diff --git a/changelog b/changelog index 4cf9a3f..7ac15d0 100644 --- a/changelog +++ b/changelog @@ -1,4 +1,13 @@ -20130723 tpd src/axiom-website/patches.html 20130722.01.tpd.patch +20130725 tpd src/axiom-website/patches.html 20130725.01.tpd.patch +20130725 tpd src/axiom-website/CATS/index.html add rich2, rich3a +20130725 tpd src/axiom-website/CATS/rich2.input added +20130725 tpd src/axiom-website/CATS/rich2.input.pdf added +20130725 tpd src/axiom-website/CATS/rich3a.input added +20130725 tpd src/axiom-website/CATS/rich3a.input.pdf added +20130725 tpd src/input/Makefile add rich2, rich3a added +20130725 tpd src/input/rich2.input added +20130725 tpd src/input/rich3a.input added +20130723 tpd src/axiom-website/patches.html 20130723.01.tpd.patch 20130723 tpd src/axiom-website/CATS/rich1b.input 20130723 tpd src/axiom-website/CATS/rich1b.input.pdf 20130723 tpd src/input/rich1b.input diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index c39c10a..e975cda 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -296,6 +296,9 @@ They have been rewritten using Axiom syntax. (a+b x)^m (A+B x) (d+e x)^p source pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 1) + source + pdf



Rich



diff --git a/src/axiom-website/CATS/rich2.input.pamphlet b/src/axiom-website/CATS/rich2.input.pamphlet new file mode 100644 index 0000000..0494093 --- /dev/null +++ b/src/axiom-website/CATS/rich2.input.pamphlet @@ -0,0 +1,36165 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich2.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (A+B x) (d+e x)^p| +There are: +\begin{itemize} +\item 249 integrals in this file. +\item 249 supplied "optimal results". +\item 230 matching answers. +\item 24 cases where Axiom supplied 2 results. +\item 34 cases that Axiom failed to integrate. +\item 6 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich2.output +)spool rich2.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1293 +t0:=x^m*(a+b*x)*(A+B*x) +--R +--R +--R 2 m +--R (1) (B b x + (A b + B a)x + A a)x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1293 +r0:=a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(2+m)/(2+m)+b*B*x^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 m + 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 m + 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 m + 1 +--R (A a m + 5A a m + 6A a)x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 +--R (A a m + 5A a m + 6A a)x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 +--R (B b m + 3B b m + 2B b)x +--R + +--R 2 2 +--R ((A b + B a)m + (4A b + 4B a)m + 3A b + 3B a)x +--R + +--R 2 +--R (A a m + 5A a m + 6A a)x +--R * +--R m log(x) +--R %e +--R + +--R 2 m + 3 +--R (- B b m - 3B b m - 2B b)x +--R + +--R 2 m + 2 +--R ((- A b - B a)m + (- 4A b - 4B a)m - 3A b - 3B a)x +--R + +--R 2 m + 1 +--R (- A a m - 5A a m - 6A a)x +--R / +--R 3 2 +--R m + 6m + 11m + 6 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1293 +t0:=x^4*(a+b*x)*(A+B*x) +--R +--R +--R 6 5 4 +--R (1) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1293 +r0:=1/5*a*A*x^5+1/6*(A*b+a*B)*x^6+1/7*b*B*x^7 +--R +--R +--R 1 7 1 1 6 1 5 +--R (2) - B b x + (- A b + - B a)x + - A a x +--R 7 6 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 1 6 1 5 +--R (3) - B b x + (- A b + - B a)x + - A a x +--R 7 6 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 1293 +t0:=x^3*(a+b*x)*(A+B*x) +--R +--R +--R 5 4 3 +--R (1) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1293 +r0:=1/4*a*A*x^4+1/5*(A*b+a*B)*x^5+1/6*b*B*x^6 +--R +--R +--R 1 6 1 1 5 1 4 +--R (2) - B b x + (- A b + - B a)x + - A a x +--R 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 1 5 1 4 +--R (3) - B b x + (- A b + - B a)x + - A a x +--R 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 1293 +t0:=x^2*(a+b*x)*(A+B*x) +--R +--R +--R 4 3 2 +--R (1) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1293 +r0:=1/3*a*A*x^3+1/4*(A*b+a*B)*x^4+1/5*b*B*x^5 +--R +--R +--R 1 5 1 1 4 1 3 +--R (2) - B b x + (- A b + - B a)x + - A a x +--R 5 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 1 4 1 3 +--R (3) - B b x + (- A b + - B a)x + - A a x +--R 5 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 1293 +t0:=x*(a+b*x)*(A+B*x) +--R +--R +--R 3 2 +--R (1) B b x + (A b + B a)x + A a x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1293 +r0:=1/2*a*A*x^2+1/3*(A*b+a*B)*x^3+1/4*b*B*x^4 +--R +--R +--R 1 4 1 1 3 1 2 +--R (2) - B b x + (- A b + - B a)x + - A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 1 3 1 2 +--R (3) - B b x + (- A b + - B a)x + - A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1293 +t0:=(a+b*x)*(A+B*x) +--R +--R +--R 2 +--R (1) B b x + (A b + B a)x + A a +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1293 +r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*b*B*x^3 +--R +--R +--R 1 3 1 1 2 +--R (2) - B b x + (- A b + - B a)x + A a x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 3 1 1 2 +--R (3) - B b x + (- A b + - B a)x + A a x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1293 +t0:=(a+b*x)*(A+B*x)/x +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1293 +r0:=a*B*x+1/2*b*(A+B*x)^2/B+a*A*log(x) +--R +--R +--R 2 2 2 2 +--R 2A B a log(x) + B b x + (2A B b + 2B a)x + A b +--R (2) ----------------------------------------------- +--R 2B +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2A a log(x) + B b x + (2A b + 2B a)x +--R (3) ------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R A b +--R (4) - --- +--R 2B +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1293 +t0:=(a+b*x)*(A+B*x)/x^2 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1293 +r0:=-a*A/x+b*B*x+(A*b+a*B)*log(x) +--R +--R +--R 2 +--R (A b + B a)x log(x) + B b x - A a +--R (2) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (A b + B a)x log(x) + B b x - A a +--R (3) ---------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1293 +t0:=(a+b*x)*(A+B*x)/x^3 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1293 +r0:=-1/2*a*A/x^2+(-A*b-a*B)/x+b*B*log(x) +--R +--R +--R 2 +--R 2B b x log(x) + (- 2A b - 2B a)x - A a +--R (2) -------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2B b x log(x) + (- 2A b - 2B a)x - A a +--R (3) -------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1293 +t0:=(a+b*x)*(A+B*x)/x^4 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1293 +r0:=-1/3*a*A/x^3+1/2*(-A*b-a*B)/x^2-b*B/x +--R +--R +--R 2 1 1 1 +--R - B b x + (- - A b - - B a)x - - A a +--R 2 2 3 +--R (2) ------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 6B b x + (- 3A b - 3B a)x - 2A a +--R (3) ----------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1293 +t0:=(a+b*x)*(A+B*x)/x^5 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1293 +r0:=-1/4*a*A/x^4+1/3*(-A*b-a*B)/x^3-1/2*b*B/x^2 +--R +--R +--R 1 2 1 1 1 +--R - - B b x + (- - A b - - B a)x - - A a +--R 2 3 3 4 +--R (2) --------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 6B b x + (- 4A b - 4B a)x - 3A a +--R (3) ----------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1293 +t0:=(a+b*x)*(A+B*x)/x^6 +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1293 +r0:=-1/5*a*A/x^5+1/4*(-A*b-a*B)/x^4-1/3*b*B/x^3 +--R +--R +--R 1 2 1 1 1 +--R - - B b x + (- - A b - - B a)x - - A a +--R 3 4 4 5 +--R (2) --------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 20B b x + (- 15A b - 15B a)x - 12A a +--R (3) --------------------------------------- +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1293 +t0:=x^m*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 3 2 2 2 2 m +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1293 +r0:=a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(2+m)/(2+m)+_ + b*(A*b+2*a*B)*x^(3+m)/(3+m)+b^2*B*x^(4+m)/(4+m) +--R +--R +--R (2) +--R 2 3 2 2 2 2 m + 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m + 8A b +--R + +--R 16B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R m + 2 +--R x +--R + +--R 2 3 2 2 2 2 m + 1 +--R (A a m + 9A a m + 26A a m + 24A a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m +--R + +--R 2 +--R 8A b + 16B a b +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R (A a m + 9A a m + 26A a m + 24A a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 4 +--R (B b m + 6B b m + 11B b m + 6B b )x +--R + +--R 2 3 2 2 2 +--R (A b + 2B a b)m + (7A b + 14B a b)m + (14A b + 28B a b)m +--R + +--R 2 +--R 8A b + 16B a b +--R * +--R 3 +--R x +--R + +--R 2 3 2 2 2 +--R (2A a b + B a )m + (16A a b + 8B a )m + (38A a b + 19B a )m +--R + +--R 2 +--R 24A a b + 12B a +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 +--R (A a m + 9A a m + 26A a m + 24A a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- B b m - 6B b m - 11B b m - 6B b )x +--R + +--R 2 3 2 2 2 +--R (- A b - 2B a b)m + (- 7A b - 14B a b)m + (- 14A b - 28B a b)m +--R + +--R 2 +--R - 8A b - 16B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 2 2 2 +--R (- 2A a b - B a )m + (- 16A a b - 8B a )m + (- 38A a b - 19B a )m +--R + +--R 2 +--R - 24A a b - 12B a +--R * +--R m + 2 +--R x +--R + +--R 2 3 2 2 2 2 m + 1 +--R (- A a m - 9A a m - 26A a m - 24A a )x +--R / +--R 4 3 2 +--R m + 10m + 35m + 50m + 24 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1293 +t0:=x^4*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 7 2 6 2 5 2 4 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 66 + +--S 67 of 1293 +r0:=1/5*a^2*A*x^5+1/6*a*(2*A*b+a*B)*x^6+1/7*b*(A*b+2*a*B)*x^7+1/8*b^2*B*x^8 +--R +--R +--R 1 2 8 1 2 2 7 1 1 2 6 1 2 5 +--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 8 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 67 + +--S 68 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 1 2 2 7 1 1 2 6 1 2 5 +--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 8 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 69 + +--S 70 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 70 + +)clear all + +--S 71 of 1293 +t0:=x^3*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 6 2 5 2 4 2 3 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1293 +r0:=1/4*a^2*A*x^4+1/5*a*(2*A*b+a*B)*x^5+1/6*b*(A*b+2*a*B)*x^6+1/7*b^2*B*x^7 +--R +--R +--R 1 2 7 1 2 1 6 2 1 2 5 1 2 4 +--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 7 6 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 72 + +--S 73 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 1 2 1 6 2 1 2 5 1 2 4 +--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 7 6 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 1293 +t0:=x^2*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 5 2 4 2 3 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1293 +r0:=1/3*a^2*A*x^3+1/4*a*(2*A*b+a*B)*x^4+1/5*b*(A*b+2*a*B)*x^5+1/6*b^2*B*x^6 +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 +--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 6 5 5 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1293 +t0:=x*(a+b*x)^2*(A+B*x) +--R +--R +--R 2 4 2 3 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1293 +r0:=1/2*a^2*A*x^2+1/3*a*(2*A*b+a*B)*x^3+1/4*b*(A*b+2*a*B)*x^4+1/5*b^2*B*x^5 +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 +--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x +--R 5 4 2 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1293 +t0:=(a+b*x)^2*(A+B*x) +--R +--R +--R 2 3 2 2 2 2 +--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1293 +r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 +--R +--R +--R (2) +--R 1 4 4 1 4 2 3 3 3 1 2 2 2 2 2 +--R - B b x + (- A b + - B a b )x + (A a b + - B a b )x + A a b x +--R 4 3 3 2 +--R + +--R 1 3 1 4 +--R - A a b - -- B a +--R 3 12 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 1 2 4 1 2 2 3 1 2 2 2 +--R (3) - B b x + (- A b + - B a b)x + (A a b + - B a )x + A a x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1293 +m0:=a0-r0 +--R +--R +--R 1 3 1 4 +--R - - A a b + -- B a +--R 3 12 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 89 + +--S 90 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 90 + +)clear all + +--S 91 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 1293 +r0:=2*a*A*b*x+1/2*A*b^2*x^2+1/3*B*(a+b*x)^3/b+a^2*A*log(x) +--R +--R +--R (2) +--R 2 3 3 3 2 2 2 2 3 +--R 6A a b log(x) + 2B b x + (3A b + 6B a b )x + (12A a b + 6B a b)x + 2B a +--R ---------------------------------------------------------------------------- +--R 6b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 2 2 +--R 6A a log(x) + 2B b x + (3A b + 6B a b)x + (12A a b + 6B a )x +--R (3) --------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1293 +m0:=a0-r0 +--R +--R +--R 3 +--R B a +--R (4) - ---- +--R 3b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^2 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 1293 +r0:=-a^2*A/x+b*(A*b+2*a*B)*x+1/2*b^2*B*x^2+a*(2*A*b+a*B)*log(x) +--R +--R +--R 2 2 3 2 2 2 +--R (4A a b + 2B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a +--R (2) -------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 2 2 +--R (4A a b + 2B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a +--R (3) -------------------------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^3 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1293 +r0:=-1/2*a^2*A/x^2-a*(2*A*b+a*B)/x+b^2*B*x+b*(A*b+2*a*B)*log(x) +--R +--R +--R 2 2 2 3 2 2 +--R (2A b + 4B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a +--R (2) --------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 3 2 2 +--R (2A b + 4B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a +--R (3) --------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^4 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1293 +r0:=-1/3*a^2*A/x^3-1/2*a*(2*A*b+a*B)/x^2-b*(A*b+2*a*B)/x+b^2*B*log(x) +--R +--R +--R 2 3 2 2 2 2 +--R 6B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a +--R (2) ------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R 6B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a +--R (3) ------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^5 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1293 +r0:=-1/4*a^2*A/x^4-1/3*a*(2*A*b+a*B)/x^3-1/2*b*(A*b+2*a*B)/x^2-b^2*B/x +--R +--R +--R 2 3 1 2 2 2 1 2 1 2 +--R - B b x + (- - A b - B a b)x + (- - A a b - - B a )x - - A a +--R 2 3 3 4 +--R (2) ---------------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 12B b x + (- 6A b - 12B a b)x + (- 8A a b - 4B a )x - 3A a +--R (3) ---------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^6 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1293 +r0:=-1/5*a^2*A/x^5-1/4*a*(2*A*b+a*B)/x^4-1/3*b*(A*b+2*a*B)/x^3-1/2*b^2*B/x^2 +--R +--R +--R 1 2 3 1 2 2 2 1 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 2 3 3 2 4 5 +--R (2) -------------------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 30B b x + (- 20A b - 40B a b)x + (- 30A a b - 15B a )x - 12A a +--R (3) -------------------------------------------------------------------- +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^7 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1293 +r0:=-1/6*a^2*A/x^6-1/5*a*(2*A*b+a*B)/x^5-1/4*b*(A*b+2*a*B)/x^4-1/3*b^2*B/x^3 +--R +--R +--R 1 2 3 1 2 1 2 2 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 3 4 2 5 5 6 +--R (2) -------------------------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 1293 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 2 2 +--R - 20B b x + (- 15A b - 30B a b)x + (- 24A a b - 12B a )x - 10A a +--R (3) -------------------------------------------------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1293 +t0:=(a+b*x)^2*(A+B*x)/x^8 +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1293 +r0:=-1/7*a^2*A/x^7-1/6*a*(2*A*b+a*B)/x^6-1/5*b*(A*b+2*a*B)/x^5-1/4*b^2*B/x^4 +--R +--R +--R 1 2 3 1 2 2 2 1 1 2 1 2 +--R - - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a +--R 4 5 5 3 6 7 +--R (2) -------------------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R - 105B b x + (- 84A b - 168B a b)x + (- 140A a b - 70B a )x - 60A a +--R ----------------------------------------------------------------------- +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1293 +t0:=x^m*(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1293 +r0:=a^3*A*x^(1+m)/(1+m)+a^2*(3*A*b+a*B)*x^(2+m)/(2+m)+_ + 3*a*b*(A*b+a*B)*x^(3+m)/(3+m)+b^2*(A*b+3*a*B)*x^(4+m)/(4+m)+_ + b^3*B*x^(5+m)/(5+m) +--R +--R +--R (2) +--R 3 4 3 3 3 2 3 3 m + 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (A b + 3B a b )m + (11A b + 33B a b )m + (41A b + 123B a b )m +--R + +--R 3 2 3 2 +--R (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R m + 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R m + 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 m + 1 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 3 3 2 3 3 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (A b + 3B a b )m + (11A b + 33B a b )m + (41A b + 123B a b )m +--R + +--R 3 2 3 2 +--R (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R * +--R m log(x) +--R %e +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 3 3 2 3 3 5 +--R (B b m + 10B b m + 35B b m + 50B b m + 24B b )x +--R + +--R 3 2 4 3 2 3 +--R (A b + 3B a b )m + (11A b + 33B a b )m +--R + +--R 3 2 2 3 2 3 2 +--R (41A b + 123B a b )m + (61A b + 183B a b )m + 30A b + 90B a b +--R * +--R 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (3A a b + 3B a b)m + (36A a b + 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (147A a b + 147B a b)m + (234A a b + 234B a b)m + 120A a b +--R + +--R 2 +--R 120B a b +--R * +--R 3 +--R x +--R + +--R 2 3 4 2 3 3 2 3 2 +--R (3A a b + B a )m + (39A a b + 13B a )m + (177A a b + 59B a )m +--R + +--R 2 3 2 3 +--R (321A a b + 107B a )m + 180A a b + 60B a +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 +--R (A a m + 14A a m + 71A a m + 154A a m + 120A a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 4 3 3 3 2 3 3 m + 5 +--R (- B b m - 10B b m - 35B b m - 50B b m - 24B b )x +--R + +--R 3 2 4 3 2 3 +--R (- A b - 3B a b )m + (- 11A b - 33B a b )m +--R + +--R 3 2 2 3 2 3 2 +--R (- 41A b - 123B a b )m + (- 61A b - 183B a b )m - 30A b - 90B a b +--R * +--R m + 4 +--R x +--R + +--R 2 2 4 2 2 3 +--R (- 3A a b - 3B a b)m + (- 36A a b - 36B a b)m +--R + +--R 2 2 2 2 2 2 +--R (- 147A a b - 147B a b)m + (- 234A a b - 234B a b)m - 120A a b +--R + +--R 2 +--R - 120B a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 4 2 3 3 +--R (- 3A a b - B a )m + (- 39A a b - 13B a )m +--R + +--R 2 3 2 2 3 2 3 +--R (- 177A a b - 59B a )m + (- 321A a b - 107B a )m - 180A a b - 60B a +--R * +--R m + 2 +--R x +--R + +--R 3 4 3 3 3 2 3 3 m + 1 +--R (- A a m - 14A a m - 71A a m - 154A a m - 120A a )x +--R / +--R 5 4 3 2 +--R m + 15m + 85m + 225m + 274m + 120 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1293 +t0:=x^4*(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 8 3 2 7 2 2 6 2 3 5 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 4 +--R A a x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1293 +r0:=1/5*a^3*A*x^5+1/6*a^2*(3*A*b+a*B)*x^6+3/7*a*b*(A*b+a*B)*x^7+_ + 1/8*b^2*(A*b+3*a*B)*x^8+1/9*b^3*B*x^9 +--R +--R +--R (2) +--R 1 3 9 1 3 3 2 8 3 2 3 2 7 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 3 6 1 3 5 +--R (- A a b + - B a )x + - A a x +--R 2 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 1 3 3 2 8 3 2 3 2 7 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 9 8 8 7 7 +--R + +--R 1 2 1 3 6 1 3 5 +--R (- A a b + - B a )x + - A a x +--R 2 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 1293 +t0:=x^3*(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 7 3 2 6 2 2 5 2 3 4 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 3 +--R A a x +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1293 +r0:=1/4*a^3*A*x^4+1/5*a^2*(3*A*b+a*B)*x^5+1/2*a*b*(A*b+a*B)*x^6+_ + 1/7*b^2*(A*b+3*a*B)*x^7+1/8*b^3*B*x^8 +--R +--R +--R (2) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A a b + - B a )x + - A a x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 8 1 3 3 2 7 1 2 1 2 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 8 7 7 2 2 +--R + +--R 3 2 1 3 5 1 3 4 +--R (- A a b + - B a )x + - A a x +--R 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +)clear all + +--S 146 of 1293 +t0:=x^2*(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 6 3 2 5 2 2 4 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 2 +--R A a x +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1293 +r0:=1/3*a^3*A*x^3+1/4*a^2*(3*A*b+a*B)*x^4+3/5*a*b*(A*b+a*B)*x^5+_ + 1/6*b^2*(A*b+3*a*B)*x^6+1/7*b^3*B*x^7 +--R +--R +--R (2) +--R 1 3 7 1 3 1 2 6 3 2 3 2 5 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 7 6 2 5 5 +--R + +--R 3 2 1 3 4 1 3 3 +--R (- A a b + - B a )x + - A a x +--R 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 147 + +--S 148 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 7 1 3 1 2 6 3 2 3 2 5 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 7 6 2 5 5 +--R + +--R 3 2 1 3 4 1 3 3 +--R (- A a b + - B a )x + - A a x +--R 4 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 149 + +--S 150 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 150 + +)clear all + +--S 151 of 1293 +t0:=x*(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 5 3 2 4 2 2 3 2 3 2 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a x +--R Type: Polynomial(Integer) +--E 151 + +--S 152 of 1293 +r0:=-1/4*a*(A*b-a*B)*(a+b*x)^4/b^3+1/5*(A*b-2*a*B)*(a+b*x)^5/b^3+_ + 1/6*B*(a+b*x)^6/b^3 +--R +--R +--R (2) +--R 1 6 6 1 6 3 5 5 3 5 3 2 4 4 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 6 5 5 4 4 +--R + +--R 2 4 1 3 3 3 1 3 3 2 1 5 1 6 +--R (A a b + - B a b )x + - A a b x - -- A a b + -- B a +--R 3 2 20 60 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +--S 153 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 6 1 3 3 2 5 3 2 3 2 4 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b)x +--R 6 5 5 4 4 +--R + +--R 2 1 3 3 1 3 2 +--R (A a b + - B a )x + - A a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 153 + +--S 154 of 1293 +m0:=a0-r0 +--R +--R +--R 1 5 1 6 +--R -- A a b - -- B a +--R 20 60 +--R (4) ------------------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 154 + +--S 155 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 155 + +)clear all + +--S 156 of 1293 +t0:=(a+b*x)^3*(A+B*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1293 +r0:=1/4*(A*b-a*B)*(a+b*x)^4/b^2+1/5*B*(a+b*x)^5/b^2 +--R +--R +--R (2) +--R 1 5 5 1 5 3 4 4 4 2 3 3 +--R - B b x + (- A b + - B a b )x + (A a b + B a b )x +--R 5 4 4 +--R + +--R 3 2 3 1 3 2 2 3 2 1 4 1 5 +--R (- A a b + - B a b )x + A a b x + - A a b - -- B a +--R 2 2 4 20 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 5 1 3 3 2 4 2 2 3 +--R - B b x + (- A b + - B a b )x + (A a b + B a b)x +--R 5 4 4 +--R + +--R 3 2 1 3 2 3 +--R (- A a b + - B a )x + A a x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1293 +m0:=a0-r0 +--R +--R +--R 1 4 1 5 +--R - - A a b + -- B a +--R 4 20 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 159 + +--S 160 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 160 + +)clear all + +--S 161 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1293 +r0:=3*a^2*A*b*x+3/2*a*A*b^2*x^2+1/3*A*b^3*x^3+1/4*B*(a+b*x)^4/b+a^3*A*log(x) +--R +--R +--R (2) +--R 3 4 4 4 3 3 3 2 2 2 +--R 12A a b log(x) + 3B b x + (4A b + 12B a b )x + (18A a b + 18B a b )x +--R + +--R 2 2 3 4 +--R (36A a b + 12B a b)x + 3B a +--R / +--R 12b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 4 3 2 3 2 2 2 +--R 12A a log(x) + 3B b x + (4A b + 12B a b )x + (18A a b + 18B a b)x +--R + +--R 2 3 +--R (36A a b + 12B a )x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1293 +m0:=a0-r0 +--R +--R +--R 4 +--R B a +--R (4) - ---- +--R 4b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1293 +r0:=-a^3*A/x+3*a*b*(A*b+a*B)*x+1/2*b^2*(A*b+3*a*B)*x^2+1/3*b^3*B*x^3+_ + a^2*(3*A*b+a*B)*log(x) +--R +--R +--R (2) +--R 2 3 3 4 3 2 3 +--R (18A a b + 6B a )x log(x) + 2B b x + (3A b + 9B a b )x +--R + +--R 2 2 2 3 +--R (18A a b + 18B a b)x - 6A a +--R / +--R 6x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 4 3 2 3 +--R (18A a b + 6B a )x log(x) + 2B b x + (3A b + 9B a b )x +--R + +--R 2 2 2 3 +--R (18A a b + 18B a b)x - 6A a +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1293 +r0:=-1/2*a^3*A/x^2-a^2*(3*A*b+a*B)/x+b^2*(A*b+3*a*B)*x+1/2*b^3*B*x^2+_ + 3*a*b*(A*b+a*B)*log(x) +--R +--R +--R (2) +--R 2 2 2 3 4 3 2 3 +--R (6A a b + 6B a b)x log(x) + B b x + (2A b + 6B a b )x +--R + +--R 2 3 3 +--R (- 6A a b - 2B a )x - A a +--R / +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 3 2 3 +--R (6A a b + 6B a b)x log(x) + B b x + (2A b + 6B a b )x +--R + +--R 2 3 3 +--R (- 6A a b - 2B a )x - A a +--R / +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^4 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1293 +r0:=-1/3*a^3*A/x^3-1/2*a^2*(3*A*b+a*B)/x^2-3*a*b*(A*b+a*B)/x+_ + b^3*B*x+b^2*(A*b+3*a*B)*log(x) +--R +--R +--R (2) +--R 3 2 3 3 4 2 2 2 +--R (6A b + 18B a b )x log(x) + 6B b x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 9A a b - 3B a )x - 2A a +--R / +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 4 2 2 2 +--R (6A b + 18B a b )x log(x) + 6B b x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 9A a b - 3B a )x - 2A a +--R / +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^5 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1293 +r0:=-1/3*a^3*B/x^3-3/2*a^2*b*B/x^2-3*a*b^2*B/x-1/4*A*(a+b*x)^4/(a*x^4)+_ + b^3*B*log(x) +--R +--R +--R (2) +--R 3 4 4 4 3 2 2 3 +--R 12B a b x log(x) - 3A b x + (- 12A a b - 36B a b )x +--R + +--R 2 2 3 2 3 4 4 +--R (- 18A a b - 18B a b)x + (- 12A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12a x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R 12B b x log(x) + (- 12A b - 36B a b )x + (- 18A a b - 18B a b)x +--R + +--R 2 3 3 +--R (- 12A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1293 +m0:=a0-r0 +--R +--R +--R 4 +--R A b +--R (4) ---- +--R 4a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^6 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1293 +r0:=-1/5*a^3*A/x^5-1/4*a^2*(3*A*b+a*B)/x^4-a*b*(A*b+a*B)/x^3-_ + 1/2*b^2*(A*b+3*a*B)/x^2-b^3*B/x +--R +--R +--R (2) +--R 3 4 1 3 3 2 3 2 2 2 +--R - B b x + (- - A b - - B a b )x + (- A a b - B a b)x +--R 2 2 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 4 4 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R - 20B b x + (- 10A b - 30B a b )x + (- 20A a b - 20B a b)x +--R + +--R 2 3 3 +--R (- 15A a b - 5B a )x - 4A a +--R / +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^7 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1293 +r0:=-1/6*a^3*A/x^6-1/5*a^2*(3*A*b+a*B)/x^5-3/4*a*b*(A*b+a*B)/x^4-_ + 1/3*b^2*(A*b+3*a*B)/x^3-1/2*b^3*B/x^2 +--R +--R +--R (2) +--R 1 3 4 1 3 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - B a b )x + (- - A a b - - B a b)x +--R 2 3 4 4 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 5 5 6 +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 192 + +--S 193 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R - 30B b x + (- 20A b - 60B a b )x + (- 45A a b - 45B a b)x +--R + +--R 2 3 3 +--R (- 36A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^8 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1293 +r0:=-1/7*a^3*A/x^7-1/6*a^2*(3*A*b+a*B)/x^6-3/5*a*b*(A*b+a*B)/x^5-_ + 1/4*b^2*(A*b+3*a*B)/x^4-1/3*b^3*B/x^3 +--R +--R +--R (2) +--R 1 3 4 1 3 3 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 3 4 4 5 5 +--R + +--R 1 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 2 6 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 197 + +--S 198 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R - 140B b x + (- 105A b - 315B a b )x + (- 252A a b - 252B a b)x +--R + +--R 2 3 3 +--R (- 210A a b - 70B a )x - 60A a +--R / +--R 7 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^9 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1293 +r0:=-1/8*a^3*A/x^8-1/7*a^2*(3*A*b+a*B)/x^7-1/2*a*b*(A*b+a*B)/x^6-_ + 1/5*b^2*(A*b+3*a*B)/x^5-1/4*b^3*B/x^4 +--R +--R +--R (2) +--R 1 3 4 1 3 3 2 3 1 2 1 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 4 5 5 2 2 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 7 7 8 +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R - 70B b x + (- 56A b - 168B a b )x + (- 140A a b - 140B a b)x +--R + +--R 2 3 3 +--R (- 120A a b - 40B a )x - 35A a +--R / +--R 8 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1293 +t0:=(a+b*x)^3*(A+B*x)/x^10 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1293 +r0:=-1/9*a^3*A/x^9-1/8*a^2*(3*A*b+a*B)/x^8-3/7*a*b*(A*b+a*B)/x^7-_ + 1/6*b^2*(A*b+3*a*B)/x^6-1/5*b^3*B/x^5 +--R +--R +--R (2) +--R 1 3 4 1 3 1 2 3 3 2 3 2 2 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - - B a b)x +--R 5 6 2 7 7 +--R + +--R 3 2 1 3 1 3 +--R (- - A a b - - B a )x - - A a +--R 8 8 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 207 + +--S 208 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 3 2 2 2 +--R - 504B b x + (- 420A b - 1260B a b )x + (- 1080A a b - 1080B a b)x +--R + +--R 2 3 3 +--R (- 945A a b - 315B a )x - 280A a +--R / +--R 9 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1293 +t0:=x^m*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1293 +r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(2+m)/(2+m)+_ + 5*a^3*b*(2*A*b+a*B)*x^(3+m)/(3+m)+10*a^2*b^2*(A*b+a*B)*x^(4+m)/(4+m)+_ + 5*a*b^3*(A*b+2*a*B)*x^(5+m)/(5+m)+b^4*(A*b+5*a*B)*x^(6+m)/(6+m)+_ + b^5*B*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m + 1764B b m +--R + +--R 5 +--R 720B b +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 5 4 4 +--R (A b + 5B a b )m + (22A b + 110B a b )m + (190A b + 950B a b )m +--R + +--R 5 4 3 5 4 2 +--R (820A b + 4100B a b )m + (1849A b + 9245B a b )m +--R + +--R 5 4 5 4 +--R (2038A b + 10190B a b )m + 840A b + 4200B a b +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5A a b + B a )m + (130A a b + 26B a )m + (1350A a b + 270B a )m +--R + +--R 4 5 3 4 5 2 +--R (7100A a b + 1420B a )m + (19645A a b + 3929B a )m +--R + +--R 4 5 4 5 +--R (26370A a b + 5274B a )m + 12600A a b + 2520B a +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m + 8028A a m +--R + +--R 5 +--R 5040A a +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m + 1764B b m +--R + +--R 5 +--R 720B b +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (A b + 5B a b )m + (22A b + 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (190A b + 950B a b )m + (820A b + 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (1849A b + 9245B a b )m + (2038A b + 10190B a b )m + 840A b +--R + +--R 4 +--R 4200B a b +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5A a b + B a )m + (130A a b + 26B a )m + (1350A a b + 270B a )m +--R + +--R 4 5 3 4 5 2 +--R (7100A a b + 1420B a )m + (19645A a b + 3929B a )m +--R + +--R 4 5 4 5 +--R (26370A a b + 5274B a )m + 12600A a b + 2520B a +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m + 8028A a m +--R + +--R 5 +--R 5040A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 5 5 4 5 3 5 2 +--R B b m + 21B b m + 175B b m + 735B b m + 1624B b m +--R + +--R 5 5 +--R 1764B b m + 720B b +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (A b + 5B a b )m + (22A b + 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (190A b + 950B a b )m + (820A b + 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (1849A b + 9245B a b )m + (2038A b + 10190B a b )m + 840A b +--R + +--R 4 +--R 4200B a b +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5A a b + 10B a b )m + (115A a b + 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035A a b + 2070B a b )m + (4625A a b + 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720A a b + 21440B a b )m + (12060A a b + 24120B a b )m +--R + +--R 4 2 3 +--R 5040A a b + 10080B a b +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10A a b + 10B a b )m + (240A a b + 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260A a b + 2260B a b )m + (10560A a b + 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450A a b + 25450B a b )m + (29520A a b + 29520B a b )m +--R + +--R 2 3 3 2 +--R 12600A a b + 12600B a b +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10A a b + 5B a b)m + (250A a b + 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470A a b + 1235B a b)m + (12190A a b + 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120A a b + 15560B a b)m + (37960A a b + 18980B a b)m +--R + +--R 3 2 4 +--R 16800A a b + 8400B a b +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (5A a b + B a )m + (130A a b + 26B a )m +--R + +--R 4 5 4 4 5 3 +--R (1350A a b + 270B a )m + (7100A a b + 1420B a )m +--R + +--R 4 5 2 4 5 4 +--R (19645A a b + 3929B a )m + (26370A a b + 5274B a )m + 12600A a b +--R + +--R 5 +--R 2520B a +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R A a m + 27A a m + 295A a m + 1665A a m + 5104A a m +--R + +--R 5 5 +--R 8028A a m + 5040A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - B b m - 21B b m - 175B b m - 735B b m - 1624B b m - 1764B b m +--R + +--R 5 +--R - 720B b +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (- A b - 5B a b )m + (- 22A b - 110B a b )m +--R + +--R 5 4 4 5 4 3 +--R (- 190A b - 950B a b )m + (- 820A b - 4100B a b )m +--R + +--R 5 4 2 5 4 5 +--R (- 1849A b - 9245B a b )m + (- 2038A b - 10190B a b )m - 840A b +--R + +--R 4 +--R - 4200B a b +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 5A a b - 10B a b )m + (- 115A a b - 230B a b )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (- 1035A a b - 2070B a b )m + (- 4625A a b - 9250B a b )m +--R + +--R 4 2 3 2 4 2 3 +--R (- 10720A a b - 21440B a b )m + (- 12060A a b - 24120B a b )m +--R + +--R 4 2 3 +--R - 5040A a b - 10080B a b +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 10A a b - 10B a b )m + (- 240A a b - 240B a b )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (- 2260A