diff --git a/changelog b/changelog index 70c0331..bd0d725 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100604 tpd src/axiom-website/patches.html 20100604.03.tpd.patch +20100604 tpd src/input/Makefile add rule-based rational integration tests +20100604 tpd src/input/richrational.input add rule-based rational integration 20100604 tpd src/axiom-website/patches.html 20100604.02.tpd.patch 20100604 tpd books/bookvol10.5 tighten array type declarations 20100604 tpd src/axiom-website/patches.html 20100604.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 5676568..e50b357 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2838,5 +2838,7 @@ books/bookvol10.3 add test and help files for all domains
books/bookvolbib add ES10 Burcin and Stein Axiom reference
20100605.02.tpd.patch books/bookvol10.5 tighten array type declarations
+20100605.03.tpd.patch +src/input/richrational.input add rule-based rational integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 6eca629..105b083 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -368,7 +368,7 @@ REGRES= ackermann.regress \ quat1.regress quat.regress r20abugs.regress r20bugs.regress \ r21bugsbig.regress r21bugs.regress radff.regress radix.regress \ realclos.regress reclos.regress reclos2.regress regset.regress \ - repa6.regress robidoux.regress \ + repa6.regress richrational.regress robidoux.regress \ roman.regress roots.regress ruleset.regress rules.regress \ rubey.regress sae.regress spline.regress \ schaum1.regress schaum2.regress schaum3.regress schaum4.regress \ @@ -552,7 +552,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/asinatan.input ${OUT}/asinhatanh.input \ ${OUT}/assign.input ${OUT}/atansqrt.input ${OUT}/axiom.input \ ${OUT}/asec.input \ - ${OUT}/bbtree.input ${OUT}/besselk.input \ + ${OUT}/bbtree.input ${OUT}/besselk.input \ ${OUT}/bern.input \ ${OUT}/bernpoly.input ${OUT}/binary.input ${OUT}/bini.input \ ${OUT}/biquat.input ${OUT}/bop.input \ @@ -679,7 +679,8 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ ${OUT}/r21bugs.input \ ${OUT}/radff.input ${OUT}/radix.input ${OUT}/realclos.input \ - ${OUT}/reclos.input ${OUT}/reclos2.input ${OUT}/regset.input \ + ${OUT}/reclos.input ${OUT}/reclos2.input ${OUT}/regset.input \ + ${OUT}/richrational.input \ ${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \ ${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/rubey.input \ ${OUT}/sae.input \ @@ -1020,7 +1021,8 @@ DOCFILES= \ ${DOC}/regset.input.dvi ${DOC}/reductio.input.dvi \ ${DOC}/regset.input.dvi ${DOC}/repa6.input.dvi \ ${DOC}/ribbon.input.dvi ${DOC}/ribbons.input.dvi \ - ${DOC}/ribbonsnew.input.dvi ${DOC}/rk4draw.input.dvi \ + ${DOC}/ribbonsnew.input.dvi ${DOC}/richrational.input.dvi \ + ${DOC}/rk4draw.input.dvi \ ${DOC}/robidoux.input.dvi ${DOC}/roman.input.dvi \ ${DOC}/romnum.as.dvi ${DOC}/roots.input.dvi \ ${DOC}/ruleset.input.dvi ${DOC}/rules.input.dvi \ diff --git a/src/input/richrational.input.pamphlet b/src/input/richrational.input.pamphlet new file mode 100644 index 0000000..6442910 --- /dev/null +++ b/src/input/richrational.input.pamphlet @@ -0,0 +1,60244 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richrational.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richrational.output +)spool richrational.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1483 +t0000:= (5-2*x)^6*(2+3*x)^3*(-16+33*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 57024x - 768960x + 4070736x - 10051008x + 8647828x + 8983380x +--R + +--R 4 3 2 +--R - 19081125x - 196250x + 11962500x - 75000x - 2000000 +--R Type: Polynomial Integer +--E 1 + +--S 2 of 1483 +r0000:= -1/2*(5-2*x)^7*(2+3*x)^4 +--R +--R +--R (2) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x - 625000 +--R 2 +--R Type: Polynomial Fraction Integer +--E 2 + +--S 3 of 1483 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x +--R 2 +--R Type: Polynomial Fraction Integer +--E 3 + +--S 4 of 1483 +m0000:=a0000-r0000 +--R +--R +--R (4) 625000 +--R Type: Polynomial Fraction Integer +--E 4 + +--S 5 of 1483 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial Fraction Integer +--E 5 + +--S 6 of 1483 +t0001:= x*(a+b*x)*(c+d*x)^16 +--R +--R +--R (6) +--R 16 18 16 15 17 15 2 14 16 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 15 3 13 4 12 14 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 13 5 11 6 10 12 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 11 7 9 8 8 10 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 9 9 7 10 6 8 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 7 11 5 12 4 6 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 5 13 3 14 2 4 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 3 15 16 2 16 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial Integer +--E 6 + +--S 7 of 1483 +r0001:= -1/5814*(c+d*x)^17*(-2*b*c^2+19*a*c*d+34*b*c*d*x-_ + 323*x*d^2*a-306*b*d^2*x^2)/d^3 +--R +--R +--R (7) +--R 1 19 19 1 19 8 18 18 16 18 120 2 17 17 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 19 18 9 17 17 +--R + +--R 15 2 17 3 16 16 112 3 16 364 4 15 15 +--R (-- a c d + 35b c d )x + (--- a c d + --- b c d )x +--R 2 3 3 +--R + +--R 4 15 5 14 14 5 14 6 13 13 +--R (130a c d + 312b c d )x + (336a c d + 616b c d )x +--R + +--R 2002 6 13 2860 7 12 12 7 12 8 11 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 1170b c d )x +--R 3 3 +--R + +--R 8 11 9 10 10 11440 9 10 8008 10 9 9 +--R (1287a c d + 1144b c d )x + (----- a c d + ---- b c d )x +--R 9 9 +--R + +--R 10 9 11 8 8 11 8 12 7 7 +--R (1001a c d + 546b c d )x + (624a c d + 260b c d )x +--R + +--R 910 12 7 280 13 6 6 13 6 14 5 5 +--R (--- a c d + --- b c d )x + (112a c d + 24b c d )x +--R 3 3 +--R + +--R 14 5 15 4 4 16 15 4 1 16 3 3 1 16 3 2 +--R (30a c d + 4b c d )x + (-- a c d + - b c d )x + - a c d x +--R 3 3 2 +--R + +--R 1 18 1 19 +--R - --- a c d + ---- b c +--R 306 2907 +--R / +--R 3 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 7 + +--S 8 of 1483 +a0001:=integrate(t0001,x) +--R +--R +--R (8) +--R 1 16 19 1 16 8 15 18 16 15 120 2 14 17 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 19 18 9 17 17 +--R + +--R 15 2 14 3 13 16 112 3 13 364 4 12 15 +--R (-- a c d + 35b c d )x + (--- a c d + --- b c d )x +--R 2 3 3 +--R + +--R 4 12 5 11 14 5 11 6 10 13 +--R (130a c d + 312b c d )x + (336a c d + 616b c d )x +--R + +--R 2002 6 10 2860 7 9 12 7 9 8 8 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 1170b c d )x +--R 3 3 +--R + +--R 8 8 9 7 10 11440 9 7 8008 10 6 9 +--R (1287a c d + 1144b c d )x + (----- a c d + ---- b c d )x +--R 9 9 +--R + +--R 10 6 11 5 8 11 5 12 4 7 +--R (1001a c d + 546b c d )x + (624a c d + 260b c d )x +--R + +--R 910 12 4 280 13 3 6 13 3 14 2 5 +--R (--- a c d + --- b c d )x + (112a c d + 24b c d )x +--R 3 3 +--R + +--R 14 2 15 4 16 15 1 16 3 1 16 2 +--R (30a c d + 4b c d)x + (-- a c d + - b c )x + - a c x +--R 3 3 2 +--R Type: Polynomial Fraction Integer +--E 8 + +--S 9 of 1483 +m0001:=a0001-r0001 +--R +--R +--R 1 18 1 19 +--R --- a c d - ---- b c +--R 306 2907 +--R (9) ----------------------- +--R 3 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 9 + +--S 10 of 1483 +d0001:=D(m0001,x) +--R +--R +--R (10) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 10 + +--S 11 of 1483 +t0002:= x*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (11) +--R 2 16 19 16 2 15 18 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 17 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 16 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 15 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 14 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 13 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 12 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 11 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 10 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 9 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 8 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 7 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 6 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 5 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 4 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 3 2 15 16 2 2 16 +--R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x +--R Type: Polynomial Integer +--E 11 + +--S 12 of 1483 +r0002:= -1/58140*(c+d*x)^17*(3*b^2*c^3-40*a*b*c^2*d+190*a^2*c*d^2-_ + 51*d*b^2*c^2*x+680*a*b*c*d^2*x-3230*a^2*d^3*x+459*d^2*b^2*c*x^2-_ + 6120*d^3*a*b*x^2-2907*d^3*b^2*x^3)/d^4 +--R +--R +--R (12) +--R 1 2 20 20 2 20 16 2 19 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 1 2 20 16 19 20 2 2 18 18 +--R (-- a d + -- a b c d + -- b c d )x +--R 18 9 3 +--R + +--R 16 2 19 240 2 18 560 2 3 17 17 +--R (-- a c d + --- a b c d + --- b c d )x +--R 17 17 17 +--R + +--R 15 2 2 18 3 17 455 2 4 16 16 +--R (-- a c d + 70a b c d + --- b c d )x +--R 2 4 +--R + +--R 112 2 3 17 728 4 16 1456 2 5 15 15 +--R (--- a c d + --- a b c d + ---- b c d )x +--R 3 3 5 +--R + +--R 2 4 16 5 15 2 6 14 14 +--R (130a c d + 624a b c d + 572b c d )x +--R + +--R 2 5 15 6 14 2 7 13 13 +--R (336a c d + 1232a b c d + 880b c d )x +--R + +--R 2002 2 6 14 5720 7 13 2145 2 8 12 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 3 3 2 +--R + +--R 2 7 13 8 12 2 9 11 11 +--R (1040a c d + 2340a b c d + 1040b c d )x +--R + +--R 2 8 12 9 11 4004 2 10 10 10 +--R (1287a c d + 2288a b c d + ---- b c d )x +--R 5 +--R + +--R 11440 2 9 11 16016 10 10 1456 2 11 9 9 +--R (----- a c d + ----- a b c d + ---- b c d )x +--R 9 9 3 +--R + +--R 2 10 10 11 9 455 2 12 8 8 +--R (1001a c d + 1092a b c d + --- b c d )x +--R 2 +--R + +--R 2 11 9 12 8 2 13 7 7 +--R (624a c d + 520a b c d + 80b c d )x +--R + +--R 910 2 12 8 560 13 7 2 14 6 6 +--R (--- a c d + --- a b c d + 20b c d )x +--R 3 3 +--R + +--R 2 13 7 14 6 16 2 15 5 5 +--R (112a c d + 48a b c d + -- b c d )x +--R 5 +--R + +--R 2 14 6 15 5 1 2 16 4 4 16 2 15 5 2 16 4 3 +--R (30a c d + 8a b c d + - b c d )x + (-- a c d + - a b c d )x +--R 4 3 3 +--R + +--R 1 2 16 4 2 1 2 18 2 2 19 1 2 20 +--R - a c d x - --- a c d + ---- a b c d - ----- b c +--R 2 306 2907 19380 +--R / +--R 4 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 12 + +--S 13 of 1483 +a0002:=integrate(t0002,x) +--R +--R +--R (13) +--R 1 2 16 20 2 16 16 2 15 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 1 2 16 16 15 20 2 2 14 18 +--R (-- a d + -- a b c d + -- b c d )x +--R 18 9 3 +--R + +--R 16 2 15 240 2 14 560 2 3 13 17 +--R (-- a c d + --- a b c d + --- b c d )x +--R 17 17 17 +--R + +--R 15 2 2 14 3 13 455 2 4 12 16 +--R (-- a c d + 70a b c d + --- b c d )x +--R 2 4 +--R + +--R 112 2 3 13 728 4 12 1456 2 5 11 15 +--R (--- a c d + --- a b c d + ---- b c d )x +--R 3 3 5 +--R + +--R 2 4 12 5 11 2 6 10 14 +--R (130a c d + 624a b c d + 572b c d )x +--R + +--R 2 5 11 6 10 2 7 9 13 +--R (336a c d + 1232a b c d + 880b c d )x +--R + +--R 2002 2 6 10 5720 7 9 2145 2 8 8 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 3 3 2 +--R + +--R 2 7 9 8 8 2 9 7 11 +--R (1040a c d + 2340a b c d + 1040b c d )x +--R + +--R 2 8 8 9 7 4004 2 10 6 10 +--R (1287a c d + 2288a b c d + ---- b c d )x +--R 5 +--R + +--R 11440 2 9 7 16016 10 6 1456 2 11 5 9 +--R (----- a c d + ----- a b c d + ---- b c d )x +--R 9 9 3 +--R + +--R 2 10 6 11 5 455 2 12 4 8 +--R (1001a c d + 1092a b c d + --- b c d )x +--R 2 +--R + +--R 2 11 5 12 4 2 13 3 7 +--R (624a c d + 520a b c d + 80b c d )x +--R + +--R 910 2 12 4 560 13 3 2 14 2 6 +--R (--- a c d + --- a b c d + 20b c d )x +--R 3 3 +--R + +--R 2 13 3 14 2 16 2 15 5 +--R (112a c d + 48a b c d + -- b c d)x +--R 5 +--R + +--R 2 14 2 15 1 2 16 4 16 2 15 2 16 3 1 2 16 2 +--R (30a c d + 8a b c d + - b c )x + (-- a c d + - a b c )x + - a c x +--R 4 3 3 2 +--R Type: Polynomial Fraction Integer +--E 13 + +--S 14 of 1483 +m0002:=a0002-r0002 +--R +--R +--R 1 2 18 2 2 19 1 2 20 +--R --- a c d - ---- a b c d + ----- b c +--R 306 2907 19380 +--R (14) ----------------------------------------- +--R 4 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 14 + +--S 15 of 1483 +d0002:=D(m0002,x) +--R +--R +--R (15) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 15 + +--S 16 of 1483 +t0003:= x^2*(a+b*x)*(c+d*x)^16 +--R +--R +--R (16) +--R 16 19 16 15 18 15 2 14 17 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 16 3 13 4 12 15 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 14 5 11 6 10 13 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 12 7 9 8 8 11 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 10 9 7 10 6 9 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 8 11 5 12 4 7 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 6 13 3 14 2 5 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 4 15 16 3 16 2 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial Integer +--E 16 + +--S 17 of 1483 +r0003:= 1/58140*(c+d*x)^17*(20*a*c^2*d-3*b*c^3-340*a*c*d^2*x+51*d*b*c^2*x-_ + 459*d^2*b*c*x^2+3060*d^3*a*x^2+2907*d^3*b*x^3)/d^4 +--R +--R +--R (17) +--R 1 20 20 1 20 16 19 19 8 19 20 2 18 18 +--R -- b d x + (-- a d + -- b c d )x + (- a c d + -- b c d )x +--R 20 19 19 9 3 +--R + +--R 120 2 18 560 3 17 17 3 17 455 4 16 16 +--R (--- a c d + --- b c d )x + (35a c d + --- b c d )x +--R 17 17 4 +--R + +--R 364 4 16 1456 5 15 15 5 15 6 14 14 +--R (--- a c d + ---- b c d )x + (312a c d + 572b c d )x +--R 3 5 +--R + +--R 6 14 7 13 13 2860 7 13 2145 8 12 12 +--R (616a c d + 880b c d )x + (---- a c d + ---- b c d )x +--R 3 2 +--R + +--R 8 12 9 11 11 9 11 4004 10 10 10 +--R (1170a c d + 1040b c d )x + (1144a c d + ---- b c d )x +--R 5 +--R + +--R 8008 10 10 1456 11 9 9 11 9 455 12 8 8 +--R (---- a c d + ---- b c d )x + (546a c d + --- b c d )x +--R 9 3 2 +--R + +--R 12 8 13 7 7 280 13 7 14 6 6 +--R (260a c d + 80b c d )x + (--- a c d + 20b c d )x +--R 3 +--R + +--R 14 6 16 15 5 5 15 5 1 16 4 4 1 16 4 3 +--R (24a c d + -- b c d )x + (4a c d + - b c d )x + - a c d x +--R 5 4 3 +--R + +--R 1 19 1 20 +--R ---- a c d - ----- b c +--R 2907 19380 +--R / +--R 4 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 17 + +--S 18 of 1483 +a0003:=integrate(t0003,x) +--R +--R +--R (18) +--R 1 16 20 1 16 16 15 19 8 15 20 2 14 18 +--R -- b d x + (-- a d + -- b c d )x + (- a c d + -- b c d )x +--R 20 19 19 9 3 +--R + +--R 120 2 14 560 3 13 17 3 13 455 4 12 16 +--R (--- a c d + --- b c d )x + (35a c d + --- b c d )x +--R 17 17 4 +--R + +--R 364 4 12 1456 5 11 15 5 11 6 10 14 +--R (--- a c d + ---- b c d )x + (312a c d + 572b c d )x +--R 3 5 +--R + +--R 6 10 7 9 13 2860 7 9 2145 8 8 12 +--R (616a c d + 880b c d )x + (---- a c d + ---- b c d )x +--R 3 2 +--R + +--R 8 8 9 7 11 9 7 4004 10 6 10 +--R (1170a c d + 1040b c d )x + (1144a c d + ---- b c d )x +--R 5 +--R + +--R 8008 10 6 1456 11 5 9 11 5 455 12 4 8 +--R (---- a c d + ---- b c d )x + (546a c d + --- b c d )x +--R 9 3 2 +--R + +--R 12 4 13 3 7 280 13 3 14 2 6 +--R (260a c d + 80b c d )x + (--- a c d + 20b c d )x +--R 3 +--R + +--R 14 2 16 15 5 15 1 16 4 1 16 3 +--R (24a c d + -- b c d)x + (4a c d + - b c )x + - a c x +--R 5 4 3 +--R Type: Polynomial Fraction Integer +--E 18 + +--S 19 of 1483 +m0003:=a0003-r0003 +--R +--R +--R 1 19 1 20 +--R - ---- a c d + ----- b c +--R 2907 19380 +--R (19) --------------------------- +--R 4 +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 19 + +--S 20 of 1483 +d0003:=D(m0003,x) +--R +--R +--R (20) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 20 + +--S 21 of 1483 +t0004:= (b+2*c*x)*(a+b*x+c*x^2)^7 +--R +--R +--R (21) +--R 8 15 7 14 7 2 6 13 6 3 5 12 +--R 2c x + 15b c x + (14a c + 49b c )x + (91a b c + 91b c )x +--R + +--R 2 6 2 5 4 4 11 2 5 3 4 5 3 10 +--R (42a c + 252a b c + 105b c )x + (231a b c + 385a b c + 77b c )x +--R + +--R 3 5 2 2 4 4 3 6 2 9 +--R (70a c + 525a b c + 350a b c + 35b c )x +--R + +--R 3 4 2 3 3 5 2 7 8 +--R (315a b c + 630a b c + 189a b c + 9b c)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 7 +--R (70a c + 560a b c + 420a b c + 56a b c + b )x +--R + +--R 4 3 3 3 2 2 5 7 6 +--R (245a b c + 490a b c + 147a b c + 7a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 5 +--R (42a c + 315a b c + 210a b c + 21a b )x +--R + +--R 5 2 4 3 3 5 4 6 2 5 2 4 4 3 +--R (105a b c + 175a b c + 35a b )x + (14a c + 84a b c + 35a b )x +--R + +--R 6 5 3 2 7 6 2 7 +--R (21a b c + 21a b )x + (2a c + 7a b )x + a b +--R Type: Polynomial Integer +--E 21 + +--S 22 of 1483 +r0004:= 1/8*(a+b*x+c*x^2)^8 +--R +--R +--R (22) +--R 1 8 16 7 15 7 7 2 6 14 6 3 5 13 +--R - c x + b c x + (a c + - b c )x + (7a b c + 7b c )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 12 2 5 3 4 5 3 11 +--R (- a c + 21a b c + -- b c )x + (21a b c + 35a b c + 7b c )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 10 +--R (7a c + --- a b c + 35a b c + - b c )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (35a b c + 70a b c + 21a b c + b c)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 8 +--R (-- a c + 70a b c + --- a b c + 7a b c + - b )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 7 +--R (35a b c + 70a b c + 21a b c + a b )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 6 5 2 4 3 3 5 5 +--R (7a c + --- a b c + 35a b c + - a b )x + (21a b c + 35a b c + 7a b )x +--R 2 2 +--R + +--R 7 6 2 5 2 35 4 4 4 6 5 3 3 7 7 6 2 2 +--R (- a c + 21a b c + -- a b )x + (7a b c + 7a b )x + (a c + - a b )x +--R 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 22 + +--S 23 of 1483 +a0004:=integrate(t0004,x) +--R +--R +--R (23) +--R 1 8 16 7 15 7 7 2 6 14 6 3 5 13 +--R - c x + b c x + (a c + - b c )x + (7a b c + 7b c )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 12 2 5 3 4 5 3 11 +--R (- a c + 21a b c + -- b c )x + (21a b c + 35a b c + 7b c )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 10 +--R (7a c + --- a b c + 35a b c + - b c )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (35a b c + 70a b c + 21a b c + b c)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 8 +--R (-- a c + 70a b c + --- a b c + 7a b c + - b )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 7 +--R (35a b c + 70a b c + 21a b c + a b )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 6 5 2 4 3 3 5 5 +--R (7a c + --- a b c + 35a b c + - a b )x + (21a b c + 35a b c + 7a b )x +--R 2 2 +--R + +--R 7 6 2 5 2 35 4 4 4 6 5 3 3 7 7 6 2 2 +--R (- a c + 21a b c + -- a b )x + (7a b c + 7a b )x + (a c + - a b )x +--R 2 4 2 +--R + +--R 7 +--R a b x +--R Type: Polynomial Fraction Integer +--E 23 + +--S 24 of 1483 +m0004:=a0004-r0004 +--R +--R +--R 1 8 +--R (24) - - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 24 + +--S 25 of 1483 +d0004:=D(m0004,x) +--R +--R +--R (25) 0 +--R Type: Polynomial Fraction Integer +--E 25 + +--S 26 of 1483 +t0005:= (b+2*c*x+3*d*x^2)*(a+b*x+c*x^2+d*x^3)^7 +--R +--R +--R (26) +--R 8 23 7 22 7 2 6 21 +--R 3d x + 23c d x + (22b d + 77c d )x +--R + +--R 7 6 3 5 20 +--R (21a d + 147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 +--R ((140a c + 70b )d + 420b c d + 175c d )x +--R + +--R 6 2 2 5 3 4 5 3 18 +--R (133a b d + (399a c + 399b c)d + 665b c d + 133c d )x +--R + +--R 2 6 3 5 3 2 2 4 4 3 +--R 63a d + (756a b c + 126b )d + (630a c + 945b c )d + 630b c d +--R + +--R 6 2 +--R 63c d +--R * +--R 17 +--R x +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (357a c + 357a b )d + (1785a b c + 595b c)d + (595a c + 1190b c )d +--R + +--R 5 2 7 +--R 357b c d + 17c d +--R * +--R 16 +--R x +--R + +--R 2 5 2 2 2 4 4 3 3 2 3 +--R 336a b d + (840a c + 1680a b c + 140b )d + (2240a b c + 1120b c )d +--R + +--R 5 2 4 2 6 8 +--R (336a c + 840b c )d + 112b c d + 2c +--R * +--R 15 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 105a d + (1575a b c + 525a b )d + (1050a c + 3150a b c + 525b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (1575a b c + 1050b c )d + (105a c + 315b c )d + 15b c +--R * +--R 14 +--R x +--R + +--R 3 2 2 4 2 2 3 5 3 +--R (490a c + 735a b )d + (2940a b c + 1960a b c + 98b )d +--R + +--R 2 4 2 3 4 2 2 5 3 4 7 +--R (735a c + 2940a b c + 735b c )d + (588a b c + 490b c )d + 14a c +--R + +--R 2 6 +--R 49b c +--R * +--R 13 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 455a b d + (910a c + 2730a b c + 455a b )d +--R + +--R 2 3 3 2 5 2 +--R (2730a b c + 2730a b c + 273b c)d +--R + +--R 2 5 2 4 4 3 6 3 5 +--R (273a c + 1365a b c + 455b c )d + 91a b c + 91b c +--R * +--R 12 +--R x +--R + +--R 4 4 3 2 3 3 +--R 105a d + (1680a b c + 840a b )d +--R + +--R 3 3 2 2 2 4 6 2 +--R (840a c + 3780a b c + 1260a b c + 42b )d +--R + +--R 2 4 3 3 5 2 2 6 2 5 4 4 +--R (1260a b c + 1680a b c + 252b c )d + 42a c + 252a b c + 105b c +--R * +--R 11 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (385a c + 770a b )d + (2310a b c + 2310a b c + 231a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 +--R (385a c + 2310a b c + 1155a b c + 77b c)d + 231a b c + 385a b c +--R + +--R 5 3 +--R 77b c +--R * +--R 10 +--R x +--R + +--R 4 3 4 2 3 2 2 4 2 +--R 350a b d + (525a c + 2100a b c + 525a b )d +--R + +--R 3 3 2 3 2 5 7 3 5 2 2 4 +--R (1400a b c + 2100a b c + 420a b c + 10b )d + 70a c + 525a b c +--R + +--R 4 3 6 2 +--R 350a b c + 35b c +--R * +--R 9 +--R x +--R + +--R 5 3 4 3 3 2 +--R 63a d + (945a b c + 630a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (315a c + 1890a b c + 945a b c + 63a b )d + 315a b c + 630a b c +--R + +--R 5 2 7 +--R 189a b c + 9b c +--R * +--R 8 +--R x +--R + +--R 5 4 2 2 4 2 3 3 2 5 4 4 +--R (168a c + 420a b )d + (840a b c + 1120a b c + 168a b )d + 70a c +--R + +--R 3 2 3 2 4 2 6 8 +--R 560a b c + 420a b c + 56a b c + b +--R * +--R 7 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 147a b d + (147a c + 735a b c + 245a b )d + 245a b c + 490a b c +--R + +--R 2 5 7 +--R 147a b c + 7a b +--R * +--R 6 +--R x +--R + +--R 6 2 5 4 3 5 3 4 2 2 3 4 2 6 5 +--R (21a d + (252a b c + 210a b )d + 42a c + 315a b c + 210a b c + 21a b )x +--R + +--R 6 5 2 5 2 4 3 3 5 4 +--R ((35a c + 105a b )d + 105a b c + 175a b c + 35a b )x +--R + +--R 6 6 2 5 2 4 4 3 7 6 5 3 2 +--R (28a b d + 14a c + 84a b c + 35a b )x + (3a d + 21a b c + 21a b )x +--R + +--R 7 6 2 7 +--R (2a c + 7a b )x + a b +--R Type: Polynomial Integer +--E 26 + +--S 27 of 1483 +r0005:= 1/8*(a+b*x+c*x^2+d*x^3)^8 +--R +--R +--R (27) +--R 1 8 24 7 23 7 7 2 6 22 7 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (a d + 7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 +--R ((7a c + - b )d + 21b c d + -- c d )x +--R 2 4 +--R + +--R 6 2 2 5 3 4 5 3 19 +--R (7a b d + (21a c + 21b c)d + 35b c d + 7c d )x +--R + +--R 7 2 6 3 5 3 105 2 2 4 4 3 7 6 2 18 +--R (- a d + (42a b c + 7b )d + (35a c + --- b c )d + 35b c d + - c d )x +--R 2 2 2 +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (21a c + 21a b )d + (105a b c + 35b c)d + (35a c + 70b c )d +--R + +--R 5 2 7 +--R 21b c d + c d +--R * +--R 17 +--R x +--R + +--R 2 5 105 2 2 2 35 4 4 3 3 2 3 +--R 21a b d + (--- a c + 105a b c + -- b )d + (140a b c + 70b c )d +--R 2 4 +--R + +--R 5 105 2 4 2 6 1 8 +--R (21a c + --- b c )d + 7b c d + - c +--R 2 8 +--R * +--R 16 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 7a d + (105a b c + 35a b )d + (70a c + 210a b c + 35b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (105a b c + 70b c )d + (7a c + 21b c )d + b c +--R * +--R 15 +--R x +--R + +--R 3 105 2 2 4 2 2 3 5 3 +--R (35a c + --- a b )d + (210a b c + 140a b c + 7b )d +--R 2 +--R + +--R 105 2 4 2 3 105 4 2 2 5 3 4 7 +--R (--- a c + 210a b c + --- b c )d + (42a b c + 35b c )d + a c +--R 2 2 +--R + +--R 7 2 6 +--R - b c +--R 2 +--R * +--R 14 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 35a b d + (70a c + 210a b c + 35a b )d +--R + +--R 2 3 3 2 5 2 2 5 2 4 4 3 +--R (210a b c + 210a b c + 21b c)d + (21a c + 105a b c + 35b c )d +--R + +--R 6 3 5 +--R 7a b c + 7b c +--R * +--R 13 +--R x +--R + +--R 35 4 4 3 2 3 3 +--R -- a d + (140a b c + 70a b )d +--R 4 +--R + +--R 3 3 2 2 2 4 7 6 2 +--R (70a c + 315a b c + 105a b c + - b )d +--R 2 +--R + +--R 2 4 3 3 5 2 7 2 6 2 5 35 4 4 +--R (105a b c + 140a b c + 21b c )d + - a c + 21a b c + -- b c +--R 2 4 +--R * +--R 12 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (35a c + 70a b )d + (210a b c + 210a b c + 21a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 5 3 +--R (35a c + 210a b c + 105a b c + 7b c)d + 21a b c + 35a b c + 7b c +--R * +--R 11 +--R x +--R + +--R 4 3 105 4 2 3 2 105 2 4 2 +--R 35a b d + (--- a c + 210a b c + --- a b )d +--R 2 2 +--R + +--R 3 3 2 3 2 5 7 3 5 105 2 2 4 4 3 +--R (140a b c + 210a b c + 42a b c + b )d + 7a c + --- a b c + 35a b c +--R 2 +--R + +--R 7 6 2 +--R - b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 5 3 4 3 3 2 +--R 7a d + (105a b c + 70a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (35a c + 210a b c + 105a b c + 7a b )d + 35a b c + 70a b c +--R + +--R 5 2 7 +--R 21a b c + b c +--R * +--R 9 +--R x +--R + +--R 5 105 4 2 2 4 2 3 3 2 5 35 4 4 +--R (21a c + --- a b )d + (105a b c + 140a b c + 21a b )d + -- a c +--R 2 4 +--R + +--R 3 2 3 105 2 4 2 6 1 8 +--R 70a b c + --- a b c + 7a b c + - b +--R 2 8 +--R * +--R 8 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 21a b d + (21a c + 105a b c + 35a b )d + 35a b c + 70a b c +--R + +--R 2 5 7 +--R 21a b c + a b +--R * +--R 7 +--R x +--R + +--R 7 6 2 5 4 3 5 3 105 4 2 2 3 4 7 2 6 6 +--R (- a d + (42a b c + 35a b )d + 7a c + --- a b c + 35a b c + - a b )x +--R 2 2 2 +--R + +--R 6 5 2 5 2 4 3 3 5 5 +--R ((7a c + 21a b )d + 21a b c + 35a b c + 7a b )x +--R + +--R 6 7 6 2 5 2 35 4 4 4 7 6 5 3 3 +--R (7a b d + - a c + 21a b c + -- a b )x + (a d + 7a b c + 7a b )x +--R 2 4 +--R + +--R 7 7 6 2 2 7 1 8 +--R (a c + - a b )x + a b x + - a +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 27 + +--S 28 of 1483 +a0005:=integrate(t0005,x) +--R +--R +--R (28) +--R 1 8 24 7 23 7 7 2 6 22 7 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (a d + 7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 +--R ((7a c + - b )d + 21b c d + -- c d )x +--R 2 4 +--R + +--R 6 2 2 5 3 4 5 3 19 +--R (7a b d + (21a c + 21b c)d + 35b c d + 7c d )x +--R + +--R 7 2 6 3 5 3 105 2 2 4 4 3 7 6 2 18 +--R (- a d + (42a b c + 7b )d + (35a c + --- b c )d + 35b c d + - c d )x +--R 2 2 2 +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (21a c + 21a b )d + (105a b c + 35b c)d + (35a c + 70b c )d +--R + +--R 5 2 7 +--R 21b c d + c d +--R * +--R 17 +--R x +--R + +--R 2 5 105 2 2 2 35 4 4 3 3 2 3 +--R 21a b d + (--- a c + 105a b c + -- b )d + (140a b c + 70b c )d +--R 2 4 +--R + +--R 5 105 2 4 2 6 1 8 +--R (21a c + --- b c )d + 7b c d + - c +--R 2 8 +--R * +--R 16 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 7a d + (105a b c + 35a b )d + (70a c + 210a b c + 35b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (105a b c + 70b c )d + (7a c + 21b c )d + b c +--R * +--R 15 +--R x +--R + +--R 3 105 2 2 4 2 2 3 5 3 +--R (35a c + --- a b )d + (210a b c + 140a b c + 7b )d +--R 2 +--R + +--R 105 2 4 2 3 105 4 2 2 5 3 4 7 +--R (--- a c + 210a b c + --- b c )d + (42a b c + 35b c )d + a c +--R 2 2 +--R + +--R 7 2 6 +--R - b c +--R 2 +--R * +--R 14 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 35a b d + (70a c + 210a b c + 35a b )d +--R + +--R 2 3 3 2 5 2 2 5 2 4 4 3 +--R (210a b c + 210a b c + 21b c)d + (21a c + 105a b c + 35b c )d +--R + +--R 6 3 5 +--R 7a b c + 7b c +--R * +--R 13 +--R x +--R + +--R 35 4 4 3 2 3 3 +--R -- a d + (140a b c + 70a b )d +--R 4 +--R + +--R 3 3 2 2 2 4 7 6 2 +--R (70a c + 315a b c + 105a b c + - b )d +--R 2 +--R + +--R 2 4 3 3 5 2 7 2 6 2 5 35 4 4 +--R (105a b c + 140a b c + 21b c )d + - a c + 21a b c + -- b c +--R 2 4 +--R * +--R 12 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (35a c + 70a b )d + (210a b c + 210a b c + 21a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 5 3 +--R (35a c + 210a b c + 105a b c + 7b c)d + 21a b c + 35a b c + 7b c +--R * +--R 11 +--R x +--R + +--R 4 3 105 4 2 3 2 105 2 4 2 +--R 35a b d + (--- a c + 210a b c + --- a b )d +--R 2 2 +--R + +--R 3 3 2 3 2 5 7 3 5 105 2 2 4 4 3 +--R (140a b c + 210a b c + 42a b c + b )d + 7a c + --- a b c + 35a b c +--R 2 +--R + +--R 7 6 2 +--R - b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 5 3 4 3 3 2 +--R 7a d + (105a b c + 70a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (35a c + 210a b c + 105a b c + 7a b )d + 35a b c + 70a b c +--R + +--R 5 2 7 +--R 21a b c + b c +--R * +--R 9 +--R x +--R + +--R 5 105 4 2 2 4 2 3 3 2 5 35 4 4 +--R (21a c + --- a b )d + (105a b c + 140a b c + 21a b )d + -- a c +--R 2 4 +--R + +--R 3 2 3 105 2 4 2 6 1 8 +--R 70a b c + --- a b c + 7a b c + - b +--R 2 8 +--R * +--R 8 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 21a b d + (21a c + 105a b c + 35a b )d + 35a b c + 70a b c +--R + +--R 2 5 7 +--R 21a b c + a b +--R * +--R 7 +--R x +--R + +--R 7 6 2 5 4 3 5 3 105 4 2 2 3 4 7 2 6 6 +--R (- a d + (42a b c + 35a b )d + 7a c + --- a b c + 35a b c + - a b )x +--R 2 2 2 +--R + +--R 6 5 2 5 2 4 3 3 5 5 +--R ((7a c + 21a b )d + 21a b c + 35a b c + 7a b )x +--R + +--R 6 7 6 2 5 2 35 4 4 4 7 6 5 3 3 +--R (7a b d + - a c + 21a b c + -- a b )x + (a d + 7a b c + 7a b )x +--R 2 4 +--R + +--R 7 7 6 2 2 7 +--R (a c + - a b )x + a b x +--R 2 +--R Type: Polynomial Fraction Integer +--E 28 + +--S 29 of 1483 +m0005:=a0005-r0005 +--R +--R +--R 1 8 +--R (29) - - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 29 + +--S 30 of 1483 +d0005:=D(m0005,x) +--R +--R +--R (30) 0 +--R Type: Polynomial Fraction Integer +--E 30 + +--S 31 of 1483 +t0006:= (b+2*c*x+3*d*x^2)*(b*x+c*x^2+d*x^3)^7 +--R +--R +--R (31) +--R 8 23 7 22 7 2 6 21 6 3 5 20 +--R 3d x + 23c d x + (22b d + 77c d )x + (147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 2 5 3 4 5 3 18 +--R (70b d + 420b c d + 175c d )x + (399b c d + 665b c d + 133c d )x +--R + +--R 3 5 2 2 4 4 3 6 2 17 +--R (126b d + 945b c d + 630b c d + 63c d )x +--R + +--R 3 4 2 3 3 5 2 7 16 +--R (595b c d + 1190b c d + 357b c d + 17c d)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 15 +--R (140b d + 1120b c d + 840b c d + 112b c d + 2c )x +--R + +--R 4 3 3 3 2 2 5 7 14 +--R (525b c d + 1050b c d + 315b c d + 15b c )x +--R + +--R 5 3 4 2 2 3 4 2 6 13 +--R (98b d + 735b c d + 490b c d + 49b c )x +--R + +--R 5 2 4 3 3 5 12 6 2 5 2 4 4 11 +--R (273b c d + 455b c d + 91b c )x + (42b d + 252b c d + 105b c )x +--R + +--R 6 5 3 10 7 6 2 9 7 8 8 7 +--R (77b c d + 77b c )x + (10b d + 35b c )x + 9b c x + b x +--R Type: Polynomial Integer +--E 31 + +--S 32 of 1483 +r0006:= 1/8*x^8*(b+c*x+d*x^2)^8 +--R +--R +--R (32) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 32 + +--S 33 of 1483 +a0006:=integrate(t0006,x) +--R +--R +--R (33) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 33 + +--S 34 of 1483 +m0006:=a0006-r0006 +--R +--R +--R (34) 0 +--R Type: Polynomial Fraction Integer +--E 34 + +--S 35 of 1483 +d0006:=D(m0006,x) +--R +--R +--R (35) 0 +--R Type: Polynomial Fraction Integer +--E 35 + +--S 36 of 1483 +t0007:= (b+2*c*x+3*d*x^2)*x^7*(b+c*x+d*x^2)^7 +--R +--R +--R (36) +--R 8 23 7 22 7 2 6 21 6 3 5 20 +--R 3d x + 23c d x + (22b d + 77c d )x + (147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 2 5 3 4 5 3 18 +--R (70b d + 420b c d + 175c d )x + (399b c d + 665b c d + 133c d )x +--R + +--R 3 5 2 2 4 4 3 6 2 17 +--R (126b d + 945b c d + 630b c d + 63c d )x +--R + +--R 3 4 2 3 3 5 2 7 16 +--R (595b c d + 1190b c d + 357b c d + 17c d)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 15 +--R (140b d + 1120b c d + 840b c d + 112b c d + 2c )x +--R + +--R 4 3 3 3 2 2 5 7 14 +--R (525b c d + 1050b c d + 315b c d + 15b c )x +--R + +--R 5 3 4 2 2 3 4 2 6 13 +--R (98b d + 735b c d + 490b c d + 49b c )x +--R + +--R 5 2 4 3 3 5 12 6 2 5 2 4 4 11 +--R (273b c d + 455b c d + 91b c )x + (42b d + 252b c d + 105b c )x +--R + +--R 6 5 3 10 7 6 2 9 7 8 8 7 +--R (77b c d + 77b c )x + (10b d + 35b c )x + 9b c x + b x +--R Type: Polynomial Integer +--E 36 + +--S 37 of 1483 +r0007:= 1/8*x^8*(b+c*x+d*x^2)^8 +--R +--R +--R (37) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 37 + +--S 38 of 1483 +a0007:=integrate(t0007,x) +--R +--R +--R (38) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 38 + +--S 39 of 1483 +m0007:=a0007-r0007 +--R +--R +--R (39) 0 +--R Type: Polynomial Fraction Integer +--E 39 + +--S 40 of 1483 +d0007:=D(m0007,x) +--R +--R +--R (40) 0 +--R Type: Polynomial Fraction Integer +--E 40 + +--S 41 of 1483 +t0008:= (b+3*d*x^2)*(a+b*x+d*x^3)^7 +--R +--R +--R (41) +--R 8 23 7 21 7 20 2 6 19 6 18 +--R 3d x + 22b d x + 21a d x + 70b d x + 133a b d x +--R + +--R 2 6 3 5 17 2 5 16 2 5 4 4 15 +--R (63a d + 126b d )x + 357a b d x + (336a b d + 140b d )x +--R + +--R 3 5 3 4 14 2 2 4 5 3 13 +--R (105a d + 525a b d )x + (735a b d + 98b d )x +--R + +--R 3 4 4 3 12 4 4 2 3 3 6 2 11 +--R (455a b d + 455a b d )x + (105a d + 840a b d + 42b d )x +--R + +--R 3 2 3 5 2 10 4 3 2 4 2 7 9 +--R (770a b d + 231a b d )x + (350a b d + 525a b d + 10b d)x +--R + +--R 5 3 3 3 2 6 8 4 2 2 2 5 8 7 +--R (63a d + 630a b d + 63a b d)x + (420a b d + 168a b d + b )x +--R + +--R 5 2 3 4 7 6 6 2 4 3 2 6 5 +--R (147a b d + 245a b d + 7a b )x + (21a d + 210a b d + 21a b )x +--R + +--R 5 2 3 5 4 6 4 4 3 7 5 3 2 6 2 +--R (105a b d + 35a b )x + (28a b d + 35a b )x + (3a d + 21a b )x + 7a b x +--R + +--R 7 +--R a b +--R Type: Polynomial Integer +--E 41 + +--S 42 of 1483 +r0008:= 1/8*(a+b*x+d*x^3)^8 +--R +--R +--R (42) +--R 1 8 24 7 22 7 21 7 2 6 20 6 19 7 2 6 3 5 18 +--R - d x + b d x + a d x + - b d x + 7a b d x + (- a d + 7b d )x +--R 8 2 2 +--R + +--R 2 5 17 2 5 35 4 4 16 3 5 3 4 15 +--R 21a b d x + (21a b d + -- b d )x + (7a d + 35a b d )x +--R 4 +--R + +--R 105 2 2 4 5 3 14 3 4 4 3 13 +--R (--- a b d + 7b d )x + (35a b d + 35a b d )x +--R 2 +--R + +--R 35 4 4 2 3 3 7 6 2 12 3 2 3 5 2 11 +--R (-- a d + 70a b d + - b d )x + (70a b d + 21a b d )x +--R 4 2 +--R + +--R 4 3 105 2 4 2 7 10 5 3 3 3 2 6 9 +--R (35a b d + --- a b d + b d)x + (7a d + 70a b d + 7a b d)x +--R 2 +--R + +--R 105 4 2 2 2 5 1 8 8 5 2 3 4 7 7 +--R (--- a b d + 21a b d + - b )x + (21a b d + 35a b d + a b )x +--R 2 8 +--R + +--R 7 6 2 4 3 7 2 6 6 5 2 3 5 5 6 35 4 4 4 +--R (- a d + 35a b d + - a b )x + (21a b d + 7a b )x + (7a b d + -- a b )x +--R 2 2 4 +--R + +--R 7 5 3 3 7 6 2 2 7 1 8 +--R (a d + 7a b )x + - a b x + a b x + - a +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 42 + +--S 43 of 1483 +a0008:=integrate(t0008,x) +--R +--R +--R (43) +--R 1 8 24 7 22 7 21 7 2 6 20 6 19 7 2 6 3 5 18 +--R - d x + b d x + a d x + - b d x + 7a b d x + (- a d + 7b d )x +--R 8 2 2 +--R + +--R 2 5 17 2 5 35 4 4 16 3 5 3 4 15 +--R 21a b d x + (21a b d + -- b d )x + (7a d + 35a b d )x +--R 4 +--R + +--R 105 2 2 4 5 3 14 3 4 4 3 13 +--R (--- a b d + 7b d )x + (35a b d + 35a b d )x +--R 2 +--R + +--R 35 4 4 2 3 3 7 6 2 12 3 2 3 5 2 11 +--R (-- a d + 70a b d + - b d )x + (70a b d + 21a b d )x +--R 4 2 +--R + +--R 4 3 105 2 4 2 7 10 5 3 3 3 2 6 9 +--R (35a b d + --- a b d + b d)x + (7a d + 70a b d + 7a b d)x +--R 2 +--R + +--R 105 4 2 2 2 5 1 8 8 5 2 3 4 7 7 +--R (--- a b d + 21a b d + - b )x + (21a b d + 35a b d + a b )x +--R 2 8 +--R + +--R 7 6 2 4 3 7 2 6 6 5 2 3 5 5 6 35 4 4 4 +--R (- a d + 35a b d + - a b )x + (21a b d + 7a b )x + (7a b d + -- a b )x +--R 2 2 4 +--R + +--R 7 5 3 3 7 6 2 2 7 +--R (a d + 7a b )x + - a b x + a b x +--R 2 +--R Type: Polynomial Fraction Integer +--E 43 + +--S 44 of 1483 +m0008:=a0008-r0008 +--R +--R +--R 1 8 +--R (44) - - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 44 + +--S 45 of 1483 +d0008:=D(m0008,x) +--R +--R +--R (45) 0 +--R Type: Polynomial Fraction Integer +--E 45 + +--S 46 of 1483 +t0009:= (2*c*x+3*d*x^2)*(a+c*x^2+d*x^3)^7 +--R +--R +--R (46) +--R 8 23 7 22 2 6 21 7 3 5 20 +--R 3d x + 23c d x + 77c d x + (21a d + 147c d )x +--R + +--R 6 4 4 19 2 5 5 3 18 +--R (140a c d + 175c d )x + (399a c d + 133c d )x +--R + +--R 2 6 3 4 6 2 17 2 5 4 3 7 16 +--R (63a d + 630a c d + 63c d )x + (357a c d + 595a c d + 17c d)x +--R + +--R 2 2 4 5 2 8 15 3 5 2 3 3 6 14 +--R (840a c d + 336a c d + 2c )x + (105a d + 1050a c d + 105a c d)x +--R + +--R 3 4 2 4 2 7 13 3 2 3 2 5 12 +--R (490a c d + 735a c d + 14a c )x + (910a c d + 273a c d)x +--R + +--R 4 4 3 3 2 2 6 11 4 3 3 4 10 +--R (105a d + 840a c d + 42a c )x + (385a c d + 385a c d)x +--R + +--R 4 2 2 3 5 9 5 3 4 3 8 5 2 4 4 7 +--R (525a c d + 70a c )x + (63a d + 315a c d)x + (168a c d + 70a c )x +--R + +--R 5 2 6 6 2 5 3 5 6 4 6 2 3 7 2 7 +--R 147a c d x + (21a d + 42a c )x + 35a c d x + 14a c x + 3a d x + 2a c x +--R Type: Polynomial Integer +--E 46 + +--S 47 of 1483 +r0009:= 1/8*(a+c*x^2+d*x^3)^8 +--R +--R +--R (47) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 1 8 +--R - a c x + a d x + a c x + - a +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 47 + +--S 48 of 1483 +a0009:=integrate(t0009,x) +--R +--R +--R (48) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 +--R - a c x + a d x + a c x +--R 2 +--R Type: Polynomial Fraction Integer +--E 48 + +--S 49 of 1483 +m0009:=a0009-r0009 +--R +--R +--R 1 8 +--R (49) - - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 49 + +--S 50 of 1483 +d0009:=D(m0009,x) +--R +--R +--R (50) 0 +--R Type: Polynomial Fraction Integer +--E 50 + +--S 51 of 1483 +t0010:= x*(2*c+3*d*x)*(a+c*x^2+d*x^3)^7 +--R +--R +--R (51) +--R 8 23 7 22 2 6 21 7 3 5 20 +--R 3d x + 23c d x + 77c d x + (21a d + 147c d )x +--R + +--R 6 4 4 19 2 5 5 3 18 +--R (140a c d + 175c d )x + (399a c d + 133c d )x +--R + +--R 2 6 3 4 6 2 17 2 5 4 3 7 16 +--R (63a d + 630a c d + 63c d )x + (357a c d + 595a c d + 17c d)x +--R + +--R 2 2 4 5 2 8 15 3 5 2 3 3 6 14 +--R (840a c d + 336a c d + 2c )x + (105a d + 1050a c d + 105a c d)x +--R + +--R 3 4 2 4 2 7 13 3 2 3 2 5 12 +--R (490a c d + 735a c d + 14a c )x + (910a c d + 273a c d)x +--R + +--R 4 4 3 3 2 2 6 11 4 3 3 4 10 +--R (105a d + 840a c d + 42a c )x + (385a c d + 385a c d)x +--R + +--R 4 2 2 3 5 9 5 3 4 3 8 5 2 4 4 7 +--R (525a c d + 70a c )x + (63a d + 315a c d)x + (168a c d + 70a c )x +--R + +--R 5 2 6 6 2 5 3 5 6 4 6 2 3 7 2 7 +--R 147a c d x + (21a d + 42a c )x + 35a c d x + 14a c x + 3a d x + 2a c x +--R Type: Polynomial Integer +--E 51 + +--S 52 of 1483 +r0010:= 1/8*(a+c*x^2+d*x^3)^8 +--R +--R +--R (52) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 1 8 +--R - a c x + a d x + a c x + - a +--R 2 8 +--R Type: Polynomial Fraction Integer +--E 52 + +--S 53 of 1483 +a0010:=integrate(t0010,x) +--R +--R +--R (53) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 +--R - a c x + a d x + a c x +--R 2 +--R Type: Polynomial Fraction Integer +--E 53 + +--S 54 of 1483 +m0010:=a0010-r0010 +--R +--R +--R 1 8 +--R (54) - - a +--R 8 +--R Type: Polynomial Fraction Integer +--E 54 + +--S 55 of 1483 +d0010:=D(m0010,x) +--R +--R +--R (55) 0 +--R Type: Polynomial Fraction Integer +--E 55 + +--S 56 of 1483 +t0011:= (-4+4*x+x^2)*(5-12*x+6*x^2+x^3) +--R +--R +--R 5 4 3 2 +--R (56) x + 10x + 8x - 67x + 68x - 20 +--R Type: Polynomial Integer +--E 56 + +--S 57 of 1483 +r0011:= 1/6*(5-12*x+6*x^2+x^3)^2 +--R +--R +--R 1 6 5 4 67 3 2 25 +--R (57) - x + 2x + 2x - -- x + 34x - 20x + -- +--R 6 3 6 +--R Type: Polynomial Fraction Integer +--E 57 + +--S 58 of 1483 +a0011:=integrate(t0011,x) +--R +--R +--R 1 6 5 4 67 3 2 +--R (58) - x + 2x + 2x - -- x + 34x - 20x +--R 6 3 +--R Type: Polynomial Fraction Integer +--E 58 + +--S 59 of 1483 +m0011:=a0011-r0011 +--R +--R +--R 25 +--R (59) - -- +--R 6 +--R Type: Polynomial Fraction Integer +--E 59 + +--S 60 of 1483 +d0011:=D(m0011,x) +--R +--R +--R (60) 0 +--R Type: Polynomial Fraction Integer +--E 60 + +--S 61 of 1483 +t0012:= (2*x+x^3)*(1+4*x^2+x^4) +--R +--R +--R 7 5 3 +--R (61) x + 6x + 9x + 2x +--R Type: Polynomial Integer +--E 61 + +--S 62 of 1483 +r0012:= 1/8*(1+4*x^2+x^4)^2 +--R +--R +--R 1 8 6 9 4 2 1 +--R (62) - x + x + - x + x + - +--R 8 4 8 +--R Type: Polynomial Fraction Integer +--E 62 + +--S 63 of 1483 +a0012:=integrate(t0012,x) +--R +--R +--R 1 8 6 9 4 2 +--R (63) - x + x + - x + x +--R 8 4 +--R Type: Polynomial Fraction Integer +--E 63 + +--S 64 of 1483 +m0012:=a0012-r0012 +--R +--R +--R 1 +--R (64) - - +--R 8 +--R Type: Polynomial Fraction Integer +--E 64 + +--S 65 of 1483 +d0012:=D(m0012,x) +--R +--R +--R (65) 0 +--R Type: Polynomial Fraction Integer +--E 65 + +--S 66 of 1483 +t0013:= (a*x+b*x^7)^5 +--R +--R +--R 5 35 4 29 2 3 23 3 2 17 4 11 5 5 +--R (66) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 66 + +--S 67 of 1483 +r0013:= 1/36*(a+b*x^6)^6/b +--R +--R +--R (67) +--R 1 6 36 1 5 30 5 2 4 24 5 3 3 18 5 4 2 12 1 5 6 1 6 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + - a b x + -- a +--R 36 6 12 9 12 6 36 +--R ----------------------------------------------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 67 + +--S 68 of 1483 +a0013:=integrate(t0013,x) +--R +--R +--R 1 5 36 1 4 30 5 2 3 24 5 3 2 18 5 4 12 1 5 6 +--R (68) -- b x + - a b x + -- a b x + - a b x + -- a b x + - a x +--R 36 6 12 9 12 6 +--R Type: Polynomial Fraction Integer +--E 68 + +--S 69 of 1483 +m0013:=a0013-r0013 +--R +--R +--R 1 6 +--R -- a +--R 36 +--R (69) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 69 + +--S 70 of 1483 +d0013:=D(m0013,x) +--R +--R +--R (70) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 70 + +--S 71 of 1483 +t0014:= (a*x^2+b*x^13)^5 +--R +--R +--R 5 65 4 54 2 3 43 3 2 32 4 21 5 10 +--R (71) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 71 + +--S 72 of 1483 +r0014:= 1/66*(a+b*x^11)^6/b +--R +--R +--R (72) +--R 1 6 66 1 5 55 5 2 4 44 10 3 3 33 5 4 2 22 1 5 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 66 11 22 33 22 11 +--R + +--R 1 6 +--R -- a +--R 66 +--R / +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 72 + +--S 73 of 1483 +a0014:=integrate(t0014,x) +--R +--R +--R (73) +--R 1 5 66 1 4 55 5 2 3 44 10 3 2 33 5 4 22 1 5 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 66 11 22 33 22 11 +--R Type: Polynomial Fraction Integer +--E 73 + +--S 74 of 1483 +m0014:=a0014-r0014 +--R +--R +--R 1 6 +--R -- a +--R 66 +--R (74) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 74 + +--S 75 of 1483 +d0014:=D(m0014,x) +--R +--R +--R (75) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 75 + +--S 76 of 1483 +t0015:= (a*x^3+b*x^19)^5 +--R +--R +--R 5 95 4 79 2 3 63 3 2 47 4 31 5 15 +--R (76) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 76 + +--S 77 of 1483 +r0015:= 1/96*(a+b*x^16)^6/b +--R +--R +--R (77) +--R 1 6 96 1 5 80 5 2 4 64 5 3 3 48 5 4 2 32 1 5 16 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 96 16 32 24 32 16 +--R + +--R 1 6 +--R -- a +--R 96 +--R / +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 77 + +--S 78 of 1483 +a0015:=integrate(t0015,x) +--R +--R +--R (78) +--R 1 5 96 1 4 80 5 2 3 64 5 3 2 48 5 4 32 1 5 16 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 96 16 32 24 32 16 +--R Type: Polynomial Fraction Integer +--E 78 + +--S 79 of 1483 +m0015:=a0015-r0015 +--R +--R +--R 1 6 +--R -- a +--R 96 +--R (79) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 79 + +--S 80 of 1483 +d0015:=D(m0015,x) +--R +--R +--R (80) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 80 + +--S 81 of 1483 +t0016:= (a+b*x)*(1+(c+a*x+1/2*b*x^2)^4) +--R +--R +--R (81) +--R 1 5 9 9 4 8 1 4 2 3 7 7 3 7 3 2 6 +--R -- b x + -- a b x + (- b c + 2a b )x + (- a b c + - a b )x +--R 16 16 2 2 2 +--R + +--R 3 3 2 2 2 4 5 15 2 2 3 5 4 +--R (- b c + 9a b c + 3a b)x + (-- a b c + 10a b c + a )x +--R 2 2 +--R + +--R 2 3 2 2 4 3 3 3 2 2 4 2 3 +--R (2b c + 12a b c + 4a c)x + (6a b c + 6a c )x + (b c + 4a c + b)x +--R + +--R 4 +--R a c + a +--R Type: Polynomial Fraction Integer +--E 81 + +--S 82 of 1483 +r0016:= c+a*x+1/2*b*x^2+1/160*(2*c+2*a*x+b*x^2)^5 +--R +--R +--R (82) +--R 1 5 10 1 4 9 1 4 1 2 3 8 1 3 1 3 2 7 +--R --- b x + -- a b x + (-- b c + - a b )x + (- a b c + - a b )x +--R 160 16 16 4 2 2 +--R + +--R 1 3 2 3 2 2 1 4 6 3 2 2 3 1 5 5 +--R (- b c + - a b c + - a b)x + (- a b c + 2a b c + - a )x +--R 4 2 2 2 5 +--R + +--R 1 2 3 2 2 4 4 3 3 2 3 1 4 2 3 1 2 +--R (- b c + 3a b c + a c)x + (2a b c + 2a c )x + (- b c + 2a c + - b)x +--R 2 2 2 +--R + +--R 4 1 5 +--R (a c + a)x + - c + c +--R 5 +--R Type: Polynomial Fraction Integer +--E 82 + +--S 83 of 1483 +a0016:=integrate(t0016,x) +--R +--R +--R (83) +--R 1 5 10 1 4 9 1 4 1 2 3 8 1 3 1 3 2 7 +--R --- b x + -- a b x + (-- b c + - a b )x + (- a b c + - a b )x +--R 160 16 16 4 2 2 +--R + +--R 1 3 2 3 2 2 1 4 6 3 2 2 3 1 5 5 +--R (- b c + - a b c + - a b)x + (- a b c + 2a b c + - a )x +--R 4 2 2 2 5 +--R + +--R 1 2 3 2 2 4 4 3 3 2 3 1 4 2 3 1 2 +--R (- b c + 3a b c + a c)x + (2a b c + 2a c )x + (- b c + 2a c + - b)x +--R 2 2 2 +--R + +--R 4 +--R (a c + a)x +--R Type: Polynomial Fraction Integer +--E 83 + +--S 84 of 1483 +m0016:=a0016-r0016 +--R +--R +--R 1 5 +--R (84) - - c - c +--R 5 +--R Type: Polynomial Fraction Integer +--E 84 + +--S 85 of 1483 +d0016:=D(m0016,x) +--R +--R +--R (85) 0 +--R Type: Polynomial Fraction Integer +--E 85 + +--S 86 of 1483 +t0017:= (a+c*x^2)*(1+(d+a*x+1/3*c*x^3)^5) +--R +--R +--R (86) +--R 1 6 17 16 5 15 5 5 14 35 2 4 13 65 4 12 +--R --- c x + --- a c x + -- c d x + -- a c x + -- a c d x +--R 243 243 81 81 81 +--R + +--R 10 4 2 40 3 3 11 110 2 3 10 100 3 2 25 4 2 9 +--R (-- c d + -- a c )x + --- a c d x + (--- a c d + -- a c )x +--R 27 27 27 27 9 +--R + +--R 10 3 3 3 2 8 40 2 2 2 8 5 7 70 2 3 35 4 6 +--R (-- c d + 10a c d)x + (-- a c d + - a c)x + (-- a c d + -- a c d)x +--R 9 3 3 9 3 +--R + +--R 5 2 4 3 2 6 5 50 2 3 5 4 20 4 4 2 3 +--R (- c d + 20a c d + a )x + (-- a c d + 5a d)x + (-- a c d + 10a d )x +--R 3 3 3 +--R + +--R 5 3 3 2 2 4 5 +--R (c d + 10a d + c)x + 5a d x + a d + a +--R Type: Polynomial Fraction Integer +--E 86 + +--S 87 of 1483 +r0017:= d+a*x+1/3*c*x^3+1/4374*(3*d+3*a*x+c*x^3)^6 +--R +--R +--R (87) +--R 1 6 18 1 5 16 1 5 15 5 2 4 14 5 4 13 +--R ---- c x + --- a c x + --- c d x + --- a c x + -- a c d x +--R 4374 243 243 162 81 +--R + +--R 5 4 2 10 3 3 12 10 2 3 11 10 3 2 5 4 2 10 +--R (--- c d + -- a c )x + -- a c d x + (-- a c d + -- a c )x +--R 162 81 27 27 18 +--R + +--R 10 3 3 10 3 2 9 5 2 2 2 1 5 8 10 2 3 5 4 7 +--R (-- c d + -- a c d)x + (- a c d + - a c)x + (-- a c d + - a c d)x +--R 81 9 3 3 9 3 +--R + +--R 5 2 4 10 3 2 1 6 6 10 2 3 5 5 +--R (-- c d + -- a c d + - a )x + (-- a c d + a d)x +--R 18 3 6 3 +--R + +--R 5 4 5 4 2 4 1 5 10 3 3 1 3 5 2 4 2 5 +--R (- a c d + - a d )x + (- c d + -- a d + - c)x + - a d x + (a d + a)x +--R 3 2 3 3 3 2 +--R + +--R 1 6 +--R - d + d +--R 6 +--R Type: Polynomial Fraction Integer +--E 87 + +--S 88 of 1483 +a0017:=integrate(t0017,x) +--R +--R +--R (88) +--R 1 6 18 1 5 16 1 5 15 5 2 4 14 5 4 13 +--R ---- c x + --- a c x + --- c d x + --- a c x + -- a c d x +--R 4374 243 243 162 81 +--R + +--R 5 4 2 10 3 3 12 10 2 3 11 10 3 2 5 4 2 10 +--R (--- c d + -- a c )x + -- a c d x + (-- a c d + -- a c )x +--R 162 81 27 27 18 +--R + +--R 10 3 3 10 3 2 9 5 2 2 2 1 5 8 10 2 3 5 4 7 +--R (-- c d + -- a c d)x + (- a c d + - a c)x + (-- a c d + - a c d)x +--R 81 9 3 3 9 3 +--R + +--R 5 2 4 10 3 2 1 6 6 10 2 3 5 5 +--R (-- c d + -- a c d + - a )x + (-- a c d + a d)x +--R 18 3 6 3 +--R + +--R 5 4 5 4 2 4 1 5 10 3 3 1 3 5 2 4 2 5 +--R (- a c d + - a d )x + (- c d + -- a d + - c)x + - a d x + (a d + a)x +--R 3 2 3 3 3 2 +--R Type: Polynomial Fraction Integer +--E 88 + +--S 89 of 1483 +m0017:=a0017-r0017 +--R +--R +--R 1 6 +--R (89) - - d - d +--R 6 +--R Type: Polynomial Fraction Integer +--E 89 + +--S 90 of 1483 +d0017:=D(m0017,x) +--R +--R +--R (90) 0 +--R Type: Polynomial Fraction Integer +--E 90 + +--S 91 of 1483 +t0018:= (b*x+c*x^2)*(1+(d+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (91) +--R 1 6 17 17 5 16 10 2 4 15 5 5 25 3 3 14 +--R --- c x + --- b c x + -- b c x + (-- c d + --- b c )x +--R 243 486 81 81 108 +--R + +--R 35 4 35 4 2 13 65 2 3 13 5 12 +--R (-- b c d + --- b c )x + (-- b c d + -- b c)x +--R 81 144 54 96 +--R + +--R 10 4 2 5 3 2 1 6 11 55 3 2 55 4 10 +--R (-- c d + - b c d + -- b )x + (-- b c d + -- b c d)x +--R 27 3 32 27 48 +--R + +--R 25 2 2 2 5 5 9 10 3 3 15 3 2 8 40 2 3 5 4 2 7 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (-- b c d + - b d )x +--R 6 16 9 4 9 4 +--R + +--R 35 2 3 6 5 2 4 5 3 3 5 25 4 4 5 2 4 3 5 2 +--R -- b c d x + (- c d + - b d )x + -- b c d x + - b d x + (c d + c)x +--R 6 3 2 6 2 +--R + +--R 5 +--R (b d + b)x +--R Type: Polynomial Fraction Integer +--E 91 + +--S 92 of 1483 +r0018:= d+1/2*b*x^2+1/3*c*x^3+1/279936*(6*d+3*b*x^2+2*c*x^3)^6 +--R +--R +--R (92) +--R 1 6 18 1 5 17 5 2 4 16 1 5 5 3 3 15 +--R ---- c x + --- b c x + --- b c x + (--- c d + --- b c )x +--R 4374 486 648 243 324 +--R + +--R 5 4 5 4 2 14 5 2 3 1 5 13 +--R (--- b c d + --- b c )x + (-- b c d + -- b c)x +--R 162 288 54 96 +--R + +--R 5 4 2 5 3 2 1 6 12 5 3 2 5 4 11 +--R (--- c d + -- b c d + --- b )x + (-- b c d + -- b c d)x +--R 162 36 384 27 48 +--R + +--R 5 2 2 2 1 5 10 10 3 3 5 3 2 9 5 2 3 5 4 2 8 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (- b c d + -- b d )x +--R 12 32 81 12 9 32 +--R + +--R 5 2 3 7 5 2 4 5 3 3 6 5 4 5 5 2 4 4 +--R - b c d x + (-- c d + -- b d )x + - b c d x + - b d x +--R 6 18 12 6 8 +--R + +--R 1 5 1 3 1 5 1 2 1 6 +--R (- c d + - c)x + (- b d + - b)x + - d + d +--R 3 3 2 2 6 +--R Type: Polynomial Fraction Integer +--E 92 + +--S 93 of 1483 +a0018:=integrate(t0018,x) +--R +--R +--R (93) +--R 1 6 18 1 5 17 5 2 4 16 1 5 5 3 3 15 +--R ---- c x + --- b c x + --- b c x + (--- c d + --- b c )x +--R 4374 486 648 243 324 +--R + +--R 5 4 5 4 2 14 5 2 3 1 5 13 +--R (--- b c d + --- b c )x + (-- b c d + -- b c)x +--R 162 288 54 96 +--R + +--R 5 4 2 5 3 2 1 6 12 5 3 2 5 4 11 +--R (--- c d + -- b c d + --- b )x + (-- b c d + -- b c d)x +--R 162 36 384 27 48 +--R + +--R 5 2 2 2 1 5 10 10 3 3 5 3 2 9 5 2 3 5 4 2 8 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (- b c d + -- b d )x +--R 12 32 81 12 9 32 +--R + +--R 5 2 3 7 5 2 4 5 3 3 6 5 4 5 5 2 4 4 +--R - b c d x + (-- c d + -- b d )x + - b c d x + - b d x +--R 6 18 12 6 8 +--R + +--R 1 5 