12a b + 4a b)cos(x) - 4b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b + 8a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 2a b + 6a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 6b + 14a b - 10a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 6b + 12a b + 6a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b - 2a b - 2a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (6b - 10a b - 8a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (2b - 6a b + 6a b - 2a b)cos(x) + 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 2 +--R (- 2a b - 2a b + 4a b )cos(x) - 6a b cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 7 2 5 4 3 6 5 +--R (2b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 7 2 5 4 3 3 +--R (2b - 4a b - 4a b )cos(x) + (- 2b - 2a b + 4a b )cos(x) +--R + +--R 7 4 3 2 +--R (- 2b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 8 +--R (- a b + a b )sin(x) +--R + +--R 2 5 4 3 6 4 3 6 7 +--R ((- a b + 2a b - a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (2a b - a b - a b )cos(x) + (2a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (a b - 3a b + 3a b - a )cos(x) + a b + a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 4 2 5 4 3 3 +--R (- 2a b - a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (3a b + 3a b )cos(x) + (3a b - 6a b + 3a b)cos(x) + a b +--R + +--R 4 3 6 +--R a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 6 3 4 3 +--R - 3a b cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 6 5 2 2 6 3 4 5 2 7 +--R (- 6a b + 3a b )cos(x) + (- 2a b + 6a b - 6a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 +--R - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b - 4a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 7 3 +--R (- 3a b + 6a b + 3a b )cos(x) + (5a b - 6a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (5a b - 4a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 3a b + a b - a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (3a b - 3a b )cos(x) + (4a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 5 2 2 +--R (- a b + a b + a b - a )cos(x) + (- a b + 2a b + 2a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 8 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 7 +--R ((- a b + 2a b - a b )cos(x) - a b + 2a b - a )sin(x) +--R + +--R 7 3 5 5 3 3 7 5 3 7 2 +--R (2a b - a b - a b )cos(x) + (2a b - 3a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 5 3 7 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 3a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 3 +--R (- 2a b + a b + a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 6 2 2 2 6 4 4 6 2 2 6 +--R (3a b - 3a b )cos(x) + (3a b - 6a b + 3a b )cos(x) + a b +--R + +--R 6 2 8 +--R - 3a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 7 4 7 3 5 3 +--R (- 3a b + 3a b)cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b + 3a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 7 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) - 2a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 2 6 4 4 3 +--R (3a b + a b - 5a b + a )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 7a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 8 +--R (- 3a b + 6a b - 3a b )cos(x) - 2a b + 3a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 7a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 9a b - 3a b - 3a b)cos(x) +--R + +--R 7 3 5 7 3 7 3 5 7 2 +--R (5a b - 6a b + a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 2 6 4 4 3 +--R (- 3a b + 4a b - 2a b + a )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 8 2 2 6 4 4 6 2 2 6 +--R (4a b - 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) + a b +--R + +--R 4 4 6 2 +--R - 2a b + a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 7 3 5 7 4 +--R (a b - a b - a b + a b)cos(x) + (a b - 3a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 7 2 +--R (- a b + a b + a b - a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 7 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 6 2 2 8 2 6 4 4 6 2 +--R (- 6a b + 6a b )cos(x) + (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 8 4 4 6 2 +--R 2b - 6a b + 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 4 +--R (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 