a b - 2260B a b )m + (- 10560A a b - 10560B a b )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 25450A a b - 25450B a b )m + (- 29520A a b - 29520B a b )m +--R + +--R 2 3 3 2 +--R - 12600A a b - 12600B a b +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 10A a b - 5B a b)m + (- 250A a b - 125B a b)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 2470A a b - 1235B a b)m + (- 12190A a b - 6095B a b)m +--R + +--R 3 2 4 2 3 2 4 +--R (- 31120A a b - 15560B a b)m + (- 37960A a b - 18980B a b)m +--R + +--R 3 2 4 +--R - 16800A a b - 8400B a b +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (- 5A a b - B a )m + (- 130A a b - 26B a )m +--R + +--R 4 5 4 4 5 3 +--R (- 1350A a b - 270B a )m + (- 7100A a b - 1420B a )m +--R + +--R 4 5 2 4 5 4 +--R (- 19645A a b - 3929B a )m + (- 26370A a b - 5274B a )m - 12600A a b +--R + +--R 5 +--R - 2520B a +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - A a m - 27A a m - 295A a m - 1665A a m - 5104A a m - 8028A a m +--R + +--R 5 +--R - 5040A a +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1293 +t0:=x^5*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 11 5 4 10 4 2 3 9 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 8 3 2 4 7 4 5 6 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 1293 +r0:=1/6*a^5*A*x^6+1/7*a^4*(5*A*b+a*B)*x^7+5/8*a^3*b*(2*A*b+a*B)*x^8+_ + 10/9*a^2*b^2*(A*b+a*B)*x^9+1/2*a*b^3*(A*b+2*a*B)*x^10+_ + 1/11*b^4*(A*b+5*a*B)*x^11+1/12*b^5*B*x^12 +--R +--R +--R (2) +--R 1 5 12 1 5 5 4 11 1 4 2 3 10 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x +--R 12 11 11 2 +--R + +--R 10 2 3 10 3 2 9 5 3 2 5 4 8 5 4 1 5 7 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 9 9 4 8 7 7 +--R + +--R 1 5 6 +--R - A a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 12 1 5 5 4 11 1 4 2 3 10 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x +--R 12 11 11 2 +--R + +--R 10 2 3 10 3 2 9 5 3 2 5 4 8 5 4 1 5 7 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 9 9 4 8 7 7 +--R + +--R 1 5 6 +--R - A a x +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 1293 +t0:=x^4*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 10 5 4 9 4 2 3 8 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 7 3 2 4 6 4 5 5 5 4 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1293 +r0:=1/5*a^5*A*x^5+1/6*a^4*(5*A*b+a*B)*x^6+5/7*a^3*b*(2*A*b+a*B)*x^7+_ + 5/4*a^2*b^2*(A*b+a*B)*x^8+5/9*a*b^3*(A*b+2*a*B)*x^9+_ + 1/10*b^4*(A*b+5*a*B)*x^10+1/11*b^5*B*x^11 +--R +--R +--R (2) +--R 1 5 11 1 5 1 4 10 5 4 10 2 3 9 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 11 10 2 9 9 +--R + +--R 5 2 3 5 3 2 8 10 3 2 5 4 7 5 4 1 5 6 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 4 4 7 7 6 6 +--R + +--R 1 5 5 +--R - A a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 11 1 5 1 4 10 5 4 10 2 3 9 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 11 10 2 9 9 +--R + +--R 5 2 3 5 3 2 8 10 3 2 5 4 7 5 4 1 5 6 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 4 4 7 7 6 6 +--R + +--R 1 5 5 +--R - A a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 1293 +t0:=x^3*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 9 5 4 8 4 2 3 7 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1293 +r0:=1/4*a^5*A*x^4+1/5*a^4*(5*A*b+a*B)*x^5+5/6*a^3*b*(2*A*b+a*B)*x^6+_ + 10/7*a^2*b^2*(A*b+a*B)*x^7+5/8*a*b^3*(A*b+2*a*B)*x^8+_ + 1/9*b^4*(A*b+5*a*B)*x^9+1/10*b^5*B*x^10 +--R +--R +--R (2) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (A a b + - B a )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - A a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b)x + (A a b + - B a )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - A a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 1293 +t0:=x^2*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 8 5 4 7 4 2 3 6 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1293 +r0:=1/6*a^2*(A*b-a*B)*(a+b*x)^6/b^4-1/7*a*(2*A*b-3*a*B)*(a+b*x)^7/b^4+_ + 1/8*(A*b-3*a*B)*(a+b*x)^8/b^4+1/9*B*(a+b*x)^9/b^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 5 8 10 2 7 7 +--R - B b x + (- A b + - B a b )x + (- A a b + -- B a b )x +--R 9 8 8 7 7 +--R + +--R 5 2 7 5 3 6 6 3 6 4 5 5 5 4 5 1 5 4 4 +--R (- A a b + - B a b )x + (2A a b + B a b )x + (- A a b + - B a b )x +--R 3 3 4 4 +--R + +--R 1 5 4 3 1 8 1 9 +--R - A a b x + --- A a b - --- B a +--R 3 168 504 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 232 + +--S 233 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 5 4 10 2 3 7 +--R - B b x + (- A b + - B a b )x + (- A a b + -- B a b )x +--R 9 8 8 7 7 +--R + +--R 5 2 3 5 3 2 6 3 2 4 5 5 4 1 5 4 +--R (- A a b + - B a b )x + (2A a b + B a b)x + (- A a b + - B a )x +--R 3 3 4 4 +--R + +--R 1 5 3 +--R - A a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1293 +m0:=a0-r0 +--R +--R +--R 1 8 1 9 +--R - --- A a b + --- B a +--R 168 504 +--R (4) ---------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 234 + +--S 235 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 235 + +)clear all + +--S 236 of 1293 +t0:=x*(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 7 5 4 6 4 2 3 5 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 4 3 2 4 3 4 5 2 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1293 +r0:=-1/6*a*(A*b-a*B)*(a+b*x)^6/b^3+1/7*(A*b-2*a*B)*(a+b*x)^7/b^3+_ + 1/8*B*(a+b*x)^8/b^3 +--R +--R +--R (2) +--R 1 8 8 1 8 5 7 7 5 7 5 2 6 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 8 7 7 6 3 +--R + +--R 2 6 3 5 5 5 3 5 5 4 4 4 5 4 4 1 5 3 3 +--R (2A a b + 2B a b )x + (- A a b + - B a b )x + (- A a b + - B a b )x +--R 2 4 3 3 +--R + +--R 1 5 3 2 1 7 1 8 +--R - A a b x - -- A a b + --- B a +--R 2 42 168 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 237 + +--S 238 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 8 1 5 5 4 7 5 4 5 2 3 6 +--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x +--R 8 7 7 6 3 +--R + +--R 2 3 3 2 5 5 3 2 5 4 4 5 4 1 5 3 +--R (2A a b + 2B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x +--R 2 4 3 3 +--R + +--R 1 5 2 +--R - A a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1293 +m0:=a0-r0 +--R +--R +--R 1 7 1 8 +--R -- A a b - --- B a +--R 42 168 +--R (4) ------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 239 + +--S 240 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 240 + +)clear all + +--S 241 of 1293 +t0:=(a+b*x)^5*(A+B*x) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 241 + +--S 242 of 1293 +r0:=1/6*(A*b-a*B)*(a+b*x)^6/b^2+1/7*B*(a+b*x)^7/b^2 +--R +--R +--R (2) +--R 1 7 7 1 7 5 6 6 6 2 5 5 +--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x +--R 7 6 6 +--R + +--R 5 2 5 5 3 4 4 10 3 4 5 4 3 3 +--R (- A a b + - B a b )x + (-- A a b + - B a b )x +--R 2 2 3 3 +--R + +--R 5 4 3 1 5 2 2 5 2 1 6 1 7 +--R (- A a b + - B a b )x + A a b x + - A a b - -- B a +--R 2 2 6 42 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 242 + +--S 243 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 7 1 5 5 4 6 4 2 3 5 +--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x +--R 7 6 6 +--R + +--R 5 2 3 5 3 2 4 10 3 2 5 4 3 5 4 1 5 2 +--R (- A a b + - B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x +--R 2 2 3 3 2 2 +--R + +--R 5 +--R A a x +--R Type: Polynomial(Fraction(Integer)) +--E 243 + +--S 244 of 1293 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 +--R - - A a b + -- B a +--R 6 42 +--R (4) ------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 244 + +--S 245 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 245 + +)clear all + +--S 246 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1293 +r0:=5*a^4*A*b*x+5*a^3*A*b^2*x^2+10/3*a^2*A*b^3*x^3+5/4*a*A*b^4*x^4+_ + 1/5*A*b^5*x^5+1/6*B*(a+b*x)^6/b+a^5*A*log(x) +--R +--R +--R (2) +--R 5 6 6 6 5 5 +--R 60A a b log(x) + 10B b x + (12A b + 60B a b )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (75A a b + 150B a b )x + (200A a b + 200B a b )x +--R + +--R 3 3 4 2 2 4 2 5 6 +--R (300A a b + 150B a b )x + (300A a b + 60B a b)x + 10B a +--R / +--R 60b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 6 5 4 5 +--R 60A a log(x) + 10B b x + (12A b + 60B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (75A a b + 150B a b )x + (200A a b + 200B a b )x +--R + +--R 3 2 4 2 4 5 +--R (300A a b + 150B a b)x + (300A a b + 60B a )x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1293 +m0:=a0-r0 +--R +--R +--R 6 +--R B a +--R (4) - ---- +--R 6b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1293 +r0:=-a^5*A/x+5*a^3*b*(2*A*b+a*B)*x+5*a^2*b^2*(A*b+a*B)*x^2+_ + 5/3*a*b^3*(A*b+2*a*B)*x^3+1/4*b^4*(A*b+5*a*B)*x^4+_ + 1/5*b^5*B*x^5+a^4*(5*A*b+a*B)*log(x) +--R +--R +--R (2) +--R 4 5 5 6 5 4 5 +--R (300A a b + 60B a )x log(x) + 12B b x + (15A b + 75B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100A a b + 200B a b )x + (300A a b + 300B a b )x +--R + +--R 3 2 4 2 5 +--R (600A a b + 300B a b)x - 60A a +--R / +--R 60x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 6 5 4 5 +--R (300A a b + 60B a )x log(x) + 12B b x + (15A b + 75B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100A a b + 200B a b )x + (300A a b + 300B a b )x +--R + +--R 3 2 4 2 5 +--R (600A a b + 300B a b)x - 60A a +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1293 +r0:=-1/2*a^5*A/x^2-a^4*(5*A*b+a*B)/x+10*a^2*b^2*(A*b+a*B)*x+_ + 5/2*a*b^3*(A*b+2*a*B)*x^2+1/3*b^4*(A*b+5*a*B)*x^3+_ + 1/4*b^5*B*x^4+5*a^3*b*(2*A*b+a*B)*log(x) +--R +--R +--R (2) +--R 3 2 4 2 5 6 5 4 5 +--R (120A a b + 60B a b)x log(x) + 3B b x + (4A b + 20B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30A a b + 60B a b )x + (120A a b + 120B a b )x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 6A a +--R / +--R 2 +--R 12x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 5 6 5 4 5 +--R (120A a b + 60B a b)x log(x) + 3B b x + (4A b + 20B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30A a b + 60B a b )x + (120A a b + 120B a b )x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 6A a +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^4 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1293 +r0:=-1/3*a^5*A/x^3-1/2*a^4*(5*A*b+a*B)/x^2-5*a^3*b*(2*A*b+a*B)/x+_ + 5*a*b^3*(A*b+2*a*B)*x+1/2*b^4*(A*b+5*a*B)*x^2+1/3*b^5*B*x^3+_ + 10*a^2*b^2*(A*b+a*B)*log(x) +--R +--R +--R (2) +--R 2 3 3 2 3 5 6 5 4 5 +--R (60A a b + 60B a b )x log(x) + 2B b x + (3A b + 15B a b )x +--R + +--R 4 2 3 4 3 2 4 2 4 5 +--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x + (- 15A a b - 3B a )x +--R + +--R 5 +--R - 2A a +--R / +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 5 6 5 4 5 +--R (60A a b + 60B a b )x log(x) + 2B b x + (3A b + 15B a b )x +--R + +--R 4 2 3 4 3 2 4 2 4 5 +--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x + (- 15A a b - 3B a )x +--R + +--R 5 +--R - 2A a +--R / +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^5 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1293 +r0:=-1/4*a^5*A/x^4-1/3*a^4*(5*A*b+a*B)/x^3-5/2*a^3*b*(2*A*b+a*B)/x^2-_ + 10*a^2*b^2*(A*b+a*B)/x+b^4*(A*b+5*a*B)*x+1/2*b^5*B*x^2+_ + 5*a*b^3*(A*b+2*a*B)*log(x) +--R +--R +--R (2) +--R 4 2 3 4 5 6 5 4 5 +--R (60A a b + 120B a b )x log(x) + 6B b x + (12A b + 60B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x +--R + +--R 4 5 5 +--R (- 20A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 5 6 5 4 5 +--R (60A a b + 120B a b )x log(x) + 6B b x + (12A b + 60B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x +--R + +--R 4 5 5 +--R (- 20A a b - 4B a )x - 3A a +--R / +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^6 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1293 +r0:=-1/5*a^5*A/x^5-1/4*a^4*(5*A*b+a*B)/x^4-5/3*a^3*b*(2*A*b+a*B)/x^3-_ + 5*a^2*b^2*(A*b+a*B)/x^2-5*a*b^3*(A*b+2*a*B)/x+b^5*B*x+_ + b^4*(A*b+5*a*B)*log(x) +--R +--R +--R (2) +--R 5 4 5 5 6 4 2 3 4 +--R (60A b + 300B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x +--R + +--R 4 5 5 +--R (- 75A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 6 4 2 3 4 +--R (60A b + 300B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x +--R + +--R 4 5 5 +--R (- 75A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^7 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1293 +r0:=-1/5*a^5*B/x^5-5/4*a^4*b*B/x^4-10/3*a^3*b^2*B/x^3-5*a^2*b^3*B/x^2-_ + 5*a*b^4*B/x-1/6*A*(a+b*x)^6/(a*x^6)+b^5*B*log(x) +--R +--R +--R (2) +--R 5 6 6 6 5 2 4 5 +--R 60B a b x log(x) - 10A b x + (- 60A a b - 300B a b )x +--R + +--R 2 4 3 3 4 3 3 4 2 3 +--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x +--R + +--R 4 2 5 2 5 6 6 +--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60a x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 4 2 3 4 +--R 60B b x log(x) + (- 60A b - 300B a b )x + (- 150A a b - 300B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 200A a b - 200B a b )x + (- 150A a b - 75B a b)x +--R + +--R 4 5 5 +--R (- 60A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1293 +m0:=a0-r0 +--R +--R +--R 6 +--R A b +--R (4) ---- +--R 6a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^8 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1293 +r0:=-1/7*A*(a+b*x)^6/(a*x^7)+1/42*(A*b-7*a*B)*(a+b*x)^6/(a^2*x^6) +--R +--R +--R (2) +--R 1 7 1 6 7 2 5 6 1 2 5 5 3 4 5 +--R (-- A b - - B a b )x - B a b x + (- - A a b - - B a b )x +--R 42 6 2 2 +--R + +--R 5 3 4 10 4 3 4 5 4 3 5 5 2 3 +--R (- - A a b - -- B a b )x + (- - A a b - - B a b )x +--R 3 3 2 2 +--R + +--R 5 2 6 2 5 6 1 7 1 7 +--R (- 2A a b - B a b)x + (- - A a b - - B a )x - - A a +--R 6 6 7 +--R / +--R 2 7 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 282 + +--S 283 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 4 2 3 4 +--R - 42B b x + (- 21A b - 105B a b )x + (- 70A a b - 140B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 105A a b - 105B a b )x + (- 84A a b - 42B a b)x +--R + +--R 4 5 5 +--R (- 35A a b - 7B a )x - 6A a +--R / +--R 7 +--R 42x +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1293 +m0:=a0-r0 +--R +--R +--R 7 6 +--R - A b + 7B a b +--R (4) ---------------- +--R 2 +--R 42a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^9 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1293 +r0:=-1/8*A*(a+b*x)^6/(a*x^8)+1/28*(A*b-4*a*B)*(a+b*x)^6/(a^2*x^7)-_ + 1/168*b*(A*b-4*a*B)*(a+b*x)^6/(a^3*x^6) +--R +--R +--R (2) +--R 1 8 1 7 8 1 3 5 6 1 3 5 5 4 4 5 +--R (- --- A b + -- B a b )x - - B a b x + (- - A a b - - B a b )x +--R 168 42 2 3 3 +--R + +--R 5 4 4 5 5 3 4 5 3 6 2 3 +--R (- - A a b - - B a b )x + (- 2A a b - 2B a b )x +--R 4 2 +--R + +--R 5 6 2 5 7 2 5 7 1 8 1 8 +--R (- - A a b - - B a b)x + (- - A a b - - B a )x - - A a +--R 3 6 7 7 8 +--R / +--R 3 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 287 + +--S 288 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 4 2 3 4 +--R - 84B b x + (- 56A b - 280B a b )x + (- 210A a b - 420B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 336A a b - 336B a b )x + (- 280A a b - 140B a b)x +--R + +--R 4 5 5 +--R (- 120A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1293 +m0:=a0-r0 +--R +--R +--R 8 7 +--R A b - 4B a b +--R (4) -------------- +--R 3 +--R 168a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^10 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1293 +r0:=-1/9*a^5*A/x^9-1/8*a^4*(5*A*b+a*B)/x^8-5/7*a^3*b*(2*A*b+a*B)/x^7-_ + 5/3*a^2*b^2*(A*b+a*B)/x^6-a*b^3*(A*b+2*a*B)/x^5-_ + 1/4*b^4*(A*b+5*a*B)/x^4-1/3*b^5*B/x^3 +--R +--R +--R (2) +--R 1 5 6 1 5 5 4 5 4 2 3 4 +--R - - B b x + (- - A b - - B a b )x + (- A a b - 2B a b )x +--R 3 4 4 +--R + +--R 5 2 3 5 3 2 3 10 3 2 5 4 2 +--R (- - A a b - - B a b )x + (- -- A a b - - B a b)x +--R 3 3 7 7 +--R + +--R 5 4 1 5 1 5 +--R (- - A a b - - B a )x - - A a +--R 8 8 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 4 2 3 4 +--R - 168B b x + (- 126A b - 630B a b )x + (- 504A a b - 1008B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 840A a b - 840B a b )x + (- 720A a b - 360B a b)x +--R + +--R 4 5 5 +--R (- 315A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^11 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1293 +r0:=-1/10*a^5*A/x^10-1/9*a^4*(5*A*b+a*B)/x^9-5/8*a^3*b*(2*A*b+a*B)/x^8-_ + 10/7*a^2*b^2*(A*b+a*B)/x^7-5/6*a*b^3*(A*b+2*a*B)/x^6-_ + 1/5*b^4*(A*b+5*a*B)/x^5-1/4*b^5*B/x^4 +--R +--R +--R (2) +--R 1 5 6 1 5 4 5 5 4 5 2 3 4 +--R - - B b x + (- - A b - B a b )x + (- - A a b - - B a b )x +--R 4 5 6 3 +--R + +--R 10 2 3 10 3 2 3 5 3 2 5 4 2 +--R (- -- A a b - -- B a b )x + (- - A a b - - B a b)x +--R 7 7 4 8 +--R + +--R 5 4 1 5 1 5 +--R (- - A a b - - B a )x - -- A a +--R 9 9 10 +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 4 2 3 4 +--R - 630B b x + (- 504A b - 2520B a b )x + (- 2100A a b - 4200B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 3600A a b - 3600B a b )x + (- 3150A a b - 1575B a b)x +--R + +--R 4 5 5 +--R (- 1400A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1293 +t0:=(a+b*x)^5*(A+B*x)/x^12 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1293 +r0:=-1/11*a^5*A/x^11-1/10*a^4*(5*A*b+a*B)/x^10-5/9*a^3*b*(2*A*b+a*B)/x^9-_ + 5/4*a^2*b^2*(A*b+a*B)/x^8-5/7*a*b^3*(A*b+2*a*B)/x^7-_ + 1/6*b^4*(A*b+5*a*B)/x^6-1/5*b^5*B/x^5 +--R +--R +--R (2) +--R 1 5 6 1 5 5 4 5 5 4 10 2 3 4 +--R - - B b x + (- - A b - - B a b )x + (- - A a b - -- B a b )x +--R 5 6 6 7 7 +--R + +--R 5 2 3 5 3 2 3 10 3 2 5 4 2 +--R (- - A a b - - B a b )x + (- -- A a b - - B a b)x +--R 4 4 9 9 +--R + +--R 1 4 1 5 1 5 +--R (- - A a b - -- B a )x - -- A a +--R 2 10 11 +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 5 +--R - 2772B b x + (- 2310A b - 11550B a b )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (- 9900A a b - 19800B a b )x + (- 17325A a b - 17325B a b )x +--R + +--R 3 2 4 2 4 5 5 +--R (- 15400A a b - 7700B a b)x + (- 6930A a b - 1386B a )x - 1260A a +--R / +--R 11 +--R 13860x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1293 +t0:=x^m*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1293 +r0:=a^10*A*x^(1+m)/(1+m)+a^9*(10*A*b+a*B)*x^(2+m)/(2+m)+_ + 5*a^8*b*(9*A*b+2*a*B)*x^(3+m)/(3+m)+_ + 15*a^7*b^2*(8*A*b+3*a*B)*x^(4+m)/(4+m)+_ + 30*a^6*b^3*(7*A*b+4*a*B)*x^(5+m)/(5+m)+_ + 42*a^5*b^4*(6*A*b+5*a*B)*x^(6+m)/(6+m)+_ + 42*a^4*b^5*(5*A*b+6*a*B)*x^(7+m)/(7+m)+_ + 30*a^3*b^6*(4*A*b+7*a*B)*x^(8+m)/(8+m)+_ + 15*a^2*b^7*(3*A*b+8*a*B)*x^(9+m)/(9+m)+_ + 5*a*b^8*(2*A*b+9*a*B)*x^(10+m)/(10+m)+_ + b^9*(A*b+10*a*B)*x^(11+m)/(11+m)+b^10*B*x^(12+m)/(12+m) +--R +--R +--R (2) +--R 10 11 10 10 10 9 10 8 10 7 +--R B b m + 66B b m + 1925B b m + 32670B b m + 357423B b m +--R + +--R 10 6 10 5 10 4 10 3 +--R 2637558B b m + 13339535B b m + 45995730B b m + 105258076B b m +--R + +--R 10 2 10 10 +--R 150917976B b m + 120543840B b m + 39916800B b +--R * +--R m + 12 +--R x +--R + +--R 10 9 11 10 9 10 +--R (A b + 10B a b )m + (67A b + 670B a b )m +--R + +--R 10 9 9 10 9 8 +--R (1980A b + 19800B a b )m + (33990A b + 339900B a b )m +--R + +--R 10 9 7 10 9 6 +--R (375573A b + 3755730B a b )m + (2795331A b + 27953310B a b )m +--R + +--R 10 9 5 +--R (14241590A b + 142415900B a b )m +--R + +--R 10 9 4 +--R (49412660A b + 494126600B a b )m +--R + +--R 10 9 3 +--R (113667576A b + 1136675760B a b )m +--R + +--R 10 9 2 +--R (163671552A b + 1636715520B a b )m +--R + +--R 10 9 10 9 +--R (131172480A b + 1311724800B a b )m + 43545600A b + 435456000B a b +--R * +--R m + 11 +--R x +--R + +--R 9 2 8 11 9 2 8 10 +--R (10A a b + 45B a b )m + (680A a b + 3060B a b )m +--R + +--R 9 2 8 9 9 2 8 8 +--R (20370A a b + 91665B a b )m + (354000A a b + 1593000B a b )m +--R + +--R 9 2 8 7 +--R (3954630A a b + 17795835B a b )m +--R + +--R 9 2 8 6 +--R (29720040A a b + 133740180B a b )m +--R + +--R 9 2 8 5 +--R (152701910A a b + 687158595B a b )m +--R + +--R 9 2 8 4 +--R (533682400A a b + 2401570800B a b )m +--R + +--R 9 2 8 3 +--R (1235244360A a b + 5558599620B a b )m +--R + +--R 9 2 8 2 +--R (1787705280A a b + 8044673760B a b )m +--R + +--R 9 2 8 9 +--R (1438542720A a b + 6473442240B a b )m + 479001600A a b +--R + +--R 2 8 +--R 2155507200B a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 3 7 11 2 8 3 7 10 +--R (45A a b + 120B a b )m + (3105A a b + 8280B a b )m +--R + +--R 2 8 3 7 9 2 8 3 7 8 +--R (94320A a b + 251520B a b )m + (1660770A a b + 4428720B a b )m +--R + +--R 2 8 3 7 7 +--R (18778905A a b + 50077080B a b )m +--R + +--R 2 8 3 7 6 +--R (142688385A a b + 380502360B a b )m +--R + +--R 2 8 3 7 5 +--R (740364930A a b + 1974306480B a b )m +--R + +--R 2 8 3 7 4 +--R (2609872380A a b + 6959659680B a b )m +--R + +--R 2 8 3 7 3 +--R (6085456200A a b + 16227883200B a b )m +--R + +--R 2 8 3 7 2 +--R (8861564160A a b + 23630837760B a b )m +--R + +--R 2 8 3 7 2 8 +--R (7166102400A a b + 19109606400B a b )m + 2395008000A a b +--R + +--R 3 7 +--R 6386688000B a b +--R * +--R m + 9 +--R x +--R + +--R 3 7 4 6 11 3 7 4 6 10 +--R (120A a b + 210B a b )m + (8400A a b + 14700B a b )m +--R + +--R 3 7 4 6 9 3 7 4 6 8 +--R (258840A a b + 452970B a b )m + (4621680A a b + 8087940B a b )m +--R + +--R 3 7 4 6 7 +--R (52962120A a b + 92683710B a b )m +--R + +--R 3 7 4 6 6 +--R (407499120A a b + 713123460B a b )m +--R + +--R 3 7 4 6 5 +--R (2138834760A a b + 3742960830B a b )m +--R + +--R 3 7 4 6 4 +--R (7617739920A a b + 13331044860B a b )m +--R + +--R 3 7 4 6 3 +--R (17922900960A a b + 31365076680B a b )m +--R + +--R 3 7 4 6 2 +--R (26298578880A a b + 46022513040B a b )m +--R + +--R 3 7 4 6 3 7 +--R (21398515200A a b + 37447401600B a b )m + 7185024000A a b +--R + +--R 4 6 +--R 12573792000B a b +--R * +--R m + 8 +--R x +--R + +--R 4 6 5 5 11 4 6 5 5 10 +--R (210A a b + 252B a b )m + (14910A a b + 17892B a b )m +--R + +--R 4 6 5 5 9 4 6 5 5 8 +--R (466200A a b + 559440B a b )m + (8448300A a b + 10137960B a b )m +--R + +--R 4 6 5 5 7 +--R (98249130A a b + 117898956B a b )m +--R + +--R 4 6 5 5 6 +--R (766849230A a b + 920219076B a b )m +--R + +--R 4 6 5 5 5 +--R (4080003900A a b + 4896004680B a b )m +--R + +--R 4 6 5 5 4 +--R (14714704200A a b + 17657645040B a b )m +--R + +--R 4 6 5 5 3 +--R (35010506160A a b + 42012607392B a b )m +--R + +--R 4 6 5 5 2 +--R (51869583360A a b + 62243500032B a b )m +--R + +--R 4 6 5 5 4 6 +--R (42540422400A a b + 51048506880B a b )m + 14370048000A a b +--R + +--R 5 5 +--R 17244057600B a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 6 4 11 5 5 6 4 10 +--R (252A a b + 210B a b )m + (18144A a b + 15120B a b )m +--R + +--R 5 5 6 4 9 5 5 6 4 8 +--R (575820A a b + 479850B a b )m + (10599120A a b + 8832600B a b )m +--R + +--R 5 5 6 4 7 +--R (125269956A a b + 104391630B a b )m +--R + +--R 5 5 6 4 6 +--R (993892032A a b + 828243360B a b )m +--R + +--R 5 5 6 4 5 +--R (5374186020A a b + 4478488350B a b )m +--R + +--R 5 5 6 4 4 +--R (19684561680A a b + 16403801400B a b )m +--R + +--R 5 5 6 4 3 +--R (47508752592A a b + 39590627160B a b )m +--R + +--R 5 5 6 4 2 +--R (71279236224A a b + 59399363520B a b )m +--R + +--R 5 5 6 4 5 5 +--R (59077589760A a b + 49231324800B a b )m + 20118067200A a b +--R + +--R 6 4 +--R 16765056000B a b +--R * +--R m + 6 +--R x +--R + +--R 6 4 7 3 11 6 4 7 3 10 +--R (210A a b + 120B a b )m + (15330A a b + 8760B a b )m +--R + +--R 6 4 7 3 9 6 4 7 3 8 +--R (493920A a b + 282240B a b )m + (9242100A a b + 5281200B a b )m +--R + +--R 6 4 7 3 7 +--R (111176730A a b + 63529560B a b )m +--R + +--R 6 4 7 3 6 +--R (898709490A a b + 513548280B a b )m +--R + +--R 6 4 7 3 5 +--R (4954401060A a b + 2831086320B a b )m +--R + +--R 6 4 7 3 4 +--R (18502726200A a b + 10572986400B a b )m +--R + +--R 6 4 7 3 3 +--R (45499804560A a b + 25999888320B a b )m +--R + +--R 6 4 7 3 2 +--R (69444103680A a b + 39682344960B a b )m +--R + +--R 6 4 7 3 6 4 +--R (58406987520A a b + 33375421440B a b )m + 20118067200A a b +--R + +--R 7 3 +--R 11496038400B a b +--R * +--R m + 5 +--R x +--R + +--R 7 3 8 2 11 7 3 8 2 10 +--R (120A a b + 45B a b )m + (8880A a b + 3330B a b )m +--R + +--R 7 3 8 2 9 7 3 8 2 8 +--R (290520A a b + 108945B a b )m + (5530320A a b + 2073870B a b )m +--R + +--R 7 3 8 2 7 +--R (67814280A a b + 25430355B a b )m +--R + +--R 7 3 8 2 6 +--R (559938960A a b + 209977110B a b )m +--R + +--R 7 3 8 2 5 +--R (3159071880A a b + 1184651955B a b )m +--R + +--R 7 3 8 2 4 +--R (12092130480A a b + 4534548930B a b )m +--R + +--R 7 3 8 2 3 +--R (30496298400A a b + 11436111900B a b )m +--R + +--R 7 3 8 2 2 +--R (47696592960A a b + 17886222360B a b )m +--R + +--R 7 3 8 2 7 3 +--R (41000774400A a b + 15375290400B a b )m + 14370048000A a b +--R + +--R 8 2 +--R 5388768000B a b +--R * +--R m + 4 +--R x +--R + +--R 8 2 9 11 8 2 9 10 +--R (45A a b + 10B a b)m + (3375A a b + 750B a b)m +--R + +--R 8 2 9 9 8 2 9 8 +--R (112140A a b + 24920B a b)m + (2173230A a b + 482940B a b)m +--R + +--R 8 2 9 7 +--R (27206145A a b + 6045810B a b)m +--R + +--R 8 2 9 6 +--R (230080095A a b + 51128910B a b)m +--R + +--R 8 2 9 5 +--R (1334320110A a b + 296515580B a b)m +--R + +--R 8 2 9 4 +--R (5270196420A a b + 1171154760B a b)m +--R + +--R 8 2 9 3 +--R (13763718360A a b + 3058604080B a b)m +--R + +--R 8 2 9 2 +--R (22339514880A a b + 4964336640B a b)m +--R + +--R 8 2 9 8 2 +--R (19901635200A a b + 4422585600B a b)m + 7185024000A a b +--R + +--R 9 +--R 1596672000B a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 11 9 10 10 +--R (10A a b + B a )m + (760A a b + 76B a )m +--R + +--R 9 10 9 9 10 8 +--R (25650A a b + 2565B a )m + (506400A a b + 50640B a )m +--R + +--R 9 10 7 9 10 6 +--R (6481830A a b + 648183B a )m + (56302680A a b + 5630268B a )m +--R + +--R 9 10 5 +--R (337296950A a b + 33729695B a )m +--R + +--R 9 10 4 +--R (1386107600A a b + 138610760B a )m +--R + +--R 9 10 3 +--R (3799853160A a b + 379985316B a )m +--R + +--R 9 10 2 +--R (6540442560A a b + 654044256B a )m +--R + +--R 9 10 9 10 +--R (6234710400A a b + 623471040B a )m + 2395008000A a b + 239500800B a +--R * +--R m + 2 +--R x +--R + +--R 10 11 10 10 10 9 10 8 10 7 +--R A a m + 77A a m + 2640A a m + 53130A a m + 696333A a m +--R + +--R 10 6 10 5 10 4 +--R 6230301A a m + 38759930A a m + 167310220A a m +--R + +--R 10 3 10 2 10 10 +--R 489896616A a m + 924118272A a m + 1007441280A a m + 479001600A a +--R * +--R m + 1 +--R x +--R / +--R 12 11 10 9 8 7 6 +--R m + 78m + 2717m + 55770m + 749463m + 6926634m + 44990231m +--R + +--R 5 4 3 2 +--R 206070150m + 657206836m + 1414014888m + 1931559552m + 1486442880m +--R + +--R 479001600 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 10 10 9 10 8 10 7 +--R B b m + 66B b m + 1925B b m + 32670B b m + 357423B b m +--R + +--R 10 6 10 5 10 4 +--R 2637558B b m + 13339535B b m + 45995730B b m +--R + +--R 10 3 10 2 10 10 +--R 105258076B b m + 150917976B b m + 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623471040B a )m + 2395008000A a b +--R + +--R 10 +--R 239500800B a +--R * +--R 2 +--R x +--R + +--R 10 11 10 10 10 9 10 8 +--R A a m + 77A a m + 2640A a m + 53130A a m +--R + +--R 10 7 10 6 10 5 +--R 696333A a m + 6230301A a m + 38759930A a m +--R + +--R 10 4 10 3 10 2 +--R 167310220A a m + 489896616A a m + 924118272A a m +--R + +--R 10 10 +--R 1007441280A a m + 479001600A a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 10 11 10 10 10 9 10 8 10 7 +--R - B b m - 66B b m - 1925B b m - 32670B b m - 357423B b m +--R + +--R 10 6 10 5 10 4 +--R - 2637558B b m - 13339535B b m - 45995730B b m +--R + +--R 10 3 10 2 10 10 +--R - 105258076B b m - 150917976B b m - 120543840B b m - 39916800B b +--R * +--R m + 12 +--R x +--R + +--R 10 9 11 10 9 10 +--R (- A b - 10B a b )m + (- 67A b - 670B a b )m +--R + +--R 10 9 9 10 9 8 +--R (- 1980A b - 19800B a b )m + (- 33990A b - 339900B a b )m +--R + +--R 10 9 7 +--R (- 375573A b - 3755730B a b )m +--R + +--R 10 9 6 +--R (- 2795331A b - 27953310B a b )m +--R + +--R 10 9 5 +--R (- 14241590A b - 142415900B a b )m +--R + +--R 10 9 4 +--R (- 49412660A b - 494126600B a b )m +--R + +--R 10 9 3 +--R (- 113667576A b - 1136675760B a b )m +--R + +--R 10 9 2 +--R (- 163671552A b - 1636715520B a b )m +--R + +--R 10 9 10 +--R (- 131172480A b - 1311724800B a b )m - 43545600A b +--R + +--R 9 +--R - 435456000B a b +--R * +--R m + 11 +--R x +--R + +--R 9 2 8 11 9 2 8 10 +--R (- 10A a b - 45B a b )m + (- 680A a b - 3060B a b )m +--R + +--R 9 2 8 9 9 2 8 8 +--R (- 20370A a b - 91665B a b )m + (- 354000A a b - 1593000B a b )m +--R + +--R 9 2 8 7 +--R (- 3954630A a b - 17795835B a b )m +--R + +--R 9 2 8 6 +--R (- 29720040A a b - 133740180B a b )m +--R + +--R 9 2 8 5 +--R (- 152701910A a b - 687158595B a b )m +--R + +--R 9 2 8 4 +--R (- 533682400A a b - 2401570800B a b )m +--R + +--R 9 2 8 3 +--R (- 1235244360A a b - 5558599620B a b )m +--R + +--R 9 2 8 2 +--R (- 1787705280A a b - 8044673760B a b )m +--R + +--R 9 2 8 9 +--R (- 1438542720A a b - 6473442240B a b )m - 479001600A a b +--R + +--R 2 8 +--R - 2155507200B a b +--R * +--R m + 10 +--R x +--R + +--R 2 8 3 7 11 2 8 3 7 10 +--R (- 45A a b - 120B a b )m + (- 3105A a b - 8280B a b )m +--R + +--R 2 8 3 7 9 +--R (- 94320A a b - 251520B a b )m +--R + +--R 2 8 3 7 8 +--R (- 1660770A a b - 4428720B a b )m +--R + +--R 2 8 3 7 7 +--R (- 18778905A a b - 50077080B a b )m +--R + +--R 2 8 3 7 6 +--R (- 142688385A a b - 380502360B a b )m +--R + +--R 2 8 3 7 5 +--R (- 740364930A a b - 1974306480B a b )m +--R + +--R 2 8 3 7 4 +--R (- 2609872380A a b - 6959659680B a b )m +--R + +--R 2 8 3 7 3 +--R (- 6085456200A a b - 16227883200B a b )m +--R + +--R 2 8 3 7 2 +--R (- 8861564160A a b - 23630837760B a b )m +--R + +--R 2 8 3 7 2 8 +--R (- 7166102400A a b - 19109606400B a b )m - 2395008000A a b +--R + +--R 3 7 +--R - 6386688000B a b +--R * +--R m + 9 +--R x +--R + +--R 3 7 4 6 11 3 7 4 6 10 +--R (- 120A a b - 210B a b )m + (- 8400A a b - 14700B a b )m +--R + +--R 3 7 4 6 9 +--R (- 258840A a b - 452970B a b )m +--R + +--R 3 7 4 6 8 +--R (- 4621680A a b - 8087940B a b )m +--R + +--R 3 7 4 6 7 +--R (- 52962120A a b - 92683710B a b )m +--R + +--R 3 7 4 6 6 +--R (- 407499120A a b - 713123460B a b )m +--R + +--R 3 7 4 6 5 +--R (- 2138834760A a b - 3742960830B a b )m +--R + +--R 3 7 4 6 4 +--R (- 7617739920A a b - 13331044860B a b )m +--R + +--R 3 7 4 6 3 +--R (- 17922900960A a b - 31365076680B a b )m +--R + +--R 3 7 4 6 2 +--R (- 26298578880A a b - 46022513040B a b )m +--R + +--R 3 7 4 6 3 7 +--R (- 21398515200A a b - 37447401600B a b )m - 7185024000A a b +--R + +--R 4 6 +--R - 12573792000B a b +--R * +--R m + 8 +--R x +--R + +--R 4 6 5 5 11 4 6 5 5 10 +--R (- 210A a b - 252B a b )m + (- 14910A a b - 17892B a b )m +--R + +--R 4 6 5 5 9 +--R (- 466200A a b - 559440B a b )m +--R + +--R 4 6 5 5 8 +--R (- 8448300A a b - 10137960B a b )m +--R + +--R 4 6 5 5 7 +--R (- 98249130A a b - 117898956B a b )m +--R + +--R 4 6 5 5 6 +--R (- 766849230A a b - 920219076B a b )m +--R + +--R 4 6 5 5 5 +--R (- 4080003900A a b - 4896004680B a b )m +--R + +--R 4 6 5 5 4 +--R (- 14714704200A a b - 17657645040B a b )m +--R + +--R 4 6 5 5 3 +--R (- 35010506160A a b - 42012607392B a b )m +--R + +--R 4 6 5 5 2 +--R (- 51869583360A a b - 62243500032B a b )m +--R + +--R 4 6 5 5 4 6 +--R (- 42540422400A a b - 51048506880B a b )m - 14370048000A a b +--R + +--R 5 5 +--R - 17244057600B a b +--R * +--R m + 7 +--R x +--R + +--R 5 5 6 4 11 5 5 6 4 10 +--R (- 252A a b - 210B a b )m + (- 18144A a b - 15120B a b )m +--R + +--R 5 5 6 4 9 +--R (- 575820A a b - 479850B a b )m +--R + +--R 5 5 6 4 8 +--R (- 10599120A a b - 8832600B a b )m +--R + +--R 5 5 6 4 7 +--R (- 125269956A a b - 104391630B a b )m +--R + +--R 5 5 6 4 6 +--R (- 993892032A a b - 828243360B a b )m +--R + +--R 5 5 6 4 5 +--R (- 5374186020A a b - 4478488350B a b )m +--R + +--R 5 5 6 4 4 +--R (- 19684561680A a b - 16403801400B a b )m +--R + +--R 5 5 6 4 3 +--R (- 47508752592A a b - 39590627160B a b )m +--R + +--R 5 5 6 4 2 +--R (- 71279236224A a b - 59399363520B a b )m +--R + +--R 5 5 6 4 5 5 +--R (- 59077589760A a b - 49231324800B a b )m - 20118067200A a b +--R + +--R 6 4 +--R - 16765056000B a b +--R * +--R m + 6 +--R x +--R + +--R 6 4 7 3 11 6 4 7 3 10 +--R (- 210A a b - 120B a b )m + (- 15330A a b - 8760B a b )m +--R + +--R 6 4 7 3 9 +--R (- 493920A a b - 282240B a b )m +--R + +--R 6 4 7 3 8 +--R (- 9242100A a b - 5281200B a b )m +--R + +--R 6 4 7 3 7 +--R (- 111176730A a b - 63529560B a b )m +--R + +--R 6 4 7 3 6 +--R (- 898709490A a b - 513548280B a b )m +--R + +--R 6 4 7 3 5 +--R (- 4954401060A a b - 2831086320B a b )m +--R + +--R 6 4 7 3 4 +--R (- 18502726200A a b - 10572986400B a b )m +--R + +--R 6 4 7 3 3 +--R (- 45499804560A a b - 25999888320B a b )m +--R + +--R 6 4 7 3 2 +--R (- 69444103680A a b - 39682344960B a b )m +--R + +--R 6 4 7 3 6 4 +--R (- 58406987520A a b - 33375421440B a b )m - 20118067200A a b +--R + +--R 7 3 +--R - 11496038400B a b +--R * +--R m + 5 +--R x +--R + +--R 7 3 8 2 11 7 3 8 2 10 +--R (- 120A a b - 45B a b )m + (- 8880A a b - 3330B a b )m +--R + +--R 7 3 8 2 9 +--R (- 290520A a b - 108945B a b )m +--R + +--R 7 3 8 2 8 +--R (- 5530320A a b - 2073870B a b )m +--R + +--R 7 3 8 2 7 +--R (- 67814280A a b - 25430355B a b )m +--R + +--R 7 3 8 2 6 +--R (- 559938960A a b - 209977110B a b )m +--R + +--R 7 3 8 2 5 +--R (- 3159071880A a b - 1184651955B a b )m +--R + +--R 7 3 8 2 4 +--R (- 12092130480A a b - 4534548930B a b )m +--R + +--R 7 3 8 2 3 +--R (- 30496298400A a b - 11436111900B a b )m +--R + +--R 7 3 8 2 2 +--R (- 47696592960A a b - 17886222360B a b )m +--R + +--R 7 3 8 2 7 3 +--R (- 41000774400A a b - 15375290400B a b )m - 14370048000A a b +--R + +--R 8 2 +--R - 5388768000B a b +--R * +--R m + 4 +--R x +--R + +--R 8 2 9 11 8 2 9 10 +--R (- 45A a b - 10B a b)m + (- 3375A a b - 750B a b)m +--R + +--R 8 2 9 9 8 2 9 8 +--R (- 112140A a b - 24920B a b)m + (- 2173230A a b - 482940B a b)m +--R + +--R 8 2 9 7 +--R (- 27206145A a b - 6045810B a b)m +--R + +--R 8 2 9 6 +--R (- 230080095A a b - 51128910B a b)m +--R + +--R 8 2 9 5 +--R (- 1334320110A a b - 296515580B a b)m +--R + +--R 8 2 9 4 +--R (- 5270196420A a b - 1171154760B a b)m +--R + +--R 8 2 9 3 +--R (- 13763718360A a b - 3058604080B a b)m +--R + +--R 8 2 9 2 +--R (- 22339514880A a b - 4964336640B a b)m +--R + +--R 8 2 9 