1 3 1 5 1 2 +--R (- c d + - c)x + (- b d + - b)x +--R 3 3 2 2 +--R Type: Polynomial Fraction Integer +--E 93 + +--S 94 of 1483 +m0018:=a0018-r0018 +--R +--R +--R 1 6 +--R (94) - - d - d +--R 6 +--R Type: Polynomial Fraction Integer +--E 94 + +--S 95 of 1483 +d0018:=D(m0018,x) +--R +--R +--R (95) 0 +--R Type: Polynomial Fraction Integer +--E 95 + +--S 96 of 1483 +t0019:= (a+b*x+c*x^2)*(1+(a*x+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (96) +--R 1 6 17 17 5 16 16 5 10 2 4 15 +--R --- c x + --- b c x + (--- a c + -- b c )x +--R 243 486 243 81 +--R + +--R 25 4 25 3 3 14 35 2 4 35 2 3 35 4 2 13 +--R (-- a b c + --- b c )x + (-- a c + -- a b c + --- b c )x +--R 54 108 81 27 144 +--R + +--R 65 2 3 65 3 2 13 5 12 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 40 3 3 2 2 2 5 4 1 6 11 +--R (-- a c + 5a b c + - a b c + -- b )x +--R 27 4 32 +--R + +--R 55 3 2 55 2 3 11 5 10 25 4 2 25 3 2 25 2 4 9 +--R (-- a b c + -- a b c + -- a b )x + (-- a c + -- a b c + -- a b )x +--R 9 12 32 9 3 16 +--R + +--R 15 4 15 3 3 8 8 5 4 2 7 7 5 6 6 5 2 +--R (-- a b c + -- a b )x + (- a c + 5a b )x + - a b x + a x + c x + b x + a +--R 2 4 3 2 +--R Type: Polynomial Fraction Integer +--E 96 + +--S 97 of 1483 +r0019:= a*x+1/2*b*x^2+1/3*c*x^3+1/279936*x^6*(6*a+3*b*x+2*c*x^2)^6 +--R +--R +--R (97) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 5 4 5 3 3 15 5 2 4 5 2 3 5 4 2 14 +--R (--- a b c + --- b c )x + (--- a c + -- a b c + --- b c )x +--R 162 324 162 54 288 +--R + +--R 5 2 3 5 3 2 1 5 13 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 10 3 3 5 2 2 2 5 4 1 6 12 +--R (-- a c + -- a b c + -- a b c + --- b )x +--R 81 12 48 384 +--R + +--R 5 3 2 5 2 3 1 5 11 5 4 2 5 3 2 5 2 4 10 +--R (- a b c + -- a b c + -- a b )x + (-- a c + - a b c + -- a b )x +--R 9 12 32 18 6 32 +--R + +--R 5 4 5 3 3 9 1 5 5 4 2 8 1 5 7 1 6 6 1 3 +--R (- a b c + -- a b )x + (- a c + - a b )x + - a b x + - a x + - c x +--R 6 12 3 8 2 6 3 +--R + +--R 1 2 +--R - b x + a x +--R 2 +--R Type: Polynomial Fraction Integer +--E 97 + +--S 98 of 1483 +a0019:=integrate(t0019,x) +--R +--R +--R (98) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 5 4 5 3 3 15 5 2 4 5 2 3 5 4 2 14 +--R (--- a b c + --- b c )x + (--- a c + -- a b c + --- b c )x +--R 162 324 162 54 288 +--R + +--R 5 2 3 5 3 2 1 5 13 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 10 3 3 5 2 2 2 5 4 1 6 12 +--R (-- a c + -- a b c + -- a b c + --- b )x +--R 81 12 48 384 +--R + +--R 5 3 2 5 2 3 1 5 11 5 4 2 5 3 2 5 2 4 10 +--R (- a b c + -- a b c + -- a b )x + (-- a c + - a b c + -- a b )x +--R 9 12 32 18 6 32 +--R + +--R 5 4 5 3 3 9 1 5 5 4 2 8 1 5 7 1 6 6 1 3 +--R (- a b c + -- a b )x + (- a c + - a b )x + - a b x + - a x + - c x +--R 6 12 3 8 2 6 3 +--R + +--R 1 2 +--R - b x + a x +--R 2 +--R Type: Polynomial Fraction Integer +--E 98 + +--S 99 of 1483 +m0019:=a0019-r0019 +--R +--R +--R (99) 0 +--R Type: Polynomial Fraction Integer +--E 99 + +--S 100 of 1483 +d0019:=D(m0019,x) +--R +--R +--R (100) 0 +--R Type: Polynomial Fraction Integer +--E 100 + +--S 101 of 1483 +t0020:= (a+b*x+c*x^2)*(1+(d+a*x+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (101) +--R 1 6 17 17 5 16 16 5 10 2 4 15 +--R --- c x + --- b c x + (--- a c + -- b c )x +--R 243 486 243 81 +--R + +--R 5 5 25 4 25 3 3 14 +--R (-- c d + -- a b c + --- b c )x +--R 81 54 108 +--R + +--R 35 4 35 2 4 35 2 3 35 4 2 13 +--R (-- b c d + -- a c + -- a b c + --- b c )x +--R 81 81 27 144 +--R + +--R 65 4 65 2 3 65 2 3 65 3 2 13 5 12 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 10 4 2 40 3 5 3 2 40 3 3 2 2 2 5 4 1 6 11 +--R (-- c d + (-- a b c + - b c )d + -- a c + 5a b c + - a b c + -- b )x +--R 27 9 3 27 4 32 +--R + +--R 55 3 2 110 2 3 55 2 2 55 4 55 3 2 55 2 3 +--R -- b c d + (--- a c + -- a b c + -- b c)d + -- a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 11 5 +--R -- a b +--R 32 +--R * +--R 10 +--R x +--R + +--R 100 3 25 2 2 2 50 2 2 25 3 5 5 25 4 2 +--R (--- a c + -- b c )d + (-- a b c + -- a b c + -- b )d + -- a c +--R 27 6 3 3 16 9 +--R + +--R 25 3 2 25 2 4 +--R -- a b c + -- a b +--R 3 16 +--R * +--R 9 +--R x +--R + +--R 10 3 3 2 15 3 2 3 2 45 2 2 45 4 +--R -- c d + (15a b c + -- b c)d + (10a c + -- a b c + -- a b )d +--R 9 4 2 16 +--R + +--R 15 4 15 3 3 +--R -- a b c + -- a b +--R 2 4 +--R * +--R 8 +--R x +--R + +--R 40 2 3 40 2 2 2 5 4 2 80 3 2 3 8 5 +--R -- b c d + (-- a c + 20a b c + - b )d + (-- a b c + 10a b )d + - a c +--R 9 3 4 3 3 +--R + +--R 4 2 +--R 5a b +--R * +--R 7 +--R x +--R + +--R 70 2 35 2 3 2 35 3 2 35 4 35 3 2 +--R (-- a c + -- b c)d + (35a b c + -- a b )d + (-- a c + -- a b )d +--R 9 6 4 3 2 +--R + +--R 7 5 +--R - a b +--R 2 +--R * +--R 6 +--R x +--R + +--R 5 2 4 5 3 3 3 45 2 2 2 4 6 5 +--R (- c d + (20a b c + - b )d + (20a c + -- a b )d + 15a b d + a )x +--R 3 2 2 +--R + +--R 25 4 50 2 25 2 3 3 2 5 4 +--R (-- b c d + (-- a c + -- a b )d + 25a b d + 5a d)x +--R 6 3 2 +--R + +--R 20 5 2 4 2 3 4 2 3 +--R ((-- a c + - b )d + 20a b d + 10a d )x +--R 3 2 +--R + +--R 5 15 4 3 3 2 5 2 4 5 +--R (c d + -- a b d + 10a d + c)x + (b d + 5a d + b)x + a d + a +--R 2 +--R Type: Polynomial Fraction Integer +--E 101 + +--S 102 of 1483 +r0020:= d+a*x+1/2*b*x^2+1/3*c*x^3+1/279936*(6*d+6*a*x+3*b*x^2+2*c*x^3)^6 +--R +--R +--R (102) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 1 5 5 4 5 3 3 15 +--R (--- c d + --- a b c + --- b c )x +--R 243 162 324 +--R + +--R 5 4 5 2 4 5 2 3 5 4 2 14 +--R (--- b c d + --- a c + -- a b c + --- b c )x +--R 162 162 54 288 +--R + +--R 5 4 5 2 3 5 2 3 5 3 2 1 5 13 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 5 4 2 10 3 5 3 2 10 3 3 5 2 2 2 5 4 +--R --- c d + (-- a b c + -- b c )d + -- a c + -- a b c + -- a b c +--R 162 27 36 81 12 48 +--R + +--R 1 6 +--R --- b +--R 384 +--R * +--R 12 +--R x +--R + +--R 5 3 2 10 2 3 5 2 2 5 4 5 3 2 5 2 3 +--R -- b c d + (-- a c + - a b c + -- b c)d + - a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 1 5 +--R -- a b +--R 32 +--R * +--R 11 +--R x +--R + +--R 10 3 5 2 2 2 5 2 2 5 3 1 5 5 4 2 +--R (-- a c + -- b c )d + (- a b c + - a b c + -- b )d + -- a c +--R 27 12 3 6 32 18 +--R + +--R 5 3 2 5 2 4 +--R - a b c + -- a b +--R 6 32 +--R * +--R 10 +--R x +--R + +--R 10 3 3 5 2 5 3 2 10 3 2 5 2 2 5 4 +--R -- c d + (- a b c + -- b c)d + (-- a c + - a b c + -- a b )d +--R 81 3 12 9 2 16 +--R + +--R 5 4 5 3 3 +--R - a b c + -- a b +--R 6 12 +--R * +--R 9 +--R x +--R + +--R 5 2 3 5 2 2 5 2 5 4 2 10 3 5 2 3 1 5 +--R - b c d + (- a c + - a b c + -- b )d + (-- a b c + - a b )d + - a c +--R 9 3 2 32 3 4 3 +--R + +--R 5 4 2 +--R - a b +--R 8 +--R * +--R 8 +--R x +--R + +--R 10 2 5 2 3 2 5 3 2 5 4 5 3 2 1 5 7 +--R ((-- a c + - b c)d + (5a b c + - a b )d + (- a c + - a b )d + - a b)x +--R 9 6 4 3 2 2 +--R + +--R 5 2 4 10 5 3 3 10 3 15 2 2 2 5 4 1 6 6 +--R (-- c d + (-- a b c + -- b )d + (-- a c + -- a b )d + - a b d + - a )x +--R 18 3 12 3 4 2 6 +--R + +--R 5 4 10 2 5 2 3 3 2 5 5 +--R (- b c d + (-- a c + - a b )d + 5a b d + a d)x +--R 6 3 2 +--R + +--R 5 5 2 4 2 3 5 4 2 4 +--R ((- a c + - b )d + 5a b d + - a d )x +--R 3 8 2 +--R + +--R 1 5 5 4 10 3 3 1 3 1 5 5 2 4 1 2 +--R (- c d + - a b d + -- a d + - c)x + (- b d + - a d + - b)x +--R 3 2 3 3 2 2 2 +--R + +--R 5 1 6 +--R (a d + a)x + - d + d +--R 6 +--R Type: Polynomial Fraction Integer +--E 102 + +--S 103 of 1483 +a0020:=integrate(t0020,x) +--R +--R +--R (103) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 1 5 5 4 5 3 3 15 +--R (--- c d + --- a b c + --- b c )x +--R 243 162 324 +--R + +--R 5 4 5 2 4 5 2 3 5 4 2 14 +--R (--- b c d + --- a c + -- a b c + --- b c )x +--R 162 162 54 288 +--R + +--R 5 4 5 2 3 5 2 3 5 3 2 1 5 13 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 5 4 2 10 3 5 3 2 10 3 3 5 2 2 2 5 4 +--R --- c d + (-- a b c + -- b c )d + -- a c + -- a b c + -- a b c +--R 162 27 36 81 12 48 +--R + +--R 1 6 +--R --- b +--R 384 +--R * +--R 12 +--R x +--R + +--R 5 3 2 10 2 3 5 2 2 5 4 5 3 2 5 2 3 +--R -- b c d + (-- a c + - a b c + -- b c)d + - a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 1 5 +--R -- a b +--R 32 +--R * +--R 11 +--R x +--R + +--R 10 3 5 2 2 2 5 2 2 5 3 1 5 5 4 2 +--R (-- a c + -- b c )d + (- a b c + - a b c + -- b )d + -- a c +--R 27 12 3 6 32 18 +--R + +--R 5 3 2 5 2 4 +--R - a b c + -- a b +--R 6 32 +--R * +--R 10 +--R x +--R + +--R 10 3 3 5 2 5 3 2 10 3 2 5 2 2 5 4 +--R -- c d + (- a b c + -- b c)d + (-- a c + - a b c + -- a b )d +--R 81 3 12 9 2 16 +--R + +--R 5 4 5 3 3 +--R - a b c + -- a b +--R 6 12 +--R * +--R 9 +--R x +--R + +--R 5 2 3 5 2 2 5 2 5 4 2 10 3 5 2 3 1 5 +--R - b c d + (- a c + - a b c + -- b )d + (-- a b c + - a b )d + - a c +--R 9 3 2 32 3 4 3 +--R + +--R 5 4 2 +--R - a b +--R 8 +--R * +--R 8 +--R x +--R + +--R 10 2 5 2 3 2 5 3 2 5 4 5 3 2 1 5 7 +--R ((-- a c + - b c)d + (5a b c + - a b )d + (- a c + - a b )d + - a b)x +--R 9 6 4 3 2 2 +--R + +--R 5 2 4 10 5 3 3 10 3 15 2 2 2 5 4 1 6 6 +--R (-- c d + (-- a b c + -- b )d + (-- a c + -- a b )d + - a b d + - a )x +--R 18 3 12 3 4 2 6 +--R + +--R 5 4 10 2 5 2 3 3 2 5 5 +--R (- b c d + (-- a c + - a b )d + 5a b d + a d)x +--R 6 3 2 +--R + +--R 5 5 2 4 2 3 5 4 2 4 +--R ((- a c + - b )d + 5a b d + - a d )x +--R 3 8 2 +--R + +--R 1 5 5 4 10 3 3 1 3 1 5 5 2 4 1 2 +--R (- c d + - a b d + -- a d + - c)x + (- b d + - a d + - b)x +--R 3 2 3 3 2 2 2 +--R + +--R 5 +--R (a d + a)x +--R Type: Polynomial Fraction Integer +--E 103 + +--S 104 of 1483 +m0020:=a0020-r0020 +--R +--R +--R 1 6 +--R (104) - - d - d +--R 6 +--R Type: Polynomial Fraction Integer +--E 104 + +--S 105 of 1483 +d0020:=D(m0020,x) +--R +--R +--R (105) 0 +--R Type: Polynomial Fraction Integer +--E 105 + +--S 106 of 1483 +t0021:= (2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14) +--R +--R +--R (106) +--R 20 19 18 17 +--R 3486784401x + 46490458680x + 294439571640x + 1177758286560x +--R + +--R 16 15 14 13 +--R 3336981811920x + 7118894532096x + 11864824220160x + 15819767221203x +--R + +--R 12 11 10 9 +--R 17138093246586x + 15233903651304x + 11171623917168x + 6770824454160x +--R + +--R 8 7 6 5 +--R 3385569848544x + 1389081063168x + 463107083481x + 123532587108x +--R + +--R 4 3 2 +--R 25748932860x + 4042307808x + 449706096x + 31617600x + 1056832 +--R Type: Polynomial Integer +--E 106 + +--S 107 of 1483 +r0021:= 1/21*(2+3*x)^7+1/42*(2+3*x)^14+1/63*(2+3*x)^21 +--R +--R +--R (107) +--R 1162261467 21 20 19 18 +--R ---------- x + 2324522934x + 15496819560x + 65431015920x +--R 7 +--R + +--R 17 16 15 15819767221203 14 +--R 196293047760x + 444930908256x + 790988281344x + -------------- x +--R 14 +--R + +--R 13 12 11 10 +--R 1318314865122x + 1269491970942x + 1015602174288x + 677082445416x +--R + +--R 9 8 7 6 +--R 376174427616x + 173635132896x + 66158154783x + 20588764518x +--R + +--R 5 4 3 2 2122112 +--R 5149786572x + 1010576952x + 149902032x + 15808800x + 1056832x + ------- +--R 63 +--R Type: Polynomial Fraction Integer +--E 107 + +--S 108 of 1483 +a0021:=integrate(t0021,x) +--R +--R +--R (108) +--R 1162261467 21 20 19 18 +--R ---------- x + 2324522934x + 15496819560x + 65431015920x +--R 7 +--R + +--R 17 16 15 15819767221203 14 +--R 196293047760x + 444930908256x + 790988281344x + -------------- x +--R 14 +--R + +--R 13 12 11 10 +--R 1318314865122x + 1269491970942x + 1015602174288x + 677082445416x +--R + +--R 9 8 7 6 +--R 376174427616x + 173635132896x + 66158154783x + 20588764518x +--R + +--R 5 4 3 2 +--R 5149786572x + 1010576952x + 149902032x + 15808800x + 1056832x +--R Type: Polynomial Fraction Integer +--E 108 + +--S 109 of 1483 +m0021:=a0021-r0021 +--R +--R +--R 2122112 +--R (109) - ------- +--R 63 +--R Type: Polynomial Fraction Integer +--E 109 + +--S 110 of 1483 +d0021:=D(m0021,x) +--R +--R +--R (110) 0 +--R Type: Polynomial Fraction Integer +--E 110 + +--S 111 of 1483 +t0022:= (2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14)^2 +--R +--R +--R (111) +--R 34 33 32 +--R 16677181699666569x + 378016118525775564x + 4158177303783531204x +--R + +--R 31 30 +--R 29569260826905110784x + 152774514272343072384x +--R + +--R 29 28 +--R 611098057089372289536x + 1969093739510199599616x +--R + +--R 27 26 +--R 5250916653945060568950x + 11814562711582707057228x +--R + +--R 25 24 +--R 22753974480193166244840x + 37923300052713558858960x +--R + +--R 23 22 +--R 55161197358098322404160x + 70483846759795477607040x +--R + +--R 21 20 +--R 79520450781314886393600x + 79520847116576754110643x +--R + +--R 19 18 +--R 70685813958589477281960x + 55960416183860517516840x +--R + +--R 17 16 +--R 39502388988265540321440x + 24872768546728823564400x +--R + +--R 15 14 +--R 13964412385079287976448x + 6982756365625215229440x +--R + +--R 13 12 +--R 3103796605675782721446x + 1222900430946085012212x +--R + +--R 11 10 +--R 425448833766864577488x + 130036362517827878112x +--R + +--R 9 8 7 +--R 34689917186099544096x + 8009483060433484224x + 1583178214811622912x +--R + +--R 6 5 4 +--R 264090004030265049x + 36466108367328612x + 4057390785756924x +--R + +--R 3 2 +--R 349626718314720x + 21898634455152x + 887139656256x + 17451466816 +--R Type: Polynomial Integer +--E 111 + +--S 112 of 1483 +r0022:= 1/21*(2+3*x)^7+1/21*(2+3*x)^14+1/21*(2+3*x)^21+1/42*(2+3*x)^28+_ + 1/105*(2+3*x)^35 +--R +--R +--R (112) +--R 16677181699666569 35 34 33 +--R ----------------- x + 11118121133111046x + 126005372841925188x +--R 35 +--R + +--R 32 31 101849676181562048256 30 +--R 924039400840784712x + 4928210137817518464x + --------------------- x +--R 5 +--R + +--R 29 2625458326972530284475 28 +--R 67899784121041365504x + ---------------------- x +--R 14 +--R + +--R 27 26 +--R 437576396725285446564x + 875152864622814086340x +--R + +--R 7584660010542711771792 25 24 +--R ---------------------- x + 2298383223254096766840x +--R 5 +--R + +--R 23 22 +--R 3064515076512846852480x + 3614565944605222108800x +--R + +--R 26506949038858918036881 21 20 +--R ----------------------- x + 3534290697929473864098x +--R 7 +--R + +--R 19 18 +--R 2945285062308448290360x + 2194577166014752240080x +--R + +--R 17 16 +--R 1463104032160519033200x + 872775774067455498528x +--R + +--R 15 14 +--R 465517091041681015296x + 221699757548270194389x +--R + +--R 13 12 11 +--R 94069263918929616324x + 35454069480572048124x + 11821487501620716192x +--R + +--R 17344958593049772048 10 9 8 +--R -------------------- x + 889942562270387136x + 197897276851452864x +--R 5 +--R + +--R 7 6 4057390785756924 5 +--R 37727143432895007x + 6077684727888102x + ---------------- x +--R 5 +--R + +--R 4 3 2 +--R 87406679578680x + 7299544818384x + 443569828128x + 17451466816x +--R + +--R 35041395328 +--R ----------- +--R 105 +--R Type: Polynomial Fraction Integer +--E 112 + +--S 113 of 1483 +a0022:=integrate(t0022,x) +--R +--R +--R (113) +--R 16677181699666569 35 34 33 +--R ----------------- x + 11118121133111046x + 126005372841925188x +--R 35 +--R + +--R 32 31 101849676181562048256 30 +--R 924039400840784712x + 4928210137817518464x + --------------------- x +--R 5 +--R + +--R 29 2625458326972530284475 28 +--R 67899784121041365504x + ---------------------- x +--R 14 +--R + +--R 27 26 +--R 437576396725285446564x + 875152864622814086340x +--R + +--R 7584660010542711771792 25 24 +--R ---------------------- x + 2298383223254096766840x +--R 5 +--R + +--R 23 22 +--R 3064515076512846852480x + 3614565944605222108800x +--R + +--R 26506949038858918036881 21 20 +--R ----------------------- x + 3534290697929473864098x +--R 7 +--R + +--R 19 18 +--R 2945285062308448290360x + 2194577166014752240080x +--R + +--R 17 16 +--R 1463104032160519033200x + 872775774067455498528x +--R + +--R 15 14 +--R 465517091041681015296x + 221699757548270194389x +--R + +--R 13 12 11 +--R 94069263918929616324x + 35454069480572048124x + 11821487501620716192x +--R + +--R 17344958593049772048 10 9 8 +--R -------------------- x + 889942562270387136x + 197897276851452864x +--R 5 +--R + +--R 7 6 4057390785756924 5 +--R 37727143432895007x + 6077684727888102x + ---------------- x +--R 5 +--R + +--R 4 3 2 +--R 87406679578680x + 7299544818384x + 443569828128x + 17451466816x +--R Type: Polynomial Fraction Integer +--E 113 + +--S 114 of 1483 +m0022:=a0022-r0022 +--R +--R +--R 35041395328 +--R (114) - ----------- +--R 105 +--R Type: Polynomial Fraction Integer +--E 114 + +--S 115 of 1483 +d0022:=D(m0022,x) +--R +--R +--R (115) 0 +--R Type: Polynomial Fraction Integer +--E 115 + +--S 116 of 1483 +t0023:= (a+b*x)^2/x^4 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (116) ------------------ +--R 4 +--R x +--R Type: Fraction Polynomial Integer +--E 116 + +--S 117 of 1483 +r0023:= -1/3*(a+b*x)^3/a/x^3 +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - - b x - a b x - a b x - - a +--R 3 3 +--R (117) -------------------------------- +--R 3 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 117 + +--S 118 of 1483 +a0023:=integrate(t0023,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (118) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression Integer,...) +--E 118 + +--S 119 of 1483 +m0023:=a0023-r0023 +--R +--R +--R 3 +--R b +--R (119) -- +--R 3a +--R Type: Expression Integer +--E 119 + +--S 120 of 1483 +d0023:=D(m0023,x) +--R +--R +--R (120) 0 +--R Type: Expression Integer +--E 120 + +--S 121 of 1483 +t0024:= x*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R (121) b x + 3a b x + 3a b x + a x +--R Type: Polynomial Integer +--E 121 + +--S 122 of 1483 +r0024:= -1/20*(a+b*x)^4*(a-4*b*x)/b^2 +--R +--R +--R 1 5 5 3 4 4 2 3 3 1 3 2 2 1 5 +--R - b x + - a b x + a b x + - a b x - -- a +--R 5 4 2 20 +--R (122) --------------------------------------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 122 + +--S 123 of 1483 +a0024:=integrate(t0024,x) +--R +--R +--R 1 3 5 3 2 4 2 3 1 3 2 +--R (123) - b x + - a b x + a b x + - a x +--R 5 4 2 +--R Type: Polynomial Fraction Integer +--E 123 + +--S 124 of 1483 +m0024:=a0024-r0024 +--R +--R +--R 1 5 +--R -- a +--R 20 +--R (124) ----- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 124 + +--S 125 of 1483 +d0024:=D(m0024,x) +--R +--R +--R (125) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 125 + +--S 126 of 1483 +t0025:= (a+b*x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (126) ---------------------------- +--R 5 +--R x +--R Type: Fraction Polynomial Integer +--E 126 + +--S 127 of 1483 +r0025:= -1/4*(a+b*x)^4/a/x^4 +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - - b x - a b x - - a b x - a b x - - a +--R 4 2 4 +--R (127) ------------------------------------------- +--R 4 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 127 + +--S 128 of 1483 +a0025:=integrate(t0025,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (128) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression Integer,...) +--E 128 + +--S 129 of 1483 +m0025:=a0025-r0025 +--R +--R +--R 4 +--R b +--R (129) -- +--R 4a +--R Type: Expression Integer +--E 129 + +--S 130 of 1483 +d0025:=D(m0025,x) +--R +--R +--R (130) 0 +--R Type: Expression Integer +--E 130 + +--S 131 of 1483 +t0026:= 1/x/(4+6*x) +--R +--R +--R 1 +--R (131) -------- +--R 2 +--R 6x + 4x +--R Type: Fraction Polynomial Integer +--E 131 + +--S 132 of 1483 +r0026:= -1/2*atanh(1+3*x) +--R +--R +--R atanh(3x + 1) +--R (132) - ------------- +--R 2 +--R Type: Expression Integer +--E 132 + +--S 133 of 1483 +a0026:=integrate(t0026,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (133) ---------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 133 + +--S 134 of 1483 +m0026:=a0026-r0026 +--R +--R +--R - log(3x + 2) + log(x) + 2atanh(3x + 1) +--R (134) --------------------------------------- +--R 4 +--R Type: Expression Integer +--E 134 + +--S 135 of 1483 +d0026:=D(m0026,x) +--R +--R +--R (135) 0 +--R Type: Expression Integer +--E 135 + +--S 136 of 1483 +t0027:= x^3*(a+b*x)^7 +--R +--R +--R (136) +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial Integer +--E 136 + +--S 137 of 1483 +r0027:= -1/1320*(a+b*x)^8*(a^3-8*a^2*b*x+36*a*b^2*x^2-120*b^3*x^3)/b^4 +--R +--R +--R (137) +--R 1 11 11 7 10 10 7 2 9 9 35 3 8 8 4 7 7 7 5 6 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 5 1 7 4 4 1 11 +--R - a b x + - a b x - ---- a +--R 5 4 1320 +--R / +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 137 + +--S 138 of 1483 +a0027:=integrate(t0027,x) +--R +--R +--R (138) +--R 1 7 11 7 6 10 7 2 5 9 35 3 4 8 4 3 7 7 5 2 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 1 7 4 +--R - a b x + - a x +--R 5 4 +--R Type: Polynomial Fraction Integer +--E 138 + +--S 139 of 1483 +m0027:=a0027-r0027 +--R +--R +--R 1 11 +--R ---- a +--R 1320 +--R (139) -------- +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 139 + +--S 140 of 1483 +d0027:=D(m0027,x) +--R +--R +--R (140) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 140 + +--S 141 of 1483 +t0028:= x^2*(a+b*x)^7 +--R +--R +--R (141) +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial Integer +--E 141 + +--S 142 of 1483 +r0028:= 1/360*(a+b*x)^8*(a^2-8*a*b*x+36*b^2*x^2)/b^3 +--R +--R +--R (142) +--R 1 10 10 7 9 9 21 2 8 8 3 7 7 35 4 6 6 21 5 5 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 4 1 7 3 3 1 10 +--R - a b x + - a b x + --- a +--R 4 3 360 +--R / +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 142 + +--S 143 of 1483 +a0028:=integrate(t0028,x) +--R +--R +--R (143) +--R 1 7 10 7 6 9 21 2 5 8 3 4 7 35 4 3 6 21 5 2 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 1 7 3 +--R - a b x + - a x +--R 4 3 +--R Type: Polynomial Fraction Integer +--E 143 + +--S 144 of 1483 +m0028:=a0028-r0028 +--R +--R +--R 1 10 +--R --- a +--R 360 +--R (144) - ------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 144 + +--S 145 of 1483 +d0028:=D(m0028,x) +--R +--R +--R (145) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 145 + +--S 146 of 1483 +t0029:= x*(a+b*x)^7 +--R +--R +--R (146) +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial Integer +--E 146 + +--S 147 of 1483 +r0029:= -1/72*(a+b*x)^8*(a-8*b*x)/b^2 +--R +--R +--R (147) +--R 1 9 9 7 8 8 2 7 7 35 3 6 6 4 5 5 21 5 4 4 7 6 3 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 2 1 9 +--R - a b x - -- a +--R 2 72 +--R / +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 147 + +--S 148 of 1483 +a0029:=integrate(t0029,x) +--R +--R +--R (148) +--R 1 7 9 7 6 8 2 5 7 35 3 4 6 4 3 5 21 5 2 4 7 6 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 +--R - a x +--R 2 +--R Type: Polynomial Fraction Integer +--E 148 + +--S 149 of 1483 +m0029:=a0029-r0029 +--R +--R +--R 1 9 +--R -- a +--R 72 +--R (149) ----- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 149 + +--S 150 of 1483 +d0029:=D(m0029,x) +--R +--R +--R (150) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 150 + +--S 151 of 1483 +t0030:= (a+b*x)^7/x^9 +--R +--R +--R (151) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 9 +--R x +--R Type: Fraction Polynomial Integer +--E 151 + +--S 152 of 1483 +r0030:= -1/8*(a+b*x)^8/a/x^8 +--R +--R +--R (152) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 8 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 152 + +--S 153 of 1483 +a0030:=integrate(t0030,x) +--R +--R +--R (153) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 8b x - 28a b x - 56a b x - 70a b x - 56a b x - 28a b x - 8a b x - a +--R ---------------------------------------------------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression Integer,...) +--E 153 + +--S 154 of 1483 +m0030:=a0030-r0030 +--R +--R +--R 8 +--R b +--R (154) -- +--R 8a +--R Type: Expression Integer +--E 154 + +--S 155 of 1483 +d0030:=D(m0030,x) +--R +--R +--R (155) 0 +--R Type: Expression Integer +--E 155 + +--S 156 of 1483 +t0031:= (a+b*x)^7/x^10 +--R +--R +--R (156) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction Polynomial Integer +--E 156 + +--S 157 of 1483 +r0031:= -1/72*(a+b*x)^8*(8*a-b*x)/a^2/x^9 +--R +--R +--R (157) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 157 + +--S 158 of 1483 +a0031:=integrate(t0031,x) +--R +--R +--R (158) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression Integer,...) +--E 158 + +--S 159 of 1483 +m0031:=a0031-r0031 +--R +--R +--R 9 +--R b +--R (159) - ---- +--R 2 +--R 72a +--R Type: Expression Integer +--E 159 + +--S 160 of 1483 +d0031:=D(m0031,x) +--R +--R +--R (160) 0 +--R Type: Expression Integer +--E 160 + +--S 161 of 1483 +t0032:= (a+b*x)^7/x^11 +--R +--R +--R (161) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 11 +--R x +--R Type: Fraction Polynomial Integer +--E 161 + +--S 162 of 1483 +r0032:= -1/360*(a+b*x)^8*(36*a^2-8*a*b*x+b^2*x^2)/a^3/x^10 +--R +--R +--R (162) +--R 1 10 10 1 3 7 7 7 4 6 6 21 5 5 5 35 6 4 4 7 3 3 +--R - --- b x - - a b x - - a b x - -- a b x - -- a b x - 5a b x +--R 360 3 4 5 6 +--R + +--R 21 8 2 2 7 9 1 10 +--R - -- a b x - - a b x - -- a +--R 8 9 10 +--R / +--R 3 10 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 162 + +--S 163 of 1483 +a0032:=integrate(t0032,x) +--R +--R +--R (163) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 120b x - 630a b x - 1512a b x - 2100a b x - 1800a b x - 945a b x +--R + +--R 6 7 +--R - 280a b x - 36a +--R / +--R 10 +--R 360x +--R Type: Union(Expression Integer,...) +--E 163 + +--S 164 of 1483 +m0032:=a0032-r0032 +--R +--R +--R 10 +--R b +--R (164) ----- +--R 3 +--R 360a +--R Type: Expression Integer +--E 164 + +--S 165 of 1483 +d0032:=D(m0032,x) +--R +--R +--R (165) 0 +--R Type: Expression Integer +--E 165 + +--S 166 of 1483 +t0033:= (a+b*x)^7/x^12 +--R +--R +--R (166) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 12 +--R x +--R Type: Fraction Polynomial Integer +--E 166 + +--S 167 of 1483 +r0033:= -1/1320*(a+b*x)^8*(120*a^3-36*a^2*b*x+8*a*b^2*x^2-b^3*x^3)/a^4/x^11 +--R +--R +--R (167) +--R 1 11 11 1 4 7 7 7 5 6 6 7 6 5 5 7 4 4 35 8 3 3 +--R ---- b x - - a b x - - a b x - - a b x - 5a b x - -- a b x +--R 1320 4 5 2 8 +--R + +--R 7 9 2 2 7 10 1 11 +--R - - a b x - -- a b x - -- a +--R 3 10 11 +--R / +--R 4 11 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 167 + +--S 168 of 1483 +a0033:=integrate(t0033,x) +--R +--R +--R (168) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 330b x - 1848a b x - 4620a b x - 6600a b x - 5775a b x +--R + +--R 5 2 2 6 7 +--R - 3080a b x - 924a b x - 120a +--R / +--R 11 +--R 1320x +--R Type: Union(Expression Integer,...) +--E 168 + +--S 169 of 1483 +m0033:=a0033-r0033 +--R +--R +--R 11 +--R b +--R (169) - ------ +--R 4 +--R 1320a +--R Type: Expression Integer +--E 169 + +--S 170 of 1483 +d0033:=D(m0033,x) +--R +--R +--R (170) 0 +--R Type: Expression Integer +--E 170 + +--S 171 of 1483 +t0034:= x^5/(a+b*x)^7 +--R +--R +--R (171) +--R 5 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction Polynomial Integer +--E 171 + +--S 172 of 1483 +r0034:= 1/6*x^6/a/(a+b*x)^6 +--R +--R +--R 1 6 +--R - x +--R 6 +--R (172) --------------------------------------------------------------- +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction Polynomial Fraction Integer +--E 172 + +--S 173 of 1483 +a0034:=integrate(t0034,x) +--R +--R +--R (173) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R ----------------------------------------------------------------------- +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression Integer,...) +--E 173 + +--S 174 of 1483 +m0034:=a0034-r0034 +--R +--R +--R 1 +--R (174) - ----- +--R 6 +--R 6a b +--R Type: Expression Integer +--E 174 + +--S 175 of 1483 +d0034:=D(m0034,x) +--R +--R +--R (175) 0 +--R Type: Expression Integer +--E 175 + +--S 176 of 1483 +t0035:= x^4/(a+b*x)^7 +--R +--R +--R (176) +--R 4 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction Polynomial Integer +--E 176 + +--S 177 of 1483 +r0035:= 1/30*x^5*(6*a+b*x)/a^2/(a+b*x)^6 +--R +--R +--R 1 6 1 5 +--R -- b x + - a x +--R 30 5 +--R (177) --------------------------------------------------------------- +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 7 8 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction Polynomial Fraction Integer +--E 177 + +--S 178 of 1483 +a0035:=integrate(t0035,x) +--R +--R +--R (178) +--R 4 4 3 3 2 2 2 3 4 +--R - 15b x - 20a b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 6 5 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression Integer,...) +--E 178 + +--S 179 of 1483 +m0035:=a0035-r0035 +--R +--R +--R 1 +--R (179) - ------ +--R 2 5 +--R 30a b +--R Type: Expression Integer +--E 179 + +--S 180 of 1483 +d0035:=D(m0035,x) +--R +--R +--R (180) 0 +--R Type: Expression Integer +--E 180 + +--S 181 of 1483 +t0036:= (a+b*x)^2*(c+d*x) +--R +--R +--R 2 3 2 2 2 2 +--R (181) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c +--R Type: Polynomial Integer +--E 181 + +--S 182 of 1483 +r0036:= -1/12*(a+b*x)^3*(-4*b*c+a*d-3*d*x*b)/b^2 +--R +--R +--R (182) +--R 1 4 4 2 3 1 4 3 1 2 2 3 2 2 2 1 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + a b c x - -- a d +--R 4 3 3 2 12 +--R + +--R 1 3 +--R - a b c +--R 3 +--R / +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 182 + +--S 183 of 1483 +a0036:=integrate(t0036,x) +--R +--R +--R 1 2 4 2 1 2 3 1 2 2 2 +--R (183) - b d x + (- a b d + - b c)x + (- a d + a b c)x + a c x +--R 4 3 3 2 +--R Type: Polynomial Fraction Integer +--E 183 + +--S 184 of 1483 +m0036:=a0036-r0036 +--R +--R +--R 1 4 1 3 +--R -- a d - - a b c +--R 12 3 +--R (184) ---------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 184 + +--S 185 of 1483 +d0036:=D(m0036,x) +--R +--R +--R (185) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 185 + +--S 186 of 1483 +t0037:= (a+b*x)^3*(c+d*x) +--R +--R +--R (186) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c +--R Type: Polynomial Integer +--E 186 + +--S 187 of 1483 +r0037:= -1/20*(a+b*x)^4*(-5*b*c+a*d-4*d*x*b)/b^2 +--R +--R +--R (187) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b d + - a b c)x + a b c x - -- a d + - a b c +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 187 + +--S 188 of 1483 +a0037:=integrate(t0037,x) +--R +--R +--R (188) +--R 1 3 5 3 2 1 3 4 2 2 3 1 3 3 2 2 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x + (- a d + - a b c)x +--R 5 4 4 2 2 +--R + +--R 3 +--R a c x +--R Type: Polynomial Fraction Integer +--E 188 + +--S 189 of 1483 +m0037:=a0037-r0037 +--R +--R +--R 1 5 1 4 +--R -- a d - - a b c +--R 20 4 +--R (189) ---------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 189 + +--S 190 of 1483 +d0037:=D(m0037,x) +--R +--R +--R (190) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 190 + +--S 191 of 1483 +t0038:= (a+b*x)^4*(c+d*x) +--R +--R +--R (191) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R Type: Polynomial Integer +--E 191 + +--S 192 of 1483 +r0038:= -1/30*(a+b*x)^5*(-6*b*c+a*d-5*d*x*b)/b^2 +--R +--R +--R (192) +--R 1 6 6 4 5 1 6 5 3 2 4 5 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x +--R 6 5 5 2 +--R + +--R 4 3 3 2 4 3 1 4 2 3 3 2 4 2 1 6 1 5 +--R (- a b d + 2a b c)x + (- a b d + 2a b c)x + a b c x - -- a d + - a b c +--R 3 2 30 5 +--R / +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 192 + +--S 193 of 1483 +a0038:=integrate(t0038,x) +--R +--R +--R (193) +--R 1 4 6 4 3 1 4 5 3 2 2 3 4 4 3 2 2 3 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + (- a b d + 2a b c)x +--R 6 5 5 2 3 +--R + +--R 1 4 3 2 4 +--R (- a d + 2a b c)x + a c x +--R 2 +--R Type: Polynomial Fraction Integer +--E 193 + +--S 194 of 1483 +m0038:=a0038-r0038 +--R +--R +--R 1 6 1 5 +--R -- a d - - a b c +--R 30 5 +--R (194) ---------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 194 + +--S 195 of 1483 +d0038:=D(m0038,x) +--R +--R +--R (195) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 195 + +--S 196 of 1483 +t0039:= (a+b*x)^5*(c+d*x) +--R +--R +--R (196) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b d x + (5a b d + b c)x + (10a b d + 5a b c)x + (10a b d + 10a b c)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b d + 10a b c)x + (a d + 5a b c)x + a c +--R Type: Polynomial Integer +--E 196 + +--S 197 of 1483 +r0039:= -1/42*(a+b*x)^6*(-7*b*c+a*d-6*d*x*b)/b^2 +--R +--R +--R (197) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b d x + (- a b d + - b c)x + (2a b d + a b c)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b d + - a b c)x + (- a b d + -- a b c)x + (- a b d + - a b c)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b c x - -- a d + - a b c +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 197 + +--S 198 of 1483 +a0039:=integrate(t0039,x) +--R +--R +--R (198) +--R 1 5 7 5 4 1 5 6 2 3 4 5 5 3 2 5 2 3 4 +--R - b d x + (- a b d + - b c)x + (2a b d + a b c)x + (- a b d + - a b c)x +--R 7 6 6 2 2 +--R + +--R 5 4 10 3 2 3 1 5 5 4 2 5 +--R (- a b d + -- a b c)x + (- a d + - a b c)x + a c x +--R 3 3 2 2 +--R Type: Polynomial Fraction Integer +--E 198 + +--S 199 of 1483 +m0039:=a0039-r0039 +--R +--R +--R 1 7 1 6 +--R -- a d - - a b c +--R 42 6 +--R (199) ---------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 199 + +--S 200 of 1483 +d0039:=D(m0039,x) +--R +--R +--R (200) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 200 + +--S 201 of 1483 +t0040:= (a+b*x)^2*(c+d*x)^2 +--R +--R +--R (201) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R Type: Polynomial Integer +--E 201 + +--S 202 of 1483 +r0040:= 1/30*(a+b*x)^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2+15*b^2*c*d*x-_ + 3*b*a*d^2*x+6*b^2*d^2*x^2)/b^3 +--R +--R +--R (202) +--R 1 5 2 5 1 4 2 1 5 4 1 2 3 2 4 4 1 5 2 3 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 3 4 2 2 2 3 2 1 5 2 1 4 1 3 2 2 +--R (a b c d + a b c )x + a b c x + -- a d - - a b c d + - a b c +--R 30 6 3 +--R / +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 202 + +--S 203 of 1483 +a0040:=integrate(t0040,x) +--R +--R +--R (203) +--R 1 2 2 5 1 2 1 2 4 1 2 2 4 1 2 2 3 +--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 2 2 2 2 +--R (a c d + a b c )x + a c x +--R Type: Polynomial Fraction Integer +--E 203 + +--S 204 of 1483 +m0040:=a0040-r0040 +--R +--R +--R 1 5 2 1 4 1 3 2 2 +--R - -- a d + - a b c d - - a b c +--R 30 6 3 +--R (204) -------------------------------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 204 + +--S 205 of 1483 +d0040:=D(m0040,x) +--R +--R +--R (205) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 205 + +--S 206 of 1483 +t0041:= (a+b*x)^3*(c+d*x)^2 +--R +--R +--R (206) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c +--R Type: Polynomial Integer +--E 206 + +--S 207 of 1483 +r0041:= 1/60*(a+b*x)^4*(15*b^2*c^2-6*a*b*c*d+a^2*d^2+24*b^2*c*d*x-_ + 4*b*a*d^2*x+10*b^2*d^2*x^2)/b^3 +--R +--R +--R (207) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b d + 2a b c d + a b c )x + (a b c d + - a b c )x + a b c x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a d - -- a b c d + - a b c +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 207 + +--S 208 of 1483 +a0041:=integrate(t0041,x) +--R +--R +--R (208) +--R 1 3 2 6 3 2 2 2 3 5 3 2 2 3 2 1 3 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 2 2 2 2 3 3 3 2 2 2 3 2 +--R (- a d + 2a b c d + a b c )x + (a c d + - a b c )x + a c x +--R 3 2 +--R Type: Polynomial Fraction Integer +--E 208 + +--S 209 of 1483 +m0041:=a0041-r0041 +--R +--R +--R 1 6 2 1 5 1 4 2 2 +--R - -- a d + -- a b c d - - a b c +--R 60 10 4 +--R (209) --------------------------------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 209 + +--S 210 of 1483 +d0041:=D(m0041,x) +--R +--R +--R (210) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 210 + +--S 211 of 1483 +t0042:= (a+b*x)^4*(c+d*x)^2 +--R +--R +--R (211) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R Type: Polynomial Integer +--E 211 + +--S 212 of 1483 +r0042:= 1/105*(a+b*x)^5*(21*b^2*c^2-7*a*b*c*d+a^2*d^2+35*b^2*c*d*x-_ + 5*b*a*d^2*x+15*b^2*d^2*x^2)/b^3 +--R +--R +--R (212) +--R 1 7 2 7 2 6 2 1 7 6 6 2 5 2 8 6 1 7 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 4 2 2 5 6 2 4 1 4 3 2 8 3 4 2 5 2 3 +--R (a b d + 3a b c d + a b c )x + (- a b d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 3 4 2 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (a b c d + 2a b c )x + a b c x + --- a d - -- a b c d + - a b c +--R 105 15 5 +--R / +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 212 + +--S 213 of 1483 +a0042:=integrate(t0042,x) +--R +--R +--R (213) +--R 1 4 2 7 2 3 2 1 4 6 6 2 2 2 8 3 1 4 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 2 2 2 3 2 4 1 4 2 8 3 2 2 2 3 +--R (a b d + 3a b c d + a b c )x + (- a d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 2 2 4 2 +--R (a c d + 2a b c )x + a c x +--R Type: Polynomial Fraction Integer +--E 213 + +--S 214 of 1483 +m0042:=a0042-r0042 +--R +--R +--R 1 7 2 1 6 1 5 2 2 +--R - --- a d + -- a b c d - - a b c +--R 105 15 5 +--R (214) ---------------------------------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 214 + +--S 215 of 1483 +d0042:=D(m0042,x) +--R +--R +--R (215) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 215 + +--S 216 of 1483 +t0043:= (a+b*x)^5*(c+d*x)^2 +--R +--R +--R (216) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b d x + (5a b d + 2b c d)x + (10a b d + 10a b c d + b c )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b d + 20a b c d + 5a b c )x + (5a b d + 20a b c d + 10a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a d + 10a b c d + 10a b c )x + (2a c d + 5a b c )x + a c +--R Type: Polynomial Integer +--E 216 + +--S 217 of 1483 +r0043:= 1/168*(a+b*x)^6*(28*b^2*c^2-8*a*b*c*d+a^2*d^2+48*b^2*c*d*x-_ + 6*b*a*d^2*x+21*b^2*d^2*x^2)/b^3 +--R +--R +--R (217) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b d + 4a b c d + a b c )x + (- a b d + 5a b c d + - a b c )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b d + -- a b c d + -- a b c )x + (a b c d + - a b c )x + a b c x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a d - -- a b c d + - a b c +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 217 + +--S 218 of 1483 +a0043:=integrate(t0043,x) +--R +--R +--R (218) +--R 1 5 2 8 5 4 2 2 5 7 5 2 3 2 5 4 1 5 2 6 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 8 7 7 3 3 6 +--R + +--R 3 2 2 2 3 4 2 5 5 4 2 3 2 5 2 3 2 4 +--R (2a b d + 4a b c d + a b c )x + (- a b d + 5a b c d + - a b c )x +--R 4 2 +--R + +--R 1 5 2 10 4 10 3 2 2 3 5 5 4 2 2 5 2 +--R (- a d + -- a b c d + -- a b c )x + (a c d + - a b c )x + a c x +--R 3 3 3 2 +--R Type: Polynomial Fraction Integer +--E 218 + +--S 219 of 1483 +m0043:=a0043-r0043 +--R +--R +--R 1 8 2 1 7 1 6 2 2 +--R - --- a d + -- a b c d - - a b c +--R 168 21 6 +--R (219) ---------------------------------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 219 + +--S 220 of 1483 +d0043:=D(m0043,x) +--R +--R +--R (220) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 220 + +--S 221 of 1483 +t0044:= (a+b*x)^3*(c+d*x)^3 +--R +--R +--R (221) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x +--R + +--R 3 2 2 3 3 3 +--R (3a c d + 3a b c )x + a c +--R Type: Polynomial Integer +--E 221 + +--S 222 of 1483 +r0044:= 1/140*(b*c-a*d)^3*(a+b*x)^4/b^4+_ + 1/35*(b*c-a*d)^2*(a+b*x)^4*(c+d*x)/b^3+_ + 1/14*(b*c-a*d)*(a+b*x)^4*(c+d*x)^2/b^2+1/7*(a+b*x)^4*(c+d*x)^3/b +--R +--R +--R (222) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b c d + 3a b c d + a b c )x + (- a b c d + - a b c )x + a b c x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 222 + +--S 223 of 1483 +a0044:=integrate(t0044,x) +--R +--R +--R (223) +--R 1 3 3 7 1 2 3 1 3 2 6 3 2 3 9 2 2 3 3 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 4 +--R (- a d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 2 2 2 2 3 3 3 3 2 3 2 3 2 3 3 +--R (a c d + 3a b c d + a b c )x + (- a c d + - a b c )x + a c x +--R 2 2 +--R Type: Polynomial Fraction Integer +--E 223 + +--S 224 of 1483 +m0044:=a0044-r0044 +--R +--R +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 140 20 20 4 +--R (224) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 224 + +--S 225 of 1483 +d0044:=D(m0044,x) +--R +--R +--R (225) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 225 + +--S 226 of 1483 +t0045:= (a+b*x)^4*(c+d*x)^3 +--R +--R +--R (226) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b d x + (4a b d + 3b c d )x + (6a b d + 12a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b d + 18a b c d + 12a b c d + b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a d + 12a b c d + 18a b c d + 4a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a c d + 12a b c d + 6a b c )x + (3a c d + 4a b c )x + a c +--R Type: Polynomial Integer +--E 226 + +--S 227 of 1483 +r0045:= 1/280*(b*c-a*d)^3*(a+b*x)^5/b^4+_ + 1/56*(b*c-a*d)^2*(a+b*x)^5*(c+d*x)/b^3+_ + 3/56*(b*c-a*d)*(a+b*x)^5*(c+d*x)^2/b^2+1/8*(a+b*x)^5*(c+d*x)^3/b +--R +--R +--R (227) +--R 1 8 3 8 4 7 3 3 8 2 7 2 6 3 7 2 1 8 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 5 3 18 2 6 2 12 7 2 1 8 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 4 3 3 5 2 9 2 6 2 7 3 4 +--R (- a b d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 4 2 3 5 2 2 6 3 3 3 4 4 2 3 5 3 2 4 4 3 +--R (a b c d + 4a b c d + 2a b c )x + (- a b c d + 2a b c )x + a b c x +--R 2 +--R + +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 280 35 10 5 +--R / +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 227 + +--S 228 of 1483 +a0045:=integrate(t0045,x) +--R +--R +--R (228) +--R 1 4 3 8 4 3 3 3 4 2 7 2 2 3 3 2 1 4 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 3 18 2 2 2 12 3 2 1 4 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 3 3 2 9 2 2 2 3 3 4 +--R (- a d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 2 3 2 2 2 3 3 3 4 2 3 3 2 4 3 +--R (a c d + 4a b c d + 2a b c )x + (- a c d + 2a b c )x + a c x +--R 2 +--R Type: Polynomial Fraction Integer +--E 228 + +--S 229 of 1483 +m0045:=a0045-r0045 +--R +--R +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 280 35 10 5 +--R (229) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 229 + +--S 230 of 1483 +d0045:=D(m0045,x) +--R +--R +--R (230) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 230 + +--S 231 of 1483 +t0046:= (a+b*x)^5*(c+d*x)^3 +--R +--R +--R (231) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b d x + (5a b d + 3b c d )x + (10a b d + 15a b c d + 3b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b d + 30a b c d + 15a b c d + b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b d + 30a b c d + 30a b c d + 5a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a d + 15a b c d + 30a b c d + 10a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a c d + 15a b c d + 10a b c )x + (3a c d + 5a b c )x + a c +--R Type: Polynomial Integer +--E 231 + +--S 232 of 1483 +r0046:= 1/504*(b*c-a*d)^3*(a+b*x)^6/b^4+_ + 1/84*(b*c-a*d)^2*(a+b*x)^6*(c+d*x)/b^3+_ + 1/24*(b*c-a*d)*(a+b*x)^6*(c+d*x)^2/b^2+1/9*(a+b*x)^6*(c+d*x)^3/b +--R +--R +--R (232) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b d x + (- a b d + - b c d )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b d + -- a b c d + - b c d)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b c d + 5a b c d + -- a b c )x + (- a b c d + - a b c )x + a b c x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 232 + +--S 233 of 1483 +a0046:=integrate(t0046,x) +--R +--R +--R (233) +--R 1 5 3 9 5 4 3 3 5 2 8 10 2 3 3 15 4 2 3 5 2 7 +--R - b d x + (- a b d + - b c d )x + (-- a b d + -- a b c d + - b c d)x +--R 9 8 8 7 7 7 +--R + +--R 5 3 2 3 2 3 2 5 4 2 1 5 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 3 15 4 2 15 3 2 2 5 2 3 3 4 +--R (- a d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 2 4 2 10 3 2 3 3 3 5 2 5 4 3 2 5 3 +--R (a c d + 5a b c d + -- a b c )x + (- a c d + - a b c )x + a c x +--R 3 2 2 +--R Type: Polynomial Fraction Integer +--E 233 + +--S 234 of 1483 +m0046:=a0046-r0046 +--R +--R +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 504 56 14 6 +--R (234) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 234 + +--S 235 of 1483 +d0046:=D(m0046,x) +--R +--R +--R (235) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 235 + +--S 236 of 1483 +t0047:= (a+b*x)^2/(c+d*x) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (236) ------------------ +--R d x + c +--R Type: Fraction Polynomial Integer +--E 236 + +--S 237 of 1483 +r0047:= -b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 +--R +--R +--R (237) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x + a d +--R ---------------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Expression Integer +--E 237 + +--S 238 of 1483 +a0047:=integrate(t0047,x) +--R +--R +--R (238) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x +--R --------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Union(Expression Integer,...) +--E 238 + +--S 239 of 1483 +m0047:=a0047-r0047 +--R +--R +--R 2 +--R a +--R (239) - -- +--R 2d +--R Type: Expression Integer +--E 239 + +--S 240 of 1483 +d0047:=D(m0047,x) +--R +--R +--R (240) 0 +--R Type: Expression Integer +--E 240 + +--S 241 of 1483 +t0048:= (a+b*x)^3/(c+d*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (241) ---------------------------- +--R d x + c +--R Type: Fraction Polynomial Integer +--E 241 + +--S 242 of 1483 +r0048:= b*(b*c-a*d)^2*x/d^3-1/2*(b*c-a*d)*(a+b*x)^2/d^2+1/3*(a+b*x)^3/d-_ + (b*c-a*d)^3*log(c+d*x)/d^4 +--R +--R +--R (242) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x + 5a d +--R + +--R 2 2 +--R - 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression Integer +--E 242 + +--S 243 of 1483 +a0048:=integrate(t0048,x) +--R +--R +--R (243) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x +--R / +--R 4 +--R 6d +--R Type: Union(Expression Integer,...) +--E 243 + +--S 244 of 1483 +m0048:=a0048-r0048 +--R +--R +--R 3 2 +--R - 5a d + 3a b c +--R (244) --------------- +--R 2 +--R 6d +--R Type: Expression Integer +--E 244 + +--S 245 of 1483 +d0048:=D(m0048,x) +--R +--R +--R (245) 0 +--R Type: Expression Integer +--E 245 + +--S 246 of 1483 +t0049:= (a+b*x)^4/(c+d*x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (246) -------------------------------------- +--R d x + c +--R Type: Fraction Polynomial Integer +--E 246 + +--S 247 of 1483 +r0049:= -b*(b*c-a*d)^3*x/d^4+1/2*(b*c-a*d)^2*(a+b*x)^2/d^3-_ + 1/3*(b*c-a*d)*(a+b*x)^3/d^2+1/4*(a+b*x)^4/d+(b*c-a*d)^4*log(c+d*x)/d^5 +--R +--R +--R (247) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x + 13a d - 16a b c d +--R + +--R 2 2 2 2 +--R 6a b c d +--R / +--R 5 +--R 12d +--R Type: Expression Integer +--E 247 + +--S 248 of 1483 +a0049:=integrate(t0049,x) +--R +--R +--R (248) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x +--R / +--R 5 +--R 12d +--R Type: Union(Expression Integer,...) +--E 248 + +--S 249 of 1483 +m0049:=a0049-r0049 +--R +--R +--R 4 2 3 2 2 2 +--R - 13a d + 16a b c d - 6a b c +--R (249) ------------------------------ +--R 3 +--R 12d +--R Type: Expression Integer +--E 249 + +--S 250 of 1483 +d0049:=D(m0049,x) +--R +--R +--R (250) 0 +--R Type: Expression Integer +--E 250 + +--S 251 of 1483 +t0050:= (a+b*x)^5/(c+d*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (251) -------------------------------------------------- +--R d x + c +--R Type: Fraction Polynomial Integer +--E 251 + +--S 252 of 1483 +r0050:= b*(b*c-a*d)^4*x/d^5-1/2*(b*c-a*d)^3*(a+b*x)^2/d^4+_ + 1/3*(b*c-a*d)^2*(a+b*x)^3/d^3-1/4*(b*c-a*d)*(a+b*x)^4/d^2+_ + 1/5*(a+b*x)^5/d-(b*c-a*d)^5*log(c+d*x)/d^6 +--R +--R +--R (252) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x + 77a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b c d + 110a b c d - 30a b c d +--R / +--R 6 +--R 60d +--R Type: Expression Integer +--E 252 + +--S 253 of 1483 +a0050:=integrate(t0050,x) +--R +--R +--R (253) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x +--R / +--R 6 +--R 60d +--R Type: Union(Expression Integer,...) +--E 253 + +--S 254 of 1483 +m0050:=a0050-r0050 +--R +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R - 77a d + 145a b c d - 110a b c d + 30a b c +--R (254) ---------------------------------------------- +--R 4 +--R 60d +--R Type: Expression Integer +--E 254 + +--S 255 of 1483 +d0050:=D(m0050,x) +--R +--R +--R (255) 0 +--R Type: Expression Integer +--E 255 + +--S 256 of 1483 +t0051:= (a+b*x)^6/(c+d*x) +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (256) ------------------------------------------------------------- +--R d x + c +--R Type: Fraction Polynomial Integer +--E 256 + +--S 257 of 1483 +r0051:= -b*(b*c-a*d)^5*x/d^6+1/2*(b*c-a*d)^4*(a+b*x)^2/d^5-_ + 1/3*(b*c-a*d)^3*(a+b*x)^3/d^4+1/4*(b*c-a*d)^2*(a+b*x)^4/d^3-_ + 1/5*(b*c-a*d)*(a+b*x)^5/d^2+1/6*(a+b*x)^6/d+(b*c-a*d)^6*log(c+d*x)/d^7 +--R +--R +--R (257) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a d - 360a b c d + 900a b c d - 1200a b c d + 900a b c d +--R + +--R 5 5 6 6 +--R - 360a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b d x + (72a b d - 12b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b d - 90a b c d + 15b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b d - 300a b c d + 120a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b d - 600a b c d + 450a b c d - 180a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b d - 900a b c d + 1200a b c d - 900a b c d + 360a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 87a d - 222a b c d + 255a b c d - 140a b c d + 30a b c d +--R / +--R 7 +--R 60d +--R Type: Expression Integer +--E 257 + +--S 258 of 1483 +a0051:=integrate(t0051,x) +--R +--R +--R (258) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a d - 360a b c d + 900a b c d - 1200a b c d + 900a b c d +--R + +--R 5 5 6 6 +--R - 360a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b d x + (72a b d - 12b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b d - 90a b c d + 15b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b d - 300a b c d + 120a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b d - 600a b c d + 450a b c d - 180a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b d - 900a b c d + 1200a b c d - 900a b c d + 360a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R / +--R 7 +--R 60d +--R Type: Union(Expression Integer,...) +--E 258 + +--S 259 of 1483 +m0051:=a0051-r0051 +--R +--R +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 87a d + 222a b c d - 255a b c d + 140a b c d - 30a b c +--R (259) ------------------------------------------------------------ +--R 5 +--R 60d +--R Type: Expression Integer +--E 259 + +--S 260 of 1483 +d0051:=D(m0051,x) +--R +--R +--R (260) 0 +--R Type: Expression Integer +--E 260 + +--S 261 of 1483 +t0052:= (a+b*x)^3/(c+d*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (261) ---------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction Polynomial Integer +--E 261 + +--S 262 of 1483 +r0052:= -2*b^2*(b*c-a*d)*x/d^3+1/2*b*(a+b*x)^2/d^2+(b*c-a*d)^3/d^4/(c+d*x)+_ + 3*b*(b*c-a*d)^2*log(c+d*x)/d^4 +--R +--R +--R (262) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (a b d + 6a b c d - 4b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R 7a b c d - 6a b c d + 2b c +--R / +--R 5 4 +--R 2d x + 2c d +--R Type: Expression Integer +--E 262 + +--S 263 of 1483 +a0052:=integrate(t0052,x) +--R +--R +--R (263) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (6a b c d - 4b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 6a b c d + 2b c +--R / +--R 5 4 +--R 2d x + 2c d +--R Type: Union(Expression Integer,...) +--E 263 + +--S 264 of 1483 +m0052:=a0052-r0052 +--R +--R +--R 2 +--R a b +--R (264) - --- +--R 2 +--R 2d +--R Type: Expression Integer +--E 264 + +--S 265 of 1483 +d0052:=D(m0052,x) +--R +--R +--R (265) 0 +--R Type: Expression Integer +--E 265 + +--S 266 of 1483 +t0053:= (a+b*x)^4/(c+d*x)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (266) -------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction Polynomial Integer +--E 266 + +--S 267 of 1483 +r0053:= 3*b^2*(b*c-a*d)^2*x/d^4-b*(b*c-a*d)*(a+b*x)^2/d^3+_ + 1/3*b*(a+b*x)^3/d^2-(b*c-a*d)^4/d^5/(c+d*x)-_ + 4*b*(b*c-a*d)^3*log(c+d*x)/d^5 +--R +--R +--R (267) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 15a b c d - 24a b c d + 9b c d)x - 3a d + 16a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 21a b c d + 12a b c d - 3b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Expression Integer +--E 267 + +--S 268 of 1483 +a0053:=integrate(t0053,x) +--R +--R +--R (268) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b c d - 24a b c d + 9b c d)x - 3a d + 12a b c d - 18a b c d +--R + +--R 3 3 4 4 +--R 12a b c d - 3b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Union(Expression Integer,...) +--E 268 + +--S 269 of 1483 +m0053:=a0053-r0053 +--R +--R +--R 3 2 2 +--R - 4a b d + 3a b c +--R (269) ----------------- +--R 3 +--R 3d +--R Type: Expression Integer +--E 269 + +--S 270 of 1483 +d0053:=D(m0053,x) +--R +--R +--R (270) 0 +--R Type: Expression Integer +--E 270 + +--S 271 of 1483 +t0054:= (a+b*x)^5/(c+d*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (271) -------------------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction Polynomial Integer +--E 271 + +--S 272 of 1483 +r0054:= -4*b^2*(b*c-a*d)^3*x/d^5+3/2*b*(b*c-a*d)^2*(a+b*x)^2/d^4-_ + 2/3*b*(b*c-a*d)*(a+b*x)^3/d^3+1/4*b*(a+b*x)^4/d^2+_ + (b*c-a*d)^5/d^6/(c+d*x)+5*b*(b*c-a*d)^4*log(c+d*x)/d^6 +--R +--R +--R (272) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (29a b d + 76a b c d - 222a b c d + 180a b c d - 48b c d)x - 12a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 89a b c d - 164a b c d + 138a b c d - 60a b c d + 12b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Expression Integer +--E 272 + +--S 273 of 1483 +a0054:=integrate(t0054,x) +--R +--R +--R (273) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (120a b c d - 240a b c d + 180a b c d - 48b c d)x - 12a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 120a b c d + 120a b c d - 60a b c d + 12b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Union(Expression Integer,...) +--E 273 + +--S 274 of 1483 +m0054:=a0054-r0054 +--R +--R +--R 4 2 3 2 2 3 2 +--R - 29a b d + 44a b c d - 18a b c +--R (274) --------------------------------- +--R 4 +--R 12d +--R Type: Expression Integer +--E 274 + +--S 275 of 1483 +d0054:=D(m0054,x) +--R +--R +--R (275) 0 +--R Type: Expression Integer +--E 275 + +--S 276 of 1483 +t0055:= (a+b*x)^6/(c+d*x)^2 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (276) ------------------------------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction Polynomial Integer +--E 276 + +--S 277 of 1483 +r0055:= 5*b^2*(b*c-a*d)^4*x/d^6-2*b*(b*c-a*d)^3*(a+b*x)^2/d^5+_ + b*(b*c-a*d)^2*(a+b*x)^3/d^4-1/2*b*(b*c-a*d)*(a+b*x)^4/d^3+_ + 1/5*b*(a+b*x)^5/d^2-(b*c-a*d)^6/d^7/(c+d*x)-_ + 6*b*(b*c-a*d)^5*log(c+d*x)/d^7 +--R +--R +--R (277) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b c d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 6 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b d x + (15a b d - 3b c d )x + (50a b d - 25a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b d - 100a b c d + 50a b c d - 10b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b d - 300a b c d + 300a b c d - 150a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 37a b d + 65a b c d - 330a b c d + 430a b c d - 240a b c d +--R + +--R 6 5 +--R 50b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a d + 97a b c d - 235a b c d + 270a b c d - 170a b c d +--R + +--R 5 5 6 6 +--R 60a b c d - 10b c +--R / +--R 8 7 +--R 10d x + 10c d +--R Type: Expression Integer +--E 277 + +--S 278 of 1483 +a0055:=integrate(t0055,x) +--R +--R +--R (278) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b c d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 6 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b d x + (15a b d - 3b c d )x + (50a b d - 25a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b d - 100a b c d + 50a b c d - 10b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b d - 300a b c d + 300a b c d - 150a b c d + 30b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (150a b c d - 400a b c d + 450a b c d - 240a b c d + 50b c d)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a d + 60a b c d - 150a b c d + 200a b c d - 150a b c d +--R + +--R 5 5 6 6 +--R 60a b c d - 10b c +--R / +--R 8 7 +--R 10d x + 10c d +--R Type: Union(Expression Integer,...) +--E 278 + +--S 279 of 1483 +m0055:=a0055-r0055 +--R +--R +--R 5 3 4 2 2 3 3 2 2 4 3 +--R - 37a b d + 85a b c d - 70a b c d + 20a b c +--R (279) ---------------------------------------------- +--R 5 +--R 10d +--R Type: Expression Integer +--E 279 + +--S 280 of 1483 +d0055:=D(m0055,x) +--R +--R +--R (280) 0 +--R Type: Expression Integer +--E 280 + +--S 281 of 1483 +t0056:= (a+b*x)^4/(c+d*x)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (281) -------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction Polynomial Integer +--E 281 + +--S 282 of 1483 +r0056:= -3*b^3*(b*c-a*d)*x/d^4+1/2*b^2*(a+b*x)^2/d^3-_ + 1/2*(b*c-a*d)^4/d^5/(c+d*x)^2+4*b*(b*c-a*d)^3/d^5/(c+d*x)+_ + 6*b^2*(b*c-a*d)^2*log(c+d*x)/d^5 +--R +--R +--R (282) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (a b d + 16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 26a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 19a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Expression Integer +--E 282 + +--S 283 of 1483 +a0056:=integrate(t0056,x) +--R +--R +--R (283) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 24a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression Integer,...) +--E 283 + +--S 284 of 1483 +m0056:=a0056-r0056 +--R +--R +--R 2 2 +--R a b +--R (284) - ---- +--R 3 +--R 2d +--R Type: Expression Integer +--E 284 + +--S 285 of 1483 +d0056:=D(m0056,x) +--R +--R +--R (285) 0 +--R Type: Expression Integer +--E 285 + +--S 286 of 1483 +t0057:= (a+b*x)^5/(c+d*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (286) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction Polynomial Integer +--E 286 + +--S 287 of 1483 +r0057:= 6*b^3*(b*c-a*d)^2*x/d^5-3/2*b^2*(b*c-a*d)*(a+b*x)^2/d^4+_ + 1/3*b^2*(a+b*x)^3/d^3+1/2*(b*c-a*d)^5/d^6/(c+d*x)^2-_ + 5*b*(b*c-a*d)^4/d^6/(c+d*x)-10*b^2*(b*c-a*d)^3*log(c+d*x)/d^6 +--R +--R +--R (287) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (11a b d + 111a b c d - 165a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 142a b c d - 138a b c d + 30a b c d + 6b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 101a b c d - 159a b c d + 105a b c d - 27b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Expression Integer +--E 287 + +--S 288 of 1483 +a0057:=integrate(t0057,x) +--R +--R +--R (288) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b c d - 165a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 120a b c d - 120a b c d + 30a b c d + 6b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 90a b c d - 150a b c d + 105a b c d - 27b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Union(Expression Integer,...) +--E 288 + +--S 289 of 1483 +m0057:=a0057-r0057 +--R +--R +--R 3 2 2 3 +--R - 11a b d + 9a b c +--R (289) ------------------ +--R 4 +--R 6d +--R Type: Expression Integer +--E 289 + +--S 290 of 1483 +d0057:=D(m0057,x) +--R +--R +--R (290) 0 +--R Type: Expression Integer +--E 290 + +--S 291 of 1483 +t0058:= (a+b*x)^6/(c+d*x)^3 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (291) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction Polynomial Integer +--E 291 + +--S 292 of 1483 +r0058:= -10*b^3*(b*c-a*d)^3*x/d^6+3*b^2*(b*c-a*d)^2*(a+b*x)^2/d^5-_ + b^2*(b*c-a*d)*(a+b*x)^3/d^4+1/4*b^2*(a+b*x)^4/d^3-_ + 1/2*(b*c-a*d)^6/d^7/(c+d*x)^2+6*b*(b*c-a*d)^5/d^7/(c+d*x)+_ + 15*b^2*(b*c-a*d)^4*log(c+d*x)/d^7 +--R +--R +--R (292) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (17a b d + 132a b c d - 318a b c d + 252a b c d - 68b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 154a b c d - 216a b c d + 84a b c d + 24a b c d +--R + +--R 6 5 +--R - 16b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 107a b c d - 228a b c d + 222a b c d +--R + +--R 5 5 6 6 +--R - 108a b c d + 22b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Expression Integer +--E 292 + +--S 293 of 1483 +a0058:=integrate(t0058,x) +--R +--R +--R (293) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b c d - 330a b c d + 252a b c d - 68b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 120a b c d - 160a b c d + 60a b c d + 24a b c d +--R + +--R 6 5 +--R - 16b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 90a b c d - 200a b c d + 210a b c d +--R + +--R 5 5 6 6 +--R - 108a b c d + 22b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Union(Expression Integer,...) +--E 293 + +--S 294 of 1483 +m0058:=a0058-r0058 +--R +--R +--R 4 2 2 3 3 2 4 2 +--R - 17a b d + 28a b c d - 12a b c +--R (294) --------------------------------- +--R 5 +--R 4d +--R Type: Expression Integer +--E 294 + +--S 295 of 1483 +d0058:=D(m0058,x) +--R +--R +--R (295) 0 +--R Type: Expression Integer +--E 295 + +--S 296 of 1483 +t0059:= (a+b*x)^4/(c+d*x)^8 +--R +--R +--R (296) +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 296 + +--S 297 of 1483 +r0059:= -1/105*(a+b*x)^5*(21*b^2*c^2-35*a*b*c*d+15*a^2*d^2+7*d*b^2*c*x-_ + 5*b*a*d^2*x+d^2*b^2*x^2)/(-b*c+a*d)^3/(c+d*x)^7 +--R +--R +--R (297) +--R 1 7 2 7 1 7 6 1 7 2 5 1 3 4 2 2 5 6 2 4 +--R - --- b d x - -- b c d x - - b c x + (- - a b d + a b c d - a b c )x +--R 105 15 5 3 +--R + +--R 4 3 2 8 3 4 2 5 2 3 6 5 2 2 4 3 3 4 2 2 +--R (- a b d + - a b c d - 2a b c )x + (- - a b d + 3a b c d - 2a b c )x +--R 3 5 +--R + +--R 2 6 2 8 5 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (- - a b d + - a b c d - a b c )x - - a d + - a b c d - - a b c +--R 3 5 7 3 5 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a d - 3a b c d + 3a b c d - b c d )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a c d - 21a b c d + 21a b c d - 7b c d )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a c d - 21a b c d + 21a b c d - 7b c d)x + a c d - 3a b c d +--R + +--R 2 9 3 10 +--R 3a b c d - b c +--R Type: Fraction Polynomial Fraction Integer +--E 297 + +--S 298 of 1483 +a0059:=integrate(t0059,x) +--R +--R +--R (298) +--R 4 4 4 3 4 4 3 3 +--R - 35b d x + (- 105a b d - 35b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 126a b d - 63a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 70a b d - 42a b c d - 21a b c d - 7b c d)x - 15a d - 10a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b c d - 3a b c d - b c +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 7 2 6 6 7 5 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression Integer,...) +--E 298 + +--S 299 of 1483 +m0059:=a0059-r0059 +--R +--R +--R 7 +--R b +--R (299) ----------------------------------------------- +--R 3 8 2 7 2 2 6 3 3 5 +--R 105a d - 315a b c d + 315a b c d - 105b c d +--R Type: Expression Integer +--E 299 + +--S 300 of 1483 +d0059:=D(m0059,x) +--R +--R +--R (300) 0 +--R Type: Expression Integer +--E 300 + +--S 301 of 1483 +t0060:= (a+b*x)^5/(c+d*x)^8 +--R +--R +--R (301) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 301 + +--S 302 of 1483 +r0060:= -1/42*(a+b*x)^6*(-7*b*c+6*a*d-d*b*x)/(-b*c+a*d)^2/(c+d*x)^7 +--R +--R +--R (302) +--R 1 7 7 1 7 6 1 2 5 6 5 5 3 4 5 2 5 4 +--R -- b d x + - b c x + (- - a b d + a b c)x + (- - a b d + - a b c)x +--R 42 6 2 3 2 +--R + +--R 5 4 3 10 3 4 3 5 2 5 4 3 2 5 6 5 2 +--R (- - a b d + -- a b c)x + (- 2a b d + - a b c)x + (- - a b d + a b c)x +--R 2 3 2 6 +--R + +--R 1 7 1 6 +--R - - a d + - a b c +--R 7 6 +--R / +--R 2 9 8 2 2 7 7 2 8 2 7 2 3 6 6 +--R (a d - 2a b c d + b c d )x + (7a c d - 14a b c d + 7b c d )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (21a c d - 42a b c d + 21b c d )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 5 4 6 3 2 7 2 2 2 6 3 7 2 2 8 +--R (21a c d - 42a b c d + 21b c d )x + (7a c d - 14a b c d + 7b c d)x +--R + +--R 2 7 2 8 2 9 +--R a c d - 2a b c d + b c +--R Type: Fraction Polynomial Fraction Integer +--E 302 + +--S 303 of 1483 +a0060:=integrate(t0060,x) +--R +--R +--R (303) +--R 5 5 5 4 5 5 4 4 +--R - 21b d x + (- 70a b d - 35b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 105a b d - 70a b c d - 35b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 84a b d - 63a b c d - 42a b c d - 21b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 35a b d - 28a b c d - 21a b c d - 14a b c d - 7b c d)x - 6a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b c d - 4a b c d - 3a b c d - 2a b c d - b c +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 +--R 42d x + 294c d x + 882c d x + 1470c d x + 1470c d x + 882c d x +--R + +--R 6 7 7 6 +--R 294c d x + 42c d +--R Type: Union(Expression Integer,...) +--E 303 + +--S 304 of 1483 +m0060:=a0060-r0060 +--R +--R +--R 7 +--R b +--R (304) - ------------------------------ +--R 2 8 7 2 2 6 +--R 42a d - 84a b c d + 42b c d +--R Type: Expression Integer +--E 304 + +--S 305 of 1483 +d0060:=D(m0060,x) +--R +--R +--R (305) 0 +--R Type: Expression Integer +--E 305 + +--S 306 of 1483 +t0061:= (a+b*x)^6/(c+d*x)^8 +--R +--R +--R (306) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 306 + +--S 307 of 1483 +r0061:= 1/7*(a+b*x)^7/(b*c-a*d)/(c+d*x)^7 +--R +--R +--R (307) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 1 7 +--R - - b x - a b x - 3a b x - 5a b x - 5a b x - 3a b x - a b x - - a +--R 7 7 +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (a d - b c d )x + (7a c d - 7b c d )x + (21a c d - 21b c d )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (35a c d - 35b c d )x + (35a c d - 35b c d )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (21a c d - 21b c d )x + (7a c d - 7b c d)x + a c d - b c +--R Type: Fraction Polynomial Fraction Integer +--E 307 + +--S 308 of 1483 +a0061:=integrate(t0061,x) +--R +--R +--R (308) +--R 6 6 6 5 6 6 5 5 +--R - 7b d x + (- 21a b d - 21b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b d - 35a b c d - 35b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 35a b d - 35a b c d - 35a b c d - 35b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 21a b d - 21a b c d - 21a b c d - 21a b c d - 21b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 7a b d - 7a b c d - 7a b c d - 7a b c d - 7a b c d - 7b c d)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - b c +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 7d x + 49c d x + 147c d x + 245c d x + 245c d x + 147c d x +--R + +--R 6 8 7 7 +--R 49c d x + 7c d +--R Type: Union(Expression Integer,...) +--E 308 + +--S 309 of 1483 +m0061:=a0061-r0061 +--R +--R +--R 7 +--R b +--R (309) --------------- +--R 8 7 +--R 7a d - 7b c d +--R Type: Expression Integer +--E 309 + +--S 310 of 1483 +d0061:=D(m0061,x) +--R +--R +--R (310) 0 +--R Type: Expression Integer +--E 310 + +--S 311 of 1483 +t0062:= (a+b*x)^7/(c+d*x)^8 +--R +--R +--R (311) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 311 + +--S 312 of 1483 +r0062:= 1/7*(b*c-a*d)^7/d^8/(c+d*x)^7-7/6*b*(b*c-a*d)^6/d^8/(c+d*x)^6+_ + 21/5*b^2*(b*c-a*d)^5/d^8/(c+d*x)^5-_ + 35/4*b^3*(b*c-a*d)^4/d^8/(c+d*x)^4+_ + 35/3*b^4*(b*c-a*d)^3/d^8/(c+d*x)^3-_ + 21/2*b^5*(b*c-a*d)^2/d^8/(c+d*x)^2+_ + 7*b^6*(b*c-a*d)/d^8/(c+d*x)+b^7*log(c+d*x)/d^8 +--R +--R +--R (312) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Expression Integer +--E 312 + +--S 313 of 1483 +a0062:=integrate(t0062,x) +--R +--R +--R (313) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Union(Expression Integer,...) +--E 313 + +--S 314 of 1483 +m0062:=a0062-r0062 +--R +--R +--R (314) 0 +--R Type: Expression Integer +--E 314 + +--S 315 of 1483 +d0062:=D(m0062,x) +--R +--R +--R (315) 0 +--R Type: Expression Integer +--E 315 + +--S 316 of 1483 +t0063:= (a+b*x)^8/(c+d*x)^8 +--R +--R +--R (316) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 316 + +--S 317 of 1483 +r0063:= b^8*x/d^8-1/7*(b*c-a*d)^8/d^9/(c+d*x)^7+_ + 4/3*b*(b*c-a*d)^7/d^9/(c+d*x)^6-28/5*b^2*(b*c-a*d)^6/d^9/(c+d*x)^5+_ + 14*b^3*(b*c-a*d)^5/d^9/(c+d*x)^4-70/3*b^4*(b*c-a*d)^4/d^9/(c+d*x)^3+_ + 28*b^5*(b*c-a*d)^3/d^9/(c+d*x)^2-28*b^6*(b*c-a*d)^2/d^9/(c+d*x)-_ + 8*b^7*(b*c-a*d)*log(c+d*x)/d^9 +--R +--R +--R (317) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Expression Integer +--E 317 + +--S 318 of 1483 +a0063:=integrate(t0063,x) +--R +--R +--R (318) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression Integer,...) +--E 318 + +--S 319 of 1483 +m0063:=a0063-r0063 +--R +--R +--R (319) 0 +--R Type: Expression Integer +--E 319 + +--S 320 of 1483 +d0063:=D(m0063,x) +--R +--R +--R (320) 0 +--R Type: Expression Integer +--E 320 + +--S 321 of 1483 +t0064:= (a+b*x)^9/(c+d*x)^8 +--R +--R +--R (321) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 321 + +--S 322 of 1483 +r0064:= -8*b^8*(b*c-a*d)*x/d^9+1/2*b^7*(a+b*x)^2/d^8+_ + 1/7*(b*c-a*d)^9/d^10/(c+d*x)^7-3/2*b*(b*c-a*d)^8/d^10/(c+d*x)^6+_ + 36/5*b^2*(b*c-a*d)^7/d^10/(c+d*x)^5-_ + 21*b^3*(b*c-a*d)^6/d^10/(c+d*x)^4+42*b^4*(b*c-a*d)^5/d^10/(c+d*x)^3-_ + 63*b^5*(b*c-a*d)^4/d^10/(c+d*x)^2+84*b^6*(b*c-a*d)^3/d^10/(c+d*x)+_ + 36*b^7*(b*c-a*d)^2*log(c+d*x)/d^10 +--R +--R +--R (322) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 +--R 35b d x + (630a b d - 315b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (35a b d + 4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17885a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 80115a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 162925a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 184975a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 121569a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43463a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6569a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Expression Integer +--E 322 + +--S 323 of 1483 +a0064:=integrate(t0064,x) +--R +--R +--R (323) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 8 8 9 2 7 7 +--R 35b d x + (630a b d - 315b c d )x + (4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17640a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 79380a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 161700a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 183750a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 120834a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43218a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6534a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Union(Expression Integer,...) +--E 323 + +--S 324 of 1483 +m0064:=a0064-r0064 +--R +--R +--R 2 7 +--R a b +--R (324) - ---- +--R 8 +--R 2d +--R Type: Expression Integer +--E 324 + +--S 325 of 1483 +d0064:=D(m0064,x) +--R +--R +--R (325) 0 +--R Type: Expression Integer +--E 325 + +--S 326 of 1483 +t0065:= (a+b*x)^7/(c+d*x) +--R +--R +--R (326) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R d x + c +--R Type: Fraction Polynomial Integer +--E 326 + +--S 327 of 1483 +r0065:= b*(b*c-a*d)^6*x/d^7-1/2*(b*c-a*d)^5*(a+b*x)^2/d^6+_ + 1/3*(b*c-a*d)^4*(a+b*x)^3/d^5-1/4*(b*c-a*d)^3*(a+b*x)^4/d^4+_ + 1/5*(b*c-a*d)^2*(a+b*x)^5/d^3-1/6*(b*c-a*d)*(a+b*x)^6/d^2+_ + 1/7*(a+b*x)^7/d-(b*c-a*d)^7*log(c+d*x)/d^8 +--R +--R +--R (327) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2940a b c d + 8820a b c d - 14700a b c d + 14700a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b c d + 2940a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (490a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b d - 588a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b d - 2205a b c d + 735a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b d - 4900a b c d + 2940a b c d - 980a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b d - 7350a b c d + 7350a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R 1470a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b d - 8820a b c d + 14700a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b c d - 2940a b c d + 420b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a d - 2163a b c d + 3339a b c d - 2765a b c d + 1190a b c d +--R + +--R 2 5 5 2 +--R - 210a b c d +--R / +--R 8 +--R 420d +--R Type: Expression Integer +--E 327 + +--S 328 of 1483 +a0065:=integrate(t0065,x) +--R +--R +--R (328) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2940a b c d + 8820a b c d - 14700a b c d + 14700a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b c d + 2940a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (490a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b d - 588a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b d - 2205a b c d + 735a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b d - 4900a b c d + 2940a b c d - 980a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b d - 7350a b c d + 7350a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R 1470a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b d - 8820a b c d + 14700a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b c d - 2940a b c d + 420b c d +--R * +--R x +--R / +--R 8 +--R 420d +--R Type: Union(Expression Integer,...) +--E 328 + +--S 329 of 1483 +m0065:=a0065-r0065 +--R +--R +--R (329) +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 669a d + 2163a b c d - 3339a b c d + 2765a b c d - 1190a b c d +--R + +--R 2 5 5 +--R 210a b c +--R / +--R 6 +--R 420d +--R Type: Expression Integer +--E 329 + +--S 330 of 1483 +d0065:=D(m0065,x) +--R +--R +--R (330) 0 +--R Type: Expression Integer +--E 330 + +--S 331 of 1483 +t0066:= (a+b*x)^7/(c+d*x)^2 +--R +--R +--R (331) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction Polynomial Integer +--E 331 + +--S 332 of 1483 +r0066:= -6*b^2*(b*c-a*d)^5*x/d^7+5/2*b*(b*c-a*d)^4*(a+b*x)^2/d^6-_ + 4/3*b*(b*c-a*d)^3*(a+b*x)^3/d^5+3/4*b*(b*c-a*d)^2*(a+b*x)^4/d^4-_ + 2/5*b*(b*c-a*d)*(a+b*x)^5/d^3+1/6*b*(a+b*x)^6/d^2+_ + (b*c-a*d)^7/d^8/(c+d*x)+7*b*(b*c-a*d)^6*log(c+d*x)/d^8 +--R +--R +--R (332) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b c d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b c d - 2520a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (84a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b d - 126a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b d - 525a b c d + 210a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b d - 1400a b c d + 1050a b c d - 420a b c d + 70b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 3150a b c d + 4200a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 1260a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 309a b d + 306a b c d - 3015a b c d + 5620a b c d - 4890a b c d +--R + +--R 6 5 2 7 6 +--R 2100a b c d - 360b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 729a b c d - 2214a b c d + 3285a b c d - 2780a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1410a b c d - 420a b c d + 60b c +--R / +--R 9 8 +--R 60d x + 60c d +--R Type: Expression Integer +--E 332 + +--S 333 of 1483 +a0066:=integrate(t0066,x) +--R +--R +--R (333) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b c d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b c d - 2520a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (84a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b d - 126a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b d - 525a b c d + 210a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b d - 1400a b c d + 1050a b c d - 420a b c d + 70b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 3150a b c d + 4200a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 1260a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b c d - 4200a b c d + 6300a b c d - 5040a b c d +--R + +--R 6 5 2 7 6 +--R 2100a b c d - 360b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 420a b c d - 1260a b c d + 2100a b c d - 2100a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1260a b c d - 420a b c d + 60b c +--R / +--R 9 8 +--R 60d x + 60c d +--R Type: Union(Expression Integer,...) +--E 333 + +--S 334 of 1483 +m0066:=a0066-r0066 +--R +--R +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R - 309a b d + 954a b c d - 1185a b c d + 680a b c d - 150a b c +--R (334) ----------------------------------------------------------------- +--R 6 +--R 60d +--R Type: Expression Integer +--E 334 + +--S 335 of 1483 +d0066:=D(m0066,x) +--R +--R +--R (335) 0 +--R Type: Expression Integer +--E 335 + +--S 336 of 1483 +t0067:= (a+b*x)^7/(c+d*x)^3 +--R +--R +--R (336) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction Polynomial Integer +--E 336 + +--S 337 of 1483 +r0067:= 15*b^3*(b*c-a*d)^4*x/d^7-5*b^2*(b*c-a*d)^3*(a+b*x)^2/d^6+_ + 2*b^2*(b*c-a*d)^2*(a+b*x)^3/d^5-3/4*b^2*(b*c-a*d)*(a+b*x)^4/d^4+_ + 1/5*b^2*(a+b*x)^5/d^3+1/2*(b*c-a*d)^7/d^8/(c+d*x)^2-_ + 7*b*(b*c-a*d)^6/d^8/(c+d*x)-21*b^2*(b*c-a*d)^5*log(c+d*x)/d^8 +--R +--R +--R (337) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R 2100a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b c d - 4200a b c d + 8400a b c d - 8400a b c d +--R + +--R 6 5 2 7 6 +--R 4200a b c d - 840b c d +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b c d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 6 7 7 +--R 2100a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b d x + (35a b d - 7b c d )x + (140a b d - 70a b c d + 14b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b d - 350a b c d + 175a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b d - 1400a b c d + 1400a b c d - 700a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 159a b d + 1005a b c d - 3510a b c d + 4310a b c d - 2380a b c d +--R + +--R 7 5 2 +--R 500b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b d + 1158a b c d - 2190a b c d + 1380a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 220a b c d - 560a b c d + 160b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 70a b c d + 789a b c d - 2145a b c d + 2790a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1990a b c d + 770a b c d - 130b c +--R / +--R 10 2 9 2 8 +--R 20d x + 40c d x + 20c d +--R Type: Expression Integer +--E 337 + +--S 338 of 1483 +a0067:=integrate(t0067,x) +--R +--R +--R (338) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R 2100a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b c d - 4200a b c d + 8400a b c d - 8400a b c d +--R + +--R 6 5 2 7 6 +--R 4200a b c d - 840b c d +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b c d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 6 7 7 +--R 2100a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b d x + (35a b d - 7b c d )x + (140a b d - 70a b c d + 14b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b d - 350a b c d + 175a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b d - 1400a b c d + 1400a b c d - 700a b c d + 140b c d )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b c d - 3850a b c d + 4410a b c d - 2380a b c d + 500b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b d + 840a b c d - 1400a b c d + 700a b c d + 420a b c d +--R + +--R 6 5 2 7 6 +--R - 560a b c d + 160b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 70a b c d + 630a b c d - 1750a b c d + 2450a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1890a b c d + 770a b c d - 130b c +--R / +--R 10 2 9 2 8 +--R 20d x + 40c d x + 20c d +--R Type: Union(Expression Integer,...) +--E 338 + +--S 339 of 1483 +m0067:=a0067-r0067 +--R +--R +--R 5 2 3 4 3 2 3 4 2 2 5 3 +--R - 159a b d + 395a b c d - 340a b c d + 100a b c +--R (339) -------------------------------------------------- +--R 6 +--R 20d +--R Type: Expression Integer +--E 339 + +--S 340 of 1483 +d0067:=D(m0067,x) +--R +--R +--R (340) 0 +--R Type: Expression Integer +--E 340 + +--S 341 of 1483 +t0068:= (a+b*x)^7/(c+d*x)^4 +--R +--R +--R (341) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R Type: Fraction Polynomial Integer +--E 341 + +--S 342 of 1483 +r0068:= -20*b^4*(b*c-a*d)^3*x/d^7+5*b^3*(b*c-a*d)^2*(a+b*x)^2/d^6-_ + 4/3*b^3*(b*c-a*d)*(a+b*x)^3/d^5+1/4*b^3*(a+b*x)^4/d^4+_ + 1/3*(b*c-a*d)^7/d^8/(c+d*x)^3-7/2*b*(b*c-a*d)^6/d^8/(c+d*x)^2+_ + 21*b^2*(b*c-a*d)^5/d^8/(c+d*x)+35*b^3*(b*c-a*d)^4*log(c+d*x)/d^8 +--R +--R +--R (342) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 5 2 +--R 1260b c d +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 6 +--R 1260b c d +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b d x + (28a b d - 7b c d )x + (126a b d - 84a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 630a b c d + 420a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (79a b d + 1124a b c d - 2586a b c d + 2044a b c d - 556b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b d + 1497a b c d - 1668a b c d - 198a b c d +--R + +--R 6 4 3 7 5 2 +--R 1092a b c d - 408b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b d - 252a b c d + 2127a b c d - 4188a b c d + 3582a b c d +--R + +--R 6 5 2 7 6 +--R - 1428a b c d + 222b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a d - 14a b c d - 84a b c d + 849a b c d - 1956a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 2034a b c d - 1036a b c d + 214b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12d x + 36c d x + 36c d x + 12c d +--R Type: Expression Integer +--E 342 + +--S 343 of 1483 +a0068:=integrate(t0068,x) +--R +--R +--R (343) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 5 2 +--R 1260b c d +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 6 +--R 1260b c d +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b d x + (28a b d - 7b c d )x + (126a b d - 84a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 630a b c d + 420a b c d - 105b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b c d - 2646a b c d + 2044a b c d - 556b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b d + 1260a b c d - 1260a b c d - 378a b c d +--R + +--R 6 4 3 7 5 2 +--R 1092a b c d - 408b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b d - 252a b c d + 1890a b c d - 3780a b c d + 3402a b c d +--R + +--R 6 5 2 7 6 +--R - 1428a b c d + 222b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a d - 14a b c d - 84a b c d + 770a b c d - 1820a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1974a b c d - 1036a b c d + 214b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12d x + 36c d x + 36c d x + 12c d +--R Type: Union(Expression Integer,...) +--E 343 + +--S 344 of 1483 +m0068:=a0068-r0068 +--R +--R +--R 4 3 2 3 4 2 5 2 +--R - 79a b d + 136a b c d - 60a b c +--R (344) ---------------------------------- +--R 6 +--R 12d +--R Type: Expression Integer +--E 344 + +--S 345 of 1483 +d0068:=D(m0068,x) +--R +--R +--R (345) 0 +--R Type: Expression Integer +--E 345 + +--S 346 of 1483 +t0069:= (a+b*x)^7/(c+d*x)^5 +--R +--R +--R (346) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c +--R Type: Fraction Polynomial Integer +--E 346 + +--S 347 of 1483 +r0069:= 15*b^5*(b*c-a*d)^2*x/d^7-5/2*b^4*(b*c-a*d)*(a+b*x)^2/d^6+_ + 1/3*b^4*(a+b*x)^3/d^5+1/4*(b*c-a*d)^7/d^8/(c+d*x)^4-_ + 7/3*b*(b*c-a*d)^6/d^8/(c+d*x)^3+21/2*b^2*(b*c-a*d)^5/d^8/(c+d*x)^2-_ + 35*b^3*(b*c-a*d)^4/d^8/(c+d*x)-35*b^4*(b*c-a*d)^3*log(c+d*x)/d^8 +--R +--R +--R (347) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 1260a b c d + 1260a b c d - 420b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d )x +--R + +--R 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (2520a b c d - 7560a b c d + 7560a b c d - 2520b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d)x +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1260a b c d + 1260a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (42a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (252a b d - 252a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (34a b d + 978a b c d - 1428a b c d + 556b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d + 1816a b c d - 1128a b c d - 672a b c d + 544b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 126a b d - 630a b c d + 3984a b c d - 5472a b c d +--R + +--R 6 4 3 7 5 2 +--R 2772a b c d - 444b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 28a b d - 84a b c d - 420a b c d + 3216a b c d - 5328a b c d +--R + +--R 6 5 2 7 6 +--R 3528a b c d - 856b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 3a d - 7a b c d - 21a b c d - 105a b c d + 909a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1647a b c d + 1197a b c d - 319b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12d x + 48c d x + 72c d x + 48c d x + 12c d +--R Type: Expression Integer +--E 347 + +--S 348 of 1483 +a0069:=integrate(t0069,x) +--R +--R +--R (348) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 1260a b c d + 1260a b c d - 420b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d )x +--R + +--R 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (2520a b c d - 7560a b c d + 7560a b c d - 2520b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d)x +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1260a b c d + 1260a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (42a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (252a b d - 252a b c d + 84b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (1008a b c d - 1428a b c d + 556b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d + 1680a b c d - 1008a b c d - 672a b c d + 544b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 126a b d - 630a b c d + 3780a b c d - 5292a b c d +--R + +--R 6 4 3 7 5 2 +--R 2772a b c d - 444b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 28a b d - 84a b c d - 420a b c d + 3080a b c d - 5208a b c d +--R + +--R 6 5 2 7 6 +--R 3528a b c d - 856b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 3a d - 7a b c d - 21a b c d - 105a b c d + 875a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1617a b c d + 1197a b c d - 319b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12d x + 48c d x + 72c d x + 48c d x + 12c d +--R Type: Union(Expression Integer,...) +--E 348 + +--S 349 of 1483 +m0069:=a0069-r0069 +--R +--R +--R 3 4 2 5 +--R - 17a b d + 15a b c +--R (349) ------------------- +--R 6 +--R 6d +--R Type: Expression Integer +--E 349 + +--S 350 of 1483 +d0069:=D(m0069,x) +--R +--R +--R (350) 0 +--R Type: Expression Integer +--E 350 + +--S 351 of 1483 +t0070:= (a+b*x)^7/(c+d*x)^6 +--R +--R +--R (351) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R d x + 6c d x + 15c d x + 20c d x + 15c d x + 6c d x + c +--R Type: Fraction Polynomial Integer +--E 351 + +--S 352 of 1483 +r0070:= -6*b^6*(b*c-a*d)*x/d^7+1/2*b^5*(a+b*x)^2/d^6+_ + 1/5*(b*c-a*d)^7/d^8/(c+d*x)^5-7/4*b*(b*c-a*d)^6/d^8/(c+d*x)^4+_ + 7*b^2*(b*c-a*d)^5/d^8/(c+d*x)^3-35/2*b^3*(b*c-a*d)^4/d^8/(c+d*x)^2+_ + 35*b^4*(b*c-a*d)^3/d^8/(c+d*x)+21*b^5*(b*c-a*d)^2*log(c+d*x)/d^8 +--R +--R +--R (352) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (2100a b c d - 4200a b c d + 2100b c d )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 3 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 2 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 5 5 2 6 6 +--R (2100a b c d - 4200a b c d + 2100b c d)x + 420a b c d - 840a b c d +--R + +--R 7 7 +--R 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (140a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (10a b d + 700a b c d - 500b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 700a b d + 2150a b c d - 700a b c d - 400b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 350a b d - 1400a b c d + 6400a b c d - 5600a b c d + 1300b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 140a b d - 350a b c d - 1400a b c d + 7800a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8400a b c d + 2700b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 35a b d - 70a b c d - 175a b c d - 700a b c d + 4425a b c d +--R + +--R 6 5 2 7 6 +--R - 5250a b c d + 1875b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 4a d - 7a b c d - 14a b c d - 35a b c d - 140a b c d + 969a b c d +--R + +--R 6 6 7 7 +--R - 1218a b c d + 459b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20d x + 100c d x + 200c d x + 200c d x + 100c d x + 20c d +--R Type: Expression Integer +--E 352 + +--S 353 of 1483 +a0070:=integrate(t0070,x) +--R +--R +--R (353) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (2100a b c d - 4200a b c d + 2100b c d )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 3 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 2 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 5 5 2 6 6 +--R (2100a b c d - 4200a b c d + 2100b c d)x + 420a b c d - 840a b c d +--R + +--R 7 7 +--R 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 6 6 7 2 5 5 +--R 10b d x + (140a b d - 70b c d )x + (700a b c d - 500b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 700a b d + 2100a b c d - 700a b c d - 400b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 350a b d - 1400a b c d + 6300a b c d - 5600a b c d + 1300b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 140a b d - 350a b c d - 1400a b c d + 7700a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8400a b c d + 2700b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 35a b d - 70a b c d - 175a b c d - 700a b c d + 4375a b c d +--R + +--R 6 5 2 7 6 +--R - 5250a b c d + 1875b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 4a d - 7a b c d - 14a b c d - 35a b c d - 140a b c d + 959a b c d +--R + +--R 6 6 7 7 +--R - 1218a b c d + 459b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20d x + 100c d x + 200c d x + 200c d x + 100c d x + 20c d +--R Type: Union(Expression Integer,...) +--E 353 + +--S 354 of 1483 +m0070:=a0070-r0070 +--R +--R +--R 2 5 +--R a b +--R (354) - ---- +--R 6 +--R 2d +--R Type: Expression Integer +--E 354 + +--S 355 of 1483 +d0070:=D(m0070,x) +--R +--R +--R (355) 0 +--R Type: Expression Integer +--E 355 + +--S 356 of 1483 +t0071:= (a+b*x)^7/(c+d*x)^7 +--R +--R +--R (356) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R Type: Fraction Polynomial Integer +--E 356 + +--S 357 of 1483 +r0071:= b^7*x/d^7+1/6*(b*c-a*d)^7/d^8/(c+d*x)^6-_ + 7/5*b*(b*c-a*d)^6/d^8/(c+d*x)^5+21/4*b^2*(b*c-a*d)^5/d^8/(c+d*x)^4-_ + 35/3*b^3*(b*c-a*d)^4/d^8/(c+d*x)^3+_ + 35/2*b^4*(b*c-a*d)^3/d^8/(c+d*x)^2-21*b^5*(b*c-a*d)^2/d^8/(c+d*x)-_ + 7*b^6*(b*c-a*d)*log(c+d*x)/d^8 +--R +--R +--R (357) +--R 6 7 7 6 6 6 6 7 2 5 5 +--R (420a b d - 420b c d )x + (2520a b c d - 2520b c d )x +--R + +--R 6 2 5 7 3 4 4 6 3 4 7 4 3 3 +--R (6300a b c d - 6300b c d )x + (8400a b c d - 8400b c d )x +--R + +--R 6 4 3 7 5 2 2 6 5 2 7 6 +--R (6300a b c d - 6300b c d )x + (2520a b c d - 2520b c d)x +--R + +--R 6 6 7 7 +--R 420a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360b c d x + (- 1260a b d + 2520a b c d - 360b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1050a b d - 3150a b c d + 9450a b c d - 4050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 700a b d - 1400a b c d - 4200a b c d + 15400a b c d +--R + +--R 7 4 3 +--R - 8200b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 315a b d - 525a b c d - 1050a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 13125a b c d - 7725b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 84a b d - 126a b c d - 210a b c d - 420a b c d - 1260a b c d +--R + +--R 6 5 2 7 6 +--R 5754a b c d - 3594b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 14a b c d - 21a b c d - 35a b c d - 70a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d + 1029a b c d - 669b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60d x + 360c d x + 900c d x + 1200c d x + 900c d x + 360c d x +--R + +--R 6 8 +--R 60c d +--R Type: Expression Integer +--E 357 + +--S 358 of 1483 +a0071:=integrate(t0071,x) +--R +--R +--R (358) +--R 6 7 7 6 6 6 6 7 2 5 5 +--R (420a b d - 420b c d )x + (2520a b c d - 2520b c d )x +--R + +--R 6 2 5 7 3 4 4 6 3 4 7 4 3 3 +--R (6300a b c d - 6300b c d )x + (8400a b c d - 8400b c d )x +--R + +--R 6 4 3 7 5 2 2 6 5 2 7 6 +--R (6300a b c d - 6300b c d )x + (2520a b c d - 2520b c d)x +--R + +--R 6 6 7 7 +--R 420a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360b c d x + (- 1260a b d + 2520a b c d - 360b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1050a b d - 3150a b c d + 9450a b c d - 4050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 700a b d - 1400a b c d - 4200a b c d + 15400a b c d +--R + +--R 7 4 3 +--R - 8200b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 315a b d - 525a b c d - 1050a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 13125a b c d - 7725b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 84a b d - 126a b c d - 210a b c d - 420a b c d - 1260a b c d +--R + +--R 6 5 2 7 6 +--R 5754a b c d - 3594b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 14a b c d - 21a b c d - 35a b c d - 70a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d + 1029a b c d - 669b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60d x + 360c d x + 900c d x + 1200c d x + 900c d x + 360c d x +--R + +--R 6 8 +--R 60c d +--R Type: Union(Expression Integer,...) +--E 358 + +--S 359 of 1483 +m0071:=a0071-r0071 +--R +--R +--R (359) 0 +--R Type: Expression Integer +--E 359 + +--S 360 of 1483 +d0071:=D(m0071,x) +--R +--R +--R (360) 0 +--R Type: Expression Integer +--E 360 + +--S 361 of 1483 +t0072:= (a+b*x)^7/(c+d*x)^8 +--R +--R +--R (361) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction Polynomial Integer +--E 361 + +--S 362 of 1483 +r0072:= 1/7*(b*c-a*d)^7/d^8/(c+d*x)^7-7/6*b*(b*c-a*d)^6/d^8/(c+d*x)^6+_ + 21/5*b^2*(b*c-a*d)^5/d^8/(c+d*x)^5-_ + 35/4*b^3*(b*c-a*d)^4/d^8/(c+d*x)^4+_ + 35/3*b^4*(b*c-a*d)^3/d^8/(c+d*x)^3-_ + 21/2*b^5*(b*c-a*d)^2/d^8/(c+d*x)^2+_ + 7*b^6*(b*c-a*d)/d^8/(c+d*x)+b^7*log(c+d*x)/d^8 +--R +--R +--R (362) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Expression Integer +--E 362 + +--S 363 of 1483 +a0072:=integrate(t0072,x) +--R +--R +--R (363) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Union(Expression Integer,...) +--E 363 + +--S 364 of 1483 +m0072:=a0072-r0072 +--R +--R +--R (364) 0 +--R Type: Expression Integer +--E 364 + +--S 365 of 1483 +d0072:=D(m0072,x) +--R +--R +--R (365) 0 +--R Type: Expression Integer +--E 365 + +--S 366 of 1483 +t0073:= (a+b*x)^7/(c+d*x)^9 +--R +--R +--R (366) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R d x + 9c d x + 36c d x + 84c d x + 126c d x + 126c d x + 84c d x +--R + +--R 7 2 2 8 9 +--R 36c d x + 9c d x + c +--R Type: Fraction Polynomial Integer +--E 366 + +--S 367 of 1483 +r0073:= 1/8*(a+b*x)^8/(b*c-a*d)/(c+d*x)^8 +--R +--R +--R (367) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 9 8 8 8 2 7 7 2 7 3 6 6 +--R (a d - b c d )x + (8a c d - 8b c d )x + (28a c d - 28b c d )x +--R + +--R 3 6 4 5 5 4 5 5 4 4 +--R (56a c d - 56b c d )x + (70a c d - 70b c d )x +--R + +--R 5 4 6 3 3 6 3 7 2 2 7 2 8 +--R (56a c d - 56b c d )x + (28a c d - 28b c d )x + (8a c d - 8b c d)x +--R + +--R 8 9 +--R a c d - b c +--R Type: Fraction Polynomial Fraction Integer +--E 367 + +--S 368 of 1483 +a0073:=integrate(t0073,x) +--R +--R +--R (368) +--R 7 7 7 6 7 7 6 6 +--R - 8b d x + (- 28a b d - 28b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 56a b d - 56a b c d - 56b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 70a b d - 70a b c d - 70a b c d - 70b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 56a b d - 56a b c d - 56a b c d - 56a b c d - 56b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 28a b d - 28a b c d - 28a b c d - 28a b c d - 28a b c d +--R + +--R 7 5 2 +--R - 28b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R - 8a b d - 8a b c d - 8a b c d - 8a b c d - 8a b c d - 8a b c d +--R + +--R 7 6 +--R - 8b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - a b c d +--R + +--R 7 7 +--R - b c +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R 8d x + 64c d x + 224c d x + 448c d x + 560c d x + 448c d x +--R + +--R 6 10 2 7 9 8 8 +--R 224c d x + 64c d x + 8c d +--R Type: Union(Expression Integer,...) +--E 368 + +--S 369 of 1483 +m0073:=a0073-r0073 +--R +--R +--R 8 +--R b +--R (369) --------------- +--R 9 8 +--R 8a d - 8b c d +--R Type: Expression Integer +--E 369 + +--S 370 of 1483 +d0073:=D(m0073,x) +--R +--R +--R (370) 0 +--R Type: Expression Integer +--E 370 + +--S 371 of 1483 +t0074:= (a+b*x)^7/(c+d*x)^10 +--R +--R +--R (371) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R Type: Fraction Polynomial Integer +--E 371 + +--S 372 of 1483 +r0074:= -1/72*(a+b*x)^8*(-9*b*c+8*a*d-b*d*x)/(-b*c+a*d)^2/(c+d*x)^9 +--R +--R +--R (372) +--R 1 9 9 1 9 8 1 2 7 8 7 7 3 6 7 2 7 6 +--R -- b d x + - b c x + (- - a b d + a b c)x + (- - a b d + - a b c)x +--R 72 8 2 3 2 +--R + +--R 21 4 5 3 6 5 5 4 35 4 5 4 +--R (- -- a b d + 7a b c)x + (- 7a b d + -- a b c)x +--R 4 4 +--R + +--R 35 6 3 5 4 3 7 2 7 6 3 2 7 8 7 2 +--R (- -- a b d + 7a b c)x + (- 3a b d + - a b c)x + (- - a b d + a b c)x +--R 6 2 8 +--R + +--R 1 9 1 8 +--R - - a d + - a b c +--R 9 8 +--R / +--R 2 11 10 2 2 9 9 2 10 2 9 2 3 8 8 +--R (a d - 2a b c d + b c d )x + (9a c d - 18a b c d + 9b c d )x +--R + +--R 2 2 9 3 8 2 4 7 7 +--R (36a c d - 72a b c d + 36b c d )x +--R + +--R 2 3 8 4 7 2 5 6 6 +--R (84a c d - 168a b c d + 84b c d )x +--R + +--R 2 4 7 5 6 2 6 5 5 +--R (126a c d - 252a b c d + 126b c d )x +--R + +--R 2 5 6 6 5 2 7 4 4 +--R (126a c d - 252a b c d + 126b c d )x +--R + +--R 2 6 5 7 4 2 8 3 3 +--R (84a c d - 168a b c d + 84b c d )x +--R + +--R 2 7 4 8 3 2 9 2 2 2 8 3 9 2 2 10 +--R (36a c d - 72a b c d + 36b c d )x + (9a c d - 18a b c d + 9b c d)x +--R + +--R 2 9 2 10 2 11 +--R a c d - 2a b c d + b c +--R Type: Fraction Polynomial Fraction Integer +--E 372 + +--S 373 of 1483 +a0074:=integrate(t0074,x) +--R +--R +--R (373) +--R 7 7 7 6 7 7 6 6 +--R - 36b d x + (- 168a b d - 84b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 378a b d - 252a b c d - 126b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 504a b d - 378a b c d - 252a b c d - 126b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d - 336a b c d - 252a b c d - 168a b c d - 84b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 216a b d - 180a b c d - 144a b c d - 108a b c d - 72a b c d +--R + +--R 7 5 2 +--R - 36b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 63a b d - 54a b c d - 45a b c d - 36a b c d - 27a b c d +--R + +--R 6 5 2 7 6 +--R - 18a b c d - 9b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 8a d - 7a b c d - 6a b c d - 5a b c d - 4a b c d - 3a b c d +--R + +--R 6 6 7 7 +--R - 2a b c d - b c +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 72d x + 648c d x + 2592c d x + 6048c d x + 9072c d x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 9072c d x + 6048c d x + 2592c d x + 648c d x + 72c d +--R Type: Union(Expression Integer,...) +--E 373 + +--S 374 of 1483 +m0074:=a0074-r0074 +--R +--R +--R 9 +--R b +--R (374) - -------------------------------- +--R 2 10 9 2 2 8 +--R 72a d - 144a b c d + 72b c d +--R Type: Expression Integer +--E 374 + +--S 375 of 1483 +d0074:=D(m0074,x) +--R +--R +--R (375) 0 +--R Type: Expression Integer +--E 375 + +--S 376 of 1483 +t0075:= (a+b*x)^5*(a*c+b*c*x)^3 +--R +--R +--R (376) +--R 8 3 8 7 3 7 2 6 3 6 3 5 3 5 4 4 3 4 5 3 3 3 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x + 56a b c x +--R + +--R 6 2 3 2 7 3 8 3 +--R 28a b c x + 8a b c x + a c +--R Type: Polynomial Integer +--E 376 + +--S 377 of 1483 +r0075:= 1/9*c^3*(a+b*x)^9/b +--R +--R +--R (377) +--R 1 9 3 9 8 3 8 2 7 3 7 28 3 6 3 6 4 5 3 5 5 4 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 3 3 3 7 2 3 2 8 3 1 9 3 +--R -- a b c x + 4a b c x + a b c x + - a c +--R 3 9 +--R / +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 377 + +--S 378 of 1483 +a0075:=integrate(t0075,x) +--R +--R +--R (378) +--R 1 8 3 9 7 3 8 2 6 3 7 28 3 5 3 6 4 4 3 5 5 3 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 2 3 3 7 3 2 8 3 +--R -- a b c x + 4a b c x + a c x +--R 3 +--R Type: Polynomial Fraction Integer +--E 378 + +--S 379 of 1483 +m0075:=a0075-r0075 +--R +--R +--R 1 9 3 +--R - a c +--R 9 +--R (379) - ------ +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 379 + +--S 380 of 1483 +d0075:=D(m0075,x) +--R +--R +--R (380) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 380 + +--S 381 of 1483 +t0076:= (a+b*x)^5*(a*c+b*c*x)^2 +--R +--R +--R (381) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 5 2 2 2 +--R b c x + 7a b c x + 21a b c x + 35a b c x + 35a b c x + 21a b c