4a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 3 7 +--R (6a b - 12a b + 6a b )cos(x) + 2a b - 6a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 6 2 4 8 2 6 4 4 6 2 3 +--R (- 6a b + 6a b )cos(x) + (- 4b + 4a b - 2a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 4b + 20a b - 4a b - 12a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 6 2 +--R (- 4b + 12a b - 12a b + 4a b )cos(x) - 4b + 6a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b + 2a b - 10a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b + 8a b - 4a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 7 +--R (- 6a b + 12a b - 6a b )cos(x) - 4a b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 14a b - 10a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 18a b - 6a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (6b - 2a b - 2a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (6b - 16a b + 2a b + 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (2b - 6a b + 6a b - 2a b )cos(x) + 2b - 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 8a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 3 5 5 3 2 +--R (- 2a b - 2a b + 4a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 8 2 6 6 2 4 +--R (2b - 2a b - 2a b + 2a b )cos(x) + (2b - 6a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 3 8 2 6 4 4 6 2 2 +--R (- 2b - 2a b + 4a b )cos(x) + (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 8 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 7 +--R ((- a b + 2a b - a b )cos(x) - a b + 2a b - a )sin(x) +--R + +--R 7 3 5 5 3 3 7 5 3 7 2 +--R (2a b - a b - a b )cos(x) + (2a b - 3a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 5 3 7 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 3a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 3 +--R (- 2a b + a b + a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 6 2 2 2 6 4 4 6 2 2 6 6 2 +--R (3a b - 3a b )cos(x) + (3a b - 6a b + 3a b )cos(x) + a b - 3a b +--R + +--R 8 +--R 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 7 4 7 3 5 3 +--R (- 3a b + 3a b)cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b + 3a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 7 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) - 2a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 8 4 +--R (2a b - 4a b + 2a b )cos(x) + (3a b + a b - 5a b + a )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 8 +--R (- 3a b + 6a b - 3a b )cos(x) - 2a b + 3a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 7a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 9a b - 3a b - 3a b)cos(x) +--R + +--R 7 3 5 7 3 7 3 5 7 2 +--R (5a b - 6a b + a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 2 6 4 4 3 +--R (- 3a b + 4a b - 2a b + a )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 8 2 2 6 4 4 6 2 2 6 +--R (4a b - 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) + a b +--R + +--R 4 4 6 2 +--R - 2a b + a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 7 3 5 7 4 +--R (a b - a b - a b + a b)cos(x) + (a b - 3a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 7 2 +--R (- a b + a b + a b - a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R / +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 2 7 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 9 4 5 6 3 2 +--R (2b - 6a b + 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (- 4b + 2a b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b + 8a b + 2a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (2b - 10a b + 18a b - 14a b + 4a b)cos(x) +--R + +--R 9 2 7 4 5 2 +--R (2b - 4a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 8 3 6 7 2 2 +--R (4a b - 6a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (a b - 3a b + 3a b - a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 5 5 7 3 2 7 +--R (2a b - 6a b + 6a b - 2a b )cos(x) sin(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (2b - 2a b - 6a b + 10a b - 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 4b + 6a b + 6a b - 14a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 6a b + 14a b - 6a b - 6a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (2b - 10a b + 18a b - 14a b + 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 2 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (4a