8 2 +--R (- 19901635200A a b - 4422585600B a b)m - 7185024000A a b +--R + +--R 9 +--R - 1596672000B a b +--R * +--R m + 3 +--R x +--R + +--R 9 10 11 9 10 10 +--R (- 10A a b - B a )m + (- 760A a b - 76B a )m +--R + +--R 9 10 9 9 10 8 +--R (- 25650A a b - 2565B a )m + (- 506400A a b - 50640B a )m +--R + +--R 9 10 7 9 10 6 +--R (- 6481830A a b - 648183B a )m + (- 56302680A a b - 5630268B a )m +--R + +--R 9 10 5 +--R (- 337296950A a b - 33729695B a )m +--R + +--R 9 10 4 +--R (- 1386107600A a b - 138610760B a )m +--R + +--R 9 10 3 +--R (- 3799853160A a b - 379985316B a )m +--R + +--R 9 10 2 +--R (- 6540442560A a b - 654044256B a )m +--R + +--R 9 10 9 +--R (- 6234710400A a b - 623471040B a )m - 2395008000A a b +--R + +--R 10 +--R - 239500800B a +--R * +--R m + 2 +--R x +--R + +--R 10 11 10 10 10 9 10 8 10 7 +--R - A a m - 77A a m - 2640A a m - 53130A a m - 696333A a m +--R + +--R 10 6 10 5 10 4 +--R - 6230301A a m - 38759930A a m - 167310220A a m +--R + +--R 10 3 10 2 10 +--R - 489896616A a m - 924118272A a m - 1007441280A a m +--R + +--R 10 +--R - 479001600A a +--R * +--R m + 1 +--R x +--R / +--R 12 11 10 9 8 7 6 +--R m + 78m + 2717m + 55770m + 749463m + 6926634m + 44990231m +--R + +--R 5 4 3 2 +--R 206070150m + 657206836m + 1414014888m + 1931559552m + 1486442880m +--R + +--R 479001600 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1293 +t0:=x^10*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 21 10 9 20 9 2 8 19 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 18 3 7 4 6 17 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 16 5 5 6 4 15 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 14 7 3 8 2 13 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 12 9 10 11 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 311 + +--S 312 of 1293 +r0:=1/11*a^10*A*x^11+1/12*a^9*(10*A*b+a*B)*x^12+_ + 5/13*a^8*b*(9*A*b+2*a*B)*x^13+15/14*a^7*b^2*(8*A*b+3*a*B)*x^14+_ + 2*a^6*b^3*(7*A*b+4*a*B)*x^15+21/8*a^5*b^4*(6*A*b+5*a*B)*x^16+_ + 42/17*a^4*b^5*(5*A*b+6*a*B)*x^17+5/3*a^3*b^6*(4*A*b+7*a*B)*x^18+_ + 15/19*a^2*b^7*(3*A*b+8*a*B)*x^19+1/4*a*b^8*(2*A*b+9*a*B)*x^20+_ + 1/21*b^9*(A*b+10*a*B)*x^21+1/22*b^10*B*x^22 +--R +--R +--R (2) +--R 1 10 22 1 10 10 9 21 1 9 9 2 8 20 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 22 21 21 2 4 +--R + +--R 45 2 8 120 3 7 19 20 3 7 35 4 6 18 +--R (-- A a b + --- B a b )x + (-- A a b + -- B a b )x +--R 19 19 3 3 +--R + +--R 210 4 6 252 5 5 17 63 5 5 105 6 4 16 +--R (--- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 4 8 +--R + +--R 6 4 7 3 15 60 7 3 45 8 2 14 +--R (14A a b + 8B a b )x + (-- A a b + -- B a b )x +--R 7 14 +--R + +--R 45 8 2 10 9 13 5 9 1 10 12 1 10 11 +--R (-- A a b + -- B a b)x + (- A a b + -- B a )x + -- A a x +--R 13 13 6 12 11 +--R Type: Polynomial(Fraction(Integer)) +--E 312 + +--S 313 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 22 1 10 10 9 21 1 9 9 2 8 20 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 22 21 21 2 4 +--R + +--R 45 2 8 120 3 7 19 20 3 7 35 4 6 18 +--R (-- A a b + --- B a b )x + (-- A a b + -- B a b )x +--R 19 19 3 3 +--R + +--R 210 4 6 252 5 5 17 63 5 5 105 6 4 16 +--R (--- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 4 8 +--R + +--R 6 4 7 3 15 60 7 3 45 8 2 14 +--R (14A a b + 8B a b )x + (-- A a b + -- B a b )x +--R 7 14 +--R + +--R 45 8 2 10 9 13 5 9 1 10 12 1 10 11 +--R (-- A a b + -- B a b)x + (- A a b + -- B a )x + -- A a x +--R 13 13 6 12 11 +--R Type: Polynomial(Fraction(Integer)) +--E 313 + +--S 314 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 314 + +--S 315 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 315 + +)clear all + +--S 316 of 1293 +t0:=x^9*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 20 10 9 19 9 2 8 18 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 17 3 7 4 6 16 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 15 5 5 6 4 14 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 13 7 3 8 2 12 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 11 9 10 10 10 9 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 316 + +--S 317 of 1293 +r0:=1/10*a^10*A*x^10+1/11*a^9*(10*A*b+a*B)*x^11+_ + 5/12*a^8*b*(9*A*b+2*a*B)*x^12+15/13*a^7*b^2*(8*A*b+3*a*B)*x^13+_ + 15/7*a^6*b^3*(7*A*b+4*a*B)*x^14+14/5*a^5*b^4*(6*A*b+5*a*B)*x^15+_ + 21/8*a^4*b^5*(5*A*b+6*a*B)*x^16+30/17*a^3*b^6*(4*A*b+7*a*B)*x^17+_ + 5/6*a^2*b^7*(3*A*b+8*a*B)*x^18+5/19*a*b^8*(2*A*b+9*a*B)*x^19+_ + 1/20*b^9*(A*b+10*a*B)*x^20+1/21*b^10*B*x^21 +--R +--R +--R (2) +--R 1 10 21 1 10 1 9 20 10 9 45 2 8 19 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 21 20 2 19 19 +--R + +--R 5 2 8 20 3 7 18 120 3 7 210 4 6 17 +--R (- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 2 3 17 17 +--R + +--R 105 4 6 63 5 5 16 84 5 5 6 4 15 +--R (--- A a b + -- B a b )x + (-- A a b + 14B a b )x +--R 8 4 5 +--R + +--R 6 4 60 7 3 14 120 7 3 45 8 2 13 +--R (15A a b + -- B a b )x + (--- A a b + -- B a b )x +--R 7 13 13 +--R + +--R 15 8 2 5 9 12 10 9 1 10 11 1 10 10 +--R (-- A a b + - B a b)x + (-- A a b + -- B a )x + -- A a x +--R 4 6 11 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 317 + +--S 318 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 21 1 10 1 9 20 10 9 45 2 8 19 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 21 20 2 19 19 +--R + +--R 5 2 8 20 3 7 18 120 3 7 210 4 6 17 +--R (- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 2 3 17 17 +--R + +--R 105 4 6 63 5 5 16 84 5 5 6 4 15 +--R (--- A a b + -- B a b )x + (-- A a b + 14B a b )x +--R 8 4 5 +--R + +--R 6 4 60 7 3 14 120 7 3 45 8 2 13 +--R (15A a b + -- B a b )x + (--- A a b + -- B a b )x +--R 7 13 13 +--R + +--R 15 8 2 5 9 12 10 9 1 10 11 1 10 10 +--R (-- A a b + - B a b)x + (-- A a b + -- B a )x + -- A a x +--R 4 6 11 11 10 +--R Type: Polynomial(Fraction(Integer)) +--E 318 + +--S 319 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 319 + +--S 320 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 320 + +)clear all + +--S 321 of 1293 +t0:=x^8*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 19 10 9 18 9 2 8 17 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 16 3 7 4 6 15 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 14 5 5 6 4 13 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 12 7 3 8 2 11 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 10 9 10 9 10 8 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 321 + +--S 322 of 1293 +r0:=1/9*a^10*A*x^9+1/10*a^9*(10*A*b+a*B)*x^10+_ + 5/11*a^8*b*(9*A*b+2*a*B)*x^11+5/4*a^7*b^2*(8*A*b+3*a*B)*x^12+_ + 30/13*a^6*b^3*(7*A*b+4*a*B)*x^13+3*a^5*b^4*(6*A*b+5*a*B)*x^14+_ + 14/5*a^4*b^5*(5*A*b+6*a*B)*x^15+15/8*a^3*b^6*(4*A*b+7*a*B)*x^16+_ + 15/17*a^2*b^7*(3*A*b+8*a*B)*x^17+5/18*a*b^8*(2*A*b+9*a*B)*x^18+_ + 1/19*b^9*(A*b+10*a*B)*x^19+1/20*b^10*B*x^20 +--R +--R +--R (2) +--R 1 10 20 1 10 10 9 19 5 9 5 2 8 18 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 20 19 19 9 2 +--R + +--R 45 2 8 120 3 7 17 15 3 7 105 4 6 16 +--R (-- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 2 8 +--R + +--R 4 6 84 5 5 15 5 5 6 4 14 +--R (14A a b + -- B a b )x + (18A a b + 15B a b )x +--R 5 +--R + +--R 210 6 4 120 7 3 13 7 3 15 8 2 12 +--R (--- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 4 +--R + +--R 45 8 2 10 9 11 9 1 10 10 1 10 9 +--R (-- A a b + -- B a b)x + (A a b + -- B a )x + - A a x +--R 11 11 10 9 +--R Type: Polynomial(Fraction(Integer)) +--E 322 + +--S 323 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 20 1 10 10 9 19 5 9 5 2 8 18 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x +--R 20 19 19 9 2 +--R + +--R 45 2 8 120 3 7 17 15 3 7 105 4 6 16 +--R (-- A a b + --- B a b )x + (-- A a b + --- B a b )x +--R 17 17 2 8 +--R + +--R 4 6 84 5 5 15 5 5 6 4 14 +--R (14A a b + -- B a b )x + (18A a b + 15B a b )x +--R 5 +--R + +--R 210 6 4 120 7 3 13 7 3 15 8 2 12 +--R (--- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 4 +--R + +--R 45 8 2 10 9 11 9 1 10 10 1 10 9 +--R (-- A a b + -- B a b)x + (A a b + -- B a )x + - A a x +--R 11 11 10 9 +--R Type: Polynomial(Fraction(Integer)) +--E 323 + +--S 324 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 324 + +--S 325 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 325 + +)clear all + +--S 326 of 1293 +t0:=x^7*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 18 10 9 17 9 2 8 16 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 15 3 7 4 6 14 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 13 5 5 6 4 12 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 11 7 3 8 2 10 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 9 9 10 8 10 7 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 326 + +--S 327 of 1293 +r0:=-1/11*a^7*(A*b-a*B)*(a+b*x)^11/b^9+_ + 1/12*a^6*(7*A*b-8*a*B)*(a+b*x)^12/b^9-_ + 7/13*a^5*(3*A*b-4*a*B)*(a+b*x)^13/b^9+_ + 1/2*a^4*(5*A*b-8*a*B)*(a+b*x)^14/b^9-_ + 7/3*a^3*(A*b-2*a*B)*(a+b*x)^15/b^9+_ + 7/16*a^2*(3*A*b-8*a*B)*(a+b*x)^16/b^9-_ + 7/17*a*(A*b-4*a*B)*(a+b*x)^17/b^9+_ + 1/18*(A*b-8*a*B)*(a+b*x)^18/b^9+1/19*B*(a+b*x)^19/b^9 +--R +--R +--R (2) +--R 1 19 19 1 19 5 18 18 10 18 45 2 17 17 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 19 18 9 17 17 +--R + +--R 45 2 17 15 3 16 16 3 16 4 15 15 +--R (-- A a b + -- B a b )x + (8A a b + 14B a b )x +--R 16 2 +--R + +--R 4 15 5 14 14 252 5 14 210 6 13 13 +--R (15A a b + 18B a b )x + (--- A a b + --- B a b )x +--R 13 13 +--R + +--R 35 6 13 7 12 12 120 7 12 45 8 11 11 +--R (-- A a b + 10B a b )x + (--- A a b + -- B a b )x +--R 2 11 11 +--R + +--R 9 8 11 9 10 10 10 9 10 1 10 9 9 1 10 9 8 +--R (- A a b + B a b )x + (-- A a b + - B a b )x + - A a b x +--R 2 9 9 8 +--R + +--R 1 18 1 19 +--R - ------ A a b + ------ B a +--R 350064 831402 +--R / +--R 9 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 19 1 10 5 9 18 10 9 45 2 8 17 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 19 18 9 17 17 +--R + +--R 45 2 8 15 3 7 16 3 7 4 6 15 +--R (-- A a b + -- B a b )x + (8A a b + 14B a b )x +--R 16 2 +--R + +--R 4 6 5 5 14 252 5 5 210 6 4 13 +--R (15A a b + 18B a b )x + (--- A a b + --- B a b )x +--R 13 13 +--R + +--R 35 6 4 7 3 12 120 7 3 45 8 2 11 +--R (-- A a b + 10B a b )x + (--- A a b + -- B a b )x +--R 2 11 11 +--R + +--R 9 8 2 9 10 10 9 1 10 9 1 10 8 +--R (- A a b + B a b)x + (-- A a b + - B a )x + - A a x +--R 2 9 9 8 +--R Type: Polynomial(Fraction(Integer)) +--E 328 + +--S 329 of 1293 +m0:=a0-r0 +--R +--R +--R 1 18 1 19 +--R ------ A a b - ------ B a +--R 350064 831402 +--R (4) ---------------------------- +--R 9 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 329 + +--S 330 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 330 + +)clear all + +--S 331 of 1293 +t0:=x^6*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 17 10 9 16 9 2 8 15 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 14 3 7 4 6 13 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 12 5 5 6 4 11 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 10 7 3 8 2 9 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 8 9 10 7 10 6 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 331 + +--S 332 of 1293 +r0:=1/11*a^6*(A*b-a*B)*(a+b*x)^11/b^8-1/12*a^5*(6*A*b-7*a*B)*(a+b*x)^12/b^8+_ + 3/13*a^4*(5*A*b-7*a*B)*(a+b*x)^13/b^8-_ + 5/14*a^3*(4*A*b-7*a*B)*(a+b*x)^14/b^8+_ + 1/3*a^2*(3*A*b-7*a*B)*(a+b*x)^15/b^8-_ + 3/16*a*(2*A*b-7*a*B)*(a+b*x)^16/b^8+_ + 1/17*(A*b-7*a*B)*(a+b*x)^17/b^8+1/18*B*(a+b*x)^18/b^8 +--R +--R +--R (2) +--R 1 18 18 1 18 10 17 17 5 17 45 2 16 16 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 18 17 17 8 16 +--R + +--R 2 16 3 15 15 60 3 15 4 14 14 +--R (3A a b + 8B a b )x + (-- A a b + 15B a b )x +--R 7 +--R + +--R 210 4 14 252 5 13 13 5 13 35 6 12 12 +--R (--- A a b + --- B a b )x + (21A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 6 12 120 7 11 11 7 11 9 8 10 10 +--R (--- A a b + --- B a b )x + (12A a b + - B a b )x +--R 11 11 2 +--R + +--R 8 10 10 9 9 9 5 9 9 1 10 8 8 1 10 8 7 +--R (5A a b + -- B a b )x + (- A a b + - B a b )x + - A a b x +--R 9 4 8 7 +--R + +--R 1 17 1 18 +--R ------ A a b - ------ B a +--R 136136 350064 +--R / +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 332 + +--S 333 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 18 1 10 10 9 17 5 9 45 2 8 16 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 18 17 17 8 16 +--R + +--R 2 8 3 7 15 60 3 7 4 6 14 +--R (3A a b + 8B a b )x + (-- A a b + 15B a b )x +--R 7 +--R + +--R 210 4 6 252 5 5 13 5 5 35 6 4 12 +--R (--- A a b + --- B a b )x + (21A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 6 4 120 7 3 11 7 3 9 8 2 10 +--R (--- A a b + --- B a b )x + (12A a b + - B a b )x +--R 11 11 2 +--R + +--R 8 2 10 9 9 5 9 1 10 8 1 10 7 +--R (5A a b + -- B a b)x + (- A a b + - B a )x + - A a x +--R 9 4 8 7 +--R Type: Polynomial(Fraction(Integer)) +--E 333 + +--S 334 of 1293 +m0:=a0-r0 +--R +--R +--R 1 17 1 18 +--R - ------ A a b + ------ B a +--R 136136 350064 +--R (4) ------------------------------ +--R 8 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 334 + +--S 335 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 335 + +)clear all + +--S 336 of 1293 +t0:=x^5*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 16 10 9 15 9 2 8 14 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 13 3 7 4 6 12 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 11 5 5 6 4 10 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 9 7 3 8 2 8 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 7 9 10 6 10 5 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 336 + +--S 337 of 1293 +r0:=-1/11*a^5*(A*b-a*B)*(a+b*x)^11/b^7+_ + 1/12*a^4*(5*A*b-6*a*B)*(a+b*x)^12/b^7-_ + 5/13*a^3*(2*A*b-3*a*B)*(a+b*x)^13/b^7+_ + 5/7*a^2*(A*b-2*a*B)*(a+b*x)^14/b^7-_ + 1/3*a*(A*b-3*a*B)*(a+b*x)^15/b^7+_ + 1/16*(A*b-6*a*B)*(a+b*x)^16/b^7+1/17*B*(a+b*x)^17/b^7 +--R +--R +--R (2) +--R 1 17 17 1 17 5 16 16 2 16 2 15 15 +--R -- B b x + (-- A b + - B a b )x + (- A a b + 3B a b )x +--R 17 16 8 3 +--R + +--R 45 2 15 60 3 14 14 120 3 14 210 4 13 13 +--R (-- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 14 7 13 13 +--R + +--R 35 4 13 5 12 12 252 5 12 210 6 11 11 +--R (-- A a b + 21B a b )x + (--- A a b + --- B a b )x +--R 2 11 11 +--R + +--R 6 11 7 10 10 40 7 10 8 9 9 +--R (21A a b + 12B a b )x + (-- A a b + 5B a b )x +--R 3 +--R + +--R 45 8 9 5 9 8 8 10 9 8 1 10 7 7 1 10 7 6 +--R (-- A a b + - B a b )x + (-- A a b + - B a b )x + - A a b x +--R 8 4 7 7 6 +--R + +--R 1 16 1 17 +--R - ----- A a b + ------ B a +--R 48048 136136 +--R / +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 17 1 10 5 9 16 2 9 2 8 15 +--R -- B b x + (-- A b + - B a b )x + (- A a b + 3B a b )x +--R 17 16 8 3 +--R + +--R 45 2 8 60 3 7 14 120 3 7 210 4 6 13 +--R (-- A a b + -- B a b )x + (--- A a b + --- B a b )x +--R 14 7 13 13 +--R + +--R 35 4 6 5 5 12 252 5 5 210 6 4 11 +--R (-- A a b + 21B a b )x + (--- A a b + --- B a b )x +--R 2 11 11 +--R + +--R 6 4 7 3 10 40 7 3 8 2 9 +--R (21A a b + 12B a b )x + (-- A a b + 5B a b )x +--R 3 +--R + +--R 45 8 2 5 9 8 10 9 1 10 7 1 10 6 +--R (-- A a b + - B a b)x + (-- A a b + - B a )x + - A a x +--R 8 4 7 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 338 + +--S 339 of 1293 +m0:=a0-r0 +--R +--R +--R 1 16 1 17 +--R ----- A a b - ------ B a +--R 48048 136136 +--R (4) --------------------------- +--R 7 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 339 + +--S 340 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 340 + +)clear all + +--S 341 of 1293 +t0:=x^4*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 15 10 9 14 9 2 8 13 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 12 3 7 4 6 11 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 10 5 5 6 4 9 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 8 7 3 8 2 7 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 6 9 10 5 10 4 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 341 + +--S 342 of 1293 +r0:=1/11*a^4*(A*b-a*B)*(a+b*x)^11/b^6-_ + 1/12*a^3*(4*A*b-5*a*B)*(a+b*x)^12/b^6+_ + 2/13*a^2*(3*A*b-5*a*B)*(a+b*x)^13/b^6-_ + 1/7*a*(2*A*b-5*a*B)*(a+b*x)^14/b^6+_ + 1/15*(A*b-5*a*B)*(a+b*x)^15/b^6+1/16*B*(a+b*x)^16/b^6 +--R +--R +--R (2) +--R 1 16 16 1 16 2 15 15 5 15 45 2 14 14 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 16 15 3 7 14 +--R + +--R 45 2 14 120 3 13 13 3 13 35 4 12 12 +--R (-- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 4 12 252 5 11 11 126 5 11 6 10 10 +--R (--- A a b + --- B a b )x + (--- A a b + 21B a b )x +--R 11 11 5 +--R + +--R 70 6 10 40 7 9 9 7 9 45 8 8 8 +--R (-- A a b + -- B a b )x + (15A a b + -- B a b )x +--R 3 3 8 +--R + +--R 45 8 8 10 9 7 7 5 9 7 1 10 6 6 1 10 6 5 +--R (-- A a b + -- B a b )x + (- A a b + - B a b )x + - A a b x +--R 7 7 3 6 5 +--R + +--R 1 15 1 16 +--R ----- A a b - ----- B a +--R 15015 48048 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 16 1 10 2 9 15 5 9 45 2 8 14 +--R -- B b x + (-- A b + - B a b )x + (- A a b + -- B a b )x +--R 16 15 3 7 14 +--R + +--R 45 2 8 120 3 7 13 3 7 35 4 