x +--R + +--R 6 2 7 2 +--R 7a b c x + a c +--R Type: Polynomial Integer +--E 381 + +--S 382 of 1483 +r0076:= 1/8*c^2*(a+b*x)^8/b +--R +--R +--R (382) +--R 1 8 2 8 7 2 7 7 2 6 2 6 3 5 2 5 35 4 4 2 4 5 3 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 2 7 2 1 8 2 +--R - a b c x + a b c x + - a c +--R 2 8 +--R / +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 382 + +--S 383 of 1483 +a0076:=integrate(t0076,x) +--R +--R +--R (383) +--R 1 7 2 8 6 2 7 7 2 5 2 6 3 4 2 5 35 4 3 2 4 5 2 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 7 2 +--R - a b c x + a c x +--R 2 +--R Type: Polynomial Fraction Integer +--E 383 + +--S 384 of 1483 +m0076:=a0076-r0076 +--R +--R +--R 1 8 2 +--R - a c +--R 8 +--R (384) - ------ +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 384 + +--S 385 of 1483 +d0076:=D(m0076,x) +--R +--R +--R (385) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 385 + +--S 386 of 1483 +t0077:= (a+b*x)^5*(a*c+b*c*x) +--R +--R +--R (386) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x + a c +--R Type: Polynomial Integer +--E 386 + +--S 387 of 1483 +r0077:= 1/7*c*(a+b*x)^7/b +--R +--R +--R (387) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x +--R 7 +--R + +--R 6 1 7 +--R a b c x + - a c +--R 7 +--R / +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 387 + +--S 388 of 1483 +a0077:=integrate(t0077,x) +--R +--R +--R (388) +--R 1 6 7 5 6 2 4 5 3 3 4 4 2 3 5 2 6 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x + a c x +--R 7 +--R Type: Polynomial Fraction Integer +--E 388 + +--S 389 of 1483 +m0077:=a0077-r0077 +--R +--R +--R 1 7 +--R - a c +--R 7 +--R (389) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 389 + +--S 390 of 1483 +d0077:=D(m0077,x) +--R +--R +--R (390) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 390 + +--S 391 of 1483 +t0078:= 2/(-1+4*x^2) +--R +--R +--R 2 +--R (391) ------- +--R 2 +--R 4x - 1 +--R Type: Fraction Polynomial Integer +--E 391 + +--S 392 of 1483 +r0078:= -atanh(2*x) +--R +--R +--R (392) - atanh(2x) +--R Type: Expression Integer +--E 392 + +--S 393 of 1483 +a0078:=integrate(t0078,x) +--R +--R +--R - log(2x + 1) + log(2x - 1) +--R (393) --------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 393 + +--S 394 of 1483 +m0078:=a0078-r0078 +--R +--R +--R - log(2x + 1) + log(2x - 1) + 2atanh(2x) +--R (394) ---------------------------------------- +--R 2 +--R Type: Expression Integer +--E 394 + +--S 395 of 1483 +d0078:=D(m0078,x) +--R +--R +--R (395) 0 +--R Type: Expression Integer +--E 395 + +--S 396 of 1483 +t0079:= x*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +--R (396) b x + 2a b x + a x +--R Type: Polynomial Integer +--E 396 + +--S 397 of 1483 +r0079:= 1/6*(a+b*x^2)^3/b +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - b x + - a b x + - a b x + - a +--R 6 2 2 6 +--R (397) ----------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 397 + +--S 398 of 1483 +a0079:=integrate(t0079,x) +--R +--R +--R 1 2 6 1 4 1 2 2 +--R (398) - b x + - a b x + - a x +--R 6 2 2 +--R Type: Polynomial Fraction Integer +--E 398 + +--S 399 of 1483 +m0079:=a0079-r0079 +--R +--R +--R 1 3 +--R - a +--R 6 +--R (399) - ---- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 399 + +--S 400 of 1483 +d0079:=D(m0079,x) +--R +--R +--R (400) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 400 + +--S 401 of 1483 +t0080:= (a+b*x^2)^2/x^7 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (401) ------------------- +--R 7 +--R x +--R Type: Fraction Polynomial Integer +--E 401 + +--S 402 of 1483 +r0080:= -1/6*(a+b*x^2)^3/a/x^6 +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 2 2 6 +--R (402) ------------------------------------- +--R 6 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 402 + +--S 403 of 1483 +a0080:=integrate(t0080,x) +--R +--R +--R 2 4 2 2 +--R - 3b x - 3a b x - a +--R (403) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression Integer,...) +--E 403 + +--S 404 of 1483 +m0080:=a0080-r0080 +--R +--R +--R 3 +--R b +--R (404) -- +--R 6a +--R Type: Expression Integer +--E 404 + +--S 405 of 1483 +d0080:=D(m0080,x) +--R +--R +--R (405) 0 +--R Type: Expression Integer +--E 405 + +--S 406 of 1483 +t0081:= x^3*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +--R (406) b x + 3a b x + 3a b x + a x +--R Type: Polynomial Integer +--E 406 + +--S 407 of 1483 +r0081:= -1/40*(a+b*x^2)^4*(a-4*b*x^2)/b^2 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 10 8 2 4 40 +--R (407) ------------------------------------------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 407 + +--S 408 of 1483 +a0081:=integrate(t0081,x) +--R +--R +--R 1 3 10 3 2 8 1 2 6 1 3 4 +--R (408) -- b x + - a b x + - a b x + - a x +--R 10 8 2 4 +--R Type: Polynomial Fraction Integer +--E 408 + +--S 409 of 1483 +m0081:=a0081-r0081 +--R +--R +--R 1 5 +--R -- a +--R 40 +--R (409) ----- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 409 + +--S 410 of 1483 +d0081:=D(m0081,x) +--R +--R +--R (410) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 410 + +--S 411 of 1483 +t0082:= x*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +--R (411) b x + 3a b x + 3a b x + a x +--R Type: Polynomial Integer +--E 411 + +--S 412 of 1483 +r0082:= 1/8*(a+b*x^2)^4/b +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - b x + - a b x + - a b x + - a b x + - a +--R 8 2 4 2 8 +--R (412) ---------------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 412 + +--S 413 of 1483 +a0082:=integrate(t0082,x) +--R +--R +--R 1 3 8 1 2 6 3 2 4 1 3 2 +--R (413) - b x + - a b x + - a b x + - a x +--R 8 2 4 2 +--R Type: Polynomial Fraction Integer +--E 413 + +--S 414 of 1483 +m0082:=a0082-r0082 +--R +--R +--R 1 4 +--R - a +--R 8 +--R (414) - ---- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 414 + +--S 415 of 1483 +d0082:=D(m0082,x) +--R +--R +--R (415) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 415 + +--S 416 of 1483 +t0083:= (a+b*x^2)^3/x^9 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (416) ----------------------------- +--R 9 +--R x +--R Type: Fraction Polynomial Integer +--E 416 + +--S 417 of 1483 +r0083:= -1/8*(a+b*x^2)^4/a/x^8 +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 8 2 4 2 8 +--R (417) ------------------------------------------------ +--R 8 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 417 + +--S 418 of 1483 +a0083:=integrate(t0083,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (418) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression Integer,...) +--E 418 + +--S 419 of 1483 +m0083:=a0083-r0083 +--R +--R +--R 4 +--R b +--R (419) -- +--R 8a +--R Type: Expression Integer +--E 419 + +--S 420 of 1483 +d0083:=D(m0083,x) +--R +--R +--R (420) 0 +--R Type: Expression Integer +--E 420 + +--S 421 of 1483 +t0084:= x^3*(a+b*x^2)^4 +--R +--R +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (421) b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Polynomial Integer +--E 421 + +--S 422 of 1483 +r0084:= -1/60*(a+b*x^2)^5*(a-5*b*x^2)/b^2 +--R +--R +--R 1 6 12 2 5 10 3 2 4 8 2 3 3 6 1 4 2 4 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x - -- a +--R 12 5 4 3 4 60 +--R (422) ------------------------------------------------------------- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 422 + +--S 423 of 1483 +a0084:=integrate(t0084,x) +--R +--R +--R 1 4 12 2 3 10 3 2 2 8 2 3 6 1 4 4 +--R (423) -- b x + - a b x + - a b x + - a b x + - a x +--R 12 5 4 3 4 +--R Type: Polynomial Fraction Integer +--E 423 + +--S 424 of 1483 +m0084:=a0084-r0084 +--R +--R +--R 1 6 +--R -- a +--R 60 +--R (424) ----- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 424 + +--S 425 of 1483 +d0084:=D(m0084,x) +--R +--R +--R (425) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 425 + +--S 426 of 1483 +t0085:= x*(a+b*x^2)^4 +--R +--R +--R 4 9 3 7 2 2 5 3 3 4 +--R (426) b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Polynomial Integer +--E 426 + +--S 427 of 1483 +r0085:= 1/10*(a+b*x^2)^5/b +--R +--R +--R 1 5 10 1 4 8 2 3 6 3 2 4 1 4 2 1 5 +--R -- b x + - a b x + a b x + a b x + - a b x + -- a +--R 10 2 2 10 +--R (427) -------------------------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 427 + +--S 428 of 1483 +a0085:=integrate(t0085,x) +--R +--R +--R 1 4 10 1 3 8 2 2 6 3 4 1 4 2 +--R (428) -- b x + - a b x + a b x + a b x + - a x +--R 10 2 2 +--R Type: Polynomial Fraction Integer +--E 428 + +--S 429 of 1483 +m0085:=a0085-r0085 +--R +--R +--R 1 5 +--R -- a +--R 10 +--R (429) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 429 + +--S 430 of 1483 +d0085:=D(m0085,x) +--R +--R +--R (430) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 430 + +--S 431 of 1483 +t0086:= x^5*(a+b*x^2)^5 +--R +--R +--R 5 15 4 13 2 3 11 3 2 9 4 7 5 5 +--R (431) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 431 + +--S 432 of 1483 +r0086:= 1/336*(a+b*x^2)^6*(a^2-6*a*b*x^2+21*b^2*x^4)/b^3 +--R +--R +--R (432) +--R 1 8 16 5 7 14 5 2 6 12 3 5 10 5 4 4 8 1 5 3 6 1 8 +--R -- b x + -- a b x + - a b x + a b x + - a b x + - a b x + --- a +--R 16 14 6 8 6 336 +--R -------------------------------------------------------------------------- +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 432 + +--S 433 of 1483 +a0086:=integrate(t0086,x) +--R +--R +--R 1 5 16 5 4 14 5 2 3 12 3 2 10 5 4 8 1 5 6 +--R (433) -- b x + -- a b x + - a b x + a b x + - a b x + - a x +--R 16 14 6 8 6 +--R Type: Polynomial Fraction Integer +--E 433 + +--S 434 of 1483 +m0086:=a0086-r0086 +--R +--R +--R 1 8 +--R --- a +--R 336 +--R (434) - ------ +--R 3 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 434 + +--S 435 of 1483 +d0086:=D(m0086,x) +--R +--R +--R (435) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 435 + +--S 436 of 1483 +t0087:= x^3*(a+b*x^2)^5 +--R +--R +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R (436) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 436 + +--S 437 of 1483 +r0087:= -1/84*(a+b*x^2)^6*(a-6*b*x^2)/b^2 +--R +--R +--R (437) +--R 1 7 14 5 6 12 2 5 10 5 3 4 8 5 4 3 6 1 5 2 4 1 7 +--R -- b x + -- a b x + a b x + - a b x + - a b x + - a b x - -- a +--R 14 12 4 6 4 84 +--R ------------------------------------------------------------------------ +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 437 + +--S 438 of 1483 +a0087:=integrate(t0087,x) +--R +--R +--R 1 5 14 5 4 12 2 3 10 5 3 2 8 5 4 6 1 5 4 +--R (438) -- b x + -- a b x + a b x + - a b x + - a b x + - a x +--R 14 12 4 6 4 +--R Type: Polynomial Fraction Integer +--E 438 + +--S 439 of 1483 +m0087:=a0087-r0087 +--R +--R +--R 1 7 +--R -- a +--R 84 +--R (439) ----- +--R 2 +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 439 + +--S 440 of 1483 +d0087:=D(m0087,x) +--R +--R +--R (440) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 440 + +--S 441 of 1483 +t0088:= x*(a+b*x^2)^5 +--R +--R +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (441) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial Integer +--E 441 + +--S 442 of 1483 +r0088:= 1/12*(a+b*x^2)^6/b +--R +--R +--R (442) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x + - a b x + -- a +--R 12 2 4 3 4 2 12 +--R ------------------------------------------------------------------------ +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 442 + +--S 443 of 1483 +a0088:=integrate(t0088,x) +--R +--R +--R 1 5 12 1 4 10 5 2 3 8 5 3 2 6 5 4 4 1 5 2 +--R (443) -- b x + - a b x + - a b x + - a b x + - a b x + - a x +--R 12 2 4 3 4 2 +--R Type: Polynomial Fraction Integer +--E 443 + +--S 444 of 1483 +m0088:=a0088-r0088 +--R +--R +--R 1 6 +--R -- a +--R 12 +--R (444) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 444 + +--S 445 of 1483 +d0088:=D(m0088,x) +--R +--R +--R (445) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 445 + +--S 446 of 1483 +t0089:= (a+b*x^2)^5/x^13 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (446) ---------------------------------------------------- +--R 13 +--R x +--R Type: Fraction Polynomial Integer +--E 446 + +--S 447 of 1483 +r0089:= -1/12*(a+b*x^2)^6/a/x^12 +--R +--R +--R (447) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R - -- b x - - a b x - - a b x - - a b x - - a b x - - a b x - -- a +--R 12 2 4 3 4 2 12 +--R -------------------------------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 447 + +--S 448 of 1483 +a0089:=integrate(t0089,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (448) -------------------------------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression Integer,...) +--E 448 + +--S 449 of 1483 +m0089:=a0089-r0089 +--R +--R +--R 6 +--R b +--R (449) --- +--R 12a +--R Type: Expression Integer +--E 449 + +--S 450 of 1483 +d0089:=D(m0089,x) +--R +--R +--R (450) 0 +--R Type: Expression Integer +--E 450 + +--S 451 of 1483 +t0090:= (a+b*x^2)^5/x^15 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (451) ---------------------------------------------------- +--R 15 +--R x +--R Type: Fraction Polynomial Integer +--E 451 + +--S 452 of 1483 +r0090:= -1/84*(a+b*x^2)^6*(6*a-b*x^2)/a^2/x^14 +--R +--R +--R (452) +--R 1 7 14 1 2 5 10 5 3 4 8 5 4 3 6 5 2 4 5 6 2 1 7 +--R -- b x - - a b x - - a b x - - a b x - a b x - -- a b x - -- a +--R 84 4 6 4 12 14 +--R ----------------------------------------------------------------------- +--R 2 14 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 452 + +--S 453 of 1483 +a0090:=integrate(t0090,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (453) ------------------------------------------------------------ +--R 14 +--R 84x +--R Type: Union(Expression Integer,...) +--E 453 + +--S 454 of 1483 +m0090:=a0090-r0090 +--R +--R +--R 7 +--R b +--R (454) - ---- +--R 2 +--R 84a +--R Type: Expression Integer +--E 454 + +--S 455 of 1483 +d0090:=D(m0090,x) +--R +--R +--R (455) 0 +--R Type: Expression Integer +--E 455 + +--S 456 of 1483 +t0091:= 1/(-1+a+a*x^2) +--R +--R +--R 1 +--R (456) ------------ +--R 2 +--R a x + a - 1 +--R Type: Fraction Polynomial Integer +--E 456 + +--S 457 of 1483 +r0091:= atanh((-a)^(1/2)*x/(-1+a)^(1/2))/(-1+a)^(1/2)/(-a)^(1/2) +--R +--R +--R +---+ +--R x\|- a +--R atanh(--------) +--R +-----+ +--R \|a - 1 +--R (457) --------------- +--R +---+ +-----+ +--R \|- a \|a - 1 +--R Type: Expression Integer +--E 457 + +--S 458 of 1483 +a0091:=integrate(t0091,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +------+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x | 2 +--R log(---------------------------------------) x\|a - a +--R 2 atan(----------) +--R a x + a - 1 a - 1 +--R (458) [--------------------------------------------,----------------] +--R +--------+ +------+ +--R | 2 | 2 +--R 2\|- a + a \|a - a +--R Type: Union(List Expression Integer,...) +--E 458 + +--S 459 of 1483 +m0091a:=a0091.1-r0091 +--R +--R +--R (459) +--R +--------+ +--R 2 | 2 2 +--R +---+ +-----+ (a x - a + 1)\|- a + a + (2a - 2a)x +--R \|- a \|a - 1 log(---------------------------------------) +--R 2 +--R a x + a - 1 +--R + +--R +--------+ +---+ +--R | 2 x\|- a +--R - 2\|- a + a atanh(--------) +--R +-----+ +--R \|a - 1 +--R / +--R +--------+ +--R | 2 +---+ +-----+ +--R 2\|- a + a \|- a \|a - 1 +--R Type: Expression Integer +--E 459 + +--S 460 of 1483 +d0091a:=D(m0091a,x) +--R +--R +--R (460) 0 +--R Type: Expression Integer +--E 460 + +--S 461 of 1483 +m0091b:=a0091.2-r0091 +--R +--R +--R +------+ +--R +------+ +---+ | 2 +--R | 2 x\|- a +---+ +-----+ x\|a - a +--R - \|a - a atanh(--------) + \|- a \|a - 1 atan(----------) +--R +-----+ a - 1 +--R \|a - 1 +--R (461) ----------------------------------------------------------- +--R +------+ +--R +---+ +-----+ | 2 +--R \|- a \|a - 1 \|a - a +--R Type: Expression Integer +--E 461 + +--S 462 of 1483 +d0091b:=D(m0091b,x) +--R +--R +--R (462) 0 +--R Type: Expression Integer +--E 462 + +--S 463 of 1483 +t0092:= x^2/(a-b*x^2)^2 +--R +--R +--R 2 +--R x +--R (463) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction Polynomial Integer +--E 463 + +--S 464 of 1483 +r0092:= 1/2*x/b/(a-b*x^2)-1/2*atanh(b^(1/2)*x/a^(1/2))/a^(1/2)/b^(3/2) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (- b x + a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (464) ------------------------------------ +--R 2 2 +-+ +-+ +--R (2b x - 2a b)\|a \|b +--R Type: Expression Integer +--E 464 + +--S 465 of 1483 +a0092:=integrate(t0092,x) +--R +--R +--R (465) +--R 2 +---+ +--R 2 (b x + a)\|a b - 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4b x - 4a b)\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (- b x + a)atan(---------) - x\|- a b +--R a +--R ---------------------------------------] +--R 2 2 +-----+ +--R (2b x - 2a b)\|- a b +--R Type: Union(List Expression Integer,...) +--E 465 + +--S 466 of 1483 +m0092a:=a0092.1-r0092 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (466) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4b\|a \|b \|a b +--R Type: Expression Integer +--E 466 + +--S 467 of 1483 +d0092a:=D(m0092a,x) +--R +--R +--R (467) 0 +--R Type: Expression Integer +--E 467 + +--S 468 of 1483 +m0092b:=a0092.2-r0092 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (468) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression Integer +--E 468 + +--S 469 of 1483 +d0092b:=D(m0092b,x) +--R +--R +--R (469) 0 +--R Type: Expression Integer +--E 469 + +--S 470 of 1483 +t0093:= 1/x^2/(a-b*x^2)^2 +--R +--R +--R 1 +--R (470) --------------------- +--R 2 6 4 2 2 +--R b x - 2a b x + a x +--R Type: Fraction Polynomial Integer +--E 470 + +--S 471 of 1483 +r0093:= -1/a^2/x+1/2*b*x/a^2/(a-b*x^2)+_ + 3/2*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (3b x - 3a x)\|b atanh(-----) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (471) --------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x - 2a x)\|a +--R Type: Expression Integer +--E 471 + +--S 472 of 1483 +a0093:=integrate(t0093,x) +--R +--R +--R (472) +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 |b \|a 2 +--R (3b x - 3a x) |- log(-------------------) - 6b x + 4a +--R \|a 2 +--R b x - a +--R [-------------------------------------------------------, +--R 2 3 3 +--R 4a b x - 4a x +--R +---+ +--R | b +--R +---+ a |- - +--R 3 | b \| a 2 +--R (- 3b x + 3a x) |- - atan(-------) - 3b x + 2a +--R \| a b x +--R ------------------------------------------------] +--R 2 3 3 +--R 2a b x - 2a x +--R Type: Union(List Expression Integer,...) +--E 472 + +--S 473 of 1483 +m0093a:=a0093.1-r0093 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 3\|a |- log(-------------------) - 6\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (473) ----------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression Integer +--E 473 + +--S 474 of 1483 +d0093a:=D(m0093a,x) +--R +--R +--R (474) 0 +--R Type: Expression Integer +--E 474 + +--S 475 of 1483 +m0093b:=a0093.2-r0093 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 3\|b atanh(-----) - 3 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (475) ---------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression Integer +--E 475 + +--S 476 of 1483 +d0093b:=D(m0093b,x) +--R +--R +--R (476) 0 +--R Type: Expression Integer +--E 476 + +--S 477 of 1483 +t0094:= x^2/(a-b*x^2)^3 +--R +--R +--R 2 +--R x +--R (477) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction Polynomial Integer +--E 477 + +--S 478 of 1483 +r0094:= 1/4*x/b/(a-b*x^2)^2-1/8*x/a/b/(a-b*x^2)-_ + 1/8*atanh(b^(1/2)*x/a^(1/2))/a^(3/2)/b^(3/2) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (- b x + 2a b x - a )atanh(-----) + (b x + a x)\|a \|b +--R +-+ +--R \|a +--R (478) ---------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x - 16a b x + 8a b)\|a \|b +--R Type: Expression Integer +--E 478 + +--S 479 of 1483 +a0094:=integrate(t0094,x) +--R +--R +--R (479) +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b - 2a b x 3 +---+ +--R (b x - 2a b x + a )log(-------------------------) + (2b x + 2a x)\|a b +--R 2 +--R b x - a +--R [--------------------------------------------------------------------------, +--R 3 4 2 2 2 3 +---+ +--R (16a b x - 32a b x + 16a b)\|a b +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (- b x + 2a b x - a )atan(---------) + (b x + a x)\|- a b +--R a +--R -------------------------------------------------------------] +--R 3 4 2 2 2 3 +-----+ +--R (8a b x - 16a b x + 8a b)\|- a b +--R Type: Union(List Expression Integer,...) +--E 479 + +--S 480 of 1483 +m0094a:=a0094.1-r0094 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (480) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 16a b\|a \|b \|a b +--R Type: Expression Integer +--E 480 + +--S 481 of 1483 +d0094a:=D(m0094a,x) +--R +--R +--R (481) 0 +--R Type: Expression Integer +--E 481 + +--S 482 of 1483 +m0094b:=a0094.2-r0094 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (482) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression Integer +--E 482 + +--S 483 of 1483 +d0094b:=D(m0094b,x) +--R +--R +--R (483) 0 +--R Type: Expression Integer +--E 483 + +--S 484 of 1483 +t0095:= 1/x^2/(a-b*x^2)^3 +--R +--R +--R 1 +--R (484) - ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction Polynomial Integer +--E 484 + +--S 485 of 1483 +r0095:= -1/a^3/x+1/4*b*x/a^2/(a-b*x^2)^2+7/8*b*x/a^3/(a-b*x^2)+_ + 15/8*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(7/2) +--R +--R +--R (485) +--R +-+ +--R 2 5 3 2 +-+ x\|b 2 4 2 2 +-+ +--R (15b x - 30a b x + 15a x)\|b atanh(-----) + (- 15b x + 25a b x - 8a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 2 5 4 3 5 +-+ +--R (8a b x - 16a b x + 8a x)\|a +--R Type: Expression Integer +--E 485 + +--S 486 of 1483 +a0095:=integrate(t0095,x) +--R +--R +--R (486) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 2 5 3 2 |b \|a 2 4 +--R (15b x - 30a b x + 15a x) |- log(-------------------) - 30b x +--R \|a 2 +--R b x - a +--R + +--R 2 2 +--R 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x - 32a b x + 16a x +--R , +--R +---+ +--R | b +--R +---+ a |- - +--R 2 5 3 2 | b \| a 2 4 2 2 +--R (- 15b x + 30a b x - 15a x) |- - atan(-------) - 15b x + 25a b x - 8a +--R \| a b x +--R --------------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x - 16a b x + 8a x +--R Type: Union(List Expression Integer,...) +--E 486 + +--S 487 of 1483 +m0095a:=a0095.1-r0095 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 15\|a |- log(-------------------) - 30\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (487) ------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression Integer +--E 487 + +--S 488 of 1483 +d0095a:=D(m0095a,x) +--R +--R +--R (488) 0 +--R Type: Expression Integer +--E 488 + +--S 489 of 1483 +m0095b:=a0095.2-r0095 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 15\|b atanh(-----) - 15 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (489) ------------------------------------------------ +--R 3 +-+ +--R 8a \|a +--R Type: Expression Integer +--E 489 + +--S 490 of 1483 +d0095b:=D(m0095b,x) +--R +--R +--R (490) 0 +--R Type: Expression Integer +--E 490 + +--S 491 of 1483 +t0096:= x^2/(a-b*x^2)^4 +--R +--R +--R 2 +--R x +--R (491) --------------------------------------- +--R 4 8 3 6 2 2 4 3 2 4 +--R b x - 4a b x + 6a b x - 4a b x + a +--R Type: Fraction Polynomial Integer +--E 491 + +--S 492 of 1483 +r0096:= 1/6*x/b/(a-b*x^2)^3-1/24*x/a/b/(a-b*x^2)^2-_ + 1/16*x/a^2/b/(a-b*x^2)-1/16*atanh(b^(1/2)*x/a^(1/2))/a^(5/2)/b^(3/2) +--R +--R +--R (492) +--R +-+ +--R 3 6 2 4 2 2 3 x\|b +--R (- 3b x + 9a b x - 9a b x + 3a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 2 5 3 2 +-+ +-+ +--R (3b x - 8a b x - 3a x)\|a \|b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +-+ +-+ +--R (48a b x - 144a b x + 144a b x - 48a b)\|a \|b +--R Type: Expression Integer +--E 492 + +--S 493 of 1483 +a0096:=integrate(t0096,x) +--R +--R +--R (493) +--R [ +--R 2 +---+ +--R 3 6 2 4 2 2 3 (b x + a)\|a b - 2a b x +--R (3b x - 9a b x + 9a b x - 3a )log(-------------------------) +--R 2 +--R b x - a +--R + +--R 2 5 3 2 +---+ +--R (6b x - 16a b x - 6a x)\|a b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +---+ +--R (96a b x - 288a b x + 288a b x - 96a b)\|a b +--R , +--R +--R +-----+ +--R 3 6 2 4 2 2 3 x\|- a b +--R (- 3b x + 9a b x - 9a b x + 3a )atan(---------) +--R a +--R + +--R 2 5 3 2 +-----+ +--R (3b x - 8a b x - 3a x)\|- a b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +-----+ +--R (48a b x - 144a b x + 144a b x - 48a b)\|- a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 493 + +--S 494 of 1483 +m0096a:=a0096.1-r0096 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (494) ------------------------------------------------------------ +--R 2 +-+ +-+ +---+ +--R 32a b\|a \|b \|a b +--R Type: Expression Integer +--E 494 + +--S 495 of 1483 +d0096a:=D(m0096a,x) +--R +--R +--R (495) 0 +--R Type: Expression Integer +--E 495 + +--S 496 of 1483 +m0096b:=a0096.2-r0096 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (496) ---------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression Integer +--E 496 + +--S 497 of 1483 +d0096b:=D(m0096b,x) +--R +--R +--R (497) 0 +--R Type: Expression Integer +--E 497 + +--S 498 of 1483 +t0097:= 1/x^2/(a-b*x^2)^4 +--R +--R +--R 1 +--R (498) ------------------------------------------ +--R 4 10 3 8 2 2 6 3 4 4 2 +--R b x - 4a b x + 6a b x - 4a b x + a x +--R Type: Fraction Polynomial Integer +--E 498 + +--S 499 of 1483 +r0097:= -1/a^4/x+1/6*b*x/a^2/(a-b*x^2)^3+11/24*b*x/a^3/(a-b*x^2)^2+_ + 19/16*b*x/a^4/(a-b*x^2)+35/16*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(9/2) +--R +--R +--R (499) +--R +-+ +--R 3 7 2 5 2 3 3 +-+ x\|b +--R (105b x - 315a b x + 315a b x - 105a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 105b x + 280a b x - 231a b x + 48a )\|a +--R / +--R 4 3 7 5 2 5 6 3 7 +-+ +--R (48a b x - 144a b x + 144a b x - 48a x)\|a +--R Type: Expression Integer +--E 499 + +--S 500 of 1483 +a0097:=integrate(t0097,x) +--R +--R +--R (500) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 7 2 5 2 3 3 |b \|a +--R (105b x - 315a b x + 315a b x - 105a x) |- log(-------------------) +--R \|a 2 +--R b x - a +--R + +--R 3 6 2 4 2 2 3 +--R - 210b x + 560a b x - 462a b x + 96a +--R / +--R 4 3 7 5 2 5 6 3 7 +--R 96a b x - 288a b x + 288a b x - 96a x +--R , +--R +--R +---+ +--R | b +--R +---+ a |- - +--R 3 7 2 5 2 3 3 | b \| a +--R (- 105b x + 315a b x - 315a b x + 105a x) |- - atan(-------) +--R \| a b x +--R + +--R 3 6 2 4 2 2 3 +--R - 105b x + 280a b x - 231a b x + 48a +--R / +--R 4 3 7 5 2 5 6 3 7 +--R 48a b x - 144a b x + 144a b x - 48a x +--R ] +--R Type: Union(List Expression Integer,...) +--E 500 + +--S 501 of 1483 +m0097a:=a0097.1-r0097 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 35\|a |- log(-------------------) - 70\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (501) ------------------------------------------------------- +--R 4 +-+ +--R 32a \|a +--R Type: Expression Integer +--E 501 + +--S 502 of 1483 +d0097a:=D(m0097a,x) +--R +--R +--R (502) 0 +--R Type: Expression Integer +--E 502 + +--S 503 of 1483 +m0097b:=a0097.2-r0097 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 35\|b atanh(-----) - 35 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (503) ------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression Integer +--E 503 + +--S 504 of 1483 +d0097b:=D(m0097b,x) +--R +--R +--R (504) 0 +--R Type: Expression Integer +--E 504 + +--S 505 of 1483 +t0098:= x^2/(a-b*x^2)^5 +--R +--R +--R 2 +--R x +--R (505) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction Polynomial Integer +--E 505 + +--S 506 of 1483 +r0098:= 1/8*x/b/(a-b*x^2)^4-1/48*x/a/b/(a-b*x^2)^3-_ + 5/192*x/a^2/b/(a-b*x^2)^2-5/128*x/a^3/b/(a-b*x^2)-_ + 5/128*atanh(b^(1/2)*x/a^(1/2))/a^(7/2)/b^(3/2) +--R +--R +--R (506) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (15b x - 55a b x + 73a b x + 15a x)\|a \|b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|a \|b +--R Type: Expression Integer +--E 506 + +--S 507 of 1483 +a0098:=integrate(t0098,x) +--R +--R +--R (507) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (15b x - 60a b x + 90a b x - 60a b x + 15a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b - 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (30b x - 110a b x + 146a b x + 30a x)\|a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a b)\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (15b x - 55a b x + 73a b x + 15a x)\|- a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|- a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 507 + +--S 508 of 1483 +m0098a:=a0098.1-r0098 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R 5\|a \|b log(-------------------------) + 10\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (508) -------------------------------------------------------------- +--R 3 +-+ +-+ +---+ +--R 256a b\|a \|b \|a b +--R Type: Expression Integer +--E 508 + +--S 509 of 1483 +d0098a:=D(m0098a,x) +--R +--R +--R (509) 0 +--R Type: Expression Integer +--E 509 + +--S 510 of 1483 +m0098b:=a0098.2-r0098 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R 5\|- a b atanh(-----) - 5\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (510) ------------------------------------------------ +--R 3 +-----+ +-+ +-+ +--R 128a b\|- a b \|a \|b +--R Type: Expression Integer +--E 510 + +--S 511 of 1483 +d0098b:=D(m0098b,x) +--R +--R +--R (511) 0 +--R Type: Expression Integer +--E 511 + +--S 512 of 1483 +t0099:= 1/x^2/(a-b*x^2)^5 +--R +--R +--R 1 +--R (512) - ------------------------------------------------------- +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction Polynomial Integer +--E 512 + +--S 513 of 1483 +r0099:= -1/a^5/x+1/8*b*x/a^2/(a-b*x^2)^4+5/16*b*x/a^3/(a-b*x^2)^3+_ + 41/64*b*x/a^4/(a-b*x^2)^2+187/128*b*x/a^5/(a-b*x^2)+_ + 315/128*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(11/2) +--R +--R +--R (513) +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ x\|b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x + 1155a b x - 1533a b x + 837a b x - 128a )\|a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +-+ +--R (128a b x - 512a b x + 768a b x - 512a b x + 128a x)\|a +--R Type: Expression Integer +--E 513 + +--S 514 of 1483 +a0099:=integrate(t0099,x) +--R +--R +--R (514) +--R [ +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 |b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x) |- +--R \|a +--R * +--R +-+ +--R |b 2 +--R 2a x |- + b x + a +--R \|a +--R log(-------------------) +--R 2 +--R b x - a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x + 2310a b x - 3066a b x + 1674a b x - 256a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 256a b x - 1024a b x + 1536a b x - 1024a b x + 256a x +--R , +--R +--R +---+ +--R 4 9 3 7 2 2 5 3 3 4 | b +--R (- 315b x + 1260a b x - 1890a b x + 1260a b x - 315a x) |- - +--R \| a +--R * +--R +---+ +--R | b +--R a |- - +--R \| a +--R atan(-------) +--R b x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 315b x + 1155a b x - 1533a b x + 837a b x - 128a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 128a b x - 512a b x + 768a b x - 512a b x + 128a x +--R ] +--R Type: Union(List Expression Integer,...) +--E 514 + +--S 515 of 1483 +m0099a:=a0099.1-r0099 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 315\|a |- log(-------------------) - 630\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (515) --------------------------------------------------------- +--R 5 +-+ +--R 256a \|a +--R Type: Expression Integer +--E 515 + +--S 516 of 1483 +d0099a:=D(m0099a,x) +--R +--R +--R (516) 0 +--R Type: Expression Integer +--E 516 + +--S 517 of 1483 +m0099b:=a0099.2-r0099 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 315\|b atanh(-----) - 315 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (517) -------------------------------------------------- +--R 5 +-+ +--R 128a \|a +--R Type: Expression Integer +--E 517 + +--S 518 of 1483 +d0099b:=D(m0099b,x) +--R +--R +--R (518) 0 +--R Type: Expression Integer +--E 518 + +--S 519 of 1483 +t0100:= (a+b*x)/(1-x^2) +--R +--R +--R - b x - a +--R (519) --------- +--R 2 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 519 + +--S 520 of 1483 +r0100:= -1/2*(a+b)*log(1-x)+1/2*(a-b)*log(1+x) +--R +--R +--R (- b + a)log(x + 1) + (- b - a)log(- x + 1) +--R (520) ------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 520 + +--S 521 of 1483 +a0100:=integrate(t0100,x) +--R +--R +--R (- b + a)log(x + 1) + (- b - a)log(x - 1) +--R (521) ----------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 521 + +--S 522 of 1483 +m0100:=a0100-r0100 +--R +--R +--R (- b - a)log(x - 1) + (b + a)log(- x + 1) +--R (522) ----------------------------------------- +--R 2 +--R Type: Expression Integer +--E 522 + +--S 523 of 1483 +d0100:=D(m0100,x) +--R +--R +--R (523) 0 +--R Type: Expression Integer +--E 523 + +--S 524 of 1483 +t0101:= 1/(a+b*x)/(a^2-b^2*x^2) +--R +--R +--R 1 +--R (524) - -------------------------- +--R 3 3 2 2 2 3 +--R b x + a b x - a b x - a +--R Type: Fraction Polynomial Integer +--E 524 + +--S 525 of 1483 +r0101:= -1/2/a/b/(a+b*x)+1/2*atanh(b*x/a)/a^2/b +--R +--R +--R b x +--R (b x + a)atanh(---) - a +--R a +--R (525) ----------------------- +--R 2 2 3 +--R 2a b x + 2a b +--R Type: Expression Integer +--E 525 + +--S 526 of 1483 +a0101:=integrate(t0101,x) +--R +--R +--R (b x + a)log(b x + a) + (- b x - a)log(b x - a) - 2a +--R (526) ---------------------------------------------------- +--R 2 2 3 +--R 4a b x + 4a b +--R Type: Union(Expression Integer,...) +--E 526 + +--S 527 of 1483 +m0101:=a0101-r0101 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (527) ----------------------------------------- +--R 2 +--R 4a b +--R Type: Expression Integer +--E 527 + +--S 528 of 1483 +d0101:=D(m0101,x) +--R +--R +--R (528) 0 +--R Type: Expression Integer +--E 528 + +--S 529 of 1483 +t0102:= 1/(a+b*x)^2/(a^2-b^2*x^2) +--R +--R +--R 1 +--R (529) - ---------------------------- +--R 4 4 3 3 3 4 +--R b x + 2a b x - 2a b x - a +--R Type: Fraction Polynomial Integer +--E 529 + +--S 530 of 1483 +r0102:= -1/4/a/b/(a+b*x)^2-1/4/a^2/b/(a+b*x)+1/4*atanh(b*x/a)/a^3/b +--R +--R +--R 2 2 2 b x 2 +--R (b x + 2a b x + a )atanh(---) - a b x - 2a +--R a +--R (530) -------------------------------------------- +--R 3 3 2 4 2 5 +--R 4a b x + 8a b x + 4a b +--R Type: Expression Integer +--E 530 + +--S 531 of 1483 +a0102:=integrate(t0102,x) +--R +--R +--R (531) +--R 2 2 2 2 2 2 +--R (b x + 2a b x + a )log(b x + a) + (- b x - 2a b x - a )log(b x - a) +--R + +--R 2 +--R - 2a b x - 4a +--R / +--R 3 3 2 4 2 5 +--R 8a b x + 16a b x + 8a b +--R Type: Union(Expression Integer,...) +--E 531 + +--S 532 of 1483 +m0102:=a0102-r0102 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (532) ----------------------------------------- +--R 3 +--R 8a b +--R Type: Expression Integer +--E 532 + +--S 533 of 1483 +d0102:=D(m0102,x) +--R +--R +--R (533) 0 +--R Type: Expression Integer +--E 533 + +--S 534 of 1483 +t0103:= (a+b*x)/(a^2-b^2*x^2)^2 +--R +--R +--R 1 +--R (534) -------------------------- +--R 3 3 2 2 2 3 +--R b x - a b x - a b x + a +--R Type: Fraction Polynomial Integer +--E 534 + +--S 535 of 1483 +r0103:= 1/2/a/b/(a-b*x)+1/2*atanh(b*x/a)/a^2/b +--R +--R +--R b x +--R (b x - a)atanh(---) - a +--R a +--R (535) ----------------------- +--R 2 2 3 +--R 2a b x - 2a b +--R Type: Expression Integer +--E 535 + +--S 536 of 1483 +a0103:=integrate(t0103,x) +--R +--R +--R (b x - a)log(b x + a) + (- b x + a)log(b x - a) - 2a +--R (536) ---------------------------------------------------- +--R 2 2 3 +--R 4a b x - 4a b +--R Type: Union(Expression Integer,...) +--E 536 + +--S 537 of 1483 +m0103:=a0103-r0103 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (537) ----------------------------------------- +--R 2 +--R 4a b +--R Type: Expression Integer +--E 537 + +--S 538 of 1483 +d0103:=D(m0103,x) +--R +--R +--R (538) 0 +--R Type: Expression Integer +--E 538 + +--S 539 of 1483 +t0104:= (a+b*x)^2/(a^2-b^2*x^2)^3 +--R +--R +--R 1 +--R (539) - ---------------------------- +--R 4 4 3 3 3 4 +--R b x - 2a b x + 2a b x - a +--R Type: Fraction Polynomial Integer +--E 539 + +--S 540 of 1483 +r0104:= 1/4/a/b/(a-b*x)^2+1/4/a^2/b/(a-b*x)+1/4*atanh(b*x/a)/a^3/b +--R +--R +--R 2 2 2 b x 2 +--R (b x - 2a b x + a )atanh(---) - a b x + 2a +--R a +--R (540) -------------------------------------------- +--R 3 3 2 4 2 5 +--R 4a b x - 8a b x + 4a b +--R Type: Expression Integer +--E 540 + +--S 541 of 1483 +a0104:=integrate(t0104,x) +--R +--R +--R (541) +--R 2 2 2 2 2 2 +--R (b x - 2a b x + a )log(b x + a) + (- b x + 2a b x - a )log(b x - a) +--R + +--R 2 +--R - 2a b x + 4a +--R / +--R 3 3 2 4 2 5 +--R 8a b x - 16a b x + 8a b +--R Type: Union(Expression Integer,...) +--E 541 + +--S 542 of 1483 +m0104:=a0104-r0104 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (542) ----------------------------------------- +--R 3 +--R 8a b +--R Type: Expression Integer +--E 542 + +--S 543 of 1483 +d0104:=D(m0104,x) +--R +--R +--R (543) 0 +--R Type: Expression Integer +--E 543 + +--S 544 of 1483 +t0105:= (a+b*x^2)/(1-x^2) +--R +--R +--R 2 +--R - b x - a +--R (544) ---------- +--R 2 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 544 + +--S 545 of 1483 +r0105:= -b*x+(a+b)*atanh(x) +--R +--R +--R (545) (b + a)atanh(x) - b x +--R Type: Expression Integer +--E 545 + +--S 546 of 1483 +a0105:=integrate(t0105,x) +--R +--R +--R (b + a)log(x + 1) + (- b - a)log(x - 1) - 2b x +--R (546) ---------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 546 + +--S 547 of 1483 +m0105:=a0105-r0105 +--R +--R +--R (b + a)log(x + 1) + (- b - a)log(x - 1) + (- 2b - 2a)atanh(x) +--R (547) ------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 547 + +--S 548 of 1483 +d0105:=D(m0105,x) +--R +--R +--R (548) 0 +--R Type: Expression Integer +--E 548 + +--S 549 of 1483 +t0106:= (a+b*x^2)/(c+d*x^2)^3 +--R +--R +--R 2 +--R b x + a +--R (549) ----------------------------- +--R 3 6 2 4 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction Polynomial Integer +--E 549 + +--S 550 of 1483 +r0106:= 1/4*a*x/c/(c+d*x^2)^2-1/4*b*x/d/(c+d*x^2)^2+_ + 1/8*(b*c+3*a*d)*x/c^2/d/(c+d*x^2)+_ + 1/8*(b*c+3*a*d)*atan(d^(1/2)*x/c^(1/2))/c^(5/2)/d^(3/2) +--R +--R +--R (550) +--R +-+ +--R 3 2 4 2 2 2 2 3 x\|d +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )atan(-----) +--R +-+ +--R \|c +--R + +--R 2 3 2 +-+ +-+ +--R ((3a d + b c d)x + (5a c d - b c )x)\|c \|d +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8c d x + 16c d x + 8c d)\|c \|d +--R Type: Expression Integer +--E 550 + +--S 551 of 1483 +a0106:=integrate(t0106,x) +--R +--R +--R (551) +--R [ +--R 3 2 4 2 2 2 2 3 +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c ) +--R * +--R 2 +-----+ +--R (d x - c)\|- c d + 2c d x +--R log(---------------------------) +--R 2 +--R d x + c +--R + +--R 2 3 2 +-----+ +--R ((6a d + 2b c d)x + (10a c d - 2b c )x)\|- c d +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16c d x + 32c d x + 16c d)\|- c d +--R , +--R +--R 3 2 4 2 2 2 2 3 +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c ) +--R * +--R +---+ +--R x\|c d +--R atan(-------) +--R c +--R + +--R 2 3 2 +---+ +--R ((3a d + b c d)x + (5a c d - b c )x)\|c d +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8c d x + 16c d x + 8c d)\|c d +--R ] +--R Type: Union(List Expression Integer,...) +--E 551 + +--S 552 of 1483 +m0106a:=a0106.1-r0106 +--R +--R +--R (552) +--R 2 +-----+ +--R +-+ +-+ (d x - c)\|- c d + 2c d x +--R (3a d + b c)\|c \|d log(---------------------------) +--R 2 +--R d x + c +--R + +--R +-+ +--R +-----+ x\|d +--R (- 6a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 16c d\|- c d \|c \|d +--R Type: Expression Integer +--E 552 + +--S 553 of 1483 +d0106a:=D(m0106a,x) +--R +--R +--R (553) 0 +--R Type: Expression Integer +--E 553 + +--S 554 of 1483 +m0106b:=a0106.2-r0106 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|d +--R (3a d + b c)\|c \|d atan(-------) + (- 3a d - b c)\|c d atan(-----) +--R c +-+ +--R \|c +--R (554) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8c d\|c \|d \|c d +--R Type: Expression Integer +--E 554 + +--S 555 of 1483 +d0106b:=D(m0106b,x) +--R +--R +--R (555) 0 +--R Type: Expression Integer +--E 555 + +--S 556 of 1483 +t0107:= x^4*(a+b*x^2)/(c+d*x^2) +--R +--R +--R 6 4 +--R b x + a x +--R (556) ----------- +--R 2 +--R d x + c +--R Type: Fraction Polynomial Integer +--E 556 + +--S 557 of 1483 +r0107:= c*(b*c-a*d)*x/d^3-1/3*(b*c-a*d)*x^3/d^2+1/5*b*x^5/d-_ + c^(3/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/d^(7/2) +--R +--R +--R (557) +--R +-+ +--R 2 +-+ x\|d +--R (15a c d - 15b c )\|c atan(-----) +--R +-+ +--R \|c +--R + +--R 2 5 2 3 2 +-+ +--R (3b d x + (5a d - 5b c d)x + (- 15a c d + 15b c )x)\|d +--R / +--R 3 +-+ +--R 15d \|d +--R Type: Expression Integer +--E 557 + +--S 558 of 1483 +a0107:=integrate(t0107,x) +--R +--R +--R (558) +--R [ +--R +---+ +--R | c 2 +--R +---+ 2d x |- - + d x - c +--R 2 | c \| d 2 5 +--R (15a c d - 15b c ) |- - log(---------------------) + 6b d x +--R \| d 2 +--R d x + c +--R + +--R 2 3 2 +--R (10a d - 10b c d)x + (- 30a c d + 30b c )x +--R / +--R 3 +--R 30d +--R , +--R +--R +-+ +--R |c +--R +-+ |- +--R 2 |c \|d 2 5 2 3 +--R (- 15a c d + 15b c ) |- atan(----) + 3b d x + (5a d - 5b c d)x +--R \|d x +--R + +--R 2 +--R (- 15a c d + 15b c )x +--R / +--R 3 +--R 15d +--R ] +--R Type: Union(List Expression Integer,...) +--E 558 + +--S 559 of 1483 +m0107a:=a0107.1-r0107 +--R +--R +--R (559) +--R +---+ +--R | c 2 +--R +---+ 2d x |- - + d x - c +--R 2 | c +-+ \| d +--R (a c d - b c ) |- - \|d log(---------------------) +--R \| d 2 +--R d x + c +--R + +--R +-+ +--R 2 +-+ x\|d +--R (- 2a c d + 2b c )\|c atan(-----) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2d \|d +--R Type: Expression Integer +--E 559 + +--S 560 of 1483 +d0107a:=D(m0107a,x) +--R +--R +--R (560) 0 +--R Type: Expression Integer +--E 560 + +--S 561 of 1483 +m0107b:=a0107.2-r0107 +--R +--R +--R +-+ +--R |c +--R +-+ +-+ |- +--R 2 +-+ x\|d 2 |c +-+ \|d +--R (- a c d + b c )\|c atan(-----) + (- a c d + b c ) |- \|d atan(----) +--R +-+ \|d x +--R \|c +--R (561) -------------------------------------------------------------------- +--R 3 +-+ +--R d \|d +--R Type: Expression Integer +--E 561 + +--S 562 of 1483 +d0107b:=D(m0107b,x) +--R +--R +--R (562) 0 +--R Type: Expression Integer +--E 562 + +--S 563 of 1483 +t0108:= x^2*(a+b*x^2)/(c+d*x^2) +--R +--R +--R 4 2 +--R b x + a x +--R (563) ----------- +--R 2 +--R d x + c +--R Type: Fraction Polynomial Integer +--E 563 + +--S 564 of 1483 +r0108:= -(b*c-a*d)*x/d^2+1/3*b*x^3/d+_ + c^(1/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/d^(5/2) +--R +--R +--R +-+ +--R +-+ x\|d 3 +-+ +--R (- 3a d + 3b c)\|c atan(-----) + (b d x + (3a d - 3b c)x)\|d +--R +-+ +--R \|c +--R (564) -------------------------------------------------------------- +--R 2 +-+ +--R 3d \|d +--R Type: Expression Integer +--E 564 + +--S 565 of 1483 +a0108:=integrate(t0108,x) +--R +--R +--R (565) +--R +---+ +--R | c 2 +--R +---+ - 2d x |- - + d x - c +--R | c \| d 3 +--R (3a d - 3b c) |- - log(-----------------------) + 2b d x + (6a d - 6b c)x +--R \| d 2 +--R d x + c +--R [--------------------------------------------------------------------------, +--R 2 +--R 6d +--R +-+ +--R |c +--R +-+ |- +--R |c \|d 3 +--R (3a d - 3b c) |- atan(----) + b d x + (3a d - 3b c)x +--R \|d x +--R -----------------------------------------------------] +--R 2 +--R 3d +--R Type: Union(List Expression Integer,...) +--E 565 + +--S 566 of 1483 +m0108a:=a0108.1-r0108 +--R +--R +--R (566) +--R +---+ +--R | c 2 +--R +---+ - 2d x |- - + d x - c +--R | c +-+ \| d +--R (a d - b c) |- - \|d log(-----------------------) +--R \| d 2 +--R d x + c +--R + +--R +-+ +--R +-+ x\|d +--R (2a d - 2b c)\|c atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2d \|d +--R Type: Expression Integer +--E 566 + +--S 567 of 1483 +d0108a:=D(m0108a,x) +--R +--R +--R (567) 0 +--R Type: Expression Integer +--E 567 + +--S 568 of 1483 +m0108b:=a0108.2-r0108 +--R +--R +--R +-+ +--R |c +--R +-+ +-+ |- +--R +-+ x\|d |c +-+ \|d +--R (a d - b c)\|c atan(-----) + (a d - b c) |- \|d atan(----) +--R +-+ \|d x +--R \|c +--R (568) ---------------------------------------------------------- +--R 2 +-+ +--R d \|d +--R Type: Expression Integer +--E 568 + +--S 569 of 1483 +d0108b:=D(m0108b,x) +--R +--R +--R (569) 0 +--R Type: Expression Integer +--E 569 + +--S 570 of 1483 +t0109:= (a+b*x^2)/x^2/(c+d*x^2) +--R +--R +--R 2 +--R b x + a +--R (570) ----------- +--R 4 2 +--R d x + c x +--R Type: Fraction Polynomial Integer +--E 570 + +--S 571 of 1483 +r0109:= -a/c/x+(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/c^(3/2)/d^(1/2) +--R +--R +--R +-+ +--R x\|d +-+ +-+ +--R (- a d + b c)x atan(-----) - a\|c \|d +--R +-+ +--R \|c +--R (571) -------------------------------------- +--R +-+ +-+ +--R c x\|c \|d +--R Type: Expression Integer +--E 571 + +--S 572 of 1483 +a0109:=integrate(t0109,x) +--R +--R +--R (572) +--R 2 +-----+ +--R (d x - c)\|- c d - 2c d x +-----+ +--R (a d - b c)x log(---------------------------) - 2a\|- c d +--R 2 +--R d x + c +--R [----------------------------------------------------------, +--R +-----+ +--R 2c x\|- c d +--R +---+ +--R x\|c d +---+ +--R (- a d + b c)x atan(-------) - a\|c d +--R c +--R --------------------------------------] +--R +---+ +--R c x\|c d +--R Type: Union(List Expression Integer,...) +--E 572 + +--S 573 of 1483 +m0109a:=a0109.1-r0109 +--R +--R +--R (573) +--R 2 +-----+ +--R +-+ +-+ (d x - c)\|- c d - 2c d x +--R (a d - b c)\|c \|d log(---------------------------) +--R 2 +--R d x + c +--R + +--R +-+ +--R +-----+ x\|d +--R (2a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|c +--R / +--R +-----+ +-+ +-+ +--R 2c\|- c d \|c \|d +--R Type: Expression Integer +--E 573 + +--S 574 of 1483 +d0109a:=D(m0109a,x) +--R +--R +--R (574) 0 +--R Type: Expression Integer +--E 574 + +--S 575 of 1483 +m0109b:=a0109.2-r0109 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|d +--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----) +--R c +-+ +--R \|c +--R (575) ----------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|c \|d \|c d +--R Type: Expression Integer +--E 575 + +--S 576 of 1483 +d0109b:=D(m0109b,x) +--R +--R +--R (576) 0 +--R Type: Expression Integer +--E 576 + +--S 577 of 1483 +t0110:= (a+b*x^2)/x^4/(c+d*x^2) +--R +--R +--R 2 +--R b x + a +--R (577) ----------- +--R 6 4 +--R d x + c x +--R Type: Fraction Polynomial Integer +--E 577 + +--S 578 of 1483 +r0110:= -1/3*a/c/x^3-(b*c-a*d)/c^2/x-_ + d^(1/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/c^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|d 2 +-+ +--R (3a d - 3b c)x \|d atan(-----) + ((3a d - 3b c)x - a c)\|c +--R +-+ +--R \|c +--R (578) ------------------------------------------------------------ +--R 2 3 +-+ +--R 3c x \|c +--R Type: Expression Integer +--E 578 + +--S 579 of 1483 +a0110:=integrate(t0110,x) +--R +--R +--R (579) +--R +---+ +--R | d 2 +--R +---+ 2c x |- - + d x - c +--R 3 | d \| c 2 +--R (3a d - 3b c)x |- - log(---------------------) + (6a d - 6b c)x - 2a c +--R \| c 2 +--R d x + c +--R [------------------------------------------------------------------------, +--R 2 3 +--R 6c x +--R +-+ +--R |d +--R +-+ c |- +--R 3 |d \|c 2 +--R (- 3a d + 3b c)x |- atan(-----) + (3a d - 3b c)x - a c +--R \|c d x +--R --------------------------------------------------------] +--R 2 3 +--R 3c x +--R Type: Union(List Expression Integer,...) +--E 579 + +--S 580 of 1483 +m0110a:=a0110.1-r0110 +--R +--R +--R (580) +--R +---+ +--R | d 2 +--R +---+ 2c x |- - + d x - c +--R | d +-+ \| c +--R (a d - b c) |- - \|c log(---------------------) +--R \| c 2 +--R d x + c +--R + +--R +-+ +--R +-+ x\|d +--R (- 2a d + 2b c)\|d atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2c \|c +--R Type: Expression Integer +--E 580 + +--S 581 of 1483 +d0110a:=D(m0110a,x) +--R +--R +--R (581) 0 +--R Type: Expression Integer +--E 581 + +--S 582 of 1483 +m0110b:=a0110.2-r0110 +--R +--R +--R +-+ +--R |d +--R +-+ +-+ c |- +--R +-+ x\|d +-+ |d \|c +--R (- a d + b c)\|d atan(-----) + (- a d + b c)\|c |- atan(-----) +--R +-+ \|c d x +--R \|c +--R (582) --------------------------------------------------------------- +--R 2 +-+ +--R c \|c +--R Type: Expression Integer +--E 582 + +--S 583 of 1483 +d0110b:=D(m0110b,x) +--R +--R +--R (583) 0 +--R Type: Expression Integer +--E 583 + +--S 584 of 1483 +t0111:= x^2*(a+b*x^3)^2 +--R +--R +--R 2 8 5 2 2 +--R (584) b x + 2a b x + a x +--R Type: Polynomial Integer +--E 584 + +--S 585 of 1483 +r0111:= 1/9*(a+b*x^3)^3/b +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - b x + - a b x + - a b x + - a +--R 9 3 3 9 +--R (585) ----------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 585 + +--S 586 of 1483 +a0111:=integrate(t0111,x) +--R +--R +--R 1 2 9 1 6 1 2 3 +--R (586) - b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial Fraction Integer +--E 586 + +--S 587 of 1483 +m0111:=a0111-r0111 +--R +--R +--R 1 3 +--R - a +--R 9 +--R (587) - ---- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 587 + +--S 588 of 1483 +d0111:=D(m0111,x) +--R +--R +--R (588) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 588 + +--S 589 of 1483 +t0112:= (a+b*x^3)^2/x^10 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (589) ------------------- +--R 10 +--R x +--R Type: Fraction Polynomial Integer +--E 589 + +--S 590 of 1483 +r0112:= -1/9*(a+b*x^3)^3/a/x^9 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - - a +--R 9 3 3 9 +--R (590) ------------------------------------- +--R 9 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 590 + +--S 591 of 1483 +a0112:=integrate(t0112,x) +--R +--R +--R 2 6 3 2 +--R - 3b x - 3a b x - a +--R (591) ---------------------- +--R 9 +--R 9x +--R Type: Union(Expression Integer,...) +--E 591 + +--S 592 of 1483 +m0112:=a0112-r0112 +--R +--R +--R 3 +--R b +--R (592) -- +--R 9a +--R