b - 10a b + 6a b + 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) + (a b - 3a b + 3a b - a b)cos(x) +--R Type: Expression Integer +--E 435 + +--S 436 of 586 +m0574b:= a0574.2-r0574 +--R +--R +--R (421) +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 +--R (- 3a b cos(x) - a b + a )sin(x) +--R + +--R 2 3 2 2 +--R (- 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 2 2 2 3 +--R ((- a b + a )cos(x) + 3a b cos(x) + a b - a )sin(x) +--R + +--R 3 2 2 2 3 2 +--R (b - a b)cos(x) + 3a b cos(x) - b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression Integer +--E 436 + +--S 437 of 586 +d0574b:= D(m0574b,x) +--R +--R +--R (422) +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 6 +--R ((- 2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - a b + a ) +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (4a b + 2a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 6a b + 4a b)cos(x) + 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b - a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (15a b + 3a b )cos(x) + (8a b - 10a b + 2a )cos(x) + 5a b +--R + +--R 4 2 6 +--R - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- a b - 5a b)cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b + 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 4a b + 14a b - 10a b)cos(x) - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 +--R (4a b - 4a b )cos(x) + (3a b + 2a b - 2a )cos(x) +--R + +--R 2 4 3 2 4 4 2 2 +--R - 24a b cos(x) + (- 27a b + 3a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 10a b + 14a b - 4a )cos(x) - 7a b + 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 14a b + 4a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (10a b - 14a b - 2a b)cos(x) + (10a b - 26a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (2a b - 10a b + 8a b)cos(x) + 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 5a b + 9a b - a )cos(x) + (16a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (15a b - 7a b - 2a )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 +--R 3a b - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - 5a b - 3a b)cos(x) + (- 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 +--R (- 2a b + 10a b + 4a b)cos(x) + (2a b - 2a b)cos(x) + a b +--R + +--R 5 +--R - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 6 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 9 +--R (- 2a b + 2a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 5 +--R ((- 8a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b + 2a b) +--R * +--R 8 +--R sin(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 6 +--R (- 16a b - 8a b )cos(x) + (4b - 12a b + 8a b )cos(x) + 4b +--R + +--R 2 4 +--R - 4a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 4 5 3 3 3 +--R (- 8a b - 4a b )cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (18a b - 4a b - 2a b)cos(x) + (16a b - 20a b + 4a b)cos(x) +--R + +--R 5 3 3 5 +--R 10a b - 8a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 10a b - 14a b )cos(x) + (- 8b - 4a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (- 8b + 44a b + 12a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 8b + 28a b - 20a b )cos(x) - 8b + 16a b - 8a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (8a b - 8a b )cos(x) + (14a b + 4a b - 6a b)cos(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (16a b - 4a b)cos(x) + (- 18a b + 28a b + 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 20a b + 28a b - 8a b)cos(x) - 14a b + 16a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (4a b - 4a b )cos(x) + (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 44a b + 16a b )cos(x) +--R + +--R 6 2 4 4 2 3 6 2 4 4 2 2 +--R (12b + 16a b + 20a b )cos(x) + (12b - 32a b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (4b - 20a b + 16a b )cos(x) + 4b - 12a b + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 20a b + 24a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 14a b + 24a b + 2a b)cos(x) + (8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (10a b - 20a b - 2a b)cos(x) + (8a b - 12a b + 4a b)cos(x) +--R + +--R 5 3 3 5 +--R 6a b - 8a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (- 4a b + 4a b )cos(x) + (4b - 8a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 4 6 