6 12 +--R (-- A a b + --- B a b )x + (10A a b + -- B a b )x +--R 13 13 2 +--R + +--R 210 4 6 252 5 5 11 126 5 5 6 4 10 +--R (--- A a b + --- B a b )x + (--- A a b + 21B a b )x +--R 11 11 5 +--R + +--R 70 6 4 40 7 3 9 7 3 45 8 2 8 +--R (-- A a b + -- B a b )x + (15A a b + -- B a b )x +--R 3 3 8 +--R + +--R 45 8 2 10 9 7 5 9 1 10 6 1 10 5 +--R (-- A a b + -- B a b)x + (- A a b + - B a )x + - A a x +--R 7 7 3 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 343 + +--S 344 of 1293 +m0:=a0-r0 +--R +--R +--R 1 15 1 16 +--R - ----- A a b + ----- B a +--R 15015 48048 +--R (4) ---------------------------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 344 + +--S 345 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 345 + +)clear all + +--S 346 of 1293 +t0:=x^3*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 14 10 9 13 9 2 8 12 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 11 3 7 4 6 10 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 9 5 5 6 4 8 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 7 7 3 8 2 6 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 5 9 10 4 10 3 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 346 + +--S 347 of 1293 +r0:=-1/11*a^3*(A*b-a*B)*(a+b*x)^11/b^5+_ + 1/12*a^2*(3*A*b-4*a*B)*(a+b*x)^12/b^5-_ + 3/13*a*(A*b-2*a*B)*(a+b*x)^13/b^5+_ + 1/14*(A*b-4*a*B)*(a+b*x)^14/b^5+1/15*B*(a+b*x)^15/b^5 +--R +--R +--R (2) +--R 1 15 15 1 15 5 14 14 10 14 45 2 13 13 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 15 14 7 13 13 +--R + +--R 15 2 13 3 12 12 120 3 12 210 4 11 11 +--R (-- A a b + 10B a b )x + (--- A a b + --- B a b )x +--R 4 11 11 +--R + +--R 4 11 126 5 10 10 5 10 70 6 9 9 +--R (21A a b + --- B a b )x + (28A a b + -- B a b )x +--R 5 3 +--R + +--R 105 6 9 7 8 8 120 7 8 45 8 7 7 +--R (--- A a b + 15B a b )x + (--- A a b + -- B a b )x +--R 4 7 7 +--R + +--R 15 8 7 5 9 6 6 9 6 1 10 5 5 1 10 5 4 +--R (-- A a b + - B a b )x + (2A a b + - B a b )x + - A a b x +--R 2 3 5 4 +--R + +--R 1 14 1 15 +--R - ---- A a b + ----- B a +--R 4004 15015 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 15 1 10 5 9 14 10 9 45 2 8 13 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 15 14 7 13 13 +--R + +--R 15 2 8 3 7 12 120 3 7 210 4 6 11 +--R (-- A a b + 10B a b )x + (--- A a b + --- B a b )x +--R 4 11 11 +--R + +--R 4 6 126 5 5 10 5 5 70 6 4 9 +--R (21A a b + --- B a b )x + (28A a b + -- B a b )x +--R 5 3 +--R + +--R 105 6 4 7 3 8 120 7 3 45 8 2 7 +--R (--- A a b + 15B a b )x + (--- A a b + -- B a b )x +--R 4 7 7 +--R + +--R 15 8 2 5 9 6 9 1 10 5 1 10 4 +--R (-- A a b + - B a b)x + (2A a b + - B a )x + - A a x +--R 2 3 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 348 + +--S 349 of 1293 +m0:=a0-r0 +--R +--R +--R 1 14 1 15 +--R ---- A a b - ----- B a +--R 4004 15015 +--R (4) ------------------------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 349 + +--S 350 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 350 + +)clear all + +--S 351 of 1293 +t0:=x^2*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 13 10 9 12 9 2 8 11 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 10 3 7 4 6 9 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 8 5 5 6 4 7 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 6 7 3 8 2 5 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 4 9 10 3 10 2 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 351 + +--S 352 of 1293 +r0:=1/11*a^2*(A*b-a*B)*(a+b*x)^11/b^4-_ + 1/12*a*(2*A*b-3*a*B)*(a+b*x)^12/b^4+_ + 1/13*(A*b-3*a*B)*(a+b*x)^13/b^4+1/14*B*(a+b*x)^14/b^4 +--R +--R +--R (2) +--R 1 14 14 1 14 10 13 13 5 13 15 2 12 12 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 14 13 13 6 4 +--R + +--R 45 2 12 120 3 11 11 3 11 4 10 10 +--R (-- A a b + --- B a b )x + (12A a b + 21B a b )x +--R 11 11 +--R + +--R 70 4 10 5 9 9 63 5 9 105 6 8 8 +--R (-- A a b + 28B a b )x + (-- A a b + --- B a b )x +--R 3 2 4 +--R + +--R 6 8 120 7 7 7 7 7 15 8 6 6 +--R (30A a b + --- B a b )x + (20A a b + -- B a b )x +--R 7 2 +--R + +--R 8 6 9 5 5 5 9 5 1 10 4 4 1 10 4 3 +--R (9A a b + 2B a b )x + (- A a b + - B a b )x + - A a b x +--R 2 4 3 +--R + +--R 1 13 1 14 +--R --- A a b - ---- B a +--R 858 4004 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 14 1 10 10 9 13 5 9 15 2 8 12 +--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x +--R 14 13 13 6 4 +--R + +--R 45 2 8 120 3 7 11 3 7 4 6 10 +--R (-- A a b + --- B a b )x + (12A a b + 21B a b )x +--R 11 11 +--R + +--R 70 4 6 5 5 9 63 5 5 105 6 4 8 +--R (-- A a b + 28B a b )x + (-- A a b + --- B a b )x +--R 3 2 4 +--R + +--R 6 4 120 7 3 7 7 3 15 8 2 6 8 2 9 5 +--R (30A a b + --- B a b )x + (20A a b + -- B a b )x + (9A a b + 2B a b)x +--R 7 2 +--R + +--R 5 9 1 10 4 1 10 3 +--R (- A a b + - B a )x + - A a x +--R 2 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 353 + +--S 354 of 1293 +m0:=a0-r0 +--R +--R +--R 1 13 1 14 +--R - --- A a b + ---- B a +--R 858 4004 +--R (4) ------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 354 + +--S 355 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 355 + +)clear all + +--S 356 of 1293 +t0:=x*(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 12 10 9 11 9 2 8 10 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 9 3 7 4 6 8 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 7 5 5 6 4 6 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 5 7 3 8 2 4 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 3 9 10 2 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a x +--R Type: Polynomial(Integer) +--E 356 + +--S 357 of 1293 +r0:=-1/11*a*(A*b-a*B)*(a+b*x)^11/b^3+1/12*(A*b-2*a*B)*(a+b*x)^12/b^3+_ + 1/13*B*(a+b*x)^13/b^3 +--R +--R +--R (2) +--R 1 13 13 1 13 5 12 12 10 12 45 2 11 11 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 13 12 6 11 11 +--R + +--R 9 2 11 3 10 10 40 3 10 70 4 9 9 +--R (- A a b + 12B a b )x + (-- A a b + -- B a b )x +--R 2 3 3 +--R + +--R 105 4 9 63 5 8 8 5 8 6 7 7 +--R (--- A a b + -- B a b )x + (36A a b + 30B a b )x +--R 4 2 +--R + +--R 6 7 7 6 6 7 6 8 5 5 +--R (35A a b + 20B a b )x + (24A a b + 9B a b )x +--R + +--R 45 8 5 5 9 4 4 10 9 4 1 10 3 3 1 10 3 2 +--R (-- A a b + - B a b )x + (-- A a b + - B a b )x + - A a b x +--R 4 2 3 3 2 +--R + +--R 1 12 1 13 +--R - --- A a b + --- B a +--R 132 858 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 357 + +--S 358 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 13 1 10 5 9 12 10 9 45 2 8 11 +--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x +--R 13 12 6 11 11 +--R + +--R 9 2 8 3 7 10 40 3 7 70 4 6 9 +--R (- A a b + 12B a b )x + (-- A a b + -- B a b )x +--R 2 3 3 +--R + +--R 105 4 6 63 5 5 8 5 5 6 4 7 +--R (--- A a b + -- B a b )x + (36A a b + 30B a b )x +--R 4 2 +--R + +--R 6 4 7 3 6 7 3 8 2 5 45 8 2 5 9 4 +--R (35A a b + 20B a b )x + (24A a b + 9B a b )x + (-- A a b + - B a b)x +--R 4 2 +--R + +--R 10 9 1 10 3 1 10 2 +--R (-- A a b + - B a )x + - A a x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 358 + +--S 359 of 1293 +m0:=a0-r0 +--R +--R +--R 1 12 1 13 +--R --- A a b - --- B a +--R 132 858 +--R (4) ---------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 359 + +--S 360 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 360 + +)clear all + +--S 361 of 1293 +t0:=(a+b*x)^10*(A+B*x) +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 1293 +r0:=1/11*(A*b-a*B)*(a+b*x)^11/b^2+1/12*B*(a+b*x)^12/b^2 +--R +--R +--R (2) +--R 1 12 12 1 12 10 11 11 11 9 2 10 10 +--R -- B b x + (-- A b + -- B a b )x + (A a b + - B a b )x +--R 12 11 11 2 +--R + +--R 2 10 40 3 9 9 3 9 105 4 8 8 +--R (5A a b + -- B a b )x + (15A a b + --- B a b )x +--R 3 4 +--R + +--R 4 8 5 7 7 5 7 6 6 6 +--R (30A a b + 36B a b )x + (42A a b + 35B a b )x +--R + +--R 6 6 7 5 5 7 5 45 8 4 4 +--R (42A a b + 24B a b )x + (30A a b + -- B a b )x +--R 4 +--R + +--R 8 4 10 9 3 3 9 3 1 10 2 2 10 2 1 11 +--R (15A a b + -- B a b )x + (5A a b + - B a b )x + A a b x + -- A a b +--R 3 2 11 +--R + +--R 1 12 +--R - --- B a +--R 132 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 362 + +--S 363 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 10 12 1 10 10 9 11 9 9 2 8 10 +--R -- B b x + (-- A b + -- B a b )x + (A a b + - B a b )x +--R 12 11 11 2 +--R + +--R 2 8 40 3 7 9 3 7 105 4 6 8 +--R (5A a b + -- B a b )x + (15A a b + --- B a b )x +--R 3 4 +--R + +--R 4 6 5 5 7 5 5 6 4 6 6 4 7 3 5 +--R (30A a b + 36B a b )x + (42A a b + 35B a b )x + (42A a b + 24B a b )x +--R + +--R 7 3 45 8 2 4 8 2 10 9 3 9 1 10 2 +--R (30A a b + -- B a b )x + (15A a b + -- B a b)x + (5A a b + - B a )x +--R 4 3 2 +--R + +--R 10 +--R A a x +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 1293 +m0:=a0-r0 +--R +--R +--R 1 11 1 12 +--R - -- A a b + --- B a +--R 11 132 +--R (4) ----------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 364 + +--S 365 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 365 + +)clear all + +--S 366 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1293 +r0:=10*a^9*A*b*x+45/2*a^8*A*b^2*x^2+40*a^7*A*b^3*x^3+_ + 105/2*a^6*A*b^4*x^4+252/5*a^5*A*b^5*x^5+35*a^4*A*b^6*x^6+_ + 120/7*a^3*A*b^7*x^7+45/8*a^2*A*b^8*x^8+10/9*a*A*b^9*x^9+_ + 1/10*A*b^10*x^10+1/11*B*(a+b*x)^11/b+a^10*A*log(x) +--R +--R +--R (2) +--R 10 11 11 11 10 10 +--R 27720A a b log(x) + 2520B b x + (2772A b + 27720B a b )x +--R + +--R 10 2 9 9 2 9 3 8 8 +--R (30800A a b + 138600B a b )x + (155925A a b + 415800B a b )x +--R + +--R 3 8 4 7 7 4 7 5 6 6 +--R (475200A a b + 831600B a b )x + (970200A a b + 1164240B a b )x +--R + +--R 5 6 6 5 5 6 5 7 4 4 +--R (1397088A a b + 1164240B a b )x + (1455300A a b + 831600B a b )x +--R + +--R 7 4 8 3 3 8 3 9 2 2 +--R (1108800A a b + 415800B a b )x + (623700A a b + 138600B a b )x +--R + +--R 9 2 10 11 +--R (277200A a b + 27720B a b)x + 2520B a +--R / +--R 27720b +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 10 11 10 9 10 +--R 27720A a log(x) + 2520B b x + (2772A b + 27720B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (30800A a b + 138600B a b )x + (155925A a b + 415800B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (475200A a b + 831600B a b )x + (970200A a b + 1164240B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (1397088A a b + 1164240B a b )x + (1455300A a b + 831600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (1108800A a b + 415800B a b )x + (623700A a b + 138600B a b)x +--R + +--R 9 10 +--R (277200A a b + 27720B a )x +--R / +--R 27720 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1293 +m0:=a0-r0 +--R +--R +--R 11 +--R B a +--R (4) - ----- +--R 11b +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^2 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1293 +r0:=-a^10*A/x+5*a^8*b*(9*A*b+2*a*B)*x+15/2*a^7*b^2*(8*A*b+3*a*B)*x^2+_ + 10*a^6*b^3*(7*A*b+4*a*B)*x^3+21/2*a^5*b^4*(6*A*b+5*a*B)*x^4+_ + 42/5*a^4*b^5*(5*A*b+6*a*B)*x^5+5*a^3*b^6*(4*A*b+7*a*B)*x^6+_ + 15/7*a^2*b^7*(3*A*b+8*a*B)*x^7+5/8*a*b^8*(2*A*b+9*a*B)*x^8+_ + 1/9*b^9*(A*b+10*a*B)*x^9+1/10*b^10*B*x^10+a^9*(10*A*b+a*B)*log(x) +--R +--R +--R (2) +--R 9 10 10 11 +--R (25200A a b + 2520B a )x log(x) + 252B b x +--R + +--R 10 9 10 9 2 8 9 +--R (280A b + 2800B a b )x + (3150A a b + 14175B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (16200A a b + 43200B a b )x + (50400A a b + 88200B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (105840A a b + 127008B a b )x + (158760A a b + 132300B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (176400A a b + 100800B a b )x + (151200A a b + 56700B a b )x +--R + +--R 8 2 9 2 10 +--R (113400A a b + 25200B a b)x - 2520A a +--R / +--R 2520x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 10 10 11 +--R (25200A a b + 2520B a )x log(x) + 252B b x +--R + +--R 10 9 10 9 2 8 9 +--R (280A b + 2800B a b )x + (3150A a b + 14175B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (16200A a b + 43200B a b )x + (50400A a b + 88200B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (105840A a b + 127008B a b )x + (158760A a b + 132300B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (176400A a b + 100800B a b )x + (151200A a b + 56700B a b )x +--R + +--R 8 2 9 2 10 +--R (113400A a b + 25200B a b)x - 2520A a +--R / +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^3 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 1293 +r0:=-1/2*a^10*A/x^2-a^9*(10*A*b+a*B)/x+15*a^7*b^2*(8*A*b+3*a*B)*x+_ + 15*a^6*b^3*(7*A*b+4*a*B)*x^2+14*a^5*b^4*(6*A*b+5*a*B)*x^3+_ + 21/2*a^4*b^5*(5*A*b+6*a*B)*x^4+6*a^3*b^6*(4*A*b+7*a*B)*x^5+_ + 5/2*a^2*b^7*(3*A*b+8*a*B)*x^6+5/7*a*b^8*(2*A*b+9*a*B)*x^7+_ + 1/8*b^9*(A*b+10*a*B)*x^8+1/9*b^10*B*x^9+5*a^8*b*(9*A*b+2*a*B)*log(x) +--R +--R +--R (2) +--R 8 2 9 2 10 11 10 9 10 +--R (22680A a b + 5040B a b)x log(x) + 56B b x + (63A b + 630B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (720A a b + 3240B a b )x + (3780A a b + 10080B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (12096A a b + 21168B a b )x + (26460A a b + 31752B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (42336A a b + 35280B a b )x + (52920A a b + 30240B a b )x +--R + +--R 7 3 8 2 3 9 10 10 +--R (60480A a b + 22680B a b )x + (- 5040A a b - 504B a )x - 252A a +--R / +--R 2 +--R 504x +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 9 2 10 11 10 9 10 +--R (22680A a b + 5040B a b)x log(x) + 56B b x + (63A b + 630B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (720A a b + 3240B a b )x + (3780A a b + 10080B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (12096A a b + 21168B a b )x + (26460A a b + 31752B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (42336A a b + 35280B a b )x + (52920A a b + 30240B a b )x +--R + +--R 7 3 8 2 3 9 10 10 +--R (60480A a b + 22680B a b )x + (- 5040A a b - 504B a )x - 252A a +--R / +--R 2 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^4 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 1293 +r0:=-1/3*a^10*A/x^3-1/2*a^9*(10*A*b+a*B)/x^2-5*a^8*b*(9*A*b+2*a*B)/x+_ + 30*a^6*b^3*(7*A*b+4*a*B)*x+21*a^5*b^4*(6*A*b+5*a*B)*x^2+_ + 14*a^4*b^5*(5*A*b+6*a*B)*x^3+15/2*a^3*b^6*(4*A*b+7*a*B)*x^4+_ + 3*a^2*b^7*(3*A*b+8*a*B)*x^5+5/6*a*b^8*(2*A*b+9*a*B)*x^6+_ + 1/7*b^9*(A*b+10*a*B)*x^7+1/8*b^10*B*x^8+15*a^7*b^2*(8*A*b+3*a*B)*log(x) +--R +--R +--R (2) +--R 7 3 8 2 3 10 11 +--R (20160A a b + 7560B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (24A b + 240B a b )x + (280A a b + 1260B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1512A a b + 4032B a b )x + (5040A a b + 8820B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (11760A a b + 14112B a b )x + (21168A a b + 17640B a b )x +--R + +--R 6 4 7 3 4 8 2 9 2 +--R (35280A a b + 20160B a b )x + (- 7560A a b - 1680B a b)x +--R + +--R 9 10 10 +--R (- 840A a b - 84B a )x - 56A a +--R / +--R 3 +--R 168x +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 8 2 3 10 11 +--R (20160A a b + 7560B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (24A b + 240B a b )x + (280A a b + 1260B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1512A a b + 4032B a b )x + (5040A a b + 8820B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (11760A a b + 14112B a b )x + (21168A a b + 17640B a b )x +--R + +--R 6 4 7 3 4 8 2 9 2 +--R (35280A a b + 20160B a b )x + (- 7560A a b - 1680B a b)x +--R + +--R 9 10 10 +--R (- 840A a b - 84B a )x - 56A a +--R / +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^5 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1293 +r0:=-1/4*a^10*A/x^4-1/3*a^9*(10*A*b+a*B)/x^3-5/2*a^8*b*(9*A*b+2*a*B)/x^2-_ + 15*a^7*b^2*(8*A*b+3*a*B)/x+42*a^5*b^4*(6*A*b+5*a*B)*x+_ + 21*a^4*b^5*(5*A*b+6*a*B)*x^2+10*a^3*b^6*(4*A*b+7*a*B)*x^3+_ + 15/4*a^2*b^7*(3*A*b+8*a*B)*x^4+a*b^8*(2*A*b+9*a*B)*x^5+_ + 1/6*b^9*(A*b+10*a*B)*x^6+1/7*b^10*B*x^7+30*a^6*b^3*(7*A*b+4*a*B)*log(x) +--R +--R +--R (2) +--R 6 4 7 3 4 10 11 +--R (17640A a b + 10080B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (14A b + 140B a b )x + (168A a b + 756B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (945A a b + 2520B a b )x + (3360A a b + 5880B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (8820A a b + 10584B a b )x + (21168A a b + 17640B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 1890A a b - 420B a b)x +--R + +--R 9 10 10 +--R (- 280A a b - 28B a )x - 21A a +--R / +--R 4 +--R 84x +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 4 7 3 4 10 11 +--R (17640A a b + 10080B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (14A b + 140B a b )x + (168A a b + 756B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (945A a b + 2520B a b )x + (3360A a b + 5880B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (8820A a b + 10584B a b )x + (21168A a b + 17640B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 1890A a b - 420B a b)x +--R + +--R 9 10 10 +--R (- 280A a b - 28B a )x - 21A a +--R / +--R 4 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^6 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1293 +r0:=-1/5*a^10*A/x^5-1/4*a^9*(10*A*b+a*B)/x^4-5/3*a^8*b*(9*A*b+2*a*B)/x^3-_ + 