Type: Expression Integer +--E 592 + +--S 593 of 1483 +d0112:=D(m0112,x) +--R +--R +--R (593) 0 +--R Type: Expression Integer +--E 593 + +--S 594 of 1483 +t0113:= x^2*(a+b*x^3)^3 +--R +--R +--R 3 11 2 8 2 5 3 2 +--R (594) b x + 3a b x + 3a b x + a x +--R Type: Polynomial Integer +--E 594 + +--S 595 of 1483 +r0113:= 1/12*(a+b*x^3)^4/b +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 12 3 2 3 12 +--R (595) ------------------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 595 + +--S 596 of 1483 +a0113:=integrate(t0113,x) +--R +--R +--R 1 3 12 1 2 9 1 2 6 1 3 3 +--R (596) -- b x + - a b x + - a b x + - a x +--R 12 3 2 3 +--R Type: Polynomial Fraction Integer +--E 596 + +--S 597 of 1483 +m0113:=a0113-r0113 +--R +--R +--R 1 4 +--R -- a +--R 12 +--R (597) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 597 + +--S 598 of 1483 +d0113:=D(m0113,x) +--R +--R +--R (598) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 598 + +--S 599 of 1483 +t0114:= (a+b*x^3)^3/x^13 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (599) ----------------------------- +--R 13 +--R x +--R Type: Fraction Polynomial Integer +--E 599 + +--S 600 of 1483 +r0114:= -1/12*(a+b*x^3)^4/a/x^12 +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R - -- b x - - a b x - - a b x - - a b x - -- a +--R 12 3 2 3 12 +--R (600) --------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction Polynomial Fraction Integer +--E 600 + +--S 601 of 1483 +a0114:=integrate(t0114,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 4b x - 6a b x - 4a b x - a +--R (601) -------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression Integer,...) +--E 601 + +--S 602 of 1483 +m0114:=a0114-r0114 +--R +--R +--R 4 +--R b +--R (602) --- +--R 12a +--R Type: Expression Integer +--E 602 + +--S 603 of 1483 +d0114:=D(m0114,x) +--R +--R +--R (603) 0 +--R Type: Expression Integer +--E 603 + +--S 604 of 1483 +t0115:= (a+b*x)^4/(c+d*x^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (604) -------------------------------------- +--R 3 +--R d x + c +--R Type: Fraction Polynomial Integer +--E 604 + +--S 605 of 1483 +r0115:= 4*a*b^3*x/d+1/2*b^4*x^2/d-1/3*b*(b^3*c-4*a^3*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(1/3)/d^(5/3)-_ + 1/3*a*(4*b^3*c-a^3*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(2/3)/d^(4/3)+_ + 1/3*b*(b^3*c-4*a^3*d)*log(c^(1/3)/d^(1/3)+x)/c^(1/3)/d^(5/3)-_ + 1/3*a*(4*b^3*c-a^3*d)*log(c^(1/3)/d^(1/3)+x)/c^(2/3)/d^(4/3)-_ + 1/6*b*(b^3*c-4*a^3*d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(1/3)/d^(5/3)+_ + 1/6*a*(4*b^3*c-a^3*d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(2/3)/d^(4/3)+2*a^2*b^2*log(c+d*x^3)/d +--R +--R +--R (605) +--R 4 3 3+-+ 3 4 3+-+ +--R ((- a d + 4a b c)\|d + (4a b d - b c)\|c ) +--R * +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|d - x\|c \|d + \|c +--R log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 4 3 3+-+ 3 4 3+-+ x\|d + \|c +--R ((2a d - 8a b c)\|d + (- 8a b d + 2b c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R 4 3 +-+3+-+ 3 4 +-+3+-+ +--R ((2a d - 8a b c)\|3 \|d + (8a b d - 2b c)\|3 \|c ) +--R * +--R +-+3+-+ +-+3+-+ +--R 2x\|3 \|d - \|3 \|c +--R atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 2 2 3 4 2 3 3+-+2 3+-+2 +--R (12a b log(d x + c) + 3b x + 24a b x)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression Integer +--E 605 + +--S 606 of 1483 +a0115:=integrate(t0115,x) +--R +--R +--R (606) +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R - d |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 2 +--R - d %%F0 + 6a b +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 2 6 3 2 +--R ((36a b c d - 9b c d )%%F0 - 3a c d - 48a b c d - 30a b c d ) +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R d |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 2 +--R - d %%F0 + 6a b +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 +--R (- 36a b c d + 9b c d )%%F0 + 3a c d + 48a b c d +--R + +--R 2 6 3 2 +--R 30a b c d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 2d %%F0 +--R * +--R log +--R 3 2 4 4 3 3 2 +--R (36a b c d - 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (3a c d - 168a b c d + 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (a d + 52a b c d - 52a b c d - b c )x + 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R 48a b c d - 66a b c d - 8a b c +--R + +--R 4 2 3 +--R b x + 8a b x +--R / +--R 2d +--R Type: Union(Expression Integer,...) +--E 606 + +--S 607 of 1483 +m0115:=a0115-r0115 +--R +--R +--R (607) +--R - +--R 3+-+2 3+-+2 +--R 3d \|c \|d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 2 2 3+-+2 3+-+2 +--R - 3d \|c \|d %%F + 18a b \|c \|d +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 2 6 3 2 +--R ((36a b c d - 9b c d )%%F0 - 3a c d - 48a b c d - 30a b c d ) +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 3+-+2 3+-+2 +--R 3d \|c \|d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 2 2 3+-+2 3+-+2 +--R - 3d \|c \|d %%F + 18a b \|c \|d +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 +--R (- 36a b c d + 9b c d )%%F0 + 3a c d + 48a b c d +--R + +--R 2 6 3 2 +--R 30a b c d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 3+-+2 3+-+2 +--R 6d \|c \|d %%F0 +--R * +--R log +--R 3 2 4 4 3 3 2 +--R (36a b c d - 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (3a c d - 168a b c d + 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (a d + 52a b c d - 52a b c d - b c )x + 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R 48a b c d - 66a b c d - 8a b c +--R + +--R 4 3 3+-+ 3 4 3+-+ +--R ((a d - 4a b c)\|d + (- 4a b d + b c)\|c ) +--R * +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|d - x\|c \|d + \|c +--R log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 4 3 3+-+ 3 4 3+-+ x\|d + \|c +--R ((- 2a d + 8a b c)\|d + (8a b d - 2b c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R 4 3 +-+3+-+ 3 4 +-+3+-+ +--R ((- 2a d + 8a b c)\|3 \|d + (- 8a b d + 2b c)\|3 \|c ) +--R * +--R +-+3+-+ +-+3+-+ +--R 2x\|3 \|d - \|3 \|c +--R atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 2 2 3 3+-+2 3+-+2 +--R - 12a b log(d x + c)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression Integer +--E 607 + +--S 608 of 1483 +d0115:=D(m0115,x) +--R +--R +--R (608) 0 +--R Type: Expression Integer +--E 608 + +--S 609 of 1483 +t0116:= (1+x)^4/(c+d*x^3) +--R +--R +--R 4 3 2 +--R x + 4x + 6x + 4x + 1 +--R (609) ----------------------- +--R 3 +--R d x + c +--R Type: Fraction Polynomial Integer +--E 609 + +--S 610 of 1483 +r0116:= 4*x/d+1/2*x^2/d-1/3*(c-4*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(1/3)/d^(5/3)-_ + 1/3*(4*c-d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(2/3)/d^(4/3)+_ + 1/3*(c-4*d)*log(c^(1/3)/d^(1/3)+x)/c^(1/3)/d^(5/3)-_ + 1/3*(4*c-d)*log(c^(1/3)/d^(1/3)+x)/c^(2/3)/d^(4/3)-_ + 1/6*(c-4*d)*log(c^(2/3)/d^(2/3)-c^(1/3)*x/d^(1/3)+_ + x^2)/c^(1/3)/d^(5/3)+1/6*(4*c-d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(2/3)/d^(4/3)+2*log(c+d*x^3)/d +--R +--R +--R (610) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3+-+ x \|d - x\|c \|d + \|c +--R ((- d + 4c)\|d + (4d - c)\|c )log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ x\|d + \|c +--R ((2d - 8c)\|d + (- 8d + 2c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ 2x\|3 \|d - \|3 \|c +--R ((2d - 8c)\|3 \|d + (8d - 2c)\|3 \|c )atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 3 2 3+-+2 3+-+2 +--R (12log(d x + c) + 3x + 24x)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression Integer +--E 610 + +--S 611 of 1483 +a0116:=integrate(t0116,x) +--R +--R +--R (611) +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R (- d |----------------------------------------------- - d %%G0 + 6) +--R | 3 +--R \| 3c d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((36c d - 9c d )%%G0 - 3c d - 48c d - 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R (d |----------------------------------------------- - d %%G0 + 6) +--R | 3 +--R \| 3c d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((- 36c d + 9c d )%%G0 + 3c d + 48c d + 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R 2d %%G0 +--R * +--R log +--R 2 4 3 3 2 4 2 3 3 2 +--R (36c d - 9c d )%%G0 + (3c d - 168c d + 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (d + 52c d - 52c d - c )x + 26c d + 48c d - 66c d - 8c +--R + +--R 2 +--R x + 8x +--R / +--R 2d +--R Type: Union(Expression Integer,...) +--E 611 + +--S 612 of 1483 +m0116:=a0116-r0116 +--R +--R +--R (612) +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R 3+-+2 3+-+2 |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R - 3d \|c \|d |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3d \|c \|d %%G + 18\|c \|d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((36c d - 9c d )%%G0 - 3c d - 48c d - 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R 3+-+2 3+-+2 |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R 3d \|c \|d |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3d \|c \|d %%G + 18\|c \|d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((- 36c d + 9c d )%%G0 + 3c d + 48c d + 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R 3+-+2 3+-+2 +--R 6d \|c \|d %%G0 +--R * +--R log +--R 2 4 3 3 2 4 2 3 3 2 +--R (36c d - 9c d )%%G0 + (3c d - 168c d + 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (d + 52c d - 52c d - c )x + 26c d + 48c d - 66c d - 8c +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3+-+ x \|d - x\|c \|d + \|c +--R ((d - 4c)\|d + (- 4d + c)\|c )log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ x\|d + \|c +--R ((- 2d + 8c)\|d + (8d - 2c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ 2x\|3 \|d - \|3 \|c +--R ((- 2d + 8c)\|3 \|d + (- 8d + 2c)\|3 \|c )atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 3 3+-+2 3+-+2 +--R - 12log(d x + c)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression Integer +--E 612 + +--S 613 of 1483 +d0116:=D(m0116,x) +--R +--R +--R (613) 0 +--R Type: Expression Integer +--E 613 + +--S 614 of 1483 +t0117:= x^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 +--R x +--R (614) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 614 + +--S 615 of 1483 +r0117:= (c+d*x)/b/d^4+3^(1/2)*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))/a^(1/3)/b^(2/3)/d^4-_ + 1/3*(a+b*c^3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(4/3)/d^4-_ + c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^4-_ + 1/3*(a+b*c^3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(4/3)/d^4+_ + 1/2*c^2*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^4+1/6*(a+b*c^3)*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(4/3)/d^4-_ + c*log(a+b*(c+d*x)^3)/b/d^4 +--R +--R +--R (615) +--R 3 3+-+ 2 3+-+ +--R ((b c + a)\|b + 3b c \|a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ 2 3+-+ (d x + c)\|b + \|a +--R ((- 2b c - 2a)\|b - 6b c \|a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 +-+3+-+ 2 +-+3+-+ +--R ((- 2b c - 2a)\|3 \|b + 6b c \|3 \|a ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R (- 6c log(b d x + 3b c d x + 3b c d x + b c + a) + 6d x + 6c)\|a \|b +--R / +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression Integer +--E 615 + +--S 616 of 1483 +a0117:=integrate(t0117,x) +--R +--R +--R (616) +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c 4 +--R (b d |--------------------------------------------- - b d %%H0 - 3c) +--R | 2 8 +--R \| a b d +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (27a b c d %%H0 + (- 3a b c + 21a b c - 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c 4 +--R - b d |--------------------------------------------- - b d %%H0 +--R | 2 8 +--R \| a b d +--R + +--R - 3c +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (- 27a b c d %%H0 + (3a b c - 21a b c + 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R 4 +--R 2b d %%H0 +--R * +--R log +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R - 27a b c d %%H0 + (- 3a b c - 60a b c - 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 +--R (b c - 24a b c + 3a b c + a )d x + b c - 9a b c - 12a b c +--R + +--R 3 +--R - 2a c +--R + +--R 2d x +--R / +--R 4 +--R 2b d +--R Type: Union(Expression Integer,...) +--E 616 + +--S 617 of 1483 +m0117:=a0117-r0117 +--R +--R +--R (617) +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 3+-+2 3+-+2 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R 3b d \|a \|b |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 4 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% - 9c \|a \|b +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (27a b c d %%H0 + (- 3a b c + 21a b c - 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 3+-+2 3+-+2 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R - 3b d \|a \|b |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 4 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% - 9c \|a \|b +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (- 27a b c d %%H0 + (3a b c - 21a b c + 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R 3 3+-+ 2 3+-+ +--R ((- b c - a)\|b - 3b c \|a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ 2 3+-+ (d x + c)\|b + \|a +--R ((2b c + 2a)\|b + 6b c \|a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b %%H0 +--R * +--R log +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R - 27a b c d %%H0 + (- 3a b c - 60a b c - 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 +--R (b c - 24a b c + 3a b c + a )d x + b c - 9a b c - 12a b c +--R + +--R 3 +--R - 2a c +--R + +--R 3 +-+3+-+ 2 +-+3+-+ +--R ((2b c + 2a)\|3 \|b - 6b c \|3 \|a ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R (6c log(b d x + 3b c d x + 3b c d x + b c + a) - 6c)\|a \|b +--R / +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression Integer +--E 617 + +--S 618 of 1483 +d0117:=D(m0117,x) +--R +--R +--R (618) 0 +--R Type: Expression Integer +--E 618 + +--S 619 of 1483 +t0118:= x^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 +--R x +--R (619) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 619 + +--S 620 of 1483 +r0118:= -2/3*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d^3+_ + 1/3*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d^3+_ + 2/3*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^3+_ + 1/3*c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d^3-_ + 1/3*c*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^3-1/6*c^2*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(1/3)/d^3+_ + 1/3*log(a+b*(c+d*x)^3)/b/d^3 +--R +--R +--R (620) +--R 2 3+-+ 3+-+ +--R (- b c \|b - 2b c\|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+ 3+-+ (d x + c)\|b + \|a +--R (2b c \|b + 4b c\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2b c \|3 \|b - 4b c\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R 2log(b d x + 3b c d x + 3b c d x + b c + a)\|a \|b +--R / +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression Integer +--E 620 + +--S 621 of 1483 +a0118:=integrate(t0118,x) +--R +--R +--R (621) +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a 3 +--R (b d |---------------------------------------- - b d %%I0 + 1) +--R | 2 6 +--R \| 3a b d +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (18a b d %%I0 + (3a b c - 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a 3 +--R (- b d |---------------------------------------- - b d %%I0 + 1) +--R | 2 6 +--R \| 3a b d +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (- 18a b d %%I0 + (- 3a b c + 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R 3 +--R 2b d %%I0 +--R * +--R log +--R 2 2 6 2 2 3 2 3 2 5 2 +--R - 18a b d %%I0 + (3a b c + 12a b)d %%I0 + (b c - 8a b c )d x +--R + +--R 2 6 3 2 +--R b c - a b c - 2a +--R / +--R 3 +--R 2b d +--R Type: Union(Expression Integer,...) +--E 621 + +--S 622 of 1483 +m0118:=a0118-r0118 +--R +--R +--R (622) +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 3+-+2 3+-+2 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R 3b d \|a \|b |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 3 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% + 3\|a \|b +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (18a b d %%I0 + (3a b c - 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 3+-+2 3+-+2 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R - 3b d \|a \|b |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 3 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% + 3\|a \|b +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (- 18a b d %%I0 + (- 3a b c + 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R 2 3+-+ 3+-+ +--R (b c \|b + 2b c\|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+ 3+-+ (d x + c)\|b + \|a +--R (- 2b c \|b - 4b c\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b %%I0 +--R * +--R log +--R 2 2 6 2 2 3 2 3 2 5 2 +--R - 18a b d %%I0 + (3a b c + 12a b)d %%I0 + (b c - 8a b c )d x +--R + +--R 2 6 3 2 +--R b c - a b c - 2a +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2b c \|3 \|b + 4b c\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R - 2log(b d x + 3b c d x + 3b c d x + b c + a)\|a \|b +--R / +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression Integer +--E 622 + +--S 623 of 1483 +d0118:=D(m0118,x) +--R +--R +--R (623) 0 +--R Type: Expression Integer +--E 623 + +--S 624 of 1483 +t0119:= x/(a+b*(c+d*x)^3) +--R +--R +--R x +--R (624) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 624 + +--S 625 of 1483 +r0119:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d^2-_ + 1/3*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d^2-_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^2-_ + 1/3*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d^2+_ + 1/6*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^2+1/6*c*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(1/3)/d^2 +--R +--R +--R (625) +--R 3+-+ 3+-+ +--R (c\|b + \|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ (d x + c)\|b + \|a +--R (- 2c\|b - 2\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2c\|3 \|b + 2\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b +--R Type: Expression Integer +--E 625 + +--S 626 of 1483 +a0119:=integrate(t0119,x) +--R +--R +--R (626) +--R +-------------------+ +--R | 4 2 +--R |- 9a b d %%J0 + 4c +--R ( |------------------- - %%J0) +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (9a b d %%J0 - 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R +-------------------+ +--R | 4 2 +--R |- 9a b d %%J0 + 4c +--R (- |------------------- - %%J0) +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (- 9a b d %%J0 + 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R 2 4 2 2 2 3 4 +--R 2%%J0 log(- 9a b d %%J0 - 3a b c d %%J0 + (b c - a)d x + b c + a c) +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 626 + +--S 627 of 1483 +m0119:=a0119-r0119 +--R +--R +--R (627) +--R +-------------------+ +--R | 4 2 +--R 2 3+-+2 3+-+2 |- 9a b d %%J0 + 4c 2 3+-+2 3+-+2 +--R (3d \|a \|b |------------------ - 3d \|a \|b %%)0 +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (9a b d %%J0 - 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R +-------------------+ +--R | 4 2 +--R 2 3+-+2 3+-+2 |- 9a b d %%J0 + 4c 2 3+-+2 3+-+2 +--R (- 3d \|a \|b |------------------ - 3d \|a \|b %%)0 +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (- 9a b d %%J0 + 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R 3+-+ 3+-+ +--R (- c\|b - \|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ (d x + c)\|b + \|a +--R (2c\|b + 2\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b %%J0 +--R * +--R 2 4 2 2 2 3 4 +--R log(- 9a b d %%J0 - 3a b c d %%J0 + (b c - a)d x + b c + a c) +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2c\|3 \|b - 2\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b +--R Type: Expression Integer +--E 627 + +--S 628 of 1483 +d0119:=D(m0119,x) +--R +--R +--R (628) 0 +--R Type: Expression Integer +--E 628 + +--S 629 of 1483 +t0120:= 1/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (629) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 629 + +--S 630 of 1483 +r0120:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d+_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d-_ + 1/6*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(2/3)/b^(1/3)/d +--R +--R +--R (630) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R (d x + c)\|b + \|a +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 2log(--------------------) + 2\|3 atan(------------------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+2 3+-+ +--R 6d \|a \|b +--R Type: Expression Integer +--E 630 + +--S 631 of 1483 +a0120:=integrate(t0120,x) +--R +--R +--R (631) +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R - \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R +-+ 3| 2 (2d x + 2c)\|3 \|a b - a\|3 +--R 2\|3 log((d x + c)\|a b + a) + 6atan(-----------------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 6d\|3 \|a b +--R Type: Union(Expression Integer,...) +--E 631 + +--S 632 of 1483 +m0120:=a0120-r0120 +--R +--R +--R (632) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 6d\|3 \|a \|b \|a b +--R Type: Expression Integer +--E 632 + +--S 633 of 1483 +d0120:=D(m0120,x) +--R +--R +--R (633) 0 +--R Type: Expression Integer +--E 633 + +--S 634 of 1483 +t0121:= 1/x/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (634) -------------------------------------------- +--R 3 4 2 3 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a)x +--R Type: Fraction Polynomial Integer +--E 634 + +--S 635 of 1483 +r0121:= -1/3*b^(1/3)*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/(a+b*c^3)-_ + 1/3*b^(2/3)*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/(a+b*c^3)+_ + log(-d*x)/(a+b*c^3)+_ + 1/3*b^(1/3)*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/(a+b*c^3)-_ + 1/3*b^(2/3)*c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/(a+b*c^3)-_ + 1/6*b^(1/3)*c*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/(a+b*c^3)+1/6*b^(2/3)*c^2*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/(a+b*c^3)-_ + log(a+b*(c+d*x)^3)/(3*a+3*b*c^3) +--R +--R +--R (635) +--R 2 3+-+2 3+-+3+-+ +--R (c \|b - c\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+2 3+-+3+-+ (d x + c)\|b + \|a +--R (- 2c \|b + 2c\|a \|b )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 +-+3+-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2c \|3 \|b - 2c\|3 \|a \|b )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 +--R (- 2log(b d x + 3b c d x + 3b c d x + b c + a) + 6log(- d x))\|a +--R / +--R 3 3+-+2 +--R (6b c + 6a)\|a +--R Type: Expression Integer +--E 635 + +--S 636 of 1483 +a0121:=integrate(t0121,x) +--R +--R +--R (636) +--R 3 +--R (- b c - a) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 +--R (- b c - a)%%L0 - 1 +--R * +--R log +--R 2 3 3 3 2 +--R ((9a b c + 9a )%%L0 + 3a b c + 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 +--R (b c + a) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 +--R (- b c - a)%%L0 - 1 +--R * +--R log +--R 2 3 3 3 2 +--R ((- 9a b c - 9a )%%L0 - 3a b c - 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 +--R (2b c + 2a)%%L0 +--R * +--R 2 3 3 2 3 2 2 3 +--R log((9a b c + 9a )%%L0 + (- 3a b c + 6a )%%L0 + b c d x + b c + a) +--R + +--R 2log(x) +--R / +--R 3 +--R 2b c + 2a +--R Type: Union(Expression Integer,...) +--E 636 + +--S 637 of 1483 +m0121:=a0121-r0121 +--R +--R +--R (637) +--R 3 3+-+2 +--R (- 3b c - 3a)\|a +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 3+-+2 3+-+2 +--R (- 3b c - 3a)\|a %%L0 - 3\|a +--R * +--R log +--R 2 3 3 3 2 +--R ((9a b c + 9a )%%L0 + 3a b c + 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 3+-+2 +--R (3b c + 3a)\|a +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 3+-+2 3+-+2 +--R (- 3b c - 3a)\|a %%L0 - 3\|a +--R * +--R log +--R 2 3 3 3 2 +--R ((- 9a b c - 9a )%%L0 - 3a b c - 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 3+-+2 +--R (6b c + 6a)\|a %%L0 +--R * +--R 2 3 3 2 3 2 2 3 +--R log((9a b c + 9a )%%L0 + (- 3a b c + 6a )%%L0 + b c d x + b c + a) +--R + +--R 2 3+-+2 3+-+3+-+ +--R (- c \|b + c\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+2 3+-+3+-+ (d x + c)\|b + \|a +--R (2c \|b - 2c\|a \|b )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 +-+3+-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2c \|3 \|b + 2c\|3 \|a \|b )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 +--R 2log(b d x + 3b c d x + 3b c d x + b c + a) + 6log(x) +--R + +--R - 6log(- d x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 3 3+-+2 +--R (6b c + 6a)\|a +--R Type: Expression Integer +--E 637 + +--S 638 of 1483 +d0121:=D(m0121,x) +--R +--R +--R (638) 0 +--R Type: Expression Integer +--E 638 + +--S 639 of 1483 +t0122:= 1/x^2/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (639) --------------------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b d x + 3b c d x + 3b c d x + (b c + a)x +--R Type: Fraction Polynomial Integer +--E 639 + +--S 640 of 1483 +r0122:= -1/(a+b*c^3)/x-1/3*b^(1/3)*(a-2*b*c^3)*d*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/(a+b*c^3)^2-_ + 1/3*b^(2/3)*c*(2*a-b*c^3)*d*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/(a+b*c^3)^2-_ + 3*b*c^2*d*log(-d*x)/(a+b*c^3)^2+_ + 1/3*b^(1/3)*(a-2*b*c^3)*d*log(a^(1/3)/b^(1/3)+c+_ + d*x)/a^(1/3)/(a+b*c^3)^2-_ + 1/3*b^(2/3)*c*(2*a-b*c^3)*d*log(a^(1/3)/b^(1/3)+c+_ + d*x)/a^(2/3)/(a+b*c^3)^2-_ + 1/6*b^(1/3)*(a-2*b*c^3)*d*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/(a+b*c^3)^2+_ + 1/6*b^(2/3)*c*(2*a-b*c^3)*d*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/(a+b*c^3)^2+_ + b*c^2*d*log(a+b*(c+d*x)^3)/(a+b*c^3)^2 +--R +--R +--R (640) +--R 4 3+-+2 3 3+-+3+-+ +--R ((- b c + 2a c)d x \|b + (2b c - a)d x\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((2b c - 4a c)d x \|b + (- 4b c + 2a)d x\|a \|b ) +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 +-+3+-+2 3 +-+3+-+3+-+ +--R ((2b c - 4a c)d x\|3 \|b + (4b c - 2a)d x\|3 \|a \|b ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 3 3 2 2 2 3 +--R 6b c d x log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 3 +--R - 18b c d x log(- d x) - 6b c - 6a +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )x \|a +--R Type: Expression Integer +--E 640 + +--S 641 of 1483 +a0122:=integrate(t0122,x) +--R +--R +--R (641) +--R 2 6 3 2 +--R (- b c - 2a b c - a )x +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 2 +--R (- b c - 2a b c - a )x %%M0 + 3b c d x +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (- 3a b c - 6a b c - 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 +--R (b c + 2a b c + a )x +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 2 +--R (- b c - 2a b c - a )x %%M0 + 3b c d x +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (3a b c + 6a b c + 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )x %%M0 +--R * +--R log +--R 2 3 9 3 2 6 5 2 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (3a b c - 48a b c + 30a b c )d %%M0 + (b c - a b)d x +--R + +--R 3 7 2 4 2 2 +--R (b c + 5a b c - 5a b c)d +--R + +--R 2 3 +--R - 6b c d x log(x) - 2b c - 2a +--R / +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )x +--R Type: Union(Expression Integer,...) +--E 641 + +--S 642 of 1483 +m0122:=a0122-r0122 +--R +--R +--R (642) +--R 2 6 3 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 3+-+2 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a %%M0 + 9b c d \|a +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (- 3a b c - 6a b c - 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 3+-+2 +--R (3b c + 6a b c + 3a )\|a +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 3+-+2 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a %%M0 + 9b c d \|a +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (3a b c + 6a b c + 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )\|a %%M0 +--R * +--R log +--R 2 3 9 3 2 6 5 2 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (3a b c - 48a b c + 30a b c )d %%M0 + (b c - a b)d x +--R + +--R 3 7 2 4 2 2 +--R (b c + 5a b c - 5a b c)d +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((b c - 2a c)d \|b + (- 2b c + a)d\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((- 2b c + 4a c)d \|b + (4b c - 2a)d\|a \|b ) +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 +-+3+-+2 3 +-+3+-+3+-+ +--R ((- 2b c + 4a c)d\|3 \|b + (- 4b c + 2a)d\|3 \|a \|b ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 3 3 2 2 2 3 +--R - 6b c d log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 2 +--R - 18b c d log(x) + 18b c d log(- d x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )\|a +--R Type: Expression Integer +--E 642 + +--S 643 of 1483 +d0122:=D(m0122,x) +--R +--R +--R (643) 0 +--R Type: Expression Integer +--E 643 + +--S 644 of 1483 +t0123:= (c+d*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (644) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Polynomial Integer +--E 644 + +--S 645 of 1483 +r0123:= 1/4*a*(c+d*x)^4/d+1/7*b*(c+d*x)^7/d +--R +--R +--R (645) +--R 1 7 7 6 6 2 5 5 3 1 4 4 4 3 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 2 6 3 1 7 1 4 +--R (3b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 7 4 +--R / +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 645 + +--S 646 of 1483 +a0123:=integrate(t0123,x) +--R +--R +--R (646) +--R 1 6 7 5 6 2 4 5 3 1 3 4 4 2 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 6 3 +--R (3b c + - a c )d x + (b c + a c )x +--R 2 +--R Type: Polynomial Fraction Integer +--E 646 + +--S 647 of 1483 +m0123:=a0123-r0123 +--R +--R +--R 1 7 1 4 +--R - - b c - - a c +--R 7 4 +--R (647) ----------------- +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 647 + +--S 648 of 1483 +d0123:=D(m0123,x) +--R +--R +--R (648) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 648 + +--S 649 of 1483 +t0124:= (c+d*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (649) +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial Integer +--E 649 + +--S 650 of 1483 +r0124:= 1/4*a^2*(c+d*x)^4/d+2/7*a*b*(c+d*x)^7/d+1/10*b^2*(c+d*x)^10/d +--R +--R +--R (650) +--R 1 2 10 10 2 9 9 9 2 2 8 8 2 3 2 7 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 6 6 126 2 5 2 5 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 4 4 2 7 4 2 3 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 2 9 6 2 3 1 2 10 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )d x + -- b c +--R 2 2 10 +--R + +--R 2 7 1 2 4 +--R - a b c + - a c +--R 7 4 +--R / +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 650 + +--S 651 of 1483 +a0124:=integrate(t0124,x) +--R +--R +--R (651) +--R 1 2 9 10 2 8 9 9 2 2 7 8 2 3 2 6 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 5 6 126 2 5 2 4 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 3 4 2 7 4 2 2 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 9 6 2 3 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial Fraction Integer +--E 651 + +--S 652 of 1483 +m0124:=a0124-r0124 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R - -- b c - - a b c - - a c +--R 10 7 4 +--R (652) ------------------------------ +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 652 + +--S 653 of 1483 +d0124:=D(m0124,x) +--R +--R +--R (653) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 653 + +--S 654 of 1483 +t0125:= (c+d*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (654) +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 3 3 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial Integer +--E 654 + +--S 655 of 1483 +r0125:= 1/4*a^3*(c+d*x)^4/d+3/7/d*a^2*b*(c+d*x)^7+3/10/d*a*b^2*(c+d*x)^10+_ + 1/13/d*b^3*(c+d*x)^13 +--R +--R +--R (655) +--R 1 3 13 13 3 12 12 3 2 11 11 3 3 3 2 10 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 9 9 3 5 27 2 2 8 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 7 7 3 7 2 4 2 6 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 1 3 13 3 2 10 3 2 7 +--R (b c + 3a b c + 3a b c + a c )d x + -- b c + -- a b c + - a b c +--R 13 10 7 +--R + +--R 1 3 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 655 + +--S 656 of 1483 +a0125:=integrate(t0125,x) +--R +--R +--R (656) +--R 1 3 12 13 3 11 12 3 2 10 11 3 3 3 2 9 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 8 9 3 5 27 2 2 7 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 6 7 3 7 2 4 2 5 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial Fraction Integer +--E 656 + +--S 657 of 1483 +m0125:=a0125-r0125 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R - -- b c - -- a b c - - a b c - - a c +--R 13 10 7 4 +--R (657) ------------------------------------------- +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 657 + +--S 658 of 1483 +d0125:=D(m0125,x) +--R +--R +--R (658) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 658 + +--S 659 of 1483 +t0126:= (c+d*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R (659) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 659 + +--S 660 of 1483 +r0126:= 1/2*(c+d*x)^2/b/d-1/3*a^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/b^(5/3)/d+_ + 1/3*a^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/b^(5/3)/d-_ + 1/6*a^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/b^(5/3)/d +--R +--R +--R (660) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R 2\|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 2\|3 \|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+2 +--R (3d x + 6c d x + 3c )\|b +--R / +--R 3+-+2 +--R 6b d \|b +--R Type: Expression Integer +--E 660 + +--S 661 of 1483 +a0126:=integrate(t0126,x) +--R +--R +--R (661) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 2 2 +--R - \|3 |-- log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a \|b 2 2 +-+ +--R 6 |-- atan(----------------------------------- + (3d x + 6c d x)\|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression Integer,...) +--E 661 + +--S 662 of 1483 +m0126:=a0126-r0126 +--R +--R +--R (662) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R - 2\|3 \|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +--+ +--R | 2 +--R +-+ |a 3+-+2 +--R \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a 3+-+2 \|b 2 +-+3+-+2 +--R 6 |-- \|b atan(----------------------------------- - 3c \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression Integer +--E 662 + +--S 663 of 1483 +d0126:=D(m0126,x) +--R +--R +--R (663) 0 +--R Type: Expression Integer +--E 663 + +--S 664 of 1483 +t0127:= (c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (664) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 664 + +--S 665 of 1483 +r0127:= (c+d*x)/b/d-1/3*a^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/b^(4/3)/d-_ + 1/3*a^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/b^(4/3)/d+_ + 1/6*a^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/b^(4/3)/d +--R +--R +--R (665) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R - 2\|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a 3+-+ +--R - 2\|3 \|a atan(------------------------------) + (6d x + 6c)\|b +--R 3+-+ +--R 3\|a +--R / +--R 3+-+ +--R 6b d\|b +--R Type: Expression Integer +--E 665 + +--S 666 of 1483 +a0127:=integrate(t0127,x) +--R +--R +--R (666) +--R +---+ +---+2 +---+ +--R +-+ | a | a | a 2 2 2 +--R - \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a | a +--R 2\|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(---------------------------- + 6d x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression Integer,...) +--E 666 + +--S 667 of 1483 +m0127:=a0127-r0127 +--R +--R +--R (667) +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 2 2 +--R - \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|3 \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R 2\|3 \|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +--R 2\|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a 3+-+ \| b +-+3+-+ +--R - 6 3|- - \|b atan(---------------------------- - 6c\|3 \|b +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression Integer +--E 667 + +--S 668 of 1483 +d0127:=D(m0127,x) +--R +--R +--R (668) 0 +--R Type: Expression Integer +--E 668 + +--S 669 of 1483 +t0128:= (c+d*x)/(a+b*(c+d*x)^3) +--R +--R +--R d x + c +--R (669) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 669 + +--S 670 of 1483 +r0128:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d-_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d+_ + 1/6*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(1/3)/b^(2/3)/d +--R +--R +--R (670) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R (d x + c)\|b + \|a +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R - 2log(--------------------) + 2\|3 atan(------------------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+3+-+2 +--R 6d\|a \|b +--R Type: Expression Integer +--E 670 + +--S 671 of 1483 +a0128:=integrate(t0128,x) +--R +--R +--R (671) +--R - +--R +-+ +--R \|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression Integer,...) +--E 671 + +--S 672 of 1483 +m0128:=a0128-r0128 +--R +--R +--R (672) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression Integer +--E 672 + +--S 673 of 1483 +d0128:=D(m0128,x) +--R +--R +--R (673) 0 +--R Type: Expression Integer +--E 673 + +--S 674 of 1483 +t0129:= 1/(c+d*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R (674) +--R 1 +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 +--R b d x + 5b c d x + 10b c d x + (10b c + a)d x + (5b c + 2a c)d x +--R + +--R 5 2 +--R b c + a c +--R Type: Fraction Polynomial Integer +--E 674 + +--S 675 of 1483 +r0129:= -1/a/d/(c+d*x)-1/3*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/d+_ + 1/3*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/d-_ + 1/6*b^(1/3)*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(4/3)/d +--R +--R +--R (675) +--R 3+-+ +--R (- d x - c)\|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R (2d x + 2c)\|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a 3+-+ +--R (- 2d x - 2c)\|3 \|b atan(------------------------------) - 6\|a +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+ +--R (6a d x + 6a c d)\|a +--R Type: Expression Integer +--E 675 + +--S 676 of 1483 +a0129:=integrate(t0129,x) +--R +--R +--R (676) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R (6a d x + 6a c d)\|3 +--R Type: Union(Expression Integer,...) +--E 676 + +--S 677 of 1483 +m0129:=a0129-r0129 +--R +--R +--R (677) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 2\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a d\|3 \|a +--R Type: Expression Integer +--E 677 + +--S 678 of 1483 +d0129:=D(m0129,x) +--R +--R +--R (678) 0 +--R Type: Expression Integer +--E 678 + +--S 679 of 1483 +t0130:= 1/(c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R (679) +--R 1 +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Fraction Polynomial Integer +--E 679 + +--S 680 of 1483 +r0130:= -1/2/a/d/(c+d*x)^2-1/3*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/d-_ + 1/3*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/d+_ + 1/6*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/d +--R +--R +--R (680) +--R 2 2 2 3+-+2 +--R (d x + 2c d x + c )\|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (d x + c)\|b + \|a +--R (- 2d x - 4c d x - 2c )\|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 2 2 +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2d x - 4c d x - 2c )\|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 +--R - 3\|a +--R / +--R 3 2 2 2 3+-+2 +--R (6a d x + 12a c d x + 6a c d)\|a +--R Type: Expression Integer +--E 680 + +--S 681 of 1483 +a0130:=integrate(t0130,x) +--R +--R +--R (681) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 2 2 2 +-+ +--R (6a d x + 12a c d x + 6a c d)\|3 +--R Type: Union(Expression Integer,...) +--E 681 + +--S 682 of 1483 +m0130:=a0130-r0130 +--R +--R +--R (682) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 2\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a d\|3 \|a +--R Type: Expression Integer +--E 682 + +--S 683 of 1483 +d0130:=D(m0130,x) +--R +--R +--R (683) 0 +--R Type: Expression Integer +--E 683 + +--S 684 of 1483 +t0131:= (c+d*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (684) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction Polynomial Integer +--E 684 + +--S 685 of 1483 +r0131:= -1/3*(c+d*x)^2/b/d/(a+b*(c+d*x)^3)+2/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(5/3)/d-_ + 2/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(5/3)/d+_ + 1/9*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(5/3)/d +--R +--R +--R (685) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c + a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+3+-+2 +--R (- 3d x - 6c d x - 3c )\|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|a \|b +--R Type: Expression Integer +--E 685 + +--S 686 of 1483 +a0131:=integrate(t0131,x) +--R +--R +--R (686) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (- 3d x - 6c d x - 3c )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression Integer,...) +--E 686 + +--S 687 of 1483 +m0131:=a0131-r0131 +--R +--R +--R (687) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression Integer +--E 687 + +--S 688 of 1483 +d0131:=D(m0131,x) +--R +--R +--R (688) 0 +--R Type: Expression Integer +--E 688 + +--S 689 of 1483 +t0132:= (c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (689) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction Polynomial Integer +--E 689 + +--S 690 of 1483 +r0132:= -1/3*(c+d*x)/b/d/(a+b*(c+d*x)^3)+1/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(4/3)/d+_ + 1/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(4/3)/d-_ + 1/18*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(2/3)/b^(4/3)/d +--R +--R +--R (690) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 3+-+ +--R (- 6d x - 6c)\|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|a \|b +--R Type: Expression Integer +--E 690 + +--S 691 of 1483 +a0132:=integrate(t0132,x) +--R +--R +--R (691) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (- 6d x - 6c)\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression Integer,...) +--E 691 + +--S 692 of 1483 +m0132:=a0132-r0132 +--R +--R +--R (692) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression Integer +--E 692 + +--S 693 of 1483 +d0132:=D(m0132,x) +--R +--R +--R (693) 0 +--R Type: Expression Integer +--E 693 + +--S 694 of 1483 +t0133:= (c+d*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (694) +--R d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction Polynomial Integer +--E 694 + +--S 695 of 1483 +r0133:= 1/3*(c+d*x)^2/a/d/(a+b*(c+d*x)^3)+1/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/b^(2/3)/d-_ + 1/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/b^(2/3)/d+_ + 1/18*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(4/3)/b^(2/3)/d +--R +--R +--R (695) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c + a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+3+-+2 +--R (6d x + 12c d x + 6c )\|a \|b +--R / +--R 4 3 3 2 2 2 3 2 3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|a \|b +--R Type: Expression Integer +--E 695 + +--S 696 of 1483 +a0133:=integrate(t0133,x) +--R +--R +--R (696) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d x + 12c d x + 6c )\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression Integer,...) +--E 696 + +--S 697 of 1483 +m0133:=a0133-r0133 +--R +--R +--R (697) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression Integer +--E 697 + +--S 698 of 1483 +d0133:=D(m0133,x) +--R +--R +--R (698) 0 +--R Type: Expression Integer +--E 698 + +--S 699 of 1483 +t0134:= 1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (699) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction Polynomial Integer +--E 699 + +--S 700 of 1483 +r0134:= 1/3*(c+d*x)/a/d/(a+b*(c+d*x)^3)+2/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/b^(1/3)/d+_ + 2/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/b^(1/3)/d-_ + 1/9*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/b^(1/3)/d +--R +--R +--R (700) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 3+-+ +--R (3d x + 3c)\|a \|b +--R / +--R 4 3 3 2 2 2 3 2 3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|a \|b +--R Type: Expression Integer +--E 700 + +--S 701 of 1483 +a0134:=integrate(t0134,x) +--R +--R +--R (701) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression Integer,...) +--E 701 + +--S 702 of 1483 +m0134:=a0134-r0134 +--R +--R +--R (702) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression Integer +--E 702 + +--S 703 of 1483 +d0134:=D(m0134,x) +--R +--R +--R (703) 0 +--R Type: Expression Integer +--E 703 + +--S 704 of 1483 +t0135:= 1/(c+d*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (704) +--R 1 +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R b d x + 8b c d x + 28b c d x + (56b c + 2a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (70b c + 10a b c)d x + (56b c + 20a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 2 8 +--R (28b c + 20a b c + a )d x + (8b c + 10a b c + 2a c)d x + b c +--R + +--R 5 2 2 +--R 2a b c + a c +--R Type: Fraction Polynomial Integer +--E 704 + +--S 705 of 1483 +r0135:= -1/a^2/d/(c+d*x)-1/3*b*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)-_ + 4/9*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(7/3)/d+_ + 4/9*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(7/3)/d-_ + 2/9*b^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(7/3)/d +--R +--R +--R (705) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 4b d x - 16b c d x - 24b c d x + (- 16b c - 4a)d x - 4b c +--R + +--R - 4a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|a +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R 3+-+ +--R \|a +--R Type: Expression Integer +--E 705 + +--S 706 of 1483 +a0135:=integrate(t0135,x) +--R +--R +--R (706) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression Integer,...) +--E 706 + +--S 707 of 1483 +m0135:=a0135-r0135 +--R +--R +--R (707) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 2\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 4\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 12\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a d\|3 \|a +--R Type: Expression Integer +--E 707 + +--S 708 of 1483 +d0135:=D(m0135,x) +--R +--R +--R (708) 0 +--R Type: Expression Integer +--E 708 + +--S 709 of 1483 +t0136:= 1/(c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (709) +--R 1 +--R / +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Fraction Polynomial Integer +--E 709 + +--S 710 of 1483 +r0136:= -1/2/a^2/d/(c+d*x)^2-1/3*b*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)-_ + 5/9*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(8/3)/d-_ + 5/9*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(8/3)/d+_ + 5/18*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(8/3)/d +--R +--R +--R (710) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|a +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R 3+-+2 +--R \|a +--R Type: Expression Integer +--E 710 + +--S 711 of 1483 +a0136:=integrate(t0136,x) +--R +--R +--R (711) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression Integer,...) +--E 711 + +--S 712 of 1483 +m0136:=a0136-r0136 +--R +--R +--R (712) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - 5\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 10\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 30\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a d\|3 \|a +--R Type: Expression Integer +--E 712 + +--S 713 of 1483 +d0136:=D(m0136,x) +--R +--R +--R (713) 0 +--R Type: Expression Integer +--E 713 + +--S 714 of 1483 +t0137:= (c+d*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (714) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction Polynomial Integer +--E 714 + +--S 715 of 1483 +r0137:= -1/6*(c+d*x)^2/b/d/(a+b*(c+d*x)^3)^2+_ + 1/9*(c+d*x)^2/a/b/d/(a+b*(c+d*x)^3)+1/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/b^(5/3)/d-_ + 1/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/b^(5/3)/d+_ + 1/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(4/3)/b^(5/3)/d +--R +--R +--R (715) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R Type: Expression Integer +--E 715 + +--S 716 of 1483 +a0137:=integrate(t0137,x) +--R +--R +--R (716) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 90b c - 36a b c)d x + (- 36b c - 36a b c )d x - 6b c +--R + +--R 3 2 +--R - 12a b c - 6a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression Integer,...) +--E 716 + +--S 717 of 1483 +m0137:=a0137-r0137 +--R +--R +--R (717) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression Integer +--E 717 + +--S 718 of 1483 +d0137:=D(m0137,x) +--R +--R +--R (718) 0 +--R Type: Expression Integer +--E 718 + +--S 719 of 1483 +t0138:= (c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (719) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction Polynomial Integer +--E 719 + +--S 720 of 1483 +r0138:= -1/6*(c+d*x)/b/d/(a+b*(c+d*x)^3)^2+_ + 1/18*(c+d*x)/a/b/d/(a+b*(c+d*x)^3)+1/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/b^(4/3)/d+_ + 1/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/b^(4/3)/d-_ + 1/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/b^(4/3)/d +--R +--R +--R (720) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R Type: Expression Integer +--E 720 + +--S 721 of 1483 +a0138:=integrate(t0138,x) +--R +--R +--R (721) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression Integer,...) +--E 721 + +--S 722 of 1483 +m0138:=a0138-r0138 +--R +--R +--R (722) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression Integer +--E 722 + +--S 723 of 1483 +d0138:=D(m0138,x) +--R +--R +--R (723) 0 +--R Type: Expression Integer +--E 723 + +--S 724 of 1483 +t0139:= (c+d*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (724) +--R