2 4 4 2 3 +--R (4b - 18a b - 10a b )cos(x) + (- 4b - 12a b - 8a b )cos(x) +--R + +--R 6 2 4 2 2 4 4 2 2 4 4 2 +--R (- 4b + 4a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 5 5 6 5 5 5 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- 8a b - 4a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 5 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 6 8 +--R ((- 2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - a b + a )sin(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (4a b + 2a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 6a b + 4a b)cos(x) + 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b - a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (15a b + 3a b )cos(x) + (8a b - 10a b + 2a )cos(x) + 5a b +--R + +--R 4 2 6 +--R - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- a b - 5a b)cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 12a b + 18a b + 6a b)cos(x) + (- 4a b + 14a b - 10a b)cos(x) +--R + +--R 5 3 3 5 +--R - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 2 4 3 +--R (4a b - 4a b )cos(x) + (3a b + 2a b - 2a )cos(x) - 24a b cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 27a b + 3a b )cos(x) + (- 10a b + 14a b - 4a )cos(x) - 7a b +--R + +--R 4 2 6 +--R 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 14a b + 4a b)cos(x) + (10a b - 14a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (10a b - 26a b - 8a b)cos(x) + (2a b - 10a b + 8a b)cos(x) +--R + +--R 5 3 3 5 +--R 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 5a b + 9a b - a )cos(x) + (16a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 2 4 +--R (15a b - 7a b - 2a )cos(x) + (4a b - 6a b + 2a )cos(x) + 3a b +--R + +--R 4 2 6 +--R - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - 5a b - 3a b)cos(x) + (- 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (- 2a b + 10a b + 4a b)cos(x) + (2a b - 2a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 6 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 2a b + 2a )cos(x) +--R / +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 2 8 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 3 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 4a b - 4a b + 4a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 10a b + 2a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 8b + 28a b - 32a b + 12a b )cos(x) +--R + +--R 8 2 6 4 4 2 +--R (- 8b + 16a b - 8a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 4a b + 10a b - 8a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 24a b + 52a b - 32a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 18a b + 34a b - 14a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b - 32a b + 52a b - 24a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 20a b + 28a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 8a b + 10a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b - 32a b + 28a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b - 22a b + 14a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (12a b - 24a b + 12a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R Type: Expression Integer +--E 437 + +--S 438 of 586 +t0575:= tan(x)/(a+a*sin(x))^2 +--R +--R +--R tan(x) +--R (423) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 438 + +--S 439 of 586 +r0575:= 1/4*atanh(sin(x))/a^2+1/4/a^2/(1+sin(x))^2-1/4/a^2/(1+sin(x)) +--R +--R +--R 2 +--R (sin(x) + 2sin(x) + 1)atanh(sin(x)) - sin(x) +--R (424) --------------------------------------------- +--R 2 2 2 2 +--R 4a sin(x) + 8a sin(x) + 4a +--R Type: Expression Integer +--E 439 + +--S 440 of 586 +a0575:= integrate(t0575,x) +--R +--R +--R (425) +--R 2 sin(x) + cos(x) + 1 +--R (2sin(x) - cos(x) + 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (- 2sin(x) + cos(x) - 2)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2 2 2 2 +--R 8a sin(x) - 4a cos(x) + 8a +--R Type: Union(Expression Integer,...) +--E 440 + +--S 441 of 586 +m0575:= a0575-r0575 +--R +--R +--R (426) +--R 3 2 2 2 2 +--R 2sin(x) + (- cos(x) + 6)sin(x) + (- 2cos(x) + 6)sin(x) - cos(x) +--R + +--R 2 +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R atanh(sin(x)) +--R + +--R 3 2 +--R - sin(x) + (- cos(x) + 1)sin(x) +--R / +--R 2 3 2 2 2 2 2 2 2 +--R 8a sin(x) + (- 4a cos(x) + 24a )sin(x) + (- 8a cos(x) + 