15/2*a^7*b^2*(8*A*b+3*a*B)/x^2-30*a^6*b^3*(7*A*b+4*a*B)/x+_ + 42*a^4*b^5*(5*A*b+6*a*B)*x+15*a^3*b^6*(4*A*b+7*a*B)*x^2+_ + 5*a^2*b^7*(3*A*b+8*a*B)*x^3+5/4*a*b^8*(2*A*b+9*a*B)*x^4+_ + 1/5*b^9*(A*b+10*a*B)*x^5+1/6*b^10*B*x^6+42*a^5*b^4*(6*A*b+5*a*B)*log(x) +--R +--R +--R (2) +--R 5 5 6 4 5 10 11 +--R (15120A a b + 12600B a b )x log(x) + 10B b x +--R + +--R 10 9 10 9 2 8 9 +--R (12A b + 120B a b )x + (150A a b + 675B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (900A a b + 2400B a b )x + (3600A a b + 6300B a b )x +--R + +--R 4 6 5 5 6 6 4 7 3 4 +--R (12600A a b + 15120B a b )x + (- 12600A a b - 7200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 3600A a b - 1350B a b )x + (- 900A a b - 200B a b)x +--R + +--R 9 10 10 +--R (- 150A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 6 4 5 10 11 +--R (15120A a b + 12600B a b )x log(x) + 10B b x +--R + +--R 10 9 10 9 2 8 9 +--R (12A b + 120B a b )x + (150A a b + 675B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (900A a b + 2400B a b )x + (3600A a b + 6300B a b )x +--R + +--R 4 6 5 5 6 6 4 7 3 4 +--R (12600A a b + 15120B a b )x + (- 12600A a b - 7200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 3600A a b - 1350B a b )x + (- 900A a b - 200B a b)x +--R + +--R 9 10 10 +--R (- 150A a b - 15B a )x - 12A a +--R / +--R 5 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^7 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1293 +r0:=-1/6*a^10*A/x^6-1/5*a^9*(10*A*b+a*B)/x^5-5/4*a^8*b*(9*A*b+2*a*B)/x^4-_ + 5*a^7*b^2*(8*A*b+3*a*B)/x^3-15*a^6*b^3*(7*A*b+4*a*B)/x^2-_ + 42*a^5*b^4*(6*A*b+5*a*B)/x+30*a^3*b^6*(4*A*b+7*a*B)*x+_ + 15/2*a^2*b^7*(3*A*b+8*a*B)*x^2+5/3*a*b^8*(2*A*b+9*a*B)*x^3+_ + 1/4*b^9*(A*b+10*a*B)*x^4+1/5*b^10*B*x^5+42*a^4*b^5*(5*A*b+6*a*B)*log(x) +--R +--R +--R (2) +--R 4 6 5 5 6 10 11 +--R (12600A a b + 15120B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (15A b + 150B a b )x + (200A a b + 900B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1350A a b + 3600B a b )x + (7200A a b + 12600B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 15120A a b - 12600B a b )x + (- 6300A a b - 3600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2400A a b - 900B a b )x + (- 675A a b - 150B a b)x +--R + +--R 9 10 10 +--R (- 120A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 5 5 6 10 11 +--R (12600A a b + 15120B a b )x log(x) + 12B b x +--R + +--R 10 9 10 9 2 8 9 +--R (15A b + 150B a b )x + (200A a b + 900B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (1350A a b + 3600B a b )x + (7200A a b + 12600B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 15120A a b - 12600B a b )x + (- 6300A a b - 3600B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2400A a b - 900B a b )x + (- 675A a b - 150B a b)x +--R + +--R 9 10 10 +--R (- 120A a b - 12B a )x - 10A a +--R / +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^8 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1293 +r0:=-1/7*a^10*A/x^7-1/6*a^9*(10*A*b+a*B)/x^6-a^8*b*(9*A*b+2*a*B)/x^5-_ + 15/4*a^7*b^2*(8*A*b+3*a*B)/x^4-10*a^6*b^3*(7*A*b+4*a*B)/x^3-_ + 21*a^5*b^4*(6*A*b+5*a*B)/x^2-42*a^4*b^5*(5*A*b+6*a*B)/x+_ + 15*a^2*b^7*(3*A*b+8*a*B)*x+5/2*a*b^8*(2*A*b+9*a*B)*x^2+_ + 1/3*b^9*(A*b+10*a*B)*x^3+1/4*b^10*B*x^4+30*a^3*b^6*(4*A*b+7*a*B)*log(x) +--R +--R +--R (2) +--R 3 7 4 6 7 10 11 +--R (10080A a b + 17640B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (28A b + 280B a b )x + (420A a b + 1890B a b )x +--R + +--R 2 8 3 7 8 4 6 5 5 6 +--R (3780A a b + 10080B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 10584A a b - 8820B a b )x + (- 5880A a b - 3360B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2520A a b - 945B a b )x + (- 756A a b - 168B a b)x +--R + +--R 9 10 10 +--R (- 140A a b - 14B a )x - 12A a +--R / +--R 7 +--R 84x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 4 6 7 10 11 +--R (10080A a b + 17640B a b )x log(x) + 21B b x +--R + +--R 10 9 10 9 2 8 9 +--R (28A b + 280B a b )x + (420A a b + 1890B a b )x +--R + +--R 2 8 3 7 8 4 6 5 5 6 +--R (3780A a b + 10080B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 10584A a b - 8820B a b )x + (- 5880A a b - 3360B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2520A a b - 945B a b )x + (- 756A a b - 168B a b)x +--R + +--R 9 10 10 +--R (- 140A a b - 14B a )x - 12A a +--R / +--R 7 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^9 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1293 +r0:=-1/8*a^10*A/x^8-1/7*a^9*(10*A*b+a*B)/x^7-5/6*a^8*b*(9*A*b+2*a*B)/x^6-_ + 3*a^7*b^2*(8*A*b+3*a*B)/x^5-15/2*a^6*b^3*(7*A*b+4*a*B)/x^4-_ + 14*a^5*b^4*(6*A*b+5*a*B)/x^3-21*a^4*b^5*(5*A*b+6*a*B)/x^2-_ + 30*a^3*b^6*(4*A*b+7*a*B)/x+5*a*b^8*(2*A*b+9*a*B)*x+_ + 1/2*b^9*(A*b+10*a*B)*x^2+1/3*b^10*B*x^3+15*a^2*b^7*(3*A*b+8*a*B)*log(x) +--R +--R +--R (2) +--R 2 8 3 7 8 10 11 +--R (7560A a b + 20160B a b )x log(x) + 56B b x +--R + +--R 10 9 10 9 2 8 9 +--R (84A b + 840B a b )x + (1680A a b + 7560B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 20160A a b - 35280B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 14112A a b - 11760B a b )x + (- 8820A a b - 5040B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 4032A a b - 1512B a b )x + (- 1260A a b - 280B a b)x +--R + +--R 9 10 10 +--R (- 240A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 3 7 8 10 11 +--R (7560A a b + 20160B a b )x log(x) + 56B b x +--R + +--R 10 9 10 9 2 8 9 +--R (84A b + 840B a b )x + (1680A a b + 7560B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 20160A a b - 35280B a b )x + (- 17640A a b - 21168B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 14112A a b - 11760B a b )x + (- 8820A a b - 5040B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 4032A a b - 1512B a b )x + (- 1260A a b - 280B a b)x +--R + +--R 9 10 10 +--R (- 240A a b - 24B a )x - 21A a +--R / +--R 8 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^10 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1293 +r0:=-1/9*a^10*A/x^9-1/8*a^9*(10*A*b+a*B)/x^8-5/7*a^8*b*(9*A*b+2*a*B)/x^7-_ + 5/2*a^7*b^2*(8*A*b+3*a*B)/x^6-6*a^6*b^3*(7*A*b+4*a*B)/x^5-_ + 21/2*a^5*b^4*(6*A*b+5*a*B)/x^4-14*a^4*b^5*(5*A*b+6*a*B)/x^3-_ + 15*a^3*b^6*(4*A*b+7*a*B)/x^2-15*a^2*b^7*(3*A*b+8*a*B)/x+_ + b^9*(A*b+10*a*B)*x+1/2*b^10*B*x^2+5*a*b^8*(2*A*b+9*a*B)*log(x) +--R +--R +--R (2) +--R 9 2 8 9 10 11 +--R (5040A a b + 22680B a b )x log(x) + 252B b x +--R + +--R 10 9 10 2 8 3 7 8 +--R (504A b + 5040B a b )x + (- 22680A a b - 60480B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 30240A a b - 52920B a b )x + (- 35280A a b - 42336B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 31752A a b - 26460B a b )x + (- 21168A a b - 12096B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 3240A a b - 720B a b)x +--R + +--R 9 10 10 +--R (- 630A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 2 8 9 10 11 +--R (5040A a b + 22680B a b )x log(x) + 252B b x +--R + +--R 10 9 10 2 8 3 7 8 +--R (504A b + 5040B a b )x + (- 22680A a b - 60480B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 30240A a b - 52920B a b )x + (- 35280A a b - 42336B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 31752A a b - 26460B a b )x + (- 21168A a b - 12096B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 10080A a b - 3780B a b )x + (- 3240A a b - 720B a b)x +--R + +--R 9 10 10 +--R (- 630A a b - 63B a )x - 56A a +--R / +--R 9 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^11 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1293 +r0:=-1/10*a^10*A/x^10-1/9*a^9*(10*A*b+a*B)/x^9-5/8*a^8*b*(9*A*b+2*a*B)/x^8-_ + 15/7*a^7*b^2*(8*A*b+3*a*B)/x^7-5*a^6*b^3*(7*A*b+4*a*B)/x^6-_ + 42/5*a^5*b^4*(6*A*b+5*a*B)/x^5-21/2*a^4*b^5*(5*A*b+6*a*B)/x^4-_ + 10*a^3*b^6*(4*A*b+7*a*B)/x^3-15/2*a^2*b^7*(3*A*b+8*a*B)/x^2-_ + 5*a*b^8*(2*A*b+9*a*B)/x+b^10*B*x+b^9*(A*b+10*a*B)*log(x) +--R +--R +--R (2) +--R 10 9 10 10 11 +--R (2520A b + 25200B a b )x log(x) + 2520B b x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 25200A a b - 113400B a b )x + (- 56700A a b - 151200B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 100800A a b - 176400B a b )x + (- 132300A a b - 158760B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 127008A a b - 105840B a b )x + (- 88200A a b - 50400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 43200A a b - 16200B a b )x + (- 14175A a b - 3150B a b)x +--R + +--R 9 10 10 +--R (- 2800A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 10 10 11 +--R (2520A b + 25200B a b )x log(x) + 2520B b x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 25200A a b - 113400B a b )x + (- 56700A a b - 151200B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 100800A a b - 176400B a b )x + (- 132300A a b - 158760B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 127008A a b - 105840B a b )x + (- 88200A a b - 50400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 43200A a b - 16200B a b )x + (- 14175A a b - 3150B a b)x +--R + +--R 9 10 10 +--R (- 2800A a b - 280B a )x - 252A a +--R / +--R 10 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^12 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1293 +r0:=-1/10*a^10*B/x^10-10/9*a^9*b*B/x^9-45/8*a^8*b^2*B/x^8-_ + 120/7*a^7*b^3*B/x^7-35*a^6*b^4*B/x^6-252/5*a^5*b^5*B/x^5-_ + 105/2*a^4*b^6*B/x^4-40*a^3*b^7*B/x^3-45/2*a^2*b^8*B/x^2-_ + 10*a*b^9*B/x-1/11*A*(a+b*x)^11/(a*x^11)+b^10*B*log(x) +--R +--R +--R (2) +--R 10 11 11 11 10 2 9 10 +--R 27720B a b x log(x) - 2520A b x + (- 27720A a b - 277200B a b )x +--R + +--R 2 9 3 8 9 3 8 4 7 8 +--R (- 138600A a b - 623700B a b )x + (- 415800A a b - 1108800B a b )x +--R + +--R 4 7 5 6 7 5 6 6 5 6 +--R (- 831600A a b - 1455300B a b )x + (- 1164240A a b - 1397088B a b )x +--R + +--R 6 5 7 4 5 7 4 8 3 4 +--R (- 1164240A a b - 970200B a b )x + (- 831600A a b - 475200B a b )x +--R + +--R 8 3 9 2 3 9 2 10 2 +--R (- 415800A a b - 155925B a b )x + (- 138600A a b - 30800B a b)x +--R + +--R 10 11 11 +--R (- 27720A a b - 2772B a )x - 2520A a +--R / +--R 11 +--R 27720a x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R 27720B b x log(x) + (- 27720A b - 277200B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 138600A a b - 623700B a b )x + (- 415800A a b - 1108800B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 831600A a b - 1455300B a b )x + (- 1164240A a b - 1397088B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 1164240A a b - 970200B a b )x + (- 831600A a b - 475200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 415800A a b - 155925B a b )x + (- 138600A a b - 30800B a b)x +--R + +--R 9 10 10 +--R (- 27720A a b - 2772B a )x - 2520A a +--R / +--R 11 +--R 27720x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1293 +m0:=a0-r0 +--R +--R +--R 11 +--R A b +--R (4) ----- +--R 11a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^13 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1293 +r0:=-1/12*A*(a+b*x)^11/(a*x^12)+1/132*(A*b-12*a*B)*(a+b*x)^11/(a^2*x^11) +--R +--R +--R (2) +--R 1 12 1 11 12 2 10 11 1 2 10 3 9 10 +--R (--- A b - -- B a b )x - B a b x + (- - A a b - 5B a b )x +--R 132 11 2 +--R + +--R 10 3 9 4 8 9 45 4 8 5 7 8 +--R (- -- A a b - 15B a b )x + (- -- A a b - 30B a b )x +--R 3 4 +--R + +--R 5 7 6 6 7 6 6 7 5 6 +--R (- 24A a b - 42B a b )x + (- 35A a b - 42B a b )x +--R + +--R 7 5 8 4 5 105 8 4 9 3 4 +--R (- 36A a b - 30B a b )x + (- --- A a b - 15B a b )x +--R 4 +--R + +--R 40 9 3 10 2 3 9 10 2 11 2 +--R (- -- A a b - 5B a b )x + (- - A a b - B a b)x +--R 3 2 +--R + +--R 10 11 1 12 1 12 +--R (- -- A a b - -- B a )x - -- A a +--R 11 11 12 +--R / +--R 2 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 427 + +--S 428 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 9 2 8 9 +--R - 132B b x + (- 66A b - 660B a b )x + (- 440A a b - 1980B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (- 1485A a b - 3960B a b )x + (- 3168A a b - 5544B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (- 4620A a b - 5544B a b )x + (- 4752A a b - 3960B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (- 3465A a b - 1980B a b )x + (- 1760A a b - 660B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (- 594A a b - 132B a b)x + (- 120A a b - 12B a )x - 11A a +--R / +--R 12 +--R 132x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1293 +m0:=a0-r0 +--R +--R +--R 12 11 +--R - A b + 12B a b +--R (4) ------------------- +--R 2 +--R 132a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^14 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 1293 +r0:=-1/13*A*(a+b*x)^11/(a*x^13)+1/156*(2*A*b-13*a*B)*(a+b*x)^11/(a^2*x^12)-_ + 1/1716*b*(2*A*b-13*a*B)*(a+b*x)^11/(a^3*x^11) +--R +--R +--R (2) +--R 1 13 1 12 13 1 3 10 11 +--R (- --- A b + --- B a b )x - - B a b x +--R 858 132 2 +--R + +--R 1 3 10 10 4 9 10 5 4 9 45 5 8 9 +--R (- - A a b - -- B a b )x + (- - A a b - -- B a b )x +--R 3 3 2 4 +--R + +--R 5 8 6 7 8 6 7 7 6 7 +--R (- 9A a b - 24B a b )x + (- 20A a b - 35B a b )x +--R + +--R 7 6 8 5 6 63 8 5 105 9 4 5 +--R (- 30A a b - 36B a b )x + (- -- A a b - --- B a b )x +--R 2 4 +--R + +--R 70 9 4 40 10 3 4 10 3 9 11 2 3 +--R (- -- A a b - -- B a b )x + (- 12A a b - - B a b )x +--R 3 3 2 +--R + +--R 45 11 2 10 12 2 5 12 1 13 1 13 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 11 11 6 12 13 +--R / +--R 3 13 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 858B b x + (- 572A b - 5720B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 4290A a b - 19305B a b )x + (- 15444A a b - 41184B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 34320A a b - 60060B a b )x + (- 51480A a b - 61776B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 54054A a b - 45045B a b )x + (- 40040A a b - 22880B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 20592A a b - 7722B a b )x + (- 7020A a b - 1560B a b)x +--R + +--R 9 10 10 +--R (- 1430A a b - 143B a )x - 132A a +--R / +--R 13 +--R 1716x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1293 +m0:=a0-r0 +--R +--R +--R 13 12 +--R 2A b - 13B a b +--R (4) ------------------ +--R 3 +--R 1716a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^15 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 1293 +r0:=-1/14*A*(a+b*x)^11/(a*x^14)+1/182*(3*A*b-14*a*B)*(a+b*x)^11/(a^2*x^13)-_ + 1/1092*b*(3*A*b-14*a*B)*(a+b*x)^11/(a^3*x^12)+_ + 1/12012*b^2*(3*A*b-14*a*B)*(a+b*x)^11/(a^4*x^11) +--R +--R +--R (2) +--R 1 14 1 13 14 1 4 10 11 +--R (---- A b - --- B a b )x - - B a b x +--R 4004 858 3 +--R + +--R 1 4 10 5 5 9 10 5 9 6 8 9 +--R (- - A a b - - B a b )x + (- 2A a b - 9B a b )x +--R 4 2 +--R + +--R 15 6 8 7 7 8 120 7 7 8 6 7 +--R (- -- A a b - 20B a b )x + (- --- A a b - 30B a b )x +--R 2 7 +--R + +--R 105 8 6 63 9 5 6 9 5 70 10 4 5 +--R (- --- A a b - -- B a b )x + (- 28A a b - -- B a b )x +--R 4 2 3 +--R + +--R 10 4 11 3 4 120 11 3 45 12 2 3 +--R (- 21A a b - 12B a b )x + (- --- A a b - -- B a b )x +--R 11 11 +--R + +--R 15 12 2 5 13 2 10 13 1 14 1 14 +--R (- -- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 4 6 13 13 14 +--R / +--R 4 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 437 + +--S 438 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 4004B b x + (- 3003A b - 30030B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 24024A a b - 108108B a b )x + (- 90090A a b - 240240B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 205920A a b - 360360B a b )x + (- 315315A a b - 378378B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 336336A a b - 280280B a b )x + (- 252252A a b - 144144B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 131040A a b - 49140B a b )x + (- 45045A a b - 10010B a b)x +--R + +--R 9 10 10 +--R (- 9240A a b - 924B a )x - 858A a +--R / +--R 14 +--R 12012x +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1293 +m0:=a0-r0 +--R +--R +--R 14 13 +--R - 3A b + 14B a b +--R (4) -------------------- +--R 4 +--R 12012a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^16 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1293 +r0:=-1/15*A*(a+b*x)^11/(a*x^15)+1/210*(4*A*b-15*a*B)*(a+b*x)^11/(a^2*x^14)-_ + 1/910*b*(4*A*b-15*a*B)*(a+b*x)^11/(a^3*x^13)+_ + 1/5460*b^2*(4*A*b-15*a*B)*(a+b*x)^11/(a^4*x^12)-_ + 1/60060*b^3*(4*A*b-15*a*B)*(a+b*x)^11/(a^5*x^11) +--R +--R +--R (2) +--R 1 15 1 14 15 1 5 10 11 +--R (- ----- A b + ---- B a b )x - - B a b x +--R 15015 4004 4 +--R + +--R 1 5 10 6 9 10 5 6 9 15 7 8 9 +--R (- - A a b - 2B a b )x + (- - A a b - -- B a b )x +--R 5 3 2 +--R + +--R 45 7 8 120 8 7 8 8 7 105 9 6 7 +--R (- -- A a b - --- B a b )x + (- 15A a b - --- B a b )x +--R 7 7 4 +--R + +--R 70 9 6 10 5 6 126 10 5 11 4 5 +--R (- -- A a b - 28B a b )x + (- --- A a b - 21B a b )x +--R 3 5 +--R + +--R 210 11 4 120 12 3 4 12 3 15 13 2 3 +--R (- --- A a b - --- B a b )x + (- 10A a b - -- B a b )x +--R 11 11 4 +--R + +--R 45 13 2 10 14 2 5 14 1 15 1 15 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 13 13 7 14 15 +--R / +--R 5 15 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 15015B b x + (- 12012A b - 120120B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 100100A a b - 