d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction Polynomial Integer +--E 724 + +--S 725 of 1483 +r0139:= 1/6*(c+d*x)^2/a/d/(a+b*(c+d*x)^3)^2+_ + 2/9*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)+2/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(7/3)/b^(2/3)/d-_ + 2/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(7/3)/b^(2/3)/d+_ + 1/27*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(7/3)/b^(2/3)/d +--R +--R +--R (725) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d x - 24b c d x - 60b c d x + (- 80b c - 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 60b c - 24a b c)d x + (- 24b c - 24a b c )d x - 4b c - 8a b c +--R + +--R 2 +--R - 4a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R Type: Expression Integer +--E 725 + +--S 726 of 1483 +a0139:=integrate(t0139,x) +--R +--R +--R (726) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 12b d x - 72b c d x - 180b c d x + (- 240b c - 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 180b c - 72a b c)d x + (- 72b c - 72a b c )d x - 12b c +--R + +--R 3 2 +--R - 24a b c - 12a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression Integer,...) +--E 726 + +--S 727 of 1483 +m0139:=a0139-r0139 +--R +--R +--R (727) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression Integer +--E 727 + +--S 728 of 1483 +d0139:=D(m0139,x) +--R +--R +--R (728) 0 +--R Type: Expression Integer +--E 728 + +--S 729 of 1483 +t0140:= 1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (729) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction Polynomial Integer +--E 729 + +--S 730 of 1483 +r0140:= 1/6*(c+d*x)/a/d/(a+b*(c+d*x)^3)^2+_ + 5/18*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)+5/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(8/3)/b^(1/3)/d+_ + 5/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(8/3)/b^(1/3)/d-_ + 5/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(8/3)/b^(1/3)/d +--R +--R +--R (730) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R Type: Expression Integer +--E 730 + +--S 731 of 1483 +a0140:=integrate(t0140,x) +--R +--R +--R (731) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression Integer,...) +--E 731 + +--S 732 of 1483 +m0140:=a0140-r0140 +--R +--R +--R (732) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 5\|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 10\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 30\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression Integer +--E 732 + +--S 733 of 1483 +d0140:=D(m0140,x) +--R +--R +--R (733) 0 +--R Type: Expression Integer +--E 733 + +--S 734 of 1483 +t0141:= 1/(c+d*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (734) +--R 1 +--R / +--R 3 11 11 3 10 10 3 2 9 9 3 3 2 8 8 +--R b d x + 11b c d x + 55b c d x + (165b c + 3a b )d x +--R + +--R 3 4 2 7 7 3 5 2 2 6 6 +--R (330b c + 24a b c)d x + (462b c + 84a b c )d x +--R + +--R 3 6 2 3 2 5 5 3 7 2 4 2 4 4 +--R (462b c + 168a b c + 3a b)d x + (330b c + 210a b c + 15a b c)d x +--R + +--R 3 8 2 5 2 2 3 3 +--R (165b c + 168a b c + 30a b c )d x +--R + +--R 3 9 2 6 2 3 3 2 2 +--R (55b c + 84a b c + 30a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 11 2 8 2 5 +--R (11b c + 24a b c + 15a b c + 2a c)d x + b c + 3a b c + 3a b c +--R + +--R 3 2 +--R a c +--R Type: Fraction Polynomial Integer +--E 734 + +--S 735 of 1483 +r0141:= -1/a^3/d/(c+d*x)-1/6*b*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)^2-_ + 5/9*b*(c+d*x)^2/a^3/d/(a+b*(c+d*x)^3)-_ + 14/27*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(10/3)/d+_ + 14/27*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(10/3)/d-_ + 7/27*b^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(10/3)/d +--R +--R +--R (735) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 28b d x - 196b c d x - 588b c d x + (- 980b c - 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 980b c - 224a b c)d x + (- 588b c - 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 196b c - 224a b c - 28a )d x - 28b c - 56a b c - 28a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R 3+-+ +--R \|a +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R 3+-+ +--R \|a +--R Type: Expression Integer +--E 735 + +--S 736 of 1483 +a0141:=integrate(t0141,x) +--R +--R +--R (736) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression Integer,...) +--E 736 + +--S 737 of 1483 +m0141:=a0141-r0141 +--R +--R +--R (737) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 7\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 14\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 42\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 27a d\|3 \|a +--R Type: Expression Integer +--E 737 + +--S 738 of 1483 +d0141:=D(m0141,x) +--R +--R +--R (738) 0 +--R Type: Expression Integer +--E 738 + +--S 739 of 1483 +t0142:= 1/(c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (739) +--R 1 +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Fraction Polynomial Integer +--E 739 + +--S 740 of 1483 +r0142:= -1/2/a^3/d/(c+d*x)^2-1/6*b*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)^2-_ + 11/18*b*(c+d*x)/a^3/d/(a+b*(c+d*x)^3)-_ + 20/27*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(11/3)/d-_ + 20/27*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(11/3)/d+_ + 10/27*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(11/3)/d +--R +--R +--R (740) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R 3+-+2 +--R \|a +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R 3+-+2 +--R \|a +--R Type: Expression Integer +--E 740 + +--S 741 of 1483 +a0142:=integrate(t0142,x) +--R +--R +--R (741) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression Integer,...) +--E 741 + +--S 742 of 1483 +m0142:=a0142-r0142 +--R +--R +--R (742) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - 10\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 20\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 60\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 27a d\|3 \|a +--R Type: Expression Integer +--E 742 + +--S 743 of 1483 +d0142:=D(m0142,x) +--R +--R +--R (743) 0 +--R Type: Expression Integer +--E 743 + +--S 744 of 1483 +t0143:= 1/(a+b*x^4) +--R +--R +--R 1 +--R (744) -------- +--R 4 +--R b x + a +--R Type: Fraction Polynomial Integer +--E 744 + +--S 745 of 1483 +r0143:= 1/2*(atan((-b)^(1/4)*x/a^(1/4))+_ + atanh((-b)^(1/4)*x/a^(1/4)))/a^(3/4)/(-b)^(1/4) +--R +--R +--R 4+---+ 4+---+ +--R x\|- b x\|- b +--R atanh(-------) + atan(-------) +--R 4+-+ 4+-+ +--R \|a \|a +--R (745) ------------------------------ +--R 4+---+4+-+3 +--R 2\|- b \|a +--R Type: Expression Integer +--E 745 + +--S 746 of 1483 +a0143:=integrate(t0143,x) +--R +--R +--R (746) +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R |- ------ log(4a |- ------ + x) - |- ------ log(- 4a |- ------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 256a b \| 256a b \| 256a b \| 256a b +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 +--R | 1 \| 256a b +--R - 2 |- ------ atan(-------------) +--R 4| 3 x +--R \| 256a b +--R Type: Union(Expression Integer,...) +--E 746 + +--S 747 of 1483 +m0143:=a0143-r0143 +--R +--R +--R (747) +--R +--------+ +--------+ +--R 4+---+ | 1 4+-+3 | 1 +--R 2\|- b |- ------ \|a log(4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a b \| 256a b +--R + +--R +--------+ +--------+ 4+---+ +--R 4+---+ | 1 4+-+3 | 1 x\|- b +--R - 2\|- b |- ------ \|a log(- 4a |- ------ + x - atanh(-------) +--R 4| 3 4| 3 4+-+ +--R \| 256a b \| 256a b \|a +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 4+---+ +--R 4+---+ | 1 4+-+3 \| 256a b x\|- b +--R - 4\|- b |- ------ \|a atan(------------- - atan(-------) +--R 4| 3 x 4+-+ +--R \| 256a b \|a +--R / +--R 4+---+4+-+3 +--R 2\|- b \|a +--R Type: Expression Integer +--E 747 + +--S 748 of 1483 +d0143:=D(m0143,x) +--R +--R +--R (748) 0 +--R Type: Expression Integer +--E 748 + +--S 749 of 1483 +t0144:= x^4/(a-b*x^4) +--R +--R +--R 4 +--R x +--R (749) - -------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 749 + +--S 750 of 1483 +r0144:= 1/2/b^(5/4)*(-2*b^(1/4)*x+_ + a^(1/4)*atan(b^(1/4)*x/a^(1/4))+a^(1/4)*atanh(b^(1/4)*x/a^(1/4))) +--R +--R +--R 4+-+ 4+-+ +--R 4+-+ x\|b 4+-+ x\|b 4+-+ +--R \|a atanh(-----) + \|a atan(-----) - 2x\|b +--R 4+-+ 4+-+ +--R \|a \|a +--R (750) ------------------------------------------- +--R 4+-+ +--R 2b\|b +--R Type: Expression Integer +--E 750 + +--S 751 of 1483 +a0144:=integrate(t0144,x) +--R +--R +--R (751) +--R +-----+ +-----+ +-----+ +-----+ +--R | a | a | a | a +--R b |----- log(4b |----- + x - b |----- log(- 4b |----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \|256b \|256b \|256b \|256b +--R + +--R +-----+ +--R | a +--R 4b |----- +--R +-----+ 4| 5 +--R | a \|256b +--R - 2b |----- atan(---------- - x +--R 4| 5 x +--R \|256b +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 751 + +--S 752 of 1483 +m0144:=a0144-r0144 +--R +--R +--R (752) +--R +-----+ +-----+ +-----+ +-----+ +--R | a 4+-+ | a | a 4+-+ | a +--R 2b |----- \|b log(4b |----- + x - 2b |----- \|b log(- 4b |----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \|256b \|256b \|256b \|256b +--R + +--R +-----+ +--R | a +--R 4b |----- +--R 4+-+ 4+-+ +-----+ 4| 5 +--R 4+-+ x\|b 4+-+ x\|b | a 4+-+ \|256b +--R - \|a atanh(-----) - \|a atan(-----) - 4b |----- \|b atan(----------) +--R 4+-+ 4+-+ 4| 5 x +--R \|a \|a \|256b +--R / +--R 4+-+ +--R 2b\|b +--R Type: Expression Integer +--E 752 + +--S 753 of 1483 +d0144:=D(m0144,x) +--R +--R +--R (753) 0 +--R Type: Expression Integer +--E 753 + +--S 754 of 1483 +t0145:= x^2/(a-b*x^4) +--R +--R +--R 2 +--R x +--R (754) - -------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 754 + +--S 755 of 1483 +r0145:= -1/2*(atan(b^(1/4)*x/a^(1/4))-_ + atanh(b^(1/4)*x/a^(1/4)))/a^(1/4)/b^(3/4) +--R +--R +--R 4+-+ 4+-+ +--R x\|b x\|b +--R atanh(-----) - atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (755) -------------------------- +--R 4+-+4+-+3 +--R 2\|a \|b +--R Type: Expression Integer +--E 755 + +--S 756 of 1483 +a0145:=integrate(t0145,x) +--R +--R +--R (756) +--R +-------+ +-------+3 +--R | 1 2 | 1 +--R |------- log(64a b |------- + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +-------+3 +--R 2 | 1 +--R 64a b |------- +--R +-------+ +-------+3 +-------+ 4| 3 +--R | 1 2 | 1 | 1 \|256a b +--R - |------- log(- 64a b |------- + x) + 2 |------- atan(-----------------) +--R 4| 3 4| 3 4| 3 x +--R \|256a b \|256a b \|256a b +--R Type: Union(Expression Integer,...) +--E 756 + +--S 757 of 1483 +m0145:=a0145-r0145 +--R +--R +--R (757) +--R +-------+ +-------+3 +--R | 1 4+-+4+-+3 2 | 1 +--R 2 |------- \|a \|b log(64a b |------- + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +-------+ +-------+3 4+-+ +--R | 1 4+-+4+-+3 2 | 1 x\|b +--R - 2 |------- \|a \|b log(- 64a b |------- + x - atanh(-----) +--R 4| 3 4| 3 4+-+ +--R \|256a b \|256a b \|a +--R + +--R +-------+3 +--R 2 | 1 +--R 64a b |------- +--R 4+-+ +-------+ 4| 3 +--R x\|b | 1 4+-+4+-+3 \|256a b +--R atan(-----) + 4 |------- \|a \|b atan(-----------------) +--R 4+-+ 4| 3 x +--R \|a \|256a b +--R / +--R 4+-+4+-+3 +--R 2\|a \|b +--R Type: Expression Integer +--E 757 + +--S 758 of 1483 +d0145:=D(m0145,x) +--R +--R +--R (758) 0 +--R Type: Expression Integer +--E 758 + +--S 759 of 1483 +t0146:= 1/(a-b*x^4) +--R +--R +--R 1 +--R (759) - -------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 759 + +--S 760 of 1483 +r0146:= 1/2*(atan(b^(1/4)*x/a^(1/4))+_ + atanh(b^(1/4)*x/a^(1/4)))/a^(3/4)/b^(1/4) +--R +--R +--R 4+-+ 4+-+ +--R x\|b x\|b +--R atanh(-----) + atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (760) -------------------------- +--R 4+-+3 4+-+ +--R 2\|a \|b +--R Type: Expression Integer +--E 760 + +--S 761 of 1483 +a0146:=integrate(t0146,x) +--R +--R +--R (761) +--R +------+ +------+ +------+ +------+ +--R | 1 | 1 | 1 | 1 +--R |------ log(4a |------ + x) - |------ log(- 4a |------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \|256a b \|256a b \|256a b \|256a b +--R + +--R +------+ +--R | 1 +--R 4a |------ +--R +------+ 4| 3 +--R | 1 \|256a b +--R - 2 |------ atan(-----------) +--R 4| 3 x +--R \|256a b +--R Type: Union(Expression Integer,...) +--E 761 + +--S 762 of 1483 +m0146:=a0146-r0146 +--R +--R +--R (762) +--R +------+ +------+ +--R | 1 4+-+3 4+-+ | 1 +--R 2 |------ \|a \|b log(4a |------ + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +------+ +------+ 4+-+ 4+-+ +--R | 1 4+-+3 4+-+ | 1 x\|b x\|b +--R - 2 |------ \|a \|b log(- 4a |------ + - atanh(-----) - atan(-----) +--R 4| 3 4| 3 4+-+ 4+-+ +--R \|256a b \|256a b \|a \|a +--R + +--R +------+ +--R | 1 +--R 4a |------ +--R +------+ 4| 3 +--R | 1 4+-+3 4+-+ \|256a b +--R - 4 |------ \|a \|b atan(-----------) +--R 4| 3 x +--R \|256a b +--R / +--R 4+-+3 4+-+ +--R 2\|a \|b +--R Type: Expression Integer +--E 762 + +--S 763 of 1483 +d0146:=D(m0146,x) +--R +--R +--R (763) 0 +--R Type: Expression Integer +--E 763 + +--S 764 of 1483 +t0147:= 1/x^4/(a-b*x^4) +--R +--R +--R 1 +--R (764) - ----------- +--R 8 4 +--R b x - a x +--R Type: Fraction Polynomial Integer +--E 764 + +--S 765 of 1483 +r0147:= -1/3/a/x^3+1/2*b^(3/4)*atan(b^(1/4)*x/a^(1/4))/a^(7/4)+_ + 1/2*b^(3/4)*atanh(b^(1/4)*x/a^(1/4))/a^(7/4) +--R +--R +--R 4+-+ 4+-+ +--R 3 4+-+3 x\|b 3 4+-+3 x\|b 4+-+3 +--R 3x \|b atanh(----- + 3x \|b atan(----- - 2\|a +--R 4+-+ 4+-+ +--R \|a \|a +--R (765) --------------------------------------------------- +--R 3 4+-+3 +--R 6a x \|a +--R Type: Expression Integer +--E 765 + +--S 766 of 1483 +a0147:=integrate(t0147,x) +--R +--R +--R (766) +--R +-----+ +-----+ +--R | 3 | 3 +--R 3 | b 2 | b +--R 3a x |----- log(4a |----- + b x) +--R 4| 7 4| 7 +--R \|256a \|256a +--R + +--R +-----+ +--R | 3 +--R 2 | b +--R +-----+ +-----+ +-----+ 4a |----- +--R | 3 | 3 | 3 4| 7 +--R 3 | b 2 | b 3 | b \|256a +--R - 3a x |----- log(- 4a |----- + b x - 6a x |----- atan(-----------) +--R 4| 7 4| 7 4| 7 b x +--R \|256a \|256a \|256a +--R + +--R - 1 +--R / +--R 3 +--R 3a x +--R Type: Union(Expression Integer,...) +--E 766 + +--S 767 of 1483 +m0147:=a0147-r0147 +--R +--R +--R (767) +--R +-----+ +-----+ +--R | 3 | 3 +--R 4+-+3 | b 2 | b +--R 2a \|a |----- log(4a |----- + b x) +--R 4| 7 4| 7 +--R \|256a \|256a +--R + +--R +-----+ +-----+ +--R | 3 | 3 4+-+ +--R 4+-+3 | b 2 | b 4+-+3 x\|b +--R - 2a \|a |----- log(- 4a |----- + b x - \|b atanh(-----) +--R 4| 7 4| 7 4+-+ +--R \|256a \|256a \|a +--R + +--R +-----+ +--R | 3 +--R 2 | b +--R +-----+ 4a |----- +--R | 3 4| 7 4+-+ +--R 4+-+3 | b \|256a 4+-+3 x\|b +--R - 4a \|a |----- atan(----------- - \|b atan(-----) +--R 4| 7 b x 4+-+ +--R \|256a \|a +--R / +--R 4+-+3 +--R 2a \|a +--R Type: Expression Integer +--E 767 + +--S 768 of 1483 +d0147:=D(m0147,x) +--R +--R +--R (768) 0 +--R Type: Expression Integer +--E 768 + +--S 769 of 1483 +t0148:= x^3*(a+b*x^4)^2 +--R +--R +--R 2 11 7 2 3 +--R (769) b x + 2a b x + a x +--R Type: Polynomial Integer +--E 769 + +--S 770 of 1483 +r0148:= 1/12*(a+b*x^4)^3/b +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R -- b x + - a b x + - a b x + -- a +--R 12 4 4 12 +--R (770) -------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 770 + +--S 771 of 1483 +a0148:=integrate(t0148,x) +--R +--R +--R 1 2 12 1 8 1 2 4 +--R (771) -- b x + - a b x + - a x +--R 12 4 4 +--R Type: Polynomial Fraction Integer +--E 771 + +--S 772 of 1483 +m0148:=a0148-r0148 +--R +--R +--R 1 3 +--R -- a +--R 12 +--R (772) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 772 + +--S 773 of 1483 +d0148:=D(m0148,x) +--R +--R +--R (773) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 773 + +--S 774 of 1483 +t0149:= x^3*(a+b*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +--R (774) b x + 3a b x + 3a b x + a x +--R Type: Polynomial Integer +--E 774 + +--S 775 of 1483 +r0149:= 1/16*(a+b*x^4)^4/b +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 16 4 8 4 16 +--R (775) -------------------------------------------------- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 775 + +--S 776 of 1483 +a0149:=integrate(t0149,x) +--R +--R +--R 1 3 16 1 2 12 3 2 8 1 3 4 +--R (776) -- b x + - a b x + - a b x + - a x +--R 16 4 8 4 +--R Type: Polynomial Fraction Integer +--E 776 + +--S 777 of 1483 +m0149:=a0149-r0149 +--R +--R +--R 1 4 +--R -- a +--R 16 +--R (777) - ----- +--R b +--R Type: Fraction Polynomial Fraction Integer +--E 777 + +--S 778 of 1483 +d0149:=D(m0149,x) +--R +--R +--R (778) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 778 + +--S 779 of 1483 +t0150:= (1+x^2)/(1+x^4) +--R +--R +--R 2 +--R x + 1 +--R (779) ------ +--R 4 +--R x + 1 +--R Type: Fraction Polynomial Integer +--E 779 + +--S 780 of 1483 +r0150:= 1/2*2^(1/2)*(atan(-1+x*2^(1/2))+atan(1+x*2^(1/2))) +--R +--R +--R +-+ +-+ +-+ +-+ +--R \|2 atan(x\|2 + 1) + \|2 atan(x\|2 - 1) +--R (780) ----------------------------------------- +--R 2 +--R Type: Expression Integer +--E 780 + +--S 781 of 1483 +a0150:=integrate(t0150,x) +--R +--R +--R +-+ 3 +--R x\|2 x + x +--R atan(-----) + atan(------) +--R 2 +-+ +--R \|2 +--R (781) -------------------------- +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 781 + +--S 782 of 1483 +m0150:=a0150-r0150 +--R +--R +--R +-+ 3 +--R +-+ +-+ x\|2 x + x +--R - atan(x\|2 + 1) - atan(x\|2 - 1) + atan(-----) + atan(------) +--R 2 +-+ +--R \|2 +--R (782) ---------------------------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 782 + +--S 783 of 1483 +d0150:=D(m0150,x) +--R +--R +--R (783) 0 +--R Type: Expression Integer +--E 783 + +--S 784 of 1483 +t0151:= (5+2*x^2)/(-1+x^4) +--R +--R +--R 2 +--R 2x + 5 +--R (784) ------- +--R 4 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 784 + +--S 785 of 1483 +r0151:= -3/2*atan(x)-7/2*atanh(x) +--R +--R +--R - 7atanh(x) - 3atan(x) +--R (785) ---------------------- +--R 2 +--R Type: Expression Integer +--E 785 + +--S 786 of 1483 +a0151:=integrate(t0151,x) +--R +--R +--R - 7log(x + 1) + 7log(x - 1) - 6atan(x) +--R (786) -------------------------------------- +--R 4 +--R Type: Union(Expression Integer,...) +--E 786 + +--S 787 of 1483 +m0151:=a0151-r0151 +--R +--R +--R - 7log(x + 1) + 7log(x - 1) + 14atanh(x) +--R (787) ---------------------------------------- +--R 4 +--R Type: Expression Integer +--E 787 + +--S 788 of 1483 +d0151:=D(m0151,x) +--R +--R +--R (788) 0 +--R Type: Expression Integer +--E 788 + +--S 789 of 1483 +t0152:= (c+d*x^2)/(a-b*x^4) +--R +--R +--R 2 +--R - d x - c +--R (789) ---------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 789 + +--S 790 of 1483 +r0152:= 1/2*(b^(1/2)*c-a^(1/2)*d)*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(b^(1/2)*c+a^(1/2)*d)*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4) +--R +--R +--R 4+-+ 4+-+ +--R +-+ +-+ x\|b +-+ +-+ x\|b +--R (c\|b + d\|a )atanh(-----) + (c\|b - d\|a )atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (790) -------------------------------------------------------- +--R 4+-+3 4+-+3 +--R 2\|a \|b +--R Type: Expression Integer +--E 790 + +--S 791 of 1483 +a0152:=integrate(t0152,x) +--R +--R +--R (791) +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 791 + +--S 792 of 1483 +m0152:=a0152-r0152 +--R +--R +--R (792) +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R 4+-+ 4+-+ +--R +-+ +-+ x\|b +-+ +-+ x\|b +--R (- c\|b - d\|a )atanh(-----) + (- c\|b + d\|a )atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R 4+-+3 4+-+3 +--R 2\|a \|b +--R Type: Expression Integer +--E 792 + +--S 793 of 1483 +d0152:=D(m0152,x) +--R +--R +--R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ +--R ((- d x - c)\|a + d x \|a )\|b + c \|a \|b +--R (793) ------------------------------------------------- +--R 4 4+-+2 4+-+2 +--R (b x - a)\|a \|b +--R Type: Expression Integer +--E 793 + +--S 794 of 1483 +t0153:= (1+x+x^2+x^3)/(1+x^4) +--R +--R +--R 3 2 +--R x + x + x + 1 +--R (794) --------------- +--R 4 +--R x + 1 +--R Type: Fraction Polynomial Integer +--E 794 + +--S 795 of 1483 +r0153:= 1/2*atan(x^2)+1/2*atan(-1+x*2^(1/2))*2^(1/2)+_ + 1/2*atan(1+x*2^(1/2))*2^(1/2)+1/4*log(1+x^4) +--R +--R +--R (795) +--R 4 +-+ +-+ +-+ +-+ 2 +--R log(x + 1) + 2\|2 atan(x\|2 + 1) + 2\|2 atan(x\|2 - 1) + 2atan(x ) +--R --------------------------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 795 + +--S 796 of 1483 +a0153:=integrate(t0153,x) +--R +--R +--R (796) +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R +---------+ (2\|2 - 2) |--------- +--R | +-+ | +-+ +--R |3\|2 + 4 \| 4\|2 +--R - 4 |--------- atan(-----------------------) +--R | +-+ +-+ +--R \| 4\|2 x\|2 - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R +---------+ (2\|2 + 2) |--------- +--R | +-+ | +-+ +--R |3\|2 - 4 \| 4\|2 +-+ 2 +--R - 4 |--------- atan(-----------------------) + log(x\|2 + x + 1) +--R | +-+ +-+ +--R \| 4\|2 x\|2 + 1 +--R + +--R +-+ 2 +--R log(- x\|2 + x + 1) +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 796 + +--S 797 of 1483 +m0153:=a0153-r0153 +--R +--R +--R (797) +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R +---------+ (2\|2 - 2) |--------- +--R | +-+ | +-+ +--R |3\|2 + 4 \| 4\|2 +--R - 4 |--------- atan(-----------------------) +--R | +-+ +-+ +--R \| 4\|2 x\|2 - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R +---------+ (2\|2 + 2) |--------- +--R | +-+ | +-+ +--R |3\|2 - 4 \| 4\|2 +-+ 2 +--R - 4 |--------- atan(-----------------------) + log(x\|2 + x + 1) +--R | +-+ +-+ +--R \| 4\|2 x\|2 + 1 +--R + +--R 4 +-+ 2 +-+ +-+ +--R - log(x + 1) + log(- x\|2 + x + 1) - 2\|2 atan(x\|2 + 1) +--R + +--R +-+ +-+ 2 +--R - 2\|2 atan(x\|2 - 1) - 2atan(x ) +--R / +--R 4 +--R Type: Expression Integer +--E 797 + +--S 798 of 1483 +d0153:=D(m0153,x) +--R +--R +--R (798) 0 +--R Type: Expression Integer +--E 798 + +--S 799 of 1483 +t0154:= (c+d*x+e*x^2+f*x^3)/(a+b*x^4) +--R +--R +--R 3 2 +--R f x + e x + d x + c +--R (799) --------------------- +--R 4 +--R b x + a +--R Type: Fraction Polynomial Integer +--E 799 + +--S 800 of 1483 +r0154:= 1/2*d*atan(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)+1/4*(b^(1/2)*c+_ + a^(1/2)*e)*atan(-1+_ + 2^(1/2)*b^(1/4)*x/a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)+_ + 1/4*(b^(1/2)*c+_ + a^(1/2)*e)*atan(1+2^(1/2)*b^(1/4)*x/a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)-_ + 1/8*(b^(1/2)*c-a^(1/2)*e)*log(a^(1/2)/b^(1/2)-_ + 2^(1/2)*a^(1/4)*x/b^(1/4)+_ + x^2)*2^(1/2)/a^(3/4)/b^(3/4)+1/8*(b^(1/2)*c-_ + a^(1/2)*e)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*x/b^(1/4)+_ + x^2)*2^(1/2)/a^(3/4)/b^(3/4)+1/4*f*log(a+b*x^4)/b +--R +--R +--R (800) +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b + x\|2 \|a \|b +--R (- a b e\|2 \|b + b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b - x\|2 \|a \|b +--R (a b e\|2 \|b - b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b + \|a +--R (2a b e\|2 \|b + 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b - \|a +--R (2a b e\|2 \|b + 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+ +--R 4+-+3 4+-+3 x \|b 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|b atan(------ + 2f log(b x + a)\|a \|a \|b \|b +--R +-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b +--R Type: Expression Integer +--E 800 + +--S 801 of 1483 +a0154:=integrate(t0154,x) +--R +--R +--R (801) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 - 6a b %%BT0 +--R + +--R 2 2 +--R 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BT1 - b %%BT0 + f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 6a b c d e - 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BT1 - b %%BT0 + f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e + 32a b c e - 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e - 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e - 6a b c d e + 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R 2b %%BT1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f - 4a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 4a b d e + 12a b c d e - 8a b c d + 4a b c +--R * +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e + 24a b c e - 48a b c d )f - 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R - 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e - 4a b c e + 3a b c d e + 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 8a b c d e - 3a b c d e + (- 2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R 2b %%BT0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e - 64a b c e + 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f + 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R 12a b d e - 16a b c e + 36a b c d e + 8a b c d + 4a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e + 4a b c e - 9a b c d e - 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e + 5a b c d e + (- 2a b d + 5a b c d)e - 5a b c d +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 801 + +--S 802 of 1483 +m0154:=a0154-r0154 +--R +--R +--R (802) +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 - 6a b %%BT0 +--R + +--R 2 2 +--R 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 4b\|a \|a \|b \|b %%BT1 - 4b\|a \|a \|b \|b %%BT0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 6a b c d e - 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 4b\|a \|a \|b \|b %%BT1 - 4b\|a \|a \|b \|b %%BT0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e + 32a b c e - 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e - 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e - 6a b c d e + 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b %%BT1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f - 4a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 4a b d e + 12a b c d e - 8a b c d + 4a b c +--R * +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e + 24a b c e - 48a b c d )f - 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R - 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e - 4a b c e + 3a b c d e + 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 8a b c d e - 3a b c d e + (- 2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b %%BT0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e - 64a b c e + 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f + 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R 12a b d e - 16a b c e + 36a b c d e + 8a b c d + 4a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e + 4a b c e - 9a b c d e - 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e + 5a b c d e + (- 2a b d + 5a b c d)e - 5a b c d +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b + x\|2 \|a \|b +--R (a b e\|2 \|b - b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b - x\|2 \|a \|b +--R (- a b e\|2 \|b + b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b + \|a +--R (- 2a b e\|2 \|b - 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b - \|a +--R (- 2a b e\|2 \|b - 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+ +--R 4+-+3 4+-+3 x \|b 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|b atan(------ - 2f log(b x + a)\|a \|a \|b \|b +--R +-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b +--R Type: Expression Integer +--E 802 + +--S 803 of 1483 +d0154:=D(m0154,x) +--R +--R +--R (803) +--R 4 2 4+-+2 +-+ +--R (- b c x + 2a e x + a c)\|a \|b +--R + +--R 4 2 +-+4+-+2 4 2 +--R (- b e x + 2b c x + a e)\|a \|a + 4a b e x + 4a b c x +--R * +--R 4+-+2 +--R \|b +--R + +--R 4 2 +-+4+-+2 4 2 2 +-+ +--R ((- 4b e x - 4b c x )\|a \|a + a b e x - 2a b c x - a e)\|b +--R + +--R 2 6 2 4 2 4+-+2 +--R (- 2b e x - 2b c x - 2a b e x - 2a b c)\|a +--R + +--R 2 6 2 4 +-+ +--R (2b e x + 3b c x + a b c)\|a +--R / +--R 2 6 2 2 4+-+2 2 6 2 +-+4+-+2 +-+ +--R (4a b x + 4a b x )\|b + (- 4b x - 4a b x )\|a \|a \|b +--R + +--R 3 8 2 4 2 4+-+2 +--R (- 2b x - 4a b x - 2a b)\|a +--R Type: Expression Integer +--E 803 + +--S 804 of 1483 +t0155:= (1+x+x^2+x^3)/(a-b*x^4) +--R +--R +--R 3 2 +--R - x - x - x - 1 +--R (804) ----------------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 804 + +--S 805 of 1483 +r0155:= -1/2*(a^(1/2)-b^(1/2))*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(a^(1/2)+b^(1/2))*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*atanh(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)-1/4*log(a-b*x^4)/b +--R +--R +--R (805) +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (2a b\|b + 2b \|a )atanh(-----) + 2b \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (- 2a b\|b + 2b \|a )atan(-----) - log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression Integer +--E 805 + +--S 806 of 1483 +a0155:=integrate(t0155,x) +--R +--R +--R (806) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R - b %%BU1 - b %%BU0 - 1 +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 + (- 8a b + 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R 2a b - 4a b + 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R - b %%BU1 - b %%BU0 - 1 +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (- 32a b %%BU0 + 8a b - 8a b )%%BU1 + (8a b - 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R - 2a b + 4a b - 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R 2b %%BU1 +--R * +--R log +--R 3 3 2 3 3 2 2 +--R (- 64a b %%BU0 + 16a b - 16a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (- 64a b %%BU0 - 64a b %%BU0 + 4a b + 8a b - 12a b)%%BU1 +--R + +--R 3 3 3 3 2 2 2 2 3 +--R - 64a b %%BU0 - 64a b %%BU0 + (24a b - 24a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x - 3a b + 6a b - 3a +--R + +--R 2b %%BU0 +--R * +--R log +--R 3 3 3 2 3 3 2 2 +--R 64a b %%BU0 + (16a b + 48a b )%%BU0 +--R + +--R 3 2 2 3 3 2 2 2 2 +--R (4a b - 16a b + 12a b)%%BU0 + (b - 2a b + a b)x + a b - 2a b +--R + +--R 3 +--R a +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 806 + +--S 807 of 1483 +m0155:=a0155-r0155 +--R +--R +--R (807) +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BU1 - 2b\|a \|a \|b \|b %%BU0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2\|a \|a \|b \|b +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 + (- 8a b + 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R 2a b - 4a b + 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BU1 - 2b\|a \|a \|b \|b %%BU0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2\|a \|a \|b \|b +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (- 32a b %%BU0 + 8a b - 8a b )%%BU1 + (8a b - 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R - 2a b + 4a b - 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BU1 +--R * +--R log +--R 3 3 2 3 3 2 2 +--R (- 64a b %%BU0 + 16a b - 16a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (- 64a b %%BU0 - 64a b %%BU0 + 4a b + 8a b - 12a b)%%BU1 +--R + +--R 3 3 3 3 2 2 2 2 3 +--R - 64a b %%BU0 - 64a b %%BU0 + (24a b - 24a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x - 3a b + 6a b - 3a +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BU0 +--R * +--R log +--R 3 3 3 2 3 3 2 2 +--R 64a b %%BU0 + (16a b + 48a b )%%BU0 +--R + +--R 3 2 2 3 3 2 2 2 2 +--R (4a b - 16a b + 12a b)%%BU0 + (b - 2a b + a b)x + a b - 2a b +--R + +--R 3 +--R a +--R + +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (- 2a b\|b - 2b \|a )atanh(-----) - 2b \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (2a b\|b - 2b \|a )atan(-----) + log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression Integer +--E 807 + +--S 808 of 1483 +d0155:=D(m0155,x) +--R +--R +--R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ +--R ((- x - 1)\|a + x \|a )\|b + \|a \|b +--R (808) ------------------------------------------- +--R 4 4+-+2 4+-+2 +--R (b x - a)\|a \|b +--R Type: Expression Integer +--E 808 + +--S 809 of 1483 +t0156:= (c+d*x+e*x^2+f*x^3)/(a-b*x^4) +--R +--R +--R 3 2 +--R - f x - e x - d x - c +--R (809) ----------------------- +--R 4 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 809 + +--S 810 of 1483 +r0156:= 1/2*(b^(1/2)*c-a^(1/2)*e)*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(b^(1/2)*c+a^(1/2)*e)*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*d*atanh(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)-1/4*f*log(a-b*x^4)/b +--R +--R +--R (810) +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (2a b e\|b + 2b c\|a )atanh(-----) + 2b d \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (- 2a b e\|b + 2b c\|a )atan(-----) - f log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression Integer +--E 810 + +--S 811 of 1483 +a0156:=integrate(t0156,x) +--R +--R +--R (811) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 - 6a b %%BV0 +--R + +--R 2 2 +--R - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BV1 - b %%BV0 - f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e + 6a b c d e - 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BV1 - b %%BV0 - f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e - 32a b c e + 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e - 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R 2b %%BV1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (24a b c d e - 16a b d e - 8a b c d)f + 4a b c e - 4a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 12a b c d e - 8a b c d - 4a b c +--R * +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e - 24a b c e + 48a b c d )f + 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- 3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e + 4a b c e - 3a b c d e - 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 8a b c d e + 3a b c d e + (2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R 2b %%BV0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e + 64a b c e - 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (24a b c d e - 16a b d e - 8a b c d)f - 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R - 12a b d e - 16a b c e + 36a b c d e + 8a b c d - 4a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e - 4a b c e + 9a b c d e + 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e - 5a b c d e + (2a b d + 5a b c d)e - 5a b c d +--R / +--R 2b +--R Type: Union(Expression Integer,...) +--E 811 + +--S 812 of 1483 +m0156:=a0156-r0156 +--R +--R +--R (812) +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 - 6a b %%BV0 +--R + +--R 2 2 +--R - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BV1 - 2b\|a \|a \|b \|b %%BV0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e + 6a b c d e - 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BV1 - 2b\|a \|a \|b \|b %%BV0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e - 32a b c e + 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e - 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BV1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (24a b c d e - 16a b d e - 8a b c d)f + 4a b c e - 4a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 12a b c d e - 8a b c d - 4a b c +--R * +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e - 24a b c e + 48a b c d )f + 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- 3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e + 4a b c e - 3a b c d e - 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 8a b c d e + 3a b c d e + (2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BV0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e + 64a b c e - 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (24a b c d e - 16a b d e - 8a b c d)f - 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R - 12a b d e - 16a b c e + 36a b c d e + 8a b c d - 4a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e - 4a b c e + 9a b c d e + 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e - 5a b c d e + (2a b d + 5a b c d)e - 5a b c d +--R + +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (- 2a b e\|b - 2b c\|a )atanh(-----) - 2b d \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (2a b e\|b - 2b c\|a )atan(-----) + f log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression Integer +--E 812 + +--S 813 of 1483 +d0156:=D(m0156,x) +--R +--R +--R 2 4+-+2 2 +-+ 4+-+2 4+-+2 +-+ +--R ((- e x - c)\|a + e x \|a )\|b + c \|a \|b +--R (813) ------------------------------------------------- +--R 4 4+-+2 4+-+2 +--R (b x - a)\|a \|b +--R Type: Expression Integer +--E 813 + +--S 814 of 1483 +t0157:= x^3/(a+b*(c+d*x)^4) +--R +--R +--R 3 +--R x +--R (814) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 814 + +--S 815 of 1483 +r0157:= 3/2*c^2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^4-_ + 1/4*c*(3*a^(1/2)+_ + b^(1/2)*c^2)*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(3/4)/d^4-1/4*c*(3*a^(1/2)+_ + b^(1/2)*c^2)*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(3/4)/d^4-1/8*c*(3*a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^4+1/8*c*(3*a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^4+1/4*log(a+b*(c+d*x)^4)/b/d^4 +--R +--R +--R (815) +--R +-+ +-+ 2 3 +-+ +-+ +--R (3a b c\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (- 3a b c\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (- 6a b c\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (- 6a b c\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R 12b c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+4+-+3 +-+ +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a)\|a \|a \|b +--R * +--R 4+-+3 +--R \|b +--R / +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b +--R Type: Expression Integer +--E 815 + +--S 816 of 1483 +a0157:=integrate(t0157,x) +--R +--R +--R (816) +--R - +--R 4 +--R b d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 4 +--R - b d %%BW1 - b d %%BW0 + 1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 150a b c + 30a b c + 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +--R b d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 4 +--R - b d %%BW1 - b d %%BW0 + 1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 2a b c + 150a b c - 30a b c - 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +--R 2b d %%BW1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 48a b c + 1056a b c - 432a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c + 348a b c - 1116a b c + 324a b)d +--R * +--R %%BW1 +--R + +--R 3 4 4 4 3 12 3 3 3 4 4 2 8 2 +--R (960a b c + 1728a b )d %%BW0 + (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 3 8 3 2 4 4 4 +--R (1800a b c + 3600a b c + 648a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 206a b c - 48a b c + 846a b c - 81a +--R + +--R 4 +--R 2b d %%BW0 +--R * +--R log +--R 3 4 4 4 3 12 3 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (- 48a b c + 2016a b c + 1296a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c - 1452a b c - 4716a b c - 324a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 26a b c - 444a b c - 390a b c + 27a +--R / +--R 4 +--R 2b d +--R Type: Union(Expression Integer,...) +--E 816 + +--S 817 of 1483 +m0157:=a0157-r0157 +--R +--R +--R (817) +--R - +--R 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|a \|b \|b +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 +-+4+-+3 +-+4+-+3 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|a \|b \|b %%BW1 - 4b d \|a \|a \|b \|b %%BW0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4\|a \|a \|b \|b +--R * +--R log +--R 3 4 4 4 3 12 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 150a b c + 30a b c + 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|a \|b \|b +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 +-+4+-+3 +-+4+-+3 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|a \|b \|b %%BW1 - 4b d \|a \|a \|b \|b %%BW0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4\|a \|a \|b \|b +--R * +--R log +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 2a b c + 150a b c - 30a b c - 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b %%BW1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 48a b c + 1056a b c - 432a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c + 348a b c - 1116a b c + 324a b)d +--R * +--R %%BW1 +--R + +--R 3 4 4 4 3 12 3 3 3 4 4 2 8 2 +--R (960a b c + 1728a b )d %%BW0 + (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 3 8 3 2 4 4 4 +--R (1800a b c + 3600a b c + 648a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 206a b c - 48a b c + 846a b c - 81a +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (- 3a b c\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (3a b c\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b %%BW0 +--R * +--R log +--R 3 4 4 4 3 12 3 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (- 48a b c + 2016a b c + 1296a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c - 1452a b c - 4716a b c - 324a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 26a b c - 444a b c - 390a b c + 27a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (6a b c\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (6a b c\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R - 12b c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R - +--R 4 4 3 3 2 2 2 3 4 +-+4+-+3 +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a)\|a \|a +--R * +--R +-+4+-+3 +--R \|b \|b +--R / +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b +--R Type: Expression Integer +--E 817 + +--S 818 of 1483 +d0157:=D(m0157,x) +--R +--R +--R (818) +--R 3 4 4 4 3 3 5 2 2 6 2 +--R b c d x + 4b c d x + (6b c - 6a c)d x + (4b c - 12a c )d x +--R + +--R 7 3 +--R b c - 7a c +--R * +--R 4+-+2 +-+ +--R \|a \|b +--R + +--R 4 4 2 3 3 3 2 2 4 5 +-+ +--R (3b c d x + 12b c d x + 16b c d x + 8b c d x + b c - 3a c)\|a +--R * +--R 4+-+2 +--R \|a +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 12a b c d x - 48a b c d x - 76a b c d x - 56a b c d x - 16a b c +--R * +--R 4+-+2 +--R \|b +--R + +--R 4 4 2 3 3 3 2 2 4 5 +-+4+-+2 +--R (12b c d x + 48b c d x + 76b c d x + 56b c d x + 16b c )\|a \|a +--R + +--R 4 4 2 3 3 3 2 2 4 5 +--R - 3a b c d x - 12a b c d x - 16a b c d x - 8a b c d x - a b c +--R + +--R 2 +--R 3a c +--R * +--R +-+ +--R \|b +--R + +--R 2 6 6 2 2 5 5 2 3 4 4 2 4 3 3 +--R 6b c d x + 36b c d x + 92b c d x + 128b c d x +--R + +--R 2 5 2 2 2 6 2 2 7 3 +--R (102b c + 6a b c)d x + (44b c + 12a b c )d x + 8b c + 8a b c +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 6 6 2 2 5 5 2 3 4 4 2 4 3 3 2 5 2 2 +--R - 6b c d x - 36b c d x - 93b c d x - 132b c d x - 108b c d x +--R + +--R 2 6 2 7 3 +--R - 48b c d x - 9b c - a b c +--R * +--R +-+ +--R \|a +--R / +--R 2 9 6 2 8 5 2 2 7 4 2 3 6 3 +--R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x +--R + +--R 2 4 2 5 2 2 5 2 4 2 6 2 2 3 +--R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 9 6 2 8 5 2 2 7 4 2 3 6 3 +--R - 4b d x - 24b c d x - 60b c d x - 80b c d x +--R + +--R 2 4 5 2 2 5 4 2 6 2 3 +--R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 3 11 8 3 10 7 3 2 9 6 3 3 8 5 +--R - 2b d x - 16b c d x - 56b c d x - 112b c d x +--R + +--R 3 4 2 7 4 3 5 2 6 3 +--R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x +--R + +--R 3 6 2 2 5 2 3 7 2 3 4 +--R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x +--R + +--R 3 8 2 4 2 3 +--R (- 2b c - 4a b c - 2a b)d +--R * +--R 4+-+2 +--R \|a +--R Type: Expression Integer +--E 818 + +--S 819 of 1483 +t0158:= x^2/(a+b*(c+d*x)^4) +--R +--R +--R 2 +--R x +--R (819) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 819 + +--S 820 of 1483 +r0158:= -c*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^3+_ + 1/4*(a^(1/2)+b^(1/2)*c^2)*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/_ + a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)/d^3+_ + 1/4*(a^(1/2)+b^(1/2)*c^2)*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/_ + a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)/d^3+_ + 1/8*(a^(1/2)-b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)-_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^3-1/8*(a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^3 +--R +--R +--R (820) +--R +-+ +-+ 2 +-+ +-+ +--R (- a\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (a\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (2a\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (2a\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R - 8c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b +--R Type: Expression Integer +--E 820 + +--S 821 of 1483 +a0158:=integrate(t0158,x) +--R +--R +--R (821) +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- - %%BX1 +--R | 6 +--R \| a b d +--R + +--R - %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 2 3 7 3 2 3 6 3 10 2 2 6 3 2 3 +--R (16a b c - 80a b c )d %%BX0 + (2a b c - 40a b c + 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R - |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R - %%BX1 - %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((- 224a b c - 32a b )d %%BX0 + (- 16a b c + 80a b c )d ) +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 +--R (- 16a b c + 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R 2%%BX1 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((- 448a b c - 64a b )d %%BX0 + (- 32a b c + 160a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (- 448a b c - 64a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c - 80a b c + 12a b c )d +--R * +--R %%BX1 +--R + +--R 3 3 4 4 2 9 3 2 2 6 3 2 3 +--R (- 448a b c - 64a b )d %%BX0 + (- 336a b c - 48a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 59a b c +--R + +--R 2 5 3 +--R 39a b c + 3a c +--R + +--R 2%%BX0 +--R * +--R log +--R 3 3 4 4 2 9 3 2 3 7 3 2 3 6 2 +--R (448a b c + 64a b )d %%BX0 + (- 32a b c + 160a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c + 256a b c + 60a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 2 5 +--R (b c - 33a b c - 33a b c + a )d x + b c - 3a b c - 9a b c +--R + +--R 3 +--R - 5a c +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 821 + +--S 822 of 1483 +m0158:=a0158-r0158 +--R +--R +--R (822) +--R 3 +-+4+-+3 +-+4+-+3 +--R 4d \|a \|a \|b \|b +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 +-+4+-+3 +-+4+-+3 3 +-+4+-+3 +-+4+-+3 +--R - 4d \|a \|a \|b \|b %%BX1 - 4d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 2 3 7 3 2 3 6 3 10 2 2 6 3 2 3 +--R (16a b c - 80a b c )d %%BX0 + (2a b c - 40a b c + 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R - +--R 3 +-+4+-+3 +-+4+-+3 +--R 4d \|a \|a \|b \|b +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 +-+4+-+3 +-+4+-+3 3 +-+4+-+3 +-+4+-+3 +--R - 4d \|a \|a \|b \|b %%BX1 - 4d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((- 224a b c - 32a b )d %%BX0 + (- 16a b c + 80a b c )d ) +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 +--R (- 16a b c + 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b %%BX1 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((- 448a b c - 64a b )d %%BX0 + (- 32a b c + 160a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (- 448a b c - 64a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c - 80a b c + 12a b c )d +--R * +--R %%BX1 +--R + +--R 3 3 4 4 2 9 3 2 2 6 3 2 3 +--R (- 448a b c - 64a b )d %%BX0 + (- 336a b c - 48a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 59a b c +--R + +--R 2 5 3 +--R 39a b c + 3a c +--R + +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 3 2 3 7 3 2 3 6 2 +--R (448a b c + 64a b )d %%BX0 + (- 32a b c + 160a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c + 256a b c + 60a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 2 5 +--R (b c - 33a b c - 33a b c + a )d x + b c - 3a b c - 9a b c +--R + +--R 3 +--R - 5a c +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (a\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (- a\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (- 2a\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (- 2a\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R 8c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b +--R Type: Expression Integer +--E 822 + +--S 823 of 1483 +d0158:=D(m0158,x) +--R +--R +--R (823) +--R 2 4 4 3 3 3 4 2 2 5 +--R - b c d x - 4b c d x + (- 6b c + 2a)d x + (- 4b c + 4a c)d x +--R + +--R 6 2 +--R - b c + 3a c +--R * +--R 4+-+2 +-+ +--R \|a \|b +--R + +--R 4 4 3 3 2 2 2 4 +-+4+-+2 4 4 +--R (- b d x - 4b c d x - 4b c d x + b c + a)\|a \|a + 4a b d x +--R + +--R 3 3 2 2 2 3 4 +--R 16a b c d x + 28a b c d x + 24a b c d x + 8a b c +--R * +--R 4+-+2 +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+4+-+2 +--R (- 4b d x - 16b c d x - 28b c d x - 24b c d x - 8b c )\|a \|a +--R + +--R 4 4 3 3 2 2 2 4 2 +--R a b d x + 4a b c d x + 4a b c d x - a b c - a +--R * +--R +-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 32b c d x - 48b c d x +--R + +--R 2 4 2 2 2 5 2 6 2 +--R (- 42b c - 2a b)d x + (- 20b c - 4a b c)d x - 4b c - 4a b c +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 +--R 2b d x + 12b c d x + 33b c d x + 52b c d x + 48b c d x +--R + +--R 2 5 2 6 2 +--R 24b c d x + 5b c + a b c +--R * +--R +-+ +--R \|a +--R / +--R 2 8 6 2 7 5 2 2 6 4 2 3 5 3 +--R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x +--R + +--R 2 4 2 4 2 2 5 2 3 2 6 2 2 2 +--R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 8 6 2 7 5 2 2 6 4 2 3 5 3 +--R - 4b d x - 24b c d x - 60b c d x - 80b c d x +--R + +--R 2 4 4 2 2 5 3 2 6 2 2 +--R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 3 10 8 3 9 7 3 2 8 6 3 3 7 5 +--R - 2b d x - 16b c d x - 56b c d x - 112b c d x +--R + +--R 3 4 2 6 4 3 5 2 5 3 +--R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x +--R + +--R 3 6 2 2 4 2 3 7 2 3 3 +--R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x +--R + +--R 3 8 2 4 2 2 +--R (- 2b c - 4a b c - 2a b)d +--R * +--R 4+-+2 +--R \|a +--R Type: Expression Integer +--E 823 + +--S 824 of 1483 +t0159:= x/(a+b*(c+d*x)^4) +--R +--R +--R x +--R (824) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 824 + +--S 825 of 1483 +r0159:= 1/2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^2-_ + 1/4*c*atan(-1+2^(1/2)*b^(1/4)*(c+_ + d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d^2-1/4*c*atan(1+_ + 