24a )sin(x) +--R + +--R 2 2 2 +--R - 4a cos(x) + 8a +--R Type: Expression Integer +--E 441 + +--S 442 of 586 +d0575:= D(m0575,x) +--R +--R +--R (427) +--R 8 2 7 +--R (2cos(x) - 8)sin(x) + (8cos(x) + 4cos(x) - 32)sin(x) +--R + +--R 4 3 2 6 +--R (- 2cos(x) - cos(x) + 12cos(x) - 12cos(x) - 40)sin(x) +--R + +--R 4 3 2 5 +--R (4cos(x) + 6cos(x) - 24cos(x) - 28cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 3cos(x) + 22cos(x) + 9cos(x) - 52cos(x) - 8cos(x) +--R + +--R 40 +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) - 2cos(x) + 16cos(x) - 12cos(x) - 40cos(x) + 12cos(x) +--R + +--R 32 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (16cos(x) + 18cos(x) - 31cos(x) - 28cos(x) + 12cos(x) + 8)sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 4cos(x) - 4cos(x) + 18cos(x) + 12cos(x) - 26cos(x) - 8cos(x) +--R + +--R 12cos(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 3cos(x) - 6cos(x) - 9cos(x) + 4cos(x) + 6cos(x) +--R / +--R 2 8 2 2 2 7 +--R 16a sin(x) + (- 16a cos(x) + 64a )sin(x) +--R + +--R 2 4 2 2 2 2 6 +--R (4a cos(x) - 64a cos(x) - 32a cos(x) + 64a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 5 +--R (24a cos(x) + 32a cos(x) - 80a cos(x) - 128a cos(x) - 64a )sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 +--R - 4a cos(x) - 8a cos(x) + 44a cos(x) + 96a cos(x) - 160a cos(x) +--R + +--R 2 +--R - 160a +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 8a cos(x) - 16a cos(x) + 16a cos(x) + 64a cos(x) + 80a cos(x) +--R + +--R 2 +--R - 64a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (- 36a cos(x) - 64a cos(x) + 64a cos(x) + 160a cos(x) + 64a )sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 8a cos(x) + 16a cos(x) - 40a cos(x) - 96a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R 128a cos(x) + 64a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) + 8a cos(x) - 12a cos(x) - 32a cos(x) + 32a cos(x) + 16a +--R Type: Expression Integer +--E 442 + +--S 443 of 586 +t0576:= tan(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R tan(x) +--R (428) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression Integer +--E 443 + +--S 444 of 586 +r0576:= 1/15/cos(x)^5/a^2*(cos(x)^4*sin(x)-7*sin(x)*cos(x)^2+6*sin(x)-6+10*cos(x)^2) +--R +--R +--R 4 2 2 +--R (cos(x) - 7cos(x) + 6)sin(x) + 10cos(x) - 6 +--R (429) ---------------------------------------------- +--R 2 5 +--R 15a cos(x) +--R Type: Expression Integer +--E 444 + +--S 445 of 586 +a0576:= integrate(t0576,x) +--R +--R +--R 2 3 2 +--R (- cos(x) + 8cos(x) + 9)sin(x) - 4cos(x) - 2cos(x) + 8cos(x) + 6 +--R (430) ------------------------------------------------------------------- +--R 2 2 3 2 +--R 30a cos(x)sin(x) - 15a cos(x) + 30a cos(x) +--R Type: Union(Expression Integer,...) +--E 445 + +--S 446 of 586 +m0576:= a0576-r0576 +--R +--R +--R (431) +--R 4 2 2 5 7 +--R (- 2cos(x) + 14cos(x) - 12)sin(x) + 8cos(x) sin(x) - 4cos(x) +--R + +--R 6 5 4 2 +--R - 2cos(x) + 8cos(x) + 16cos(x) - 26cos(x) + 12 +--R / +--R 2 5 2 7 2 5 +--R 30a cos(x) sin(x) - 15a cos(x) + 30a cos(x) +--R Type: Expression Integer +--E 446 + +--S 447 of 586 +d0576:= D(m0576,x) +--R +--R +--R (432) +--R 4 2 4 +--R (- 4cos(x) + 84cos(x) - 120)sin(x) +--R + +--R 6 4 2 3 +--R (6cos(x) - 74cos(x) + 168cos(x) - 120)sin(x) +--R + +--R 4 2 2 +--R (60cos(x) - 180cos(x) + 120)sin(x) +--R + +--R 8 6 4 2 8 +--R (6cos(x) - 80cos(x) + 242cos(x) - 288cos(x) + 120)sin(x) + 4cos(x) +--R + +--R 6 4 2 +--R - 32cos(x) + 52cos(x) - 24cos(x) +--R / +--R 2 6 2 2 8 2 6 2 10 +--R 60a cos(x) sin(x) + (- 60a cos(x) + 120a cos(x) )sin(x) + 15a cos(x) +--R + +--R 2 8 2 6 +--R - 60a cos(x) + 60a cos(x) +--R Type: Expression Integer +--E 447 + +--S 448 of 586 +t0577:= cot(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R cot(x) +--R (433) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression Integer +--E 448 + +--S 449 of 586 +r0577:= -2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2)+4*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+2*b*atanh(cos(x))/a^3-cot(x)/a^2-b*cos(x)/a^2/(a+b*sin(x)) +--R +--R +--R (434) +--R +---------+ +--R 2 | 2 2 +--R (2b sin(x) + 2a b)\|- b + a atanh(cos(x)) +--R + +--R x +--R a tan(-) + b +--R 3 2 2 3 2 +--R ((4b - 2a b)sin(x) + 4a b - 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R