2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d^2+_ + 1/8*c*log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d^2-1/8*c*log(a^(1/2)/b^(1/2)+_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d^2 +--R +--R +--R (825) +--R - +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b + \|a +--R - 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b - \|a +--R - 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+ (d x + 2c d x + c )\|b +--R 4\|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b +--R Type: Expression Integer +--E 825 + +--S 826 of 1483 +a0159:=integrate(t0159,x) +--R +--R +--R (826) +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R - |-------------------------------------------------------- - %%BY1 +--R | 4 +--R \| 2a b d +--R + +--R - %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (64a b d %%BY0 - 8a b c d )%%BY1 - 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (2a b c - 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- - %%BY1 +--R | 4 +--R \| 2a b d +--R + +--R - %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (- 2a b c + 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2%%BY1 +--R * +--R log +--R 3 6 2 2 4 2 +--R (128a b d %%BY0 - 16a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 3 6 3 +--R (128a b d %%BY0 + (- 4a b c + 8a )d )%%BY1 + 128a b d %%BY0 +--R + +--R 2 2 5 6 2 +--R 16a d %%BY0 + (b c - 4a c)d x + b c - 7a c +--R + +--R 2%%BY0 +--R * +--R log +--R 3 6 3 2 2 4 2 4 2 2 +--R - 128a b d %%BY0 - 16a b c d %%BY0 + (- 4a b c - 8a )d %%BY0 +--R + +--R 5 6 2 +--R (b c - 4a c)d x + b c + a c +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 826 + +--S 827 of 1483 +m0159:=a0159-r0159 +--R +--R +--R (827) +--R - +--R 2 +-+4+-+3 +-+4+-+ +--R 4d \|a \|a \|b \|b +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 2 +-+4+-+3 +-+4+-+ 2 +-+4+-+3 +-+4+-+ +--R - 4d \|a \|a \|b \|b %%BY1 - 4d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (64a b d %%BY0 - 8a b c d )%%BY1 - 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (2a b c - 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 4d \|a \|a \|b \|b +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 2 +-+4+-+3 +-+4+-+ 2 +-+4+-+3 +-+4+-+ +--R - 4d \|a \|a \|b \|b %%BY1 - 4d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (- 2a b c + 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b %%BY1 +--R * +--R log +--R 3 6 2 2 4 2 +--R (128a b d %%BY0 - 16a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 3 6 3 +--R (128a b d %%BY0 + (- 4a b c + 8a )d )%%BY1 + 128a b d %%BY0 +--R + +--R 2 2 5 6 2 +--R 16a d %%BY0 + (b c - 4a c)d x + b c - 7a c +--R + +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R - +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 3 2 2 4 2 4 2 2 +--R - 128a b d %%BY0 - 16a b c d %%BY0 + (- 4a b c - 8a )d %%BY0 +--R + +--R 5 6 2 +--R (b c - 4a c)d x + b c + a c +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b + \|a +--R 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b - \|a +--R 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+ (d x + 2c d x + c )\|b +--R - 4\|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b +--R Type: Expression Integer +--E 827 + +--S 828 of 1483 +d0159:=D(m0159,x) +--R +--R +--R (828) +--R 4 4 2 3 3 3 2 2 4 5 +--R (- 3b c d x - 12b c d x - 18b c d x - 12b c d x - 3b c - a c) +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 2 2 3 +--R - 2a b c d x - 4a b c d x - 2a b c +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 2 2 3 +-+4+-+2 +-+ +--R (2b c d x + 4b c d x + 2b c )\|a \|a \|b +--R + +--R 2 4 4 2 2 3 3 2 3 2 2 2 4 2 5 4+-+2 +--R (3b c d x + 12b c d x + 18b c d x + 12b c d x + 3b c + a b c)\|a +--R / +--R 2 7 6 2 6 5 2 2 5 4 2 3 4 3 +--R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x +--R + +--R 2 4 2 3 2 2 5 2 2 2 6 2 2 +--R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + (4a b c + 4a b c )d +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 7 6 2 6 5 2 2 5 4 2 3 4 3 +--R - 4b d x - 24b c d x - 60b c d x - 80b c d x +--R + +--R 2 4 3 2 2 5 2 2 6 2 +--R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x + (- 4b c - 4a b c )d +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 +--R - 2b d x - 16b c d x - 56b c d x - 112b c d x +--R + +--R 3 4 2 5 4 3 5 2 4 3 +--R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x +--R + +--R 3 6 2 2 3 2 3 7 2 3 2 +--R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x +--R + +--R 3 8 2 4 2 +--R (- 2b c - 4a b c - 2a b)d +--R * +--R 4+-+2 +--R \|a +--R Type: Expression Integer +--E 828 + +--S 829 of 1483 +t0160:= 1/(a+b*(c+d*x)^4) +--R +--R +--R 1 +--R (829) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction Polynomial Integer +--E 829 + +--S 830 of 1483 +r0160:= 1/4*atan(-1+2^(1/2)*b^(1/4)*(c+_ + d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d+_ + 1/4*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(1/4)/d-1/8*log(a^(1/2)/b^(1/2)-2^(1/2)*_ + a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d+_ + 1/8*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d +--R +--R +--R (830) +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R \|2 log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R - +--R +-+ +--R \|2 +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b + \|a +-+ (d x + c)\|2 \|b - \|a +--R 2\|2 atan(------------------------) + 2\|2 atan(------------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R 4+-+3 4+-+ +--R 8d \|a \|b +--R Type: Expression Integer +--E 830 + +--S 831 of 1483 +a0160:=integrate(t0160,x) +--R +--R +--R (831) +--R +-----------+ +-----------+ +--R | 1 | 1 +--R |- --------- log(4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-----------+ +-----------+ +--R | 1 | 1 +--R - |- --------- log(- 4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-----------+ +--R | 1 +--R 4a d |- --------- +--R +-----------+ 4| 3 4 +--R | 1 \| 256a b d +--R - 2 |- --------- atan(------------------) +--R 4| 3 4 d x + c +--R \| 256a b d +--R Type: Union(Expression Integer,...) +--E 831 + +--S 832 of 1483 +m0160:=a0160-r0160 +--R +--R +--R (832) +--R +-----------+ +-----------+ +--R | 1 4+-+3 4+-+ | 1 +--R 8d |- --------- \|a \|b log(4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R - \|2 log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R \|2 log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-----------+ +-----------+ +--R | 1 4+-+3 4+-+ | 1 +--R - 8d |- --------- \|a \|b log(- 4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b + \|a +--R - 2\|2 atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b - \|a +--R - 2\|2 atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R | 1 +--R 4a d |- --------- +--R +-----------+ 4| 3 4 +--R | 1 4+-+3 4+-+ \| 256a b d +--R - 16d |- --------- \|a \|b atan(------------------) +--R 4| 3 4 d x + c +--R \| 256a b d +--R / +--R 4+-+3 4+-+ +--R 8d \|a \|b +--R Type: Expression Integer +--E 832 + +--S 833 of 1483 +d0160:=D(m0160,x) +--R +--R +--R (833) +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +--R (3b d x + 12b c d x + 18b c d x + 12b c d x + 3b c + a)\|a \|b +--R + +--R 2 2 2 +--R 2a b d x + 4a b c d x + 2a b c +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 2 2 +-+4+-+2 +-+ +--R (- 2b d x - 4b c d x - 2b c )\|a \|a \|b +--R + +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 4+-+2 +--R (- 3b d x - 12b c d x - 18b c d x - 12b c d x - 3b c - a b)\|a +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4a b d x + 24a b c d x + 60a b c d x + 80a b c d x +--R + +--R 2 4 2 2 2 2 5 2 2 6 2 2 +--R (60a b c + 4a b)d x + (24a b c + 8a b c)d x + 4a b c + 4a b c +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d x - 24b c d x - 60b c d x - 80b c d x +--R + +--R 2 4 2 2 2 5 2 6 2 +--R (- 60b c - 4a b)d x + (- 24b c - 8a b c)d x - 4b c - 4a b c +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 3 8 8 3 7 7 3 2 6 6 3 3 5 5 +--R - 2b d x - 16b c d x - 56b c d x - 112b c d x +--R + +--R 3 4 2 4 4 3 5 2 3 3 +--R (- 140b c - 4a b )d x + (- 112b c - 16a b c)d x +--R + +--R 3 6 2 2 2 2 3 7 2 3 3 8 +--R (- 56b c - 24a b c )d x + (- 16b c - 16a b c )d x - 2b c +--R + +--R 2 4 2 +--R - 4a b c - 2a b +--R * +--R 4+-+2 +--R \|a +--R Type: Expression Integer +--E 833 + +--S 834 of 1483 +t0161:= 1/x/(a+b*(c+d*x)^4) +--R +--R +--R 1 +--R (834) -------------------------------------------------------- +--R 4 5 3 4 2 2 3 3 2 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + (b c + a)x +--R Type: Fraction Polynomial Integer +--E 834 + +--S 835 of 1483 +r0161:= -1/2*b^(1/2)*c^2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/(a+b*c^4)-_ + 1/4*b^(1/4)*c*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(1/4)/(a+b*c^4)-1/4*b^(3/4)*c^3*atan(-1+2^(1/2)*b^(1/4)*_ + (c+d*x)/a^(1/4))*2^(1/2)/a^(3/4)/(a+b*c^4)-1/4*b^(1/4)*c*_ + atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/a^(1/4)/(a+b*c^4)-_ + 1/4*b^(3/4)*c^3*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*_ + 2^(1/2)/a^(3/4)/(a+b*c^4)+log(-d*x)/(a+b*c^4)-1/8*b^(1/4)*c*_ + log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(1/4)/(a+b*c^4)+1/8*b^(3/4)*c^3*_ + log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/(a+b*c^4)+1/8*b^(1/4)*c*log(a^(1/2)/_ + b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*_ + 2^(1/2)/a^(1/4)/(a+b*c^4)-1/8*b^(3/4)*c^3*log(a^(1/2)/b^(1/2)+_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/_ + (a+b*c^4)-log(a+b*(c+d*x)^4)/(4*a+4*b*c^4) +--R +--R +--R (835) +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (- c \|2 \|a \|b + c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (c \|2 \|a \|b - c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b + \|a +--R (- 2c \|2 \|a \|b - 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b - \|a +--R (- 2c \|2 \|a \|b - 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 +-+ (d x + 2c d x + c )\|b +--R - 4c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R + +--R 8log(- d x) +--R * +--R +-+4+-+3 +--R \|a \|a +--R / +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a +--R Type: Expression Integer +--E 835 + +--S 836 of 1483 +a0161:=integrate(t0161,x) +--R +--R +--R (836) +--R 4 +--R (- b c - a) +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 4 +--R (- b c - a)%%CA1 + (- b c - a)%%CA0 - 1 +--R * +--R log +--R 3 4 4 2 4 3 +--R ((32a b c + 32a )%%CA0 + 8a b c + 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (8a b c + 8a )%%CA0 + 2a b c + 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +--R (b c + a) +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 4 +--R (- b c - a)%%CA1 + (- b c - a)%%CA0 - 1 +--R * +--R log +--R 3 4 4 2 4 3 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (- 8a b c - 8a )%%CA0 - 2a b c - 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +--R (2b c + 2a)%%CA1 +--R * +--R log +--R 3 4 4 2 4 3 2 +--R ((64a b c + 64a )%%CA0 + 16a b c + 16a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((64a b c + 64a )%%CA0 + 64a %%CA0 - 4a b c + 12a )%%CA1 +--R + +--R 3 4 4 3 3 2 2 3 4 +--R (64a b c + 64a )%%CA0 + 64a %%CA0 + 24a %%CA0 + b c d x + b c +--R + +--R 3a +--R + +--R 4 +--R (2b c + 2a)%%CA0 +--R * +--R log +--R 3 4 4 3 2 4 3 2 +--R (- 64a b c - 64a )%%CA0 + (16a b c - 48a )%%CA0 +--R + +--R 4 2 3 4 +--R (- 4a b c - 12a )%%CA0 + b c d x + b c - a +--R + +--R 2log(x) +--R / +--R 4 +--R 2b c + 2a +--R Type: Union(Expression Integer,...) +--E 836 + +--S 837 of 1483 +m0161:=a0161-r0161 +--R +--R +--R (837) +--R 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 +-+4+-+3 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a %%CA1 + (- 4b c - 4a)\|a \|a %%CA0 +--R + +--R +-+4+-+3 +--R - 4\|a \|a +--R * +--R log +--R 3 4 4 2 4 3 +--R ((32a b c + 32a )%%CA0 + 8a b c + 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (8a b c + 8a )%%CA0 + 2a b c + 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +-+4+-+3 +--R (4b c + 4a)\|a \|a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 +-+4+-+3 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a %%CA1 + (- 4b c - 4a)\|a \|a %%CA0 +--R + +--R +-+4+-+3 +--R - 4\|a \|a +--R * +--R log +--R 3 4 4 2 4 3 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (- 8a b c - 8a )%%CA0 - 2a b c - 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a %%CA1 +--R * +--R log +--R 3 4 4 2 4 3 2 +--R ((64a b c + 64a )%%CA0 + 16a b c + 16a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((64a b c + 64a )%%CA0 + 64a %%CA0 - 4a b c + 12a )%%CA1 +--R + +--R 3 4 4 3 3 2 2 3 4 +--R (64a b c + 64a )%%CA0 + 64a %%CA0 + 24a %%CA0 + b c d x + b c +--R + +--R 3a +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (c \|2 \|a \|b - c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (- c \|2 \|a \|b + c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a %%CA0 +--R * +--R log +--R 3 4 4 3 2 4 3 2 +--R (- 64a b c - 64a )%%CA0 + (16a b c - 48a )%%CA0 +--R + +--R 4 2 3 4 +--R (- 4a b c - 12a )%%CA0 + b c d x + b c - a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b + \|a +--R (2c \|2 \|a \|b + 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b - \|a +--R (2c \|2 \|a \|b + 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 +-+ (d x + 2c d x + c )\|b +--R 4c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) + 8log(x) +--R + +--R - 8log(- d x) +--R * +--R +-+4+-+3 +--R \|a \|a +--R / +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a +--R Type: Expression Integer +--E 837 + +--S 838 of 1483 +d0161:=D(m0161,x) +--R +--R +--R (838) +--R 5 4 2 4 3 3 3 2 4 2 +--R - 3b c d x - 12b c d x - 20b c d x - 16b c d x +--R + +--R 5 +--R (- 5b c - a c)d +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 2 3 5 4 2 4 4 3 2 5 3 2 +--R - 3b c d x - 12b c d x + (- 18b c - 2a b c)d x +--R + +--R 2 6 2 2 2 7 3 +--R (- 12b c - 4a b c )d x + (- 3b c - 3a b c )d +--R * +--R 4+-+2 +--R \|a +--R * +--R 4+-+2 +--R \|b +--R + +--R 2 3 5 4 2 4 4 3 2 5 3 2 +--R 3b c d x + 12b c d x + (18b c + 2a b c)d x +--R + +--R 2 6 2 2 2 7 3 +--R (12b c + 4a b c )d x + (3b c + 3a b c )d +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 5 4 2 2 4 3 2 3 3 2 2 4 2 +--R 3a b c d x + 12a b c d x + 20a b c d x + 16a b c d x +--R + +--R 2 5 2 +--R (5a b c + a b c)d +--R / +--R 2 4 6 6 2 5 5 5 +--R (4b c + 4a b)d x + (24b c + 24a b c)d x +--R + +--R 2 6 2 4 4 2 7 3 3 3 +--R (60b c + 60a b c )d x + (80b c + 80a b c )d x +--R + +--R 2 8 4 2 2 2 2 9 5 2 +--R (60b c + 64a b c + 4a )d x + (24b c + 32a b c + 8a c)d x +--R + +--R 2 10 6 2 2 +--R 4b c + 8a b c + 4a c +--R * +--R +-+4+-+2 +-+ +--R \|a \|a \|b +--R + +--R 3 4 2 8 8 3 5 2 7 7 +--R (2b c + 2a b )d x + (16b c + 16a b c)d x +--R + +--R 3 6 2 2 6 6 3 7 2 3 5 5 +--R (56b c + 56a b c )d x + (112b c + 112a b c )d x +--R + +--R 3 8 2 4 2 4 4 +--R (140b c + 144a b c + 4a b)d x +--R + +--R 3 9 2 5 2 3 3 +--R (112b c + 128a b c + 16a b c)d x +--R + +--R 3 10 2 6 2 2 2 2 +--R (56b c + 80a b c + 24a b c )d x +--R + +--R 3 11 2 7 2 3 3 12 2 8 2 4 +--R (16b c + 32a b c + 16a b c )d x + 2b c + 6a b c + 6a b c +--R + +--R 3 +--R 2a +--R * +--R 4+-+2 +--R \|a +--R * +--R 4+-+2 +--R \|b +--R + +--R 3 4 2 2 6 6 3 5 2 2 5 5 +--R (- 4a b c - 4a b )d x + (- 24a b c - 24a b c)d x +--R + +--R 3 6 2 2 2 4 4 3 7 2 2 3 3 3 +--R (- 60a b c - 60a b c )d x + (- 80a b c - 80a b c )d x +--R + +--R 3 8 2 2 4 3 2 2 3 9 2 2 5 3 +--R (- 60a b c - 64a b c - 4a b)d x + (- 24a b c - 32a b c - 8a b c)d x +--R + +--R 3 10 2 2 6 3 2 +--R - 4a b c - 8a b c - 4a b c +--R Type: Expression Integer +--E 838 + +--S 839 of 1483 +t0162:= (c+d*x)^3*(a+b*(c+d*x)^4)^3 +--R +--R +--R (839) +--R 3 15 15 3 14 14 3 2 13 13 3 3 12 12 +--R b d x + 15b c d x + 105b c d x + 455b c d x +--R + +--R 3 4 2 11 11 3 5 2 10 10 +--R (1365b c + 3a b )d x + (3003b c + 33a b c)d x +--R + +--R 3 6 2 2 9 9 3 7 2 3 8 8 +--R (5005b c + 165a b c )d x + (6435b c + 495a b c )d x +--R + +--R 3 8 2 4 2 7 7 3 9 2 5 2 6 6 +--R (6435b c + 990a b c + 3a b)d x + (5005b c + 1386a b c + 21a b c)d x +--R + +--R 3 10 2 6 2 2 5 5 +--R (3003b c + 1386a b c + 63a b c )d x +--R + +--R 3 11 2 7 2 3 4 4 +--R (1365b c + 990a b c + 105a b c )d x +--R + +--R 3 12 2 8 2 4 3 3 3 +--R (455b c + 495a b c + 105a b c + a )d x +--R + +--R 3 13 2 9 2 5 3 2 2 +--R (105b c + 165a b c + 63a b c + 3a c)d x +--R + +--R 3 14 2 10 2 6 3 2 3 15 2 11 2 7 +--R (15b c + 33a b c + 21a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Polynomial Integer +--E 839 + +--S 840 of 1483 +r0162:= 1/16*(a+b*(c+d*x)^4)^4/b/d +--R +--R +--R (840) +--R 1 4 16 16 4 15 15 15 4 2 14 14 4 3 13 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 4 4 1 3 12 12 4 5 3 11 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 4 6 33 3 2 10 10 4 7 3 3 9 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 4 8 495 3 4 3 2 2 8 8 +--R (---- b c + --- a b c + - a b )d x +--R 8 4 8 +--R + +--R 4 9 3 5 2 2 7 7 +--R (715b c + 198a b c + 3a b c)d x +--R + +--R 1001 4 10 3 6 21 2 2 2 6 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 4 11 3 7 2 2 3 5 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 4 12 495 3 8 105 2 2 4 1 3 4 4 +--R (--- b c + --- a b c + --- a b c + - a b)d x +--R 4 4 4 4 +--R + +--R 4 13 3 9 2 2 5 3 3 3 +--R (35b c + 55a b c + 21a b c + a b c)d x +--R + +--R 15 4 14 33 3 10 21 2 2 6 3 3 2 2 2 +--R (-- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 4 15 3 11 2 2 7 3 3 1 4 16 1 3 12 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c +--R 16 4 +--R + +--R 3 2 2 8 1 3 4 1 4 +--R - a b c + - a b c + -- a +--R 8 4 16 +--R / +--R b d +--R Type: Fraction Polynomial Fraction Integer +--E 840 + +--S 841 of 1483 +a0162:=integrate(t0162,x) +--R +--R +--R (841) +--R 1 3 15 16 3 14 15 15 3 2 13 14 3 3 12 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 3 4 1 2 11 12 3 5 2 10 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 3 6 33 2 2 9 10 3 7 2 3 8 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 3 8 495 2 4 3 2 7 8 3 9 2 5 2 6 7 +--R (---- b c + --- a b c + - a b)d x + (715b c + 198a b c + 3a b c)d x +--R 8 4 8 +--R + +--R 1001 3 10 2 6 21 2 2 5 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 3 11 2 7 2 3 4 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 3 12 495 2 8 105 2 4 1 3 3 4 +--R (--- b c + --- a b c + --- a b c + - a )d x +--R 4 4 4 4 +--R + +--R 3 13 2 9 2 5 3 2 3 +--R (35b c + 55a b c + 21a b c + a c)d x +--R + +--R 15 3 14 33 2 10 21 2 6 3 3 2 2 +--R (-- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 15 2 11 2 7 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial Fraction Integer +--E 841 + +--S 842 of 1483 +m0162:=a0162-r0162 +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R - -- b c - - a b c - - a b c - - a b c - -- a +--R 16 4 8 4 16 +--R (842) ---------------------------------------------------- +--R b d +--R Type: Fraction Polynomial Fraction Integer +--E 842 + +--S 843 of 1483 +d0162:=D(m0162,x) +--R +--R +--R (843) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 843 + +--S 844 of 1483 +t0163:= (c+d*x)^3*(a+b*(c+d*x)^4)^2 +--R +--R +--R (844) +--R 2 11 11 2 10 10 2 2 9 9 2 3 8 8 2 4 7 7 +--R b d x + 11b c d x + 55b c d x + 165b c d x + (330b c + 2a b)d x +--R + +--R 2 5 6 6 2 6 2 5 5 +--R (462b c + 14a b c)d x + (462b c + 42a b c )d x +--R + +--R 2 7 3 4 4 2 8 4 2 3 3 +--R (330b c + 70a b c )d x + (165b c + 70a b c + a )d x +--R + +--R 2 9 5 2 2 2 2 10 6 2 2 2 11 +--R (55b c + 42a b c + 3a c)d x + (11b c + 14a b c + 3a c )d x + b c +--R + +--R 7 2 3 +--R 2a b c + a c +--R Type: Polynomial Integer +--E 844 + +--S 845 of 1483 +r0163:= 1/12*(a+b*(c+d*x)^4)^3/b/d +--R +--R +--R (845) +--R 1 3 12 12 3 11 11 11 3 2 10 10 55 3 3 9 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 3 4 1 2 8 8 3 5 2 7 7 3 6 2 2 6 6 +--R (--- b c + - a b )d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 3 7 2 3 5 5 165 3 8 35 2 4 1 2 4 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a b)d x +--R 4 2 4 +--R + +--R 55 3 9 2 5 2 3 3 11 3 10 2 6 3 2 2 2 2 +--R (-- b c + 14a b c + a b c)d x + (-- b c + 7a b c + - a b c )d x +--R 3 2 2 +--R + +--R 3 11 2 7 2 3 1 3 12 1 2 8 1 2 4 1 3 +--R (b c + 2a b c + a b c )d x + -- b c + - a b c + - a b c + -- a +--R 12 4 4 12 +--R / +--R b d +--R Type: Fraction Polynomial Fraction Integer +--E 845 + +--S 846 of 1483 +a0163:=integrate(t0163,x) +--R +--R +--R (846) +--R 1 2 11 12 2 10 11 11 2 2 9 10 55 2 3 8 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 2 4 1 7 8 2 5 6 7 2 6 2 5 6 +--R (--- b c + - a b)d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 2 7 3 4 5 165 2 8 35 4 1 2 3 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 55 2 9 5 2 2 3 11 2 10 6 3 2 2 2 +--R (-- b c + 14a b c + a c)d x + (-- b c + 7a b c + - a c )d x +--R 3 2 2 +--R + +--R 2 11 7 2 3 +--R (b c + 2a b c + a c )x +--R Type: Polynomial Fraction Integer +--E 846 + +--S 847 of 1483 +m0163:=a0163-r0163 +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R - -- b c - - a b c - - a b c - -- a +--R 12 4 4 12 +--R (847) ---------------------------------------- +--R b d +--R Type: Fraction Polynomial Fraction Integer +--E 847 + +--S 848 of 1483 +d0163:=D(m0163,x) +--R +--R +--R (848) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 848 + +--S 849 of 1483 +t0164:= (c+d*x)^3*(a+b*(c+d*x)^4) +--R +--R +--R (849) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + 35b c d x + (35b c + a)d x +--R + +--R 5 2 2 6 2 7 3 +--R (21b c + 3a c)d x + (7b c + 3a c )d x + b c + a c +--R Type: Polynomial Integer +--E 849 + +--S 850 of 1483 +r0164:= 1/4*a*(c+d*x)^4/d+1/8*b*(c+d*x)^8/d +--R +--R +--R (850) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 1 4 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 3 3 7 6 3 2 2 2 7 3 1 8 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 850 + +--S 851 of 1483 +a0164:=integrate(t0164,x) +--R +--R +--R (851) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 1 3 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 2 3 7 6 3 2 2 7 3 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial Fraction Integer +--E 851 + +--S 852 of 1483 +m0164:=a0164-r0164 +--R +--R +--R 1 8 1 4 +--R - - b c - - a c +--R 8 4 +--R (852) ----------------- +--R d +--R Type: Fraction Polynomial Fraction Integer +--E 852 + +--S 853 of 1483 +d0164:=D(m0164,x) +--R +--R +--R (853) 0 +--R Type: Fraction Polynomial Fraction Integer +--E 853 + +--S 854 of 1483 +t0165:= 1/(a+b*x^5) +--R +--R +--R 1 +--R (854) -------- +--R 5 +--R b x + a +--R Type: Fraction Polynomial Integer +--E 854 + +--S 855 of 1483 +r0165:= 1/10*(10-2*5^(1/2))^(1/2)*atan(-(5^(1/2)+1)/(10-2*5^(1/2))^(1/2)+_ + 2*2^(1/2)/(5-5^(1/2))^(1/2)*b^(1/5)*x/a^(1/5))/a^(4/5)/b^(1/5)+_ + 1/10*(10+2*5^(1/2))^(1/2)*atan(-(1-5^(1/2))/(10+2*5^(1/2))^(1/2)+_ + 2*2^(1/2)/(5+5^(1/2))^(1/2)*b^(1/5)*x/a^(1/5))/a^(4/5)/b^(1/5)+_ + 1/5*log(a^(1/5)/b^(1/5)+x)/a^(4/5)/b^(1/5)-_ + 1/20*(1-5^(1/2))*log(2*a^(2/5)/b^(2/5)-(1-5^(1/2))*a^(1/5)*x/b^(1/5)+_ + 2*x^2)/a^(4/5)/b^(1/5)-1/20*(5^(1/2)+1)*log(2*a^(2/5)/b^(2/5)-_ + (5^(1/2)+1)*a^(1/5)*x/b^(1/5)+2*x^2)/a^(4/5)/b^(1/5) +--R +--R +--R (855) +--R 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 2x \|b + (x\|5 - x)\|a \|b + 2\|a +--R (\|5 - 1)log(---------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 2x \|b + (- x\|5 - x)\|a \|b + 2\|a +--R (- \|5 - 1)log(-----------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R 5+-+ 5+-+ +--R x\|b + \|a +--R 4log(------------) +--R 5+-+ +--R \|b +--R + +--R +----------+ +--R | +-+ +--R 2\|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|a \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|b \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|a +--R + +--R +------------+ +--R | +-+ +--R 2\|- 2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (2x\|2 \|5 + 10x\|2 )\|- \|5 + 5 \|b +--R + +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (- 3\|5 - 5)\|- 2\|5 + 10 \|a +--R / +--R 5+-+ +--R 20\|a +--R / +--R 5+-+4 5+-+ +--R 20\|a \|b +--R Type: Expression Integer +--E 855 + +--S 856 of 1483 +a0165:=integrate(t0165,x) +--R +--R +--R (856) +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R - 5\|a b %%CC1 - 5\|a b %%CC0 - 1 +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R - 5\|a b %%CC1 - 5\|a b %%CC0 - 1 +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R 10\|a b %%CC1 log(5a %%CC1 + x) + 10\|a b %%CC0 log(5a %%CC0 + x) +--R + +--R +---+ +--R 5| 4 +--R 2log(x\|a b + a) +--R / +--R +---+ +--R 5| 4 +--R 10\|a b +--R Type: Union(Expression Integer,...) +--E 856 + +--S 857 of 1483 +m0165:=a0165-r0165 +--R +--R +--R (857) +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 10\|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+5| 4 5+-+4 5+-+ +--R - 10\|a \|b \|a b %%CC - 10\|a \|b \|a b %%CC - 2\|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 10\|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+5| 4 5+-+4 5+-+ +--R - 10\|a \|b \|a b %%CC - 10\|a \|b \|a b %%CC - 2\|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 20\|a \|b \|a b %%CC1 log(5a %%CC1 + x) +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+ 5| 4 +--R 20\|a \|b \|a b %%CC0 log(5a %%CC0 + x + 4\|a \|b log(x\|a b + a) +--R + +--R +---+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 5| 4 2x \|b + (x\|5 - x)\|a \|b + 2\|a +--R (- \|5 + 1)\|a b log(---------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R +---+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 5| 4 2x \|b + (- x\|5 - x)\|a \|b + 2\|a +--R (\|5 + 1)\|a b log(-----------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R +---+ 5+-+ 5+-+ +--R 5| 4 x\|b + \|a +--R - 4\|a b log(------------) +--R 5+-+ +--R \|b +--R + +--R - +--R +---+ +----------+ +--R 5| 4 | +-+ +--R 2\|a b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|a \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|b \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|a +--R + +--R - +--R +------------+ +---+ +--R | +-+ 5| 4 +--R 2\|- 2\|5 + 10 \|a b +--R * +--R atan +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (2x\|2 \|5 + 10x\|2 )\|- \|5 + 5 \|b +--R + +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (- 3\|5 - 5)\|- 2\|5 + 10 \|a +--R / +--R 5+-+ +--R 20\|a +--R / +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 20\|a \|b \|a b +--R Type: Expression Integer +--E 857 + +--S 858 of 1483 +d0165:=D(m0165,x) +--R +--R +--R (858) +--R +------------+ +----------+ +--R 2 | +-+ | +-+ 7 2 +-+ 5+-+4 +--R (a x \|- 2\|5 + 10 \|- \|5 + 5 + (2b x + 2a x )\|2 )\|b +--R + +--R +------------+ +----------+ +--R 6 | +-+ | +-+ +--R (- b x - a x)\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 6 +-+ +-+ 6 +-+ +--R (- 3b x - 3a x)\|2 \|5 + (5b x + 5a x)\|2 +--R * +--R 5+-+5+-+3 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 5 | +-+ | +-+ 5 +-+ 5+-+2 5+-+2 +--R (b x \|- 2\|5 + 10 \|- \|5 + 5 + (2b x + 2a)\|2 )\|a \|b +--R + +--R 4 +-+ +-+ 4 +-+ 5+-+3 5+-+ +--R (- 3b x \|2 \|5 + 5b x \|2 )\|a \|b +--R + +--R 3 +-+ +-+ 3 +-+ 5+-+4 +--R (- 3b x \|2 \|5 + 5b x \|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 7 2 +-+ | +-+ | +-+ 7 2 5+-+4 +--R ((2b x + 2a x )\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 40b x - 80a x )\|b +--R + +--R +------------+ +--R 6 +-+ +-+ 6 +-+ | +-+ +--R ((3b x + 3a x)\|2 \|5 + (5b x + 5a x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R +------------+ +----------+ +--R 5 +-+ | +-+ | +-+ 5 5+-+2 5+-+2 +--R ((2b x + 2a)\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 80b x - 40a)\|a \|b +--R + +--R +------------+ +----------+ +--R 4 +-+ +-+ 4 +-+ | +-+ | +-+ 4 5+-+3 +--R ((3b x \|2 \|5 + 5b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40b x )\|a +--R * +--R 5+-+ +--R \|b +--R + +--R +------------+ +----------+ +--R 3 +-+ +-+ 3 +-+ | +-+ | +-+ 3 5+-+4 +--R ((3b x \|2 \|5 + 5b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40b x )\|a +--R / +--R +------------+ +----------+ +--R 7 2 2 | +-+ | +-+ 5+-+4 +--R (2a b x + 2a x )\|- 2\|5 + 10 \|- \|5 + 5 \|b +--R + +--R 6 2 +-+ +-+ 6 2 +-+ 5+-+5+-+3 +--R ((- 6a b x - 6a x)\|2 \|5 + (10a b x + 10a x)\|2 )\|a \|b +--R + +--R 2 8 3 +-+ +-+ 2 8 3 +-+ 5+-+4 +--R ((- 6b x - 6a b x )\|2 \|5 + (10b x + 10a b x )\|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R 7 2 2 5+-+4 +--R (- 160a b x - 160a x )\|b +--R + +--R +------------+ +--R 6 2 +-+ +-+ 6 2 +-+ | +-+ +--R ((6a b x + 6a x)\|2 \|5 + (10a b x + 10a x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R 5 2 5+-+2 5+-+2 2 9 4 5+-+3 5+-+ +--R (- 80a b x - 80a )\|a \|b + (- 80b x - 80a b x )\|a \|b +--R + +--R +------------+ +--R 2 8 3 +-+ +-+ 2 8 3 +-+ | +-+ +--R ((6b x + 6a b x )\|2 \|5 + (10b x + 10a b x )\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+4 +--R \|- \|5 + 5 \|a +--R Type: Expression Integer +--E 858 + +--S 859 of 1483 +t0166:= 1/(1-x^5) +--R +--R +--R 1 +--R (859) - ------ +--R 5 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 859 + +--S 860 of 1483 +r0166:= 1/10*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x)/(10+2*5^(1/2))^(1/2))+1/10*(10-2*5^(1/2))^(1/2)*atan((1+_ + 5^(1/2)+4*x)/(10-2*5^(1/2))^(1/2))-1/5*log(1-x)+1/20*(1-_ + 5^(1/2))*log(2+(1-5^(1/2))*x+2*x^2)+1/20*(5^(1/2)+1)*log(2+_ + (5^(1/2)+1)*x+2*x^2) +--R +--R +--R (860) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R - 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (\|5 + 1)log(x\|5 + 2x + x + 2) - 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (- \|5 + 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression Integer +--E 860 + +--S 861 of 1483 +a0166:=integrate(t0166,x) +--R +--R +--R (861) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R 10%%CD1 log(5%%CD1 + x) + 10%%CD0 log(5%%CD0 + x) - 2log(x - 1) +--R / +--R 10 +--R Type: Union(Expression Integer,...) +--E 861 + +--S 862 of 1483 +m0166:=a0166-r0166 +--R +--R +--R (862) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R 2\|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - 2\|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R 20%%CD1 log(5%%CD1 + x) + 20%%CD0 log(5%%CD0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R - 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (- \|5 - 1)log(x\|5 + 2x + x + 2) - 4log(x - 1) + 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (\|5 - 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression Integer +--E 862 + +--S 863 of 1483 +d0166:=D(m0166,x) +--R +--R +--R (863) 0 +--R Type: Expression Integer +--E 863 + +--S 864 of 1483 +t0167:= 1/x^2/(1-x^5) +--R +--R +--R 1 +--R (864) - ------- +--R 7 2 +--R x - x +--R Type: Fraction Polynomial Integer +--E 864 + +--S 865 of 1483 +r0167:= -1/x-1/10*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+4*x)/_ + (10+2*5^(1/2))^(1/2))-1/10*(10-2*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x)/(10-2*5^(1/2))^(1/2))-1/5*log(1-x)+_ + 1/20*(1-5^(1/2))*log(2+(1-5^(1/2))*x+2*x^2)+_ + 1/20*(5^(1/2)+1)*log(2+(5^(1/2)+1)*x+2*x^2) +--R +--R +--R (865) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R 2x\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R - 2x\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (x\|5 + x)log(x\|5 + 2x + x + 2) - 4x log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (- x\|5 + x)log(- x\|5 + 2x + x + 2) - 20 +--R / +--R 20x +--R Type: Expression Integer +--E 865 + +--S 866 of 1483 +a0167:=integrate(t0167,x) +--R +--R +--R (866) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - x\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 5x %%CE1 - 5x %%CE0 + x +--R * +--R log +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R x\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 5x %%CE1 - 5x %%CE0 + x +--R * +--R log +--R - +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R 10x %%CE1 +--R * +--R log +--R 2 2 3 +--R 125%%CE0 %%CE1 + (125%%CE0 - 25%%CE0)%%CE1 + 125%%CE0 +--R + +--R 2 +--R - 25%%CE0 + 5%%CE0 + x +--R + +--R 3 2 +--R 10x %%CE0 log(- 125%%CE0 + 25%%CE0 - 5%%CE0 + x + 1) - 2x log(x - 1) - 10 +--R / +--R 10x +--R Type: Union(Expression Integer,...) +--E 866 + +--S 867 of 1483 +m0167:=a0167-r0167 +--R +--R +--R (867) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - 2\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2 +--R * +--R log +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R 2\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2 +--R * +--R log +--R - +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R 20%%CE1 +--R * +--R log +--R 2 2 3 +--R 125%%CE0 %%CE1 + (125%%CE0 - 25%%CE0)%%CE1 + 125%%CE0 +--R + +--R 2 +--R - 25%%CE0 + 5%%CE0 + x +--R + +--R 3 2 +--R 20%%CE0 log(- 125%%CE0 + 25%%CE0 - 5%%CE0 + x + 1) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R - 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (- \|5 - 1)log(x\|5 + 2x + x + 2) - 4log(x - 1) + 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (\|5 - 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression Integer +--E 867 + +--S 868 of 1483 +d0167:=D(m0167,x) +--R +--R +--R (868) 0 +--R Type: Expression Integer +--E 868 + +--S 869 of 1483 +t0168:= x^8/(1-x^6) +--R +--R +--R 8 +--R x +--R (869) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 869 + +--S 870 of 1483 +r0168:= -1/3*x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R atanh(x ) - x +--R (870) -------------- +--R 3 +--R Type: Expression Integer +--E 870 + +--S 871 of 1483 +a0168:=integrate(t0168,x) +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2x +--R (871) ------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 871 + +--S 872 of 1483 +m0168:=a0168-r0168 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (872) -------------------------------------- +--R 6 +--R Type: Expression Integer +--E 872 + +--S 873 of 1483 +d0168:=D(m0168,x) +--R +--R +--R (873) 0 +--R Type: Expression Integer +--E 873 + +--S 874 of 1483 +t0169:= x^7/(1-x^6) +--R +--R +--R 7 +--R x +--R (874) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 874 + +--S 875 of 1483 +r0169:= -1/2*x^2+1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R There are 2 exposed and 5 unexposed library operations named atan +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 875 + +--S 876 of 1483 +a0169:=integrate(t0169,x) +--R +--R +--R (875) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression Integer,...) +--E 876 + +--S 877 of 1483 +m0169:=a0169-r0169 +--R +--R +--R (876) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) +--R 3 +--R + +--R 2 +-+ +--R (- 6x - 12r0169)\|3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression Integer +--E 877 + +--S 878 of 1483 +d0169:=D(m0169,x) +--R +--R +--R 7 +--R x +--R (877) - ------ +--R 6 +--R x - 1 +--R Type: Expression Integer +--E 878 + +--S 879 of 1483 +t0170:= x^5/(1-x^6) +--R +--R +--R 5 +--R x +--R (878) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 879 + +--S 880 of 1483 +r0170:= -1/6*log(1-x^6) +--R +--R +--R 6 +--R log(- x + 1) +--R (879) - ------------- +--R 6 +--R Type: Expression Integer +--E 880 + +--S 881 of 1483 +a0170:=integrate(t0170,x) +--R +--R +--R 6 +--R log(x - 1) +--R (880) - ----------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 881 + +--S 882 of 1483 +m0170:=a0170-r0170 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (881) ----------------------------- +--R 6 +--R Type: Expression Integer +--E 882 + +--S 883 of 1483 +d0170:=D(m0170,x) +--R +--R +--R (882) 0 +--R Type: Expression Integer +--E 883 + +--S 884 of 1483 +t0171:= x^3/(1-x^6) +--R +--R +--R 3 +--R x +--R (883) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 884 + +--S 885 of 1483 +r0171:= -1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R There are 2 exposed and 5 unexposed library operations named atan +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 885 + +--S 886 of 1483 +a0171:=integrate(t0171,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) +--R 3 +--R (884) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression Integer,...) +--E 886 + +--S 887 of 1483 +m0171:=a0171-r0171 +--R +--R +--R (885) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) - 12r0171\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression Integer +--E 887 + +--S 888 of 1483 +d0171:=D(m0171,x) +--R +--R +--R 3 +--R x +--R (886) - ------ +--R 6 +--R x - 1 +--R Type: Expression Integer +--E 888 + +--S 889 of 1483 +t0172:= x^2/(1-x^6) +--R +--R +--R 2 +--R x +--R (887) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 889 + +--S 890 of 1483 +r0172:= 1/3*atanh(x^3) +--R +--R +--R 3 +--R atanh(x ) +--R (888) --------- +--R 3 +--R Type: Expression Integer +--E 890 + +--S 891 of 1483 +a0172:=integrate(t0172,x) +--R +--R +--R 3 3 +--R log(x + 1) - log(x - 1) +--R (889) ------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 891 + +--S 892 of 1483 +m0172:=a0172-r0172 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (890) -------------------------------------- +--R 6 +--R Type: Expression Integer +--E 892 + +--S 893 of 1483 +d0172:=D(m0172,x) +--R +--R +--R (891) 0 +--R Type: Expression Integer +--E 893 + +--S 894 of 1483 +t0173:= x/(1-x^6) +--R +--R +--R x +--R (892) - ------ +--R 6 +--R x - 1 +--R Type: Fraction Polynomial Integer +--E 894 + +--S 895 of 1483 +r0173:= 1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R There are 2 exposed and 5 unexposed library operations named atan +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 895 + +--S 896 of 1483 +a0173:=integrate(t0173,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) +--R 3 +--R (893) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression Integer,...) +--E 896 + +--S 897 of 1483 +m0173:=a0173-r0173 +--R +--R +--R (894) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 12r0173\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression Integer +--E 897 + +--S 898 of 1483 +d0173:=D(m0173,x) +--R +--R +--R x +--R (895) - ------ +--R 6 +--R x - 1 +--R Type: Expression Integer +--E 898 + +--S 899 of 1483 +t0174:= 1/x/(1-x^6) +--R +--R +--R 1 +--R (896) - ------ +--R 7 +--R x - x +--R Type: Fraction Polynomial Integer +--E 899 + +--S 900 of 1483 +r0174:= log(x)-1/6*log(1-x^6) +--R +--R +--R 6 +--R 6log(x) - log(- x + 1) +--R (897) ----------------------- +--R 6 +--R Type: Expression Integer +--E 900 + +--S 901 of 1483 +a0174:=integrate(t0174,x) +--R +--R +--R 6 +--R - log(x - 1) + 6log(x) +--R (898) ----------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 901 + +--S 902 of 1483 +m0174:=a0174-r0174 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (899) ----------------------------- +--R 6 +--R Type: Expression Integer +--E 902 + +--S 903 of 1483 +d0174:=D(m0174,x) +--R +--R +--R (900) 0 +--R Type: Expression Integer +--E 903 + +--S 904 of 1483 +t0175:= 1/x^3/(1-x^6) +--R +--R +--R 1 +--R (901) - ------- +--R 9 3 +--R x - x +--R Type: Fraction Polynomial Integer +--E 904 + +--S 905 of 1483 +r0175:= -1/2/x^2-1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R There are 2 exposed and 5 unexposed library operations named atan +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 905 + +--S 906 of 1483 +a0175:=integrate(t0175,x) +--R +--R +--R (902) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression Integer,...) +--E 906 + +--S 907 of 1483 +m0175:=a0175-r0175 +--R +--R +--R (903) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) +--R 3 +--R + +--R 2 +-+ +--R (- 12r0175 x - 6)\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Expression Integer +--E 907 + +--S 908 of 1483 +d0175:=D(m0175,x) +--R +--R +--R 1 +--R (904) - ------- +--R 9 3 +--R x - x +--R Type: Expression Integer +--E 908 + +--S 909 of 1483 +t0176:= 1/x^4/(1-x^6) +--R +--R +--R 1 +--R (905) - -------- +--R 10 4 +--R x - x +--R Type: Fraction Polynomial Integer +--E 909 + +--S 910 of 1483 +r0176:= -1/3/x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R x atanh(x ) - 1 +--R (906) --------------- +--R 3 +--R 3x +--R Type: Expression Integer +--E 910 + +--S 911 of 1483 +a0176:=integrate(t0176,x) +--R +--R +--R 3 3 3 3 +--R x log(x + 1) - x log(x - 1) - 2 +--R (907) --------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression Integer,...) +--E 911 + +--S 912 of 1483 +m0176:=a0176-r0176 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (908) -------------------------------------- +--R 6 +--R Type: Expression Integer +--E 912 + +--S 913 of 1483 +d0176:=D(m0176,x) +--R +--R +--R (909) 0 +--R Type: Expression Integer +--E 913 + +--S 914 of 1483 +t0177:= 1/x^5/(1-x^6) +--R +--R +--R 1 +--R (910) - -------- +--R 11 5 +--R x - x +--R Type: Fraction Polynomial Integer +--E 914 + +--S 915 of 1483 +r0177:= -1/4/x^4+1/6*atan(1/3*(1+2*x^2)*3^(1/2))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R There are 2 exposed and 5 unexposed library operations named atan +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 915 + +--S 916 of 1483 +a0177:=integrate(t0177,x) +--R +--R +--R (911) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression Integer,...) +--E 916 + +--S 917 of 1483 +m0177:=a0177-r0177 +--R +--R +--R (912) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) +--R 3 +--R + +--R 4 +-+ +--R (- 12r0177 x - 3)\|3 +--R / +--R 4 +-+ +--R 12x \|3 +--R Type: Expression Integer +--E 917 + +--S 918 of 1483 +d0177:=D(m0177,x) +--R +--R +--R 1 +--R (913) - -------- +--R 11 5 +--R x - x +--R Type: Expression Integer +--E 918 + +--S 919 of 1483 +t0178:= 1/(a+b*x^6) +--R +--R +--R 1 +--R (914) -------- +--R 6 +--R b x + a +--R Type: Fraction Polynomial Integer +--E 919 + +--S 920 of 1483 +r0178:= -1/12*(-4*atan(b^(1/6)*x/a^(1/6))-_ + 2*atan((-3^(1/2)*a^(1/6)+2*b^(1/6)*x)/a^(1/6))-_ + 2*atan((3^(1/2)*a^(1/6)+2*b^(1/6)*x)/a^(1/6))+log(-(-a^(1/3)+_ + 3^(1/2)*a^(1/6)*x*b^(1/6)-b^(1/3)*x^2)/b^(1/3))*3^(1/2)-_ + log(1/b^(1/3)*(a^(1/3)+3^(1/2)*a^(1/6)*x*b^(1/6)+_ + b^(1/3)*x^2))*3^(1/2))/a^(5/6)/b^(1/6) +--R +--R +--R (915) +--R +-+6+-+6+-+ 2 3+-+ 3+-+ +--R +-+ x\|3 \|a \|b + x \|b + \|a +--R \|3 log(-----------------------------) +--R 3+-+ +--R \|b +--R + +--R +-+6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +-+6+-+ +--R +-+ - x\|3 \|a \|b + x \|b + \|a 2x\|b + \|3 \|a +--R - \|3 log(-------------------------------) + 2atan(-----------------) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R 6+-+ +-+6+-+ 6+-+ +--R 2x\|b - \|3 \|a x\|b +--R 2atan(-----------------) + 4atan(-----) +--R 6+-+ 6+-+ +--R \|a \|a +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression Integer +--E 920 + +--S 921 of 1483 +a0178:=integrate(t0178,x) +--R +--R +--R (916) +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R |- -------- log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R - |- -------- log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R 2 |- -------- log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R - 2 |- -------- log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 921 + +--S 922 of 1483 +m0178:=a0178-r0178 +--R +--R +--R (917) +--R +-+6+-+6+-+ 2 3+-+ 3+-+ +--R +-+ x\|3 \|a \|b + x \|b + \|a +--R - \|3 log(-----------------------------) +--R 3+-+ +--R \|b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R 6 |- -------- \|a \|b log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R - 6 |- -------- \|a \|b log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 6+-+5 6+-+ | 1 +--R 12 |- -------- \|a \|b log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 6+-+5 6+-+ | 1 +--R - 12 |- -------- \|a \|b log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-+6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +-+6+-+ +--R +-+ - x\|3 \|a \|b + x \|b + \|a 2x\|b + \|3 \|a +--R \|3 log(-------------------------------) - 2atan(-----------------) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R 6+-+ +-+6+-+ 6+-+ +--R 2x\|b - \|3 \|a x\|b +--R - 2atan(-----------------) - 4atan(-----) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \| 46656a b +--R 12\|3 |- -------- \|a \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \| 46656a b +--R - 12\|3 |- -------- \|a \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression Integer +--E 922 + +--S 923 of 1483 +d0178:=D(m0178,x) +--R +--R +--R (918) +--R 2 6+-+4 +--R 3a x \|b +--R + +--R 4 6+-+4 3+-+2 2 3+-+6+-+4 8 2 3+-+ 3+-+2 6+-+4 +--R - x \|a \|b + (- 2x \|a \|a - b x - a x )\|b - \|a \|a +--R + +--R 6 6+-+2 6 3+-+ +--R - 3b x \|a + (b x + a)\|a +--R * +--R 6+-+2 +--R \|b +--R + +--R 8 3+-+2 6 3+-+3+-+ 4 3+-+2 +--R b x \|b + 2b x \|a \|b + b x \|a +--R / +--R 8 2 2 6+-+4 +--R (6a b x + 6a x )\|b +--R + +--R 10 4 6+-+4 3+-+2 8 2 3+-+6+-+4 3+-+ +--R (- 2b x - 2a x )\|a \|b + (- 4b x - 4a x )\|a \|a \|b +--R + +--R 6 3+-+2 6+-+4 +--R (- 2b x - 2a)\|a \|a +--R * +--R 6+-+2 +--R \|b +--R Type: Expression Integer +--E 923 + +--S 924 of 1483 +t0179:= 1/x^2/(a+b*x^6) +--R +--R +--R 1 +--R (919) ----------- +--R 8 2 +--R b x + a x +--R Type: Fraction Polynomial Integer +--E 924 + +--S 925 of 1483 +r0179:= -1/a/x-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/6*b^(1/6)*atan(-3^(1/2)+2*b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/6*b^(1/6)*atan(3^(1/2)+2*b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/12*b^(1/6)*log(a^(1/3)/b^(1/3)-3^(1/2)*a^(1/6)*x/b^(1/6)+_ + x^2)*3^(1/2)/a^(7/6)+1/12*b^(1/6)*log(a^(1/3)/b^(1/3)+_ + 3^(1/2)*a^(1/6)*x/b^(1/6)+x^2)*3^(1/2)/a^(7/6) +--R +--R +--R (920) +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b + x\|3 \|a \|b +--R x\|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b - x\|3 \|a \|b +--R - x\|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 6+-+ +-+6+-+ 6+-+ +-+6+-+ +--R 6+-+ 2x\|b + \|3 \|a 6+-+ 2x\|b - \|3 \|a +--R - 2x\|b atan(-----------------) - 2x\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R 6+-+ +--R 6+-+ x\|b 6+-+ +--R - 4x\|b atan(-----) - 12\|a +--R 6+-+ +--R \|a +--R / +--R 6+-+ +--R 12a x\|a +--R Type: Expression Integer +--E 925 + +--S 926 of 1483 +a0179:=integrate(t0179,x) +--R +--R +--R (921) +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R - 2a x |- ------- log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R 2a x |- ------- log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R a x |- ------- log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a x\|3 |- ------- atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a x\|3 |- ------- atan(------------------------- - 2 +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 2a x +--R Type: Union(Expression Integer,...) +--E 926 + +--S 927 of 1483 +m0179:=a0179-r0179 +--R +--R +--R (922) +--R - +--R +---------+ +--R | b 6+-+ +--R 6a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R - 12a |- ------- \|a log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b + x\|3 \|a \|b +--R - \|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b - x\|3 \|a \|b +--R \|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R 12a |- ------- \|a log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R | b 6+-+ +--R 6a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 6+-+ +-+6+-+ 6+-+ +-+6+-+ +--R 6+-+ 2x\|b + \|3 \|a 6+-+ 2x\|b - \|3 \|a +--R 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R 6+-+ +---------+ 6| 7 +--R 6+-+ x\|b +-+ | b 6+-+ \| 46656a +--R 4\|b atan(-----) + 12a\|3 |- ------- \|a atan(-------------------------) +--R 6+-+ 6| 7 +---------+5 +--R \|a \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 12a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression Integer +--E 927 + +--S 928 of 1483 +d0179:=D(m0179,x) +--R +--R +--R (923) +--R 4 3+-+2 2 3+-+3+-+ 3+-+2 6+-+4 +--R (a x \|b + 2a x \|a \|b + a \|a )\|b +--R + +--R 2 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 4 3+-+2 6+-+6+-+2 +--R (- 2a x \|a \|b + (- 3b x - a)\|a \|a \|b - b x \|a \|a)\|b +--R + +--R 6 6+-+4 3+-+2 +--R 3b x \|a \|b +--R / +--R 10 2 4 6+-+2 3+-+2 8 2 2 3+-+6+-+2 3+-+ +--R (2a b x + 2a x )\|a \|b + (4a b x + 4a x )\|a \|a \|b +--R + +--R 6 2 3+-+2 6+-+2 +--R (2a b x + 2a )\|a \|a +--R * +--R 6+-+2 +--R \|b +--R + +--R 8 2 2 6+-+4 3+-+2 +--R (- 6a b x - 6a x )\|a \|b +--R Type: Expression Integer +--E 928 + +--S 929 of 1483 +t0180:= 1/(a-b*x^6) +--R +--R +--R 1 +--R (924) - -------- +--R 6 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 929 + +--S 930 of 1483 +r0180:= 1/12*(2*atan(1/3*3^(1/2)*(-a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ + 2*atan(1/3*3^(1/2)*(a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ + 4*atanh(b^(1/6)*x/a^(1/6))-log(1/b^(1/3)*(a^(1/3)-_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))+log(1/b^(1/3)*(a^(1/3)+_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2)))/a^(5/6)/b^(1/6) +--R +--R +--R (925) +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+6+-+ 2 3+-+ 3+-+ +--R x\|a \|b + x \|b + \|a - x\|a \|b + x \|b + \|a +--R log(-------------------------) - log(---------------------------) +--R 3+-+ 3+-+ +--R \|b \|b +--R + +--R 6+-+ +-+6+-+ +-+6+-+ +--R x\|b +-+ 2x\|3 \|b + \|3 \|a +--R 4atanh(-----) + 2\|3 atan(---------------------) +--R 6+-+ 6+-+ +--R \|a 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+ 2x\|3 \|b - \|3 \|a +--R 2\|3 atan(---------------------) +--R 6+-+ +--R 3\|a +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression Integer +--E 930 + +--S 931 of 1483 +a0180:=integrate(t0180,x) +--R +--R +--R (926) +--R +--------+ +--------+2 +--------+ +--R | 1 2 | 1 | 1 2 +--R |-------- log(36a |-------- + 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 2 | 1 | 1 2 +--R - |-------- log(36a |-------- - 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R 2 |-------- log(6a |-------- + x - 2 |-------- log(- 6a |-------- + x) +--R 6| 5 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 \|46656a b +--R 2\|3 |-------- atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- - x +--R 6| 5 +--R \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 \|46656a b +--R - 2\|3 |-------- atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- + x +--R 6| 5 +--R \|46656a b +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 931 + +--S 932 of 1483 +m0180:=a0180-r0180 +--R +--R +--R (927) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R x\|a \|b + x \|b + \|a +--R - log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R 6 |-------- \|a \|b log(36a |-------- + 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R - 6 |-------- \|a \|b log(36a |-------- - 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--R | 1 6+-+5 6+-+ | 1 +--R 12 |-------- \|a \|b log(6a |-------- + x) +--R 6| 5 6| 5 +--R \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--R | 1 6+-+5 6+-+ | 1 +--R - 12 |-------- \|a \|b log(- 6a |-------- + x) +--R 6| 5 6| 5 +--R \|46656a b \|46656a b +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R - x\|a \|b + x \|b + \|a x\|b +--R log(---------------------------) - 4atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +-+6+-+ +-+6+-+ +--R +-+ 2x\|3 \|b + \|3 \|a +-+ 2x\|3 \|b - \|3 \|a +--R - 2\|3 atan(---------------------) - 2\|3 atan(---------------------) +--R 6+-+ 6+-+ +--R 3\|a 3\|a +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \|46656a b +--R 12\|3 |-------- \|a \|b atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- - x +--R 6| 5 +--R \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \|46656a b +--R - 12\|3 |-------- \|a \|b atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- + x +--R 6| 5 +--R \|46656a b +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression Integer +--E 932 + +--S 933 of 1483 +d0180:=D(m0180,x) +--R +--R +--R (928) +--R 6 6+-+2 3+-+2 4 3+-+6+-+2 3+-+ 2 3+-+2 6+-+2 2 6+-+4 +--R (- 2x \|a \|b - 4x \|a \|a \| - 2x \|a \|a - a x )\|b +--R + +--R 4 6+-+4 3+-+2 2 3+-+6+-+4 8 2 3+-+ 3+-+2 6+-+4 +--R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a +--R + +--R 6 6+-+2 6 3+-+ +--R - b x \|a + (b x - a)\|a +--R * +--R 6+-+2 +--R \|b +--R + +--R 8 3+-+2 6 3+-+3+-+ 4 6+-+4 4 3+-+2 +--R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a +--R / +--R 8 2 2 6+-+4 +--R (6a b x - 6a x )\|b +--R + +--R 10 4 6+-+4 3+-+2 8 2 3+-+6+-+4 3+-+ +--R (- 6b x + 6a x )\|a \|b + (- 12b x + 12a x )\|a \|a \|b +--R + +--R 6 3+-+2 6+-+4 +--R (- 6b x + 6a)\|a \|a +--R * +--R 6+-+2 +--R \|b +--R Type: Expression Integer +--E 933 + +--S 934 of 1483 +t0181:= 1/x^2/(a-b*x^6) +--R +--R +--R 1 +--R (929) - ----------- +--R 8 2 +--R b x - a x +--R Type: Fraction Polynomial Integer +--E 934 + +--S 935 of 1483 +r0181:= -1/12/a^(7/6)*(12*a^(1/6)+2*b^(1/6)*atan(1/3*3^(1/2)*(-a^(1/6)+_ + 2*b^(1/6)*x)/a^(1/6))*3^(1/2)*x+2*b^(1/6)*atan(1/3*3^(1/2)*_ + (a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)*x-4*b^(1/6)*_ + atanh(b^(1/6)*x/a^(1/6))*x+b^(1/6)*log(1/b^(1/3)*(a^(1/3)-_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))*x-b^(1/6)*log(1/b^(1/3)*_ + (a^(1/3)+a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))*x)/x +--R +--R +--R (930) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R 6+-+ x\|a \|b + x \|b + \|a +--R x\|b log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R 6+-+ - x\|a \|b + x \|b + \|a 6+-+ x\|b +--R - x\|b log(---------------------------) + 4x\|b atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b + \|3 \|a +--R - 2x\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b - \|3 \|a 6+-+ +--R - 2x\|3 \|b atan(---------------------) - 12\|a +--R 6+-+ +--R 3\|a +--R / +--R 6+-+ +--R 12a x\|a +--R Type: Expression Integer +--E 935 + +--S 936 of 1483 +a0181:=integrate(t0181,x) +--R +--R +--R (931) +--R +-------+ +-------+5 +-------+4 +--R | b 6 | b 5 | b 2 +--R a x |------- log(7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R | b 6 | b +--R 2a x |------- log(7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R | b 6 | b +--R - 2a x |------- log(- 7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +-------+4 +--R | b 6 | b 5 | b 2 +--R - a x |------- log(- 7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+ | b \|46656a +--R - 2a x\|3 |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- - b x +--R 6| 7 +--R \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+ | b \|46656a +--R 2a x\|3 |------- atan(----------------------- - 2 +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- + b x +--R 6| 7 +--R \|46656a +--R / +--R 2a x +--R Type: Union(Expression Integer,...) +--E 936 + +--S 937 of 1483 +m0181:=a0181-r0181 +--R +--R +--R (932) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R 6+-+ x\|a \|b + x \|b + \|a +--R - \|b log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R +-------+ +-------+5 +-------+4 +--R 6+-+ | b 6 | b 5 | b 2 +--R 6a\|a |------- log(7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R 6+-+ | b 6 | b +--R 12a\|a |------- log(7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R 6+-+ | b 6 | b +--R - 12a\|a |------- log(- 7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +-------+4 +--R 6+-+ | b 6 | b 5 | b 2 +--R - 6a\|a |------- log(- 7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R 6+-+ - x\|a \|b + x \|b + \|a 6+-+ x\|b +--R \|b log(---------------------------) - 4\|b atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b + \|3 \|a +--R 2\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b - \|3 \|a +--R 2\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+6+-+ | b \|46656a +--R - 12a\|3 \|a |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- - b x +--R 6| 7 +--R \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+6+-+ | b \|46656a +--R 12a\|3 \|a |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- + b x +--R 6| 7 +--R \|46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression Integer +--E 937 + +--S 938 of 1483 +d0181:=D(m0181,x) +--R +--R +--R (933) +--R 6 6+-+4 3+-+2 4 3+-+6+-+4 3+-+ 2 3+-+2 6+-+4 2 6+-+26+-+4 +--R (- 2x \|a \|b - 4x \|a \|a \| - 2x \|a \|a - a x \|a )\|b +--R + +--R 4 3+-+2 8 2 6+-+2 2 3+-+3+-+ 6 6+-+4 +--R a x \|b + ((- b x + a x )\|a + 2a x \|a)\|b - b x \|a +--R + +--R 6 3+-+6+-+2 3+-+2 +--R (b x - a)\|a \|a + a \|a +--R * +--R 6+-+2 +--R \|b +--R + +--R 8 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 4 3+-+2 6+-+2 4 +--R b x \|a \|b + 2b x \|a \|a \| + b x \|a \|a + 2a b x +--R / +--R 8 2 2 6+-+4 6+-+2 10 2 4 6+-+2 3+-+2 +--R (6a b x - 6a x )\|a \|b + (- 6a b x + 6a x )\|a \|b +--R + +--R 8 2 2 3+-+6+-+2 3+-+ 6 2 3+-+2 6+-+2 +--R (- 12a b x + 12a x )\|a \|a \|b + (- 6a b x + 6a )\|a \|a +--R Type: Expression Integer +--E 938 + +--S 939 of 1483 +t0182:= 1/(a-b*x^8) +--R +--R +--R 1 +--R (934) - -------- +--R 8 +--R b x - a +--R Type: Fraction Polynomial Integer +--E 939 + +--S 940 of 1483 +r0182:= 1/16*(4*atan(b^(1/8)*x/a^(1/8))+2*atan((-a^(1/8)+2^(1/2)*_ + b^(1/8)*x)/a^(1/8))*2^(1/2)+2*atan((a^(1/8)+2^(1/2)*b^(1/8)*x)/_ + a^(1/8))*2^(1/2)+4*atanh(b^(1/8)*x/a^(1/8))-log((a^(1/4)-2^(1/2)*_ + a^(1/8)*x*b^(1/8)+x^2*b^(1/4))/b^(1/4))*2^(1/2)+log(1/b^(1/4)*_ + (a^(1/4)+2^(1/2)*a^(1/8)*x*b^(1/8)+x^2*b^(1/4)))*2^(1/2))/_ + a^(7/8)/b^(1/8) +--R +--R +--R (935) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R +-+ x\|2 \|a \|b + x \|b + \|a +--R \|2 log(-----------------------------) +--R 4+-+ +--R \|b +--R + +--R +-+8+-+8+-+ 2 4+-+ 4+-+ 8+-+ +--R +-+ - x\|2 \|a \|b + x \|b + \|a x\|b +--R - \|2 log(-------------------------------) + 4atanh(-----) +--R 4+-+ 8+-+ +--R \|b \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R +-+ x\|2 \|b + \|a +-+ x\|2 \|b - \|a x\|b +--R 2\|2 atan(----------------) + 2\|2 atan(----------------) + 4atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R / +--R 8+-+7 8+-+ +--R 16\|a \|b +--R Type: Expression Integer +--E 940 + +--S 941 of 1483 +a0182:=integrate(t0182,x) +--R +--R +--R (936) +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R |----------- log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R - |----------- log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R \|2 |----------- log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R - \|2 |----------- log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 \|16777216a b +--R - 2\|2 |----------- atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R - 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 941 + +--S 942 of 1483 +m0182:=a0182-r0182 +--R +--R +--R (937) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R x\|2 \|a \|b + x \|b + \|a +--R - log(-----------------------------) +--R 4+-+ +--R \|b +--R + +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R - +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R 8\|2 |----------- \|a \|b log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R - 8\|2 |----------- \|a \|b log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-+8+-+8+-+ 2 4+-+ 4+-+ 8+-+ +--R - x\|2 \|a \|b + x \|b + \|a +-+ x\|b +--R log(-------------------------------) - 2\|2 atanh(-----) +--R 4+-+ 8+-+ +--R \|b \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R x\|2 \|b + \|a x\|2 \|b - \|a +-+ x\|b +--R - 2atan(----------------) - 2atan(----------------) - 2\|2 atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 8+-+7 8+-+ \|16777216a b +--R - 16\|2 |----------- \|a \|b atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R - 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression Integer +--E 942 + +--S 943 of 1483 +d0182:=D(m0182,x) +--R +--R +--R (938) +--R 8 8+-+2 4+-+2 6 4+-+8+-+2 4+-+ 4 8+-+6 4 4+-+2 8+-+8+-+6 +--R (- x \|a \|b - 2x \|a \|a \| + 2x \|a - x \|a \|a)\|b +--R + +--R 6 8+-+4 4+-+2 4 4+-+8+-+4 4+-+ 2 4+-+2 8+-+4 2 8+-+4 +--R (- x \|a \|b - 2x \|a \|a \| - x \|a \|a - 2a x )\|b +--R + +--R 4 8+-+6 4+-+2 2 4+-+8+-+6 10 2 4+-+ 4+-+2 8+-+6 +--R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a +--R + +--R 8 8+-+2 8 4+-+ +--R - 2b x \|a + (b x - a)\|a +--R * +--R 8+-+2 +--R \|b +--R + +--R 10 4+-+2 8 4+-+4+-+ 6 8+-+4 6 4+-+2 +--R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a +--R / +--R 10 2 2 8+-+4 +--R (8a b x - 8a x )\|b +--R + +--R 12 4 8+-+6 4+-+2 10 2 4+-+8+-+6 4+-+ +--R (- 4b x + 4a x )\|a \|b + (- 8b x + 8a x )\|a \|a \|b +--R + +--R 8 4+-+2 8+-+6 +--R (- 4b x + 4a)\|a \|a +--R * +--R 8+-+2 +--R \|b +--R Type: Expression Integer +--E 943 + +--S 944 of 1483 +t0183:= x^5/(9-x^12) +--R +--R +--R 5 +--R x +--R (939) - ------- +--R 12 +--R x - 9 +--R Type: Fraction Polynomial Integer +--E 944 + +--S 945 of 1483 +r0183:= 1/18*atanh(1/3*x^6) +--R +--R +--R 6 +--R x +--R atanh(--) +--R 3 +--R (940) --------- +--R 18 +--R Type: Expression Integer +--E 945 + +--S 946 of 1483 +a0183:=integrate(t0183,x) +--R +--R +--R 6 6 +--R log(x + 3) - log(x - 3) +--R (941) ------------------------- +--R 36 +--R Type: Union(Expression Integer,...) +--E 946 + +--S 947 of 1483 +m0183:=a0183-r0183 +--R +--R +--R 6 +--R 6 6 x +--R log(x + 3) - log(x - 3) - 2atanh(--) +--R 3 +--R (942) -------------------------------------- +--R 36 +--R Type: Expression Integer +--E 947 + +--S 948 of 1483 +d0183:=D(m0183,x) +--R +--R +--R (943) 0 +--R Type: Expression Integer +--E 948 + +--S 949 of 1483 +t0184:= (a+b/x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (944) ----------------------------- +--R 9 +--R x +--R Type: Fraction Polynomial Integer +--E 949 + +--S 950 of 1483 +r0184:= -1/8*(a+b/x^2)^4/b +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (945) ----------------------------------------- +--R 8 +--R 8b x +--R Type: Fraction Polynomial Integer +--E 950 + +--S 951 of 1483 +a0184:=integrate(t0184,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (946) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression Integer,...) +--E 951 + +--S 952 of 1483 +m0184:=a0184-r0184 +--R +--R +--R 4 +--R a +--R (947) -- +--R 8b +--R Type: Expression Integer +--E 952 + +--S 953 of 1483 +d0184:=D(m0184,x) +--R +--R +--R (948) 0 +--R Type: Expression Integer +--E 953 + +--S 954 of 1483 +t0185:= 1/x^3/(a+b/x^2)^3 +--R +--R +--R 3 +--R x +--R (949) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction Polynomial Integer +--E 954 + +--S 955 of 1483 +r0185:= 1/4/b/(a+b/x^2)^2 +--R +--R +--R 1 4 +--R - x +--R 4 +--R (950) --------------------- +--R 2 4 2 2 3 +--R a b x + 2a b x + b +--R Type: Fraction Polynomial Fraction Integer +--E 955 + +--S 956 of 1483 +a0185:=integrate(t0185,x) +--R +--R +--R 2 +--R - 2a x - b +--R (951) ----------------------- +--R 4 4 3 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression Integer,...) +--E 956 + +--S 957 of 1483 +m0185:=a0185-r0185 +--R +--R +--R 1 +--R (952) - ---- +--R 2 +--R 4a b +--R Type: Expression Integer +--E 957 + +--S 958 of 1483 +d0185:=D(m0185,x) +--R +--R +--R (953) 0 +--R Type: Expression Integer +--E 958 + +--S 959 of 1483 +t0186:= 1/(a+b/x^5) +--R +--R +--R 5 +--R x +--R (954) -------- +--R 5 +--R a x + b +--R Type: Fraction Polynomial Integer +--E 959 + +--S 960 of 1483 +r0186:= x/a-1/10*(10-2*5^(1/2))^(1/2)*b^(1/5)*atan(-(5^(1/2)+1)/_ + (10-2*5^(1/2))^(1/2)+2*2^(1/2)/(5-5^(1/2))^(1/2)*a^(1/5)*x/b^(1/5))/_ + a^(6/5)-1/10*(10+2*5^(1/2))^(1/2)*b^(1/5)*atan(-(1-5^(1/2))/_ + (10+2*5^(1/2))^(1/2)+2*2^(1/2)/(5+5^(1/2))^(1/2)*a^(1/5)*x/b^(1/5))/_ + a^(6/5)-1/5*b^(1/5)*log(b^(1/5)/a^(1/5)+x)/a^(6/5)+_ + 1/20*(1-5^(1/2))*b^(1/5)*log(2*b^(2/5)/a^(2/5)-(1-5^(1/2))*b^(1/5)*x/_ + a^(1/5)+2*x^2)/a^(6/5)+1/20*(5^(1/2)+1)*b^(1/5)*_ + log(2*b^(2/5)/a^(2/5)-(5^(1/2)+1)*b^(1/5)*x/a^(1/5)+2*x^2)/a^(6/5) +--R +--R +--R (955) +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (x\|5 - x)\|a \|b + 2x \|a +--R (- \|5 + 1)\|b log(---------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (- x\|5 - x)\|a \|b + 2x \|a +--R (\|5 + 1)\|b log(-----------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+ 5+-+ +--R 5+-+ \|b + x\|a +--R - 4\|b log(------------) +--R 5+-+ +--R \|a +--R + +--R - +--R +----------+ +--R 5+-+ | +-+ +--R 2\|b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|b \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|a \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|b +--R + +--R +------------+ +--R | +-+ 5+-+ +--R 2\|- 2\|5 + 10 \|b +--R * +--R atan +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (3\|5 + 5)\|- 2\|5 + 10 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|a +--R / +--R 5+-+ +--R 20\|b +--R + +--R 5+-+ +--R 20x\|a +--R / +--R 5+-+ +--R 20a\|a +--R Type: Expression Integer +--E 960 + +--S 961 of 1483 +a0186:=integrate(t0186,x) +--R +--R +--R (956) +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CL1 - 5a %%CL0 - 5|- - +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 - 75a %%CL0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CL1 - 5a %%CL0 - 5|- - +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 10a %%CL1 log(- 5a %%CL1 + x) + 10a %%CL0 log(- 5a %%CL0 + x) +--R + +--R +---+ +---+ +--R | b | b +--R 2 5|- - log(- 5|- - + x + 10x +--R \| a \| a +--R / +--R 10a +--R Type: Union(Expression Integer,...) +--E 961 + +--S 962 of 1483 +m0186:=a0186-r0186 +--R +--R +--R (957) +--R - +--R 5+-+ +--R 10a\|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R 5+-+ 5+-+ | b 5+-+ +--R - 10a\|a %%CL1 - 10a\|a %%CL0 - 2 5|- - \|a +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5+-+ +--R 10a\|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 - 75a %%CL0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R 5+-+ 5+-+ | b 5+-+ +--R - 10a\|a %%CL1 - 10a\|a %%CL0 - 2 5|- - \|a +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5+-+ 5+-+ +--R 20a\|a %%CL1 log(- 5a %%CL1 + x) + 20a\|a %%CL0 log(- 5a %%CL0 + x) +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (x\|5 - x)\|a \|b + 2x \|a +--R (\|5 - 1)\|b log(---------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (- x\|5 - x)\|a \|b + 2x \|a +--R (- \|5 - 1)\|b log(-----------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+ 5+-+ +---+ +---+ +--R 5+-+ \|b + x\|a | b 5+-+ | b +--R 4\|b log(------------) + 4 5|- - \|a log(- 5|- - + x) +--R 5+-+ \| a \| a +--R \|a +--R + +--R +----------+ +--R 5+-+ | +-+ +--R 2\|b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|b \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|a \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|b +--R + +--R - +--R +------------+ +--R | +-+ 5+-+ +--R 2\|- 2\|5 + 10 \|b +--R * +--R atan +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (3\|5 + 5)\|- 2\|5 + 10 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|a +--R / +--R 5+-+ +--R 20\|b +--R / +--R 5+-+ +--R 20a\|a +--R Type: Expression Integer +--E 962 + +--S 963 of 1483 +d0186:=D(m0186,x) +--R +--R +--R (958) +--R +------------+ +----------+ +--R 5 | +-+ | +-+ 5 +-+ 5+-+2 5+-+4 +--R (a x \|- 2\|5 + 10 \|- \|5 + 5 + (2a x + 2b)\|2 )\|a \|b +--R + +--R +------------+ +----------+ +--R 6 | +-+ | +-+ +--R (- a x - b x)\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 6 +-+ +-+ 6 +-+ +--R (- 3a x - 3b x)\|2 \|5 + (5a x + 5b x)\|2 +--R * +--R 5+-+3 5+-+3 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 2 | +-+ | +-+ 7 2 +-+ 5+-+4 5+-+2 +--R (b x \|- 2\|5 + 10 \|- \|5 + 5 + (2a x + 2b x )\|2 )\|a \|b +--R + +--R 3 +-+ +-+ 3 +-+ 5+-+ +--R (- 3a b x \|2 \|5 + 5a b x \|2 )\|b +--R + +--R 4 +-+ +-+ 4 +-+ 5+-+ +--R (- 3a b x \|2 \|5 + 5a b x \|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 5 +-+ | +-+ | +-+ 5 5+-+2 5+-+4 +--R ((2a x + 2b)\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 80a x - 40b)\|a \|b +--R + +--R +------------+ +--R 6 +-+ +-+ 6 +-+ | +-+ +--R ((3a x + 3b x)\|2 \|5 + (5a x + 5b x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+3 5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R +------------+ +----------+ +--R 7 2 +-+ | +-+ | +-+ 7 2 +--R ((2a x + 2b x )\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 40a x - 80b x ) +--R * +--R 5+-+4 5+-+2 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 3 +-+ +-+ 3 +-+ | +-+ | +-+ +--R (3a b x \|2 \|5 + 5a b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 3 +--R - 40a b x +--R * +--R 5+-+ +--R \|b +--R + +--R +------------+ +----------+ +--R 4 +-+ +-+ 4 +-+ | +-+ | +-+ +--R (3a b x \|2 \|5 + 5a b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 4 +--R - 40a b x +--R * +--R 5+-+ +--R \|a +--R / +--R 2 6 +-+ +-+ 2 6 +-+ 5+-+3 5+-+3 +--R ((6a x + 6a b x)\|2 \|5 + (- 10a x - 10a b x)\|2 )\|a \|b +--R + +--R +------------+ +----------+ +--R 2 7 2 | +-+ | +-+ 5+-+4 5+-+2 +--R (- 2a x - 2a b x )\|- 2\|5 + 10 \|- \|5 + 5 \|a \|b +--R + +--R 3 8 2 3 +-+ +-+ 3 8 2 3 +-+ 5+-+ +--R ((6a x + 6a b x )\|2 \|5 + (- 10a x - 10a b x )\|2 )\|b +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R 2 5 5+-+2 5+-+4 +--R (80a x + 80a b)\|a \|b +--R + +--R +------------+ +--R 2 6 +-+ +-+ 2 6 +-+ | +-+ +--R ((- 6a x - 6a b x)\|2 \|5 + (- 10a x - 10a b x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+3 5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R 2 7 2 5+-+4 5+-+2 +--R (160a x + 160a b x )\|a \|b +--R + +--R 3 8 2 3 +-+ +-+ 3 8 2 3 +-+ +--R ((- 6a x - 6a b x )\|2 \|5 + (- 10a x - 10a b x )\|2 ) +--R * +--R +------------+ +----------+ +--R | +-+ | +-+ 5+-+ +--R \|- 2\|5 + 10 \|- \|5 + 5 \|b +--R + +--R 3 9 2 4 5+-+ +--R (80a x + 80a b x )\|a +--R Type: Expression Integer +--E 963 + +--S 964 of 1483 +t0187:= 1/(a+b/x^6) +--R +--R +--R 6 +--R x +--R (959) -------- +--R 6 +--R a x + b +--R Type: Fraction Polynomial Integer +--E 964 + +--S 965 of 1483 +r0187:= x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ + atan(-3^(1/2)+2*a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ + atan(3^(1/2)+2*a^(1/6)*x/b^(1/6))/a^(7/6)+1/12*b^(1/6)*_ + log(b^(1/3)/a^(1/3)-b^(1/6)*x*3^(1/2)/a^(1/6)+x^2)*3^(1/2)/a^(7/6)-_ + 1/12*b^(1/6)*log(b^(1/3)/a^(1/3)+b^(1/6)*x*3^(1/2)/a^(1/6)+_ + x^2)*3^(1/2)/a^(7/6) +--R +--R +--R (960) +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a +--R - \|3 \|b log(-------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ - x\|3 \|a \|b + \|a \|b + x \|a \|a +--R \|3 \|b log(---------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +-+6+-+ 6+-+ +-+6+-+ 6+-+ +--R 6+-+ \|3 \|b + 2x\|a 6+-+ \|3 \|b - 2x\|a +--R - 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|b \|b +--R + +--R 6+-+ +--R 6+-+ x\|a 6+-+ +--R - 4\|b atan(-----) + 12x\|a +--R 6+-+ +--R \|b +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression Integer +--E 965 + +--S 966 of 1483 +a0187:=integrate(t0187,x) +--R +--R +--R (961) +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R - a |- ------- log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R a |- ------- log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R - 2a |- ------- log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R 2a |- ------- log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 2a +--R Type: Union(Expression Integer,...) +--E 966 + +--S 967 of 1483 +m0187:=a0187-r0187 +--R +--R +--R (962) +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a +--R \|3 \|b log(-------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 6+-+ 2 | b | b 2 +--R - 6a |- ------- \|a log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 6+-+ 2 | b | b 2 +--R 6a |- ------- \|a log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b 6+-+ | b +--R - 12a |- ------- \|a log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b 6+-+ | b +--R 12a |- ------- \|a log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ - x\|3 \|a \|b + \|a \|b + x \|a \|a +--R - \|3 \|b log(---------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 12a\|3 |- ------- \|a atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +-+6+-+ 6+-+ +-+6+-+ 6+-+ +--R 6+-+ \|3 \|b + 2x\|a 6+-+ \|3 \|b - 2x\|a +--R 2\|b atan(-----------------) - 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|b \|b +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 6+-+ +--R +-+ | b 6+-+ \| 46656a 6+-+ x\|a +--R 12a\|3 |- ------- \|a atan(------------------ + 4\|b atan(-----) +--R 6| 7 +---------+ 6+-+ +--R \| 46656a | b \|b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression Integer +--E 967 + +--S 968 of 1483 +d0187:=D(m0187,x) +--R +--R +--R (963) +--R 6 3+-+2 6+-+4 +--R 3a x \|a \|b +--R + +--R 4 6+-+2 3+-+2 6 3+-+6+-+2 3+-+ 2 3+-+2 6+-+6+-+2 +--R (- a x \|a \|b + (- 3a x - b)\|a \|a \|b - 2b x \|a \|a)\|b +--R + +--R 6+-+4 3+-+2 2 3+-+6+-+4 3+-+ 4 3+-+2 6+-+4 +--R b \|a \|b + 2b x \|a \|a \| + b x \|a \|a +--R / +--R 2 8 2 3+-+2 6+-+2 6+-+2 2 6 6+-+4 3+-+2 +--R (6a x + 6a b x )\|a \|a \|b + (- 2a x - 2a b)\|a \|b +--R + +--R 2 8 2 3+-+6+-+4 3+-+ 2 10 4 3+-+2 6+-+4 +--R (- 4a x - 4a b x )\|a \|a \|b + (- 2a x - 2a b x )\|a \|a +--R Type: Expression Integer +--E 968 + +--S 969 of 1483 +t0188:= (a+b/x^2)/(c+d/x^2) +--R +--R +--R 2 +--R a x + b +--R (964) -------- +--R 2 +--R c x + d +--R Type: Fraction Polynomial Integer +--E 969 + +--S 970 of 1483 +r0188:= a*x/c+(b*c-a*d)*atan(c^(1/2)*x/d^(1/2))/c^(3/2)/d^(1/2) +--R +--R +--R +-+ +--R x\|c +-+ +-+ +--R (- a d + b c)atan(-----) + a x\|c \|d +--R +-+ +--R \|d +--R (965) -------------------------------------- +--R +-+ +-+ +--R c\|c \|d +--R Type: Expression Integer +--E 970 + +--S 971 of 1483 +a0188:=integrate(t0188,x) +--R +--R +--R (966) +--R 2 +-----+ +--R (c x - d)\|- c d - 2c d x +-----+ +--R (a d - b c)log(---------------------------) + 2a x\|- c d +--R 2 +--R c x + d +--R [----------------------------------------------------------, +--R +-----+ +--R 2c\|- c d +--R +---+ +--R x\|c d +---+ +--R (- a d + b c)atan(-------) + a x\|c d +--R d +--R --------------------------------------] +--R +---+ +--R c\|c d +--R Type: Union(List Expression Integer,...) +--E 971 + +--S 972 of 1483 +m0188a:=a0188.1-r0188 +--R +--R +--R (967) +--R 2 +-----+ +--R +-+ +-+ (c x - d)\|- c d - 2c d x +--R (a d - b c)\|c \|d log(---------------------------) +--R 2 +--R c x + d +--R + +--R +-+ +--R +-----+ x\|c +--R (2a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|d +--R / +--R +-----+ +-+ +-+ +--R 2c\|- c d \|c \|d +--R Type: Expression Integer +--E 972 + +--S 973 of 1483 +d0188a:=D(m0188a,x) +--R +--R +--R (968) 0 +--R Type: Expression Integer +--E 973 + +--S 974 of 1483 +m0188b:=a0188.2-r0188 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|c +--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----) +--R d +-+ +--R \|d +--R (969) ----------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|c \|d \|c d +--R Type: Expression Integer +--E 974 + +--S 975 of 1483 +d0188b:=D(m0188b,x) +--R +--R +--R (970) 0 +--R Type: Expression Integer +--E 975 + +--S 976 of 1483 +t0189:= (a+b/x^3)/(c+d/x^3) +--R +--R +--R 3 +--R a x + b +--R (971) -------- +--R 3 +--R c x + d +--R Type: Fraction Polynomial Integer +--E 976 + +--S 977 of 1483 +r0189:= a*x/c+1/3*(b*c-a*d)*atan(-1/3*3^(1/2)+2/3*c^(1/3)*_ + x*3^(1/2)/d^(1/3))*3^(1/2)/c^(4/3)/d^(2/3)+1/3*(b*c-a*d)*_ + log(d^(1/3)/c^(1/3)+x)/c^(4/3)/d^(2/3)-1/6*(b*c-a*d)*_ + log(d^(2/3)/c^(2/3)-d^(1/3)*x/c^(1/3)+x^2)/c^(4/3)/d^(2/3) +--R +--R +--R (972) +--R 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|d - x\|c \|d + x \|c +--R (a d - b c)log(---------------------------) +--R 3+-+2 +--R \|c +--R + +--R 3+-+ 3+-+ +--R \|d + x\|c +--R (- 2a d + 2b c)log(------------) +--R 3+-+ +--R \|c +--R + +--R +-+3+-+ +-+3+-+ +--R +-+ \|3 \|d - 2x\|3 \|c 3+-+3+-+2 +--R (2a d - 2b c)\|3 atan(---------------------) + 6a x\|c \|d +--R 3+-+ +--R 3\|d +--R / +--R 3+-+3+-+2 +--R 6c\|c \|d +--R Type: Expression Integer +--E 977 + +--S 978 of 1483 +a0189:=integrate(t0189,x) +--R +--R +--R (973) +--R +------+2 +------+ +--R +-+ 2 3| 2 3| 2 2 +--R (- a d + b c)\|3 log(x \|- c d + d x\|- c d + d ) +--R + +--R +------+ +--R +-+ 3| 2 +--R (2a d - 2b c)\|3 log(x\|- c d - d) +--R + +--R +------+ +--R +-+3| 2 +-+ +------+ +--R 2x\|3 \|- c d + d\|3 +-+3| 2 +--R (- 6a d + 6b c)atan(-----------------------) + 6a x\|3 \|- c d +--R 3d +--R / +--R +------+ +--R +-+3| 2 +--R 6c\|3 \|- c d +--R Type: Union(Expression Integer,...) +--E 978 + +--S 979 of 1483 +m0189:=a0189-r0189 +--R +--R +--R (974) +--R +------+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R +-+3| 2 \|d - x\|c \|d + x \|c +--R (- a d + b c)\|3 \|- c d log(---------------------------) +--R 3+-+2 +--R \|c +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 \|d + x\|c +--R (2a d - 2b c)\|3 \|- c d log(------------) +--R 3+-+ +--R \|c +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R (- a d + b c)\|3 \|c \|d log(x \|- c d + d x\|- c d + d ) +--R + +--R +------+ +--R +-+3+-+3+-+2 3| 2 +--R (2a d - 2b c)\|3 \|c \|d log(x\|- c d - d) +--R + +--R +------+ +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- c d + d\|3 +--R (- 6a d + 6b c)\|c \|d atan(-----------------------) +--R 3d +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 \|3 \|d - 2x\|3 \|c +--R (- 6a d + 6b c)\|- c d atan(---------------------) +--R 3+-+ +--R 3\|d +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6c\|3 \|- c d \|c \|d +--R Type: Expression Integer +--E 979 + +--S 980 of 1483 +d0189:=D(m0189,x) +--R +--R +--R (975) 0 +--R Type: Expression Integer +--E 980 + +--S 981 of 1483 +t0190:= 1/(a+b*(c+d*x)^2)^2 +--R +--R +--R (976) +--R 1 +--R / +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R b d x + 4b c d x + (6b c + 2a b)d x + (4b c + 4a b c)d x + b c +--R + +--R 2 2 +--R 2a b c + a +--R Type: Fraction Polynomial Integer +--E 981 + +--S 982 of 1483 +r0190:= 1/2*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+1/2*_ + atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(3/2)/b^(1/2)/d +--R +--R +--R (977) +--R +-+ +--R 2 2 2 (d x + c)\|b +-+ +-+ +--R (b d x + 2b c d x + b c + a)atan(-------------) + (d x + c)\|a \|b +--R +-+ +--R \|a +--R --------------------------------------------------------------------- +--R 3 2 2 2 2 +-+ +-+ +--R (2a b d x + 4a b c d x + (2a b c + 2a )d)\|a \|b +--R Type: Expression Integer +--E 982 + +--S 983 of 1483 +a0190:=integrate(t0190,x) +--R +--R +--R (978) +--R [ +--R 2 2 2 +--R (b d x + 2b c d x + b c + a) +--R * +--R 2 2 2 +-----+ +--R (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-----+ +--R (2d x + 2c)\|- a b +--R / +--R 3 2 2 2 2 +-----+ +--R (4a b d x + 8a b c d x + (4a b c + 4a )d)\|- a b +--R , +--R +---+ +--R 2 2 2 (d x + c)\|a b +---+ +--R (b d x + 2b c d x + b c + a)atan(---------------) + (d x + c)\|a b +--R a +--R ---------------------------------------------------------------------] +--R 3 2 2 2 2 +---+ +--R (2a b d x + 4a b c d x + (2a b c + 2a )d)\|a b +--R Type: Union(List Expression Integer,...) +--E 983 + +--S 984 of 1483 +m0190a:=a0190.1-r0190 +--R +--R +--R (979) +--R 2 2 2 +-----+ +--R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R \|a \|b log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-+ +--R +-----+ (d x + c)\|b +--R - 2\|- a b atan(-------------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 4a d\|- a b \|a \|b +--R Type: Expression Integer +--E 984 + +--S 985 of 1483 +d0190a:=D(m0190a,x) +--R +--R +--R (980) 0 +--R Type: Expression Integer +--E 985 + +--S 986 of 1483 +m0190b:=a0190.2-r0190 +--R +--R +--R +---+ +-+ +--R +-+ +-+ (d x + c)\|a b +---+ (d x + c)\|b +--R \|a \|b atan(---------------) - \|a b atan(-------------) +--R a +-+ +--R \|a +--R (981) --------------------------------------------------------- +--R +-+ +-+ +---+ +--R 2a d\|a \|b \|a b +--R Type: Expression Integer +--E 986 + +--S 987 of 1483 +d0190b:=D(m0190b,x) +--R +--R +--R (982) 0 +--R Type: Expression Integer +--E 987 + +--S 988 of 1483 +t0191:= 1/(a+b*(c+d*x)^2)^3 +--R +--R +--R (983) +--R 1 +--R / +--R 3 6 6 3 5 5 3 2 2 4 4 3 3 2 3 3 +--R b d x + 6b c d x + (15b c + 3a b )d x + (20b c + 12a b c)d x +--R + +--R 3 4 2 2 2 2 2 3 5 2 3 2 3 6 +--R (15b c + 18a b c + 3a b)d x + (6b c + 12a b c + 6a b c)d x + b c +--R + +--R 2 4 2 2 3 +--R 3a b c + 3a b c + a +--R Type: Fraction Polynomial Integer +--E 988 + +--S 989 of 1483 +r0191:= 1/4*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)^2+_ + 3/8*(c+d*x)/a^2/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+_ + 3/8*atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(5/2)/b^(1/2)/d +--R +--R +--R (984) +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R +-+ +--R (d x + c)\|b +--R atan(-------------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (3b d x + 9b c d x + (9b c + 5a)d x + 3b c + 5a c)\|a \|b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 8a b d x + 32a b c d x + (48a b c + 16a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (32a b c + 32a b c)d x + (8a b c + 16a b c + 8a )d +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression Integer +--E 989 + +--S 990 of 1483 +a0191:=integrate(t0191,x) +--R +--R +--R (985) +--R [ +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R 2 2 2 +-----+ +--R (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R 3 3 2 2 2 3 +-----+ +--R (6b d x + 18b c d x + (18b c + 10a)d x + 6b c + 10a c)\|- a b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 16a b d x + 64a b c d x + (96a b c + 32a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (64a b c + 64a b c)d x + (16a b c + 32a b c + 16a )d +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R +---+ +--R (d x + c)\|a b +--R atan(---------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +--R (3b d x + 9b c d x + (9b c + 5a)d x + 3b c + 5a c)\|a b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 8a b d x + 32a b c d x + (48a b c + 16a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (32a b c + 32a b c)d x + (8a b c + 16a b c + 8a )d +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List Expression Integer,...) +--E 990 + +--S 991 of 1483 +m0191a:=a0191.1-r0191 +--R +--R +--R (986) +--R 2 2 2 +-----+ +--R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R 3\|a \|b log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-+ +--R +-----+ (d x + c)\|b +--R - 6\|- a b atan(-------------) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 16a d\|- a b \|a \|b +--R Type: Expression Integer +--E 991 + +--S 992 of 1483 +d0191a:=D(m0191a,x) +--R +--R +--R (987) 0 +--R Type: Expression Integer +--E 992 + +--S 993 of 1483 +m0191b:=a0191.2-r0191 +--R +--R +--R +---+ +-+ +--R +-+ +-+ (d x + c)\|a b +---+ (d x + c)\|b +--R 3\|a \|b atan(---------------) - 3\|a b atan(-------------) +--R a +-+ +--R \|a +--R (988) ----------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a d\|a \|b \|a b +--R Type: Expression Integer +--E 993 + +--S 994 of 1483 +d0191b:=D(m0191b,x) +--R +--R +--R (989) 0 +--R Type: Expression Integer +--E 994 + +--S 995 of 1483 +t0192:= 1/(1-(c+d*x)^2) +--R +--R +--R 1 +--R (990) - ---------------------- +--R 2 2 2 +--R d x + 2c d x + c - 1 +--R Type: Fraction Polynomial Integer +--E 995 + +--S 996 of 1483 +r0192:= atanh(c+d*x)/d +--R +--R +--R atanh(d x + c) +--R (991) -------------- +--R d +--R Type: Expression Integer +--E 996 + +--S 997 of 1483 +a0192:=integrate(t0192,x) +--R +--R +--R log(d x + c + 1) - log(d x + c - 1) +--R (992) ----------------------------------- +--R 2d +--R Type: Union(Expression Integer,...) +--E 997 + +--S 998 of 1483 +m0192:=a0192-r0192 +--R +--R +--R log(d x + c + 1) - log(d x + c - 1) - 2atanh(d x + c) +--R (993) ----------------------------------------------------- +--R 2d +--R Type: Expression Integer +--E 998 + +--S 999 of 1483 +d0192:=D(m0192,x) +--R +--R +--R (994) 0 +--R Type: Expression Integer +--E 999 + +--S 1000 of 1483 +t0193:= 1/(1-(1+x)^2) +--R +--R +--R 1 +--R (995) - ------- +--R 2 +--R x + 2x +--R Type: Fraction Polynomial Integer +--E 1000 + +--S 1001 of 1483 +r0193:= atanh(1+x) +--R +--R +--R (996) atanh(x + 1) +--R Type: Expression Integer +--E 1001 + +--S 1002 of 1483 +a0193:=integrate(t0193,x) +--R +--R +--R log(x + 2) - log(x) +--R (997) ------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 1002 + +--S 1003 of 1483 +m0193:=a0193-r0193 +--R +--R +--R log(x + 2) - log(x) - 2atanh(x + 1) +--R (998) ----------------------------------- +--R 2 +--R Type: Expression Integer +--E 1003 + +--S 1004 of 1483 +d0193:=D(m0193,x) +--R +--R +--R (999) 0 +--R Type: Expression Integer +--E 1004 + +--S 1005 of 1483 +t0194:= x^3/(a+b*x+c*x^2) +--R +--R +--R 3 +--R x +--R (1000) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction Polynomial Integer +--E 1005 + +--S 1006 of 1483 +r0194:= -b*x/c^2+1/2*x^2/c+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^3/(b^2-4*a*c)^(1/2)+_ + 1/2*(b^2-a*c)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (1001) +--R 3 2c x + b +--R (- 6a b c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E 1006 + +--S 1007 of 1483 +a0194:=integrate(t0194,x) +--R +--R +--R (1002) +--R [ +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 3 (2c x + b)\|4a c - b +--R (6a b c - 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 1007 + +--S 1008 of 1483 +m0194a:=a0194.1-r0194 +--R +--R +--R (1003) +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2c x + b +--R (6a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E 1008 + +--S 1009 of 1483 +d0194a:=D(m0194a,x) +--R +--R +--R (1004) 0 +--R Type: Expression Integer +--E 1009 + +--S 1010 of 1483 +m0194b:=a0194.2-r0194 +--R +--R +--R (1005) +--R +---------+ +--R 3 | 2 2c x + b +--R (3a b c - b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2c x + b)\|4a c - b +--R (3a b c - b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E 1010 + +--S 1011 of 1483 +d0194b:=D(m0194b,x) +--R +--R +--R (1006) 0 +--R Type: Expression Integer +--E 1011 + +--S 1012 of 1483 +t0195:= x^2/(a+b*x+c*x^2) +--R +--R +--R 2 +--R x +--R (1007) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction Polynomial Integer +--E 1012 + +--S 1013 of 1483 +r0195:= x/c-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + c^2/(b^2-4*a*c)^(1/2)-1/2*b*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1008) +--R 2 2c x + b +--R (4a c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E 1013 + +--S 1014 of 1483 +a0195:=integrate(t0195,x) +--R +--R +--R (1009) +--R [ +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (- 4a c + 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 1014 + +--S 1015 of 1483 +m0195a:=a0195.1-r0195 +--R +--R +--R (1010) +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression Integer +--E 1015 + +--S 1016 of 1483 +d0195a:=D(m0195a,x) +--R +--R +--R (1011) 0 +--R Type: Expression Integer +--E 1016 + +--S 1017 of 1483 +m0195b:=a0195.2-r0195 +--R +--R +--R (1012) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2a c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2a c + b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E 1017 + +--S 1018 of 1483 +d0195b:=D(m0195b,x) +--R +--R +--R (1013) 0 +--R Type: Expression Integer +--E 1018 + +--S 1019 of 1483 +t0196:= 1/((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*cos((%pi-2*k*%pi)/n)) +--R +--R +--R 1 +--R (1014) ----------------------------------- +--R 2 1 +--R - - +--R a n (2k - 1)%pi a n 2 +--R (-) - 2x cos(-----------)(-) + x +--R b n b +--R Type: Expression Integer +--E 1019 + +--S 1020 of 1483 +r0196:= -atan((-x+(a/b)^(1/n)*cos((%pi-2*k*%pi)/n))/((a/b)^(1/n))/_ + sin((%pi-2*k*%pi)/n))/((a/b)^(1/n))/sin((%pi-2*k*%pi)/n) +--R +--R +--R 1 +--R - +--R (2k - 1)%pi a n +--R cos(-----------)(-) - x +--R n b +--R atan(------------------------) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R (1015) - ------------------------------ +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R Type: Expression Integer +--E 1020 + +--S 1021 of 1483 +a0196:=integrate(t0196,x) +--R +--R +--R (1016) +--R [ +--R log +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) + 3cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R - cos(-----------) ((-) ) +--R n b +--R * +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(cos(-----------) - 1)(-) +--R \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2cos(-----------) - 2cos(-----------))(-) +--R n n b +--R + +--R (2k - 1)%pi 2 +--R - 2x cos(-----------) + 2x +--R n +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 5 (2k - 1)%pi 3 a n +--R (- 2cos(-----------) + 2cos(-----------) )((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (2x cos(-----------) - 2x cos(-----------) )((-) ) +--R n n b +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R / +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) - cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R cos(-----------) ((-) ) +--R n b +--R / +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R 2 |(cos(-----------) - 1)(-) +--R \| n b +--R , +--R +--R atan +--R 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R (cos(-----------) (-) - x cos(-----------) + 2x)(-) +--R n b n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R +-----------------------------+ +--R 2 | 2 +--R - | - +--R a n 2 | (2k - 1)%pi 2 a n +--R ((-) - x ) |(- cos(-----------) + 1)(-) +--R b \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi a n +--R cos(-----------)(-) + x +--R n b +--R - atan(--------------------------------) +--R +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R / +--R +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R ] +--R Type: Union(List Expression Integer,...) +--E 1021 + +--S 1022 of 1483 +m0196a:=a0196.1-r0196 +--R +--R +--R (1017) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R * +--R log +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) + 3cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R - cos(-----------) ((-) ) +--R n b +--R * +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(cos(-----------) - 1)(-) +--R \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2cos(-----------) - 2cos(-----------))(-) +--R n n b +--R + +--R (2k - 1)%pi 2 +--R - 2x cos(-----------) + 2x +--R n +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 5 (2k - 1)%pi 3 a n +--R (- 2cos(-----------) + 2cos(-----------) )((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (2x cos(-----------) - 2x cos(-----------) )((-) ) +--R n n b +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R / +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) - cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R cos(-----------) ((-) ) +--R n b +--R + +--R 1 +--R - +---------------------------+ +--R (2k - 1)%pi a n | 2 +--R cos(-----------)(-) - x | - +--R n b | (2k - 1)%pi 2 a n +--R 2atan(------------------------) |(cos(-----------) - 1)(-) +--R 1 \| n b +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R / +--R +---------------------------+ +--R 1 | 2 +--R - | - +--R (2k - 1)%pi a n | (2k - 1)%pi 2 a n +--R 2sin(-----------)(-) |(cos(-----------) - 1)(-) +--R n b \| n b +--R Type: Expression Integer +--E 1022 + +--S 1023 of 1483 +d0196a:=D(m0196a,x) +--R +--R +--R (1018) +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (sin(-----------) + cos(-----------) + 2cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 +--R - 2x cos(-----------) (-) + x cos(-----------) +--R n b n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 4 a n +--R (- cos(-----------) sin(-----------) - 2cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 a n +--R 2x cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R 1 2 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 2 a n +--R (sin(-----------) + cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi a n 2 +--R - 2x cos(-----------)(-) + x +--R n b +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 +--R (- cos(-----------) - cos(-----------) )sin(-----------) +--R n n n +--R + +--R (2k - 1)%pi 6 (2k - 1)%pi 4 +--R - cos(-----------) - cos(-----------) +--R n n +--R * +--R 1 4 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 +--R (2x cos(-----------) - 2x cos(-----------))sin(-----------) +--R n n n +--R + +--R (2k - 1)%pi 5 +--R 4x cos(-----------) +--R n +--R * +--R 1 3 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 +--R (- x cos(-----------) + x )sin(-----------) +--R n n +--R + +--R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 +--R - 6x cos(-----------) + 4x cos(-----------) +--R n n +--R * +--R 1 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 +--R - +--R 3 (2k - 1)%pi 3 3 (2k - 1)%pi a n +--R (4x cos(-----------) - 4x cos(-----------))(-) +--R n n b +--R + +--R 4 (2k - 1)%pi 2 4 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 6 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 6 a n +--R (cos(-----------) sin(-----------) + cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 5 1 4 +--R - - +--R (2k - 1)%pi 5 a n 2 (2k - 1)%pi 4 a n +--R - 2x cos(-----------) ((-) ) + x cos(-----------) ((-) ) +--R n b n b +--R Type: Expression Integer +--E 1023 + +--S 1024 of 1483 +m0196b:=a0196.2-r0196 +--R +--R +--R (1019) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R * +--R atan +--R 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R (cos(-----------) (-) - x cos(-----------) + 2x)(-) +--R n b n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R +-----------------------------+ +--R 2 | 2 +--R - | - +--R a n 2 | (2k - 1)%pi 2 a n +--R ((-) - x ) |(- cos(-----------) + 1)(-) +--R b \| n b +--R + +--R 1 +--R - +--R 1 (2k - 1)%pi a n +--R - cos(-----------)(-) + x +--R (2k - 1)%pi a n n b +--R - sin(-----------)(-) atan(--------------------------------) +--R n b +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R + +--R 1 +--R - +-----------------------------+ +--R (2k - 1)%pi a n | 2 +--R cos(-----------)(-) - x | - +--R n b | (2k - 1)%pi 2 a n +--R atan(------------------------) |(- cos(-----------) + 1)(-) +--R 1 \| n b +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R / +--R +-----------------------------+ +--R 1 | 2 +--R - | - +--R (2k - 1)%pi a n | (2k - 1)%pi 2 a n +--R sin(-----------)(-) |(- cos(-----------) + 1)(-) +--R n b \| n b +--R Type: Expression Integer +--E 1024 + +--S 1025 of 1483 +d0196b:=D(m0196b,x) +--R +--R +--R (1020) +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (sin(-----------) + cos(-----------) + 2cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 +--R - 2x cos(-----------) (-) + x cos(-----------) +--R n b n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 2 (2k - 1)%pi 4 a n +--R (- cos(-----------) sin(-----------) - 2cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n 2 (2k - 1)%pi 2 a n +--R 2x cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R 1 2 +--R - +--R (2k - 1)%pi 2 (2k - 1)%pi 2 a n +--R (sin(-----------) + cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi a n 2 +--R - 2x cos(-----------)(-) + x +--R n b +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 2 +--R (- cos(-----------) - cos(-----------) )sin(-----------) +--R n n n +--R + +--R (2k - 1)%pi 6 (2k - 1)%pi 4 +--R - cos(-----------) - cos(-----------) +--R n n +--R * +--R 1 4 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R (2k - 1)%pi 3 (2k - 1)%pi (2k - 1)%pi 2 +--R (2x cos(-----------) - 2x cos(-----------))sin(-----------) +--R n n n +--R + +--R (2k - 1)%pi 5 +--R 4x cos(-----------) +--R n +--R * +--R 1 3 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 2 (2k - 1)%pi 2 2 (2k - 1)%pi 2 +--R (- x cos(-----------) + x )sin(-----------) +--R n n +--R + +--R 2 (2k - 1)%pi 4 2 (2k - 1)%pi 2 +--R - 6x cos(-----------) + 4x cos(-----------) +--R n n +--R * +--R 1 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 +--R - +--R 3 (2k - 1)%pi 3 3 (2k - 1)%pi a n +--R (4x cos(-----------) - 4x cos(-----------))(-) +--R n n b +--R + +--R 4 (2k - 1)%pi 2 4 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 6 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 (2k - 1)%pi 6 a n +--R (cos(-----------) sin(-----------) + cos(-----------) )((-) ) +--R n n n b +--R + +--R 1 5 1 4 +--R - - +--R (2k - 1)%pi 5 a n 2 (2k - 1)%pi 4 a n +--R - 2x cos(-----------) ((-) ) + x cos(-----------) ((-) ) +--R n b n b +--R Type: Expression Integer +--E 1025 + +--S 1026 of 1483 +t0197:= 1/x^2/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (1021) ------------------ +--R 4 3 2 +--R c x + b x + a x +--R Type: Fraction Polynomial Integer +--E 1026 + +--S 1027 of 1483 +r0197:= -1/a/x-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/_ + (b^2-4*a*c)^(1/2)-b*log(x)/a^2+1/2*b*log(a+b*x+c*x^2)/a^2 +--R +--R +--R (1022) +--R 2 2c x + b +--R (4a c - 2b )x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R Type: Expression Integer +--E 1027 + +--S 1028 of 1483 +a0197:=integrate(t0197,x) +--R +--R +--R (1023) +--R [ +--R 2 +--R (2a c - b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (- 4a c + 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2a x\|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 1028 + +--S 1029 of 1483 +m0197a:=a0197.1-r0197 +--R +--R +--R (1024) +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression Integer +--E 1029 + +--S 1030 of 1483 +d0197a:=D(m0197a,x) +--R +--R +--R (1025) 0 +--R Type: Expression Integer +--E 1030 + +--S 1031 of 1483 +m0197b:=a0197.2-r0197 +--R +--R +--R (1026) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2a c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2a c + b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E 1031 + +--S 1032 of 1483 +d0197b:=D(m0197b,x) +--R +--R +--R (1027) 0 +--R Type: Expression Integer +--E 1032 + +--S 1033 of 1483 +t0198:= 1/x^3/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (1028) ------------------ +--R 5 4 3 +--R c x + b x + a x +--R Type: Fraction Polynomial Integer +--E 1033 + +--S 1034 of 1483 +r0198:= -1/2/a/x^2+b/a^2/x+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/a^3/(b^2-4*a*c)^(1/2)+(b^2-a*c)*_ + log(x)/a^3-1/2*(b^2-a*c)*log(a+b*x+c*x^2)/a^3 +--R +--R +--R (1029) +--R 3 2 2c x + b +--R (- 6a b c + 2b )x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R Type: Expression Integer +--E 1034 + +--S 1035 of 1483 +a0198:=integrate(t0198,x) +--R +--R +--R (1030) +--R [ +--R 3 2 +--R (3a b c - b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 3 2 (2c x + b)\|4a c - b +--R (6a b c - 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 | 2 +--R 2a x \|4a c - b +--R ] +--R Type: Union(List Expression Integer,...) +--E 1035 + +--S 1036 of 1483 +m0198a:=a0198.1-r0198 +--R +--R +--R (1031) +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2c x + b +--R (6a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2a \|- 4a c + b +--R Type: Expression Integer +--E 1036 + +--S 1037 of 1483 +d0198a:=D(m0198a,x) +--R +--R +--R (1032) 0 +--R Type: Expression Integer +--E 1037 + +--S 1038 of 1483 +m0198b:=a0198.2-r0198 +--R +--R +--R (1033) +--R +---------+ +--R 3 | 2 2c x + b +--R (3a b c - b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2c x + b)\|4a c - b +--R (3a b c - b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression Integer +--E 1038 + +--S 1039 of 1483 +d0198b:=D(m0198b,x) +--R +--R +--R (1034) 0 +--R Type: Expression Integer +--E 1039 + +--S 1040 of 1483 +t0199:= x^3/(a+b*x+c*x^2)^2 +--R +--R +--R 3 +--R x +--R (1035) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction Polynomial Integer +--E 1040 + +--S 1041 of 1483 +r0199:= -1/2*(b^2-a*c)/c^3/(a+b*x+c*x^2)+1/2*b*(b^2-3*a*c)*(b+2*c*x)/_ + c^3/(b^2-4*a*c)/(a+b*x+c*x^2)+3*b*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^2/(b^2-4*a*c)^(1/2)-2*b*(b^2-3*a*c)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^2/(b^2-4*a*c)^(3/2)+_ + 1/2*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1036) +--R 2 3 2 2 4 2 3 +--R ((12a b c - 2b c)x + (12a b c - 2b )x + 12a b c - 2a b ) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 3 2 2 2 +--R ((4a c - b c)x + (4a b c - b )x + 4a c - a b )log(c x + b x + a) +--R + +--R 3 2 2 +--R (6a b c - 2b )x + 4a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 2 3 3 2 2 3 2 2 | 2 +--R ((8a c - 2b c )x + (8a b c - 2b c )x + 8a c - 2a b c )\|- 4a c + b +--R Type: Expression Integer +--E 1041 + +--S 1042 of 1483 +a0199:=integrate(t0199,x) +--R +--R +--R (1037) +--R [ +--R 2 3 2 2 4 2 3 +--R ((6a b c - b c)x + (6a b c - b )x + 6a b c - a b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R