450450B a b )x + (- 386100A a b - 1029600B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 900900A a b - 1576575B a b )x + (- 1401400A a b - 1681680B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 1513512A a b - 1261260B a b )x + (- 1146600A a b - 655200B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 600600A a b - 225225B a b )x + (- 207900A a b - 46200B a b)x +--R + +--R 9 10 10 +--R (- 42900A a b - 4290B a )x - 4004A a +--R / +--R 15 +--R 60060x +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1293 +m0:=a0-r0 +--R +--R +--R 15 14 +--R 4A b - 15B a b +--R (4) ------------------ +--R 5 +--R 60060a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^17 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 1293 +r0:=-1/16*A*(a+b*x)^11/(a*x^16)+1/240*(5*A*b-16*a*B)*(a+b*x)^11/(a^2*x^15)-_ + 1/840*b*(5*A*b-16*a*B)*(a+b*x)^11/(a^3*x^14)+_ + 1/3640*b^2*(5*A*b-16*a*B)*(a+b*x)^11/(a^4*x^13)-_ + 1/21840*b^3*(5*A*b-16*a*B)*(a+b*x)^11/(a^5*x^12)+_ + 1/240240*b^4*(5*A*b-16*a*B)*(a+b*x)^11/(a^6*x^11) +--R +--R +--R (2) +--R 1 16 1 15 16 1 6 10 11 +--R (----- A b - ----- B a b )x - - B a b x +--R 48048 15015 5 +--R + +--R 1 6 10 5 7 9 10 10 7 9 45 8 8 9 +--R (- - A a b - - B a b )x + (- -- A a b - -- B a b )x +--R 6 3 7 7 +--R + +--R 45 8 8 9 7 8 40 9 7 70 10 6 7 +--R (- -- A a b - 15B a b )x + (- -- A a b - -- B a b )x +--R 8 3 3 +--R + +--R 10 6 126 11 5 6 252 11 5 210 12 4 5 +--R (- 21A a b - --- B a b )x + (- --- A a b - --- B a b )x +--R 5 11 11 +--R + +--R 35 12 4 13 3 4 120 13 3 45 14 2 3 +--R (- -- A a b - 10B a b )x + (- --- A a b - -- B a b )x +--R 2 13 13 +--R + +--R 45 14 2 5 15 2 2 15 1 16 1 16 +--R (- -- A a b - - B a b)x + (- - A a b - -- B a )x - -- A a +--R 14 7 3 15 16 +--R / +--R 6 16 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 48048B b x + (- 40040A b - 400400B a b )x +--R + +--R 9 2 8 9 2 8 3 7 8 +--R (- 343200A a b - 1544400B a b )x + (- 1351350A a b - 3603600B a b )x +--R + +--R 3 7 4 6 7 4 6 5 5 6 +--R (- 3203200A a b - 5605600B a b )x + (- 5045040A a b - 6054048B a b )x +--R + +--R 5 5 6 4 5 6 4 7 3 4 +--R (- 5503680A a b - 4586400B a b )x + (- 4204200A a b - 2402400B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 2217600A a b - 831600B a b )x + (- 772200A a b - 171600B a b)x +--R + +--R 9 10 10 +--R (- 160160A a b - 16016B a )x - 15015A a +--R / +--R 16 +--R 240240x +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1293 +m0:=a0-r0 +--R +--R +--R 16 15 +--R - 5A b + 16B a b +--R (4) -------------------- +--R 6 +--R 240240a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^18 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 1293 +r0:=-1/17*A*(a+b*x)^11/(a*x^17)+1/272*(6*A*b-17*a*B)*(a+b*x)^11/(a^2*x^16)-_ + 1/816*b*(6*A*b-17*a*B)*(a+b*x)^11/(a^3*x^15)+_ + 1/2856*b^2*(6*A*b-17*a*B)*(a+b*x)^11/(a^4*x^14)-_ + 1/12376*b^3*(6*A*b-17*a*B)*(a+b*x)^11/(a^5*x^13)+_ + 1/74256*b^4*(6*A*b-17*a*B)*(a+b*x)^11/(a^6*x^12)-_ + 1/816816*b^5*(6*A*b-17*a*B)*(a+b*x)^11/(a^7*x^11) +--R +--R +--R (2) +--R 1 17 1 16 17 1 7 10 11 +--R (- ------ A b + ----- B a b )x - - B a b x +--R 136136 48048 6 +--R + +--R 1 7 10 10 8 9 10 5 8 9 45 9 8 9 +--R (- - A a b - -- B a b )x + (- - A a b - -- B a b )x +--R 7 7 4 8 +--R + +--R 9 8 40 10 7 8 10 7 11 6 7 +--R (- 5A a b - -- B a b )x + (- 12A a b - 21B a b )x +--R 3 +--R + +--R 210 11 6 252 12 5 6 12 5 35 13 4 5 +--R (- --- A a b - --- B a b )x + (- 21A a b - -- B a b )x +--R 11 11 2 +--R + +--R 210 13 4 120 14 3 4 60 14 3 45 15 2 3 +--R (- --- A a b - --- B a b )x + (- -- A a b - -- B a b )x +--R 13 13 7 14 +--R + +--R 15 2 2 16 2 5 16 1 17 1 17 +--R (- 3A a b - - B a b)x + (- - A a b - -- B a )x - -- A a +--R 3 8 16 17 +--R / +--R 7 17 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 136136B b x + (- 116688A b - 1166880B a b )x +--R + +--R 9 2 8 9 +--R (- 1021020A a b - 4594590B a b )x +--R + +--R 2 8 3 7 8 +--R (- 4084080A a b - 10890880B a b )x +--R + +--R 3 7 4 6 7 +--R (- 9801792A a b - 17153136B a b )x +--R + +--R 4 6 5 5 6 +--R (- 15593760A a b - 18712512B a b )x +--R + +--R 5 5 6 4 5 +--R (- 17153136A a b - 14294280B a b )x +--R + +--R 6 4 7 3 4 +--R (- 13194720A a b - 7539840B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 7001280A a b - 2625480B a b )x + (- 2450448A a b - 544544B a b)x +--R + +--R 9 10 10 +--R (- 510510A a b - 51051B a )x - 48048A a +--R / +--R 17 +--R 816816x +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1293 +m0:=a0-r0 +--R +--R +--R 17 16 +--R 6A b - 17B a b +--R (4) ------------------ +--R 7 +--R 816816a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^19 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 1293 +r0:=-1/18*a^10*A/x^18-1/17*a^9*(10*A*b+a*B)/x^17-_ + 5/16*a^8*b*(9*A*b+2*a*B)/x^16-a^7*b^2*(8*A*b+3*a*B)/x^15-_ + 15/7*a^6*b^3*(7*A*b+4*a*B)/x^14-42/13*a^5*b^4*(6*A*b+5*a*B)/x^13-_ + 7/2*a^4*b^5*(5*A*b+6*a*B)/x^12-30/11*a^3*b^6*(4*A*b+7*a*B)/x^11-_ + 3/2*a^2*b^7*(3*A*b+8*a*B)/x^10-5/9*a*b^8*(2*A*b+9*a*B)/x^9-_ + 1/8*b^9*(A*b+10*a*B)/x^8-1/7*b^10*B/x^7 +--R +--R +--R (2) +--R 1 10 11 1 10 5 9 10 10 9 2 8 9 +--R - - B b x + (- - A b - - B a b )x + (- -- A a b - 5B a b )x +--R 7 8 4 9 +--R + +--R 9 2 8 3 7 8 120 3 7 210 4 6 7 +--R (- - A a b - 12B a b )x + (- --- A a b - --- B a b )x +--R 2 11 11 +--R + +--R 35 4 6 5 5 6 252 5 5 210 6 4 5 +--R (- -- A a b - 21B a b )x + (- --- A a b - --- B a b )x +--R 2 13 13 +--R + +--R 6 4 60 7 3 4 7 3 8 2 3 +--R (- 15A a b - -- B a b )x + (- 8A a b - 3B a b )x +--R 7 +--R + +--R 45 8 2 5 9 2 10 9 1 10 1 10 +--R (- -- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 16 8 17 17 18 +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 350064B b x + (- 306306A b - 3063060B a b )x +--R + +--R 9 2 8 9 +--R (- 2722720A a b - 12252240B a b )x +--R + +--R 2 8 3 7 8 +--R (- 11027016A a b - 29405376B a b )x +--R + +--R 3 7 4 6 7 +--R (- 26732160A a b - 46781280B a b )x +--R + +--R 4 6 5 5 6 +--R (- 42882840A a b - 51459408B a b )x +--R + +--R 5 5 6 4 5 +--R (- 47500992A a b - 39584160B a b )x +--R + +--R 6 4 7 3 4 +--R (- 36756720A a b - 21003840B a b )x +--R + +--R 7 3 8 2 3 8 2 9 2 +--R (- 19603584A a b - 7351344B a b )x + (- 6891885A a b - 1531530B a b)x +--R + +--R 9 10 10 +--R (- 1441440A a b - 144144B a )x - 136136A a +--R / +--R 18 +--R 2450448x +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^20 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 1293 +r0:=-1/19*a^10*A/x^19-1/18*a^9*(10*A*b+a*B)/x^18-_ + 5/17*a^8*b*(9*A*b+2*a*B)/x^17-15/16*a^7*b^2*(8*A*b+3*a*B)/x^16-_ + 2*a^6*b^3*(7*A*b+4*a*B)/x^15-3*a^5*b^4*(6*A*b+5*a*B)/x^14-_ + 42/13*a^4*b^5*(5*A*b+6*a*B)/x^13-5/2*a^3*b^6*(4*A*b+7*a*B)/x^12-_ + 15/11*a^2*b^7*(3*A*b+8*a*B)/x^11-1/2*a*b^8*(2*A*b+9*a*B)/x^10-_ + 1/9*b^9*(A*b+10*a*B)/x^9-1/8*b^10*B/x^8 +--R +--R +--R (2) +--R 1 10 11 1 10 10 9 10 9 9 2 8 9 +--R - - B b x + (- - A b - -- B a b )x + (- A a b - - B a b )x +--R 8 9 9 2 +--R + +--R 45 2 8 120 3 7 8 3 7 35 4 6 7 +--R (- -- A a b - --- B a b )x + (- 10A a b - -- B a b )x +--R 11 11 2 +--R + +--R 210 4 6 252 5 5 6 5 5 6 4 5 +--R (- --- A a b - --- B a b )x + (- 18A a b - 15B a b )x +--R 13 13 +--R + +--R 6 4 7 3 4 15 7 3 45 8 2 3 +--R (- 14A a b - 8B a b )x + (- -- A a b - -- B a b )x +--R 2 16 +--R + +--R 45 8 2 10 9 2 5 9 1 10 1 10 +--R (- -- A a b - -- B a b)x + (- - A a b - -- B a )x - -- A a +--R 17 17 9 18 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 831402B b x + (- 739024A b - 7390240B a b )x +--R + +--R 9 2 8 9 +--R (- 6651216A a b - 29930472B a b )x +--R + +--R 2 8 3 7 8 +--R (- 27209520A a b - 72558720B a b )x +--R + +--R 3 7 4 6 7 +--R (- 66512160A a b - 116396280B a b )x +--R + +--R 4 6 5 5 6 +--R (- 107442720A a b - 128931264B a b )x +--R + +--R 5 5 6 4 5 +--R (- 119721888A a b - 99768240B a b )x +--R + +--R 6 4 7 3 4 +--R (- 93117024A a b - 53209728B a b )x +--R + +--R 7 3 8 2 3 +--R (- 49884120A a b - 18706545B a b )x +--R + +--R 8 2 9 2 9 10 +--R (- 17606160A a b - 3912480B a b)x + (- 3695120A a b - 369512B a )x +--R + +--R 10 +--R - 350064A a +--R / +--R 19 +--R 6651216x +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1293 +t0:=(a+b*x)^10*(A+B*x)/x^21 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 1293 +r0:=-1/20*a^10*A/x^20-1/19*a^9*(10*A*b+a*B)/x^19-_ + 5/18*a^8*b*(9*A*b+2*a*B)/x^18-15/17*a^7*b^2*(8*A*b+3*a*B)/x^17-_ + 15/8*a^6*b^3*(7*A*b+4*a*B)/x^16-14/5*a^5*b^4*(6*A*b+5*a*B)/x^15-_ + 3*a^4*b^5*(5*A*b+6*a*B)/x^14-30/13*a^3*b^6*(4*A*b+7*a*B)/x^13-_ + 5/4*a^2*b^7*(3*A*b+8*a*B)/x^12-5/11*a*b^8*(2*A*b+9*a*B)/x^11-_ + 1/10*b^9*(A*b+10*a*B)/x^10-1/9*b^10*B/x^9 +--R +--R +--R (2) +--R 1 10 11 1 10 9 10 10 9 45 2 8 9 +--R - - B b x + (- -- A b - B a b )x + (- -- A a b - -- B a b )x +--R 9 10 11 11 +--R + +--R 15 2 8 3 7 8 120 3 7 210 4 6 7 +--R (- -- A a b - 10B a b )x + (- --- A a b - --- B a b )x +--R 4 13 13 +--R + +--R 4 6 5 5 6 84 5 5 6 4 5 +--R (- 15A a b - 18B a b )x + (- -- A a b - 14B a b )x +--R 5 +--R + +--R 105 6 4 15 7 3 4 120 7 3 45 8 2 3 +--R (- --- A a b - -- B a b )x + (- --- A a b - -- B a b )x +--R 8 2 17 17 +--R + +--R 5 8 2 5 9 2 10 9 1 10 1 10 +--R (- - A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a +--R 2 9 19 19 20 +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 10 9 10 +--R - 1847560B b x + (- 1662804A b - 16628040B a b )x +--R + +--R 9 2 8 9 +--R (- 15116400A a b - 68023800B a b )x +--R + +--R 2 8 3 7 8 +--R (- 62355150A a b - 166280400B a b )x +--R + +--R 3 7 4 6 7 +--R (- 153489600A a b - 268606800B a b )x +--R + +--R 4 6 5 5 6 +--R (- 249420600A a b - 299304720B a b )x +--R + +--R 5 5 6 4 5 +--R (- 279351072A a b - 232792560B a b )x +--R + +--R 6 4 7 3 4 +--R (- 218243025A a b - 124710300B a b )x +--R + +--R 7 3 8 2 3 +--R (- 117374400A a b - 44015400B a b )x +--R + +--R 8 2 9 2 9 10 +--R (- 41570100A a b - 9237800B a b)x + (- 8751600A a b - 875160B a )x +--R + +--R 10 +--R - 831402A a +--R / +--R 20 +--R 16628040x +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1293 +t0:=(a+b*x)^10*(A+B*x)/(d+e*x)^22 +--R +--R +--R (1) +--R 10 11 10 9 10 9 2 8 9 +--R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x +--R + +--R 2 8 3 7 8 3 7 4 6 7 +--R (45A a b + 120B a b )x + (120A a b + 210B a b )x +--R + +--R 4 6 5 5 6 5 5 6 4 5 +--R (210A a b + 252B a b )x + (252A a b + 210B a b )x +--R + +--R 6 4 7 3 4 7 3 8 2 3 +--R (210A a b + 120B a b )x + (120A a b + 45B a b )x +--R + +--R 8 2 9 2 9 10 10 +--R (45A a b + 10B a b)x + (10A a b + B a )x + A a +--R / +--R 22 22 21 21 2 20 20 3 19 19 4 18 18 +--R e x + 22d e x + 231d e x + 1540d e x + 7315d e x +--R + +--R 5 17 17 6 16 16 7 15 15 8 14 14 +--R 26334d e x + 74613d e x + 170544d e x + 319770d e x +--R + +--R 9 13 13 10 12 12 11 11 11 12 10 10 +--R 497420d e x + 646646d e x + 705432d e x + 646646d e x +--R + +--R 13 9 9 14 8 8 15 7 7 16 6 6 +--R 497420d e x + 319770d e x + 170544d e x + 74613d e x +--R + +--R 17 5 5 18 4 4 19 3 3 20 2 2 21 22 +--R 26334d e x + 7315d e x + 1540d e x + 231d e x + 22d e x + d +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 1293 +r0:=1/21*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^21)-_ + 1/20*(b*d-a*e)^9*(11*b*B*d-10*A*b*e-a*B*e)/(e^12*(d+e*x)^20)+_ + 5/19*b*(b*d-a*e)^8*(11*b*B*d-9*A*b*e-2*a*B*e)/(e^12*(d+e*x)^19)-_ + 5/6*b^2*(b*d-a*e)^7*(11*b*B*d-8*A*b*e-3*a*B*e)/(e^12*(d+e*x)^18)+_ + 30/17*b^3*(b*d-a*e)^6*(11*b*B*d-7*A*b*e-4*a*B*e)/(e^12*(d+e*x)^17)-_ + 21/8*b^4*(b*d-a*e)^5*(11*b*B*d-6*A*b*e-5*a*B*e)/(e^12*(d+e*x)^16)+_ + 14/5*b^5*(b*d-a*e)^4*(11*b*B*d-5*A*b*e-6*a*B*e)/(e^12*(d+e*x)^15)-_ + 15/7*b^6*(b*d-a*e)^3*(11*b*B*d-4*A*b*e-7*a*B*e)/(e^12*(d+e*x)^14)+_ + 15/13*b^7*(b*d-a*e)^2*(11*b*B*d-3*A*b*e-8*a*B*e)/(e^12*(d+e*x)^13)-_ + 5/12*b^8*(b*d-a*e)*(11*b*B*d-2*A*b*e-9*a*B*e)/(e^12*(d+e*x)^12)+_ + 1/11*b^9*(11*b*B*d-A*b*e-10*a*B*e)/(e^12*(d+e*x)^11)-_ + 1/10*b^10*B/(e^12*(d+e*x)^10) +--R +--R +--R (2) +--R 1 10 11 11 1 10 10 9 11 1 10 10 10 +--R - -- B b e x + ((- -- A b - -- B a b )e - -- B b d e )x +--R 10 11 11 10 +--R + +--R 5 9 15 2 8 11 5 10 25 9 10 +--R (- - A a b - -- B a b )e + (- -- A b - -- B a b )d e +--R 6 4 66 33 +--R + +--R 1 10 2 9 +--R - -- B b d e +--R 12 +--R * +--R 9 +--R x +--R + +--R 45 2 8 120 3 7 11 15 9 135 2 8 10 +--R (- -- A a b - --- B a b )e + (- -- A a b - --- B a b )d e +--R 13 13 26 52 +--R + +--R 15 10 75 9 2 9 3 10 3 8 +--R (- --- A b - --- B a b )d e - -- B b d e +--R 286 143 52 +--R * +--R 8 +--R x +--R + +--R 60 3 7 4 6 11 180 2 8 480 3 7 10 +--R (- -- A a b - 15B a b )e + (- --- A a b - --- B a b )d e +--R 7 91 91 +--R + +--R 30 9 135 2 8 2 9 30 10 300 9 3 8 +--R (- -- A a b - --- B a b )d e + (- ---- A b - ---- B a b )d e +--R 91 91 1001 1001 +--R + +--R 3 10 4 7 +--R - -- B b d e +--R 91 +--R * +--R 7 +--R x +--R + +--R 4 6 84 5 5 11 3 7 4 6 10 +--R (- 14A a b - -- B a b )e + (- 4A a b - 7B a b )d e +--R 5 +--R + +--R 12 2 8 32 3 7 2 9 2 9 9 2 8 3 8 +--R (- -- A a b - -- B a b )d e + (- -- A a b - -- B a b )d e +--R 13 13 13 13 +--R + +--R 2 10 20 9 4 7 1 10 5 6 +--R (- --- A b - --- B a b )d e - -- B b d e +--R 143 143 65 +--R * +--R 6 +--R x +--R + +--R 63 5 5 105 6 4 11 21 4 6 63 5 5 10 +--R (- -- A a b - --- B a b )e + (- -- A a b - -- B a b )d e +--R 4 8 4 10 +--R + +--R 3 3 7 21 4 6 2 9 9 2 8 12 3 7 3 8 +--R (- - A a b - -- B a b )d e + (- -- A a b - -- B a b )d e +--R 2 8 26 13 +--R + +--R 3 9 27 2 8 4 7 3 10 15 9 5 6 +--R (- -- A a b - --- B a b )d e + (- --- A b - --- B a b )d e +--R 52 104 572 286 +--R + +--R 3 10 6 5 +--R - --- B b d e +--R 520 +--R * +--R 5 +--R x +--R + +--R 210 6 4 120 7 3 11 315 5 5 525 6 4 10 +--R (- --- A a b - --- B a b )e + (- --- A a b - --- B a b )d e +--R 17 17 68 136 +--R + +--R 105 4 6 63 5 5 2 9 15 3 7 105 4 6 3 8 +--R (- --- A a b - -- B a b )d e + (- -- A a b - --- B a b )d e +--R 68 34 34 136 +--R + +--R 45 2 8 60 3 7 4 7 15 9 135 2 8 5 6 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 442 221 884 1768 +--R + +--R 15 10 75 9 6 5 3 10 7 4 +--R (- ---- A b - ---- B a b )d e - ---- B b d e +--R 9724 4862 1768 +--R * +--R 4 +--R x +--R + +--R 20 7 3 5 8 2 11 140 6 4 80 7 3 10 +--R (- -- A a b - - B a b )e + (- --- A a b - -- B a b )d e +--R 3 2 51 51 +--R + +--R 35 5 5 175 6 4 2 9 35 4 6 7 5 5 3 8 +--R (- -- A a b - --- B a b )d e + (- --- A a b - -- B a b )d e +--R 34 204 102 17 +--R + +--R 5 3 7 35 4 6 4 7 5 2 8 40 3 7 5 6 +--R (- -- A a b - --- B a b )d e + (- --- A a b - --- B a b )d e +--R 51 204 221 663 +--R + +--R 5 9 15 2 8 6 5 5 10 25 9 7 4 +--R (- ---- A a b - --- B a b )d e + (- ----- A b - ---- B a b )d e +--R 1326 884 14586 7293 +--R + +--R 1 10 8 3 +--R - ---- B b d e +--R 2652 +--R * +--R 3 +--R x +--R + +--R 45 8 2 10 9 11 20 7 3 15 8 2 10 +--R (- -- A a b - -- B a b)e + (- -- A a b - -- B a b )d e +--R 19 19 19 38 +--R + +--R 140 6 4 80 7 3 2 9 105 5 5 175 6 4 3 8 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 323 323 646 1292 +--R + +--R 35 4 6 21 5 5 4 7 5 3 7 35 4 6 5 6 +--R (- --- A a b - --- B a b )d e + (- --- A a b - ---- B a b )d e +--R 646 323 323 1292 +--R + +--R 15 2 8 40 3 7 6 5 +--R (- ---- A a b - ---- B a b )d e +--R 4199 4199 +--R + +--R 5 9 45 2 8 7 4 +--R (- ---- A a b - ----- B a b )d e +--R 8398 16796 +--R + +--R 5 10 25 9 8 3 1 10 9 2 +--R (- ----- A b - ----- B a b )d e - ----- B b d e +--R 92378 46189 16796 +--R * +--R 2 +--R x +--R + +--R 1 9 1 10 11 9 8 2 1 9 10 +--R (- - A a b - -- B a )e + (- -- A a b - -- B a b)d e +--R 2 20 38 19 +--R + +--R 2 7 3 3 8 2 2 9 14 6 4 8 7 3 3 8 +--R (- -- A a b - -- B a b )d e + (- --- A a b - --- B a b )d e +--R 19 76 323 323 +--R + +--R 21 5 5 35 6 4 4 7 7 4 6 21 5 5 5 6 +--R (- ---- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 1292 2584 1292 3230 +--R + +--R 1 3 7 7 4 6 6 5 3 2 8 4 3 7 7 4 +--R (- --- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 646 2584 8398 4199 +--R + +--R 1 9 9 2 8 8 3 +--R (- ----- A a b - ----- B a b )d e +--R 16796 33592 +--R + +--R 1 10 5 9 9 2 1 10 10 +--R (- ------ A b - ----- B a b )d e - ------ B b d e +--R 184756 92378 167960 +--R * +--R x +--R + +--R 1 10 11 1 9 1 10 10 +--R - -- A a e + (- -- A a b - --- B a )d e +--R 21 42 420 +--R + +--R 3 8 2 1 9 2 9 2 7 3 1 8 2 3 8 +--R (- --- A a b - --- B a b)d e + (- --- A a b - --- B a b )d e +--R 266 399 399 532 +--R + +--R 2 6 4 8 7 3 4 7 1 5 5 5 6 4 5 6 +--R (- --- A a b - ---- B a b )d e + (- ---- A a b - ---- B a b )d e +--R 969 6783 1292 7752 +--R + +--R 1 4 6 1 5 5 6 5 1 3 7 1 4 6 7 4 +--R (- ---- A a b - ---- B a b )d e + (- ----- A a b - ---- B a b )d e +--R 3876 3230 13566 7752 +--R + +--R 1 2 8 4 3 7 8 3 +--R (- ----- A a b - ----- B a b )d e +--R 58786 88179 +--R + +--R 1 9 3 2 8 9 2 +--R (- ------ A a b - ------ B a b )d e +--R 352716 235144 +--R + +--R 1 10 5 9 10 1 10 11 +--R (- ------- A b - ------- B a b )d e - ------- B b d +--R 3879876 1939938 3527160 +--R / +--R 33 21 32 20 2 31 19 3 30 18 4 29 17 +--R e x + 21d e x + 210d e x + 1330d e x + 5985d e x +--R + +--R 5 28 16 6 27 15 7 26 14 8 25 13 +--R 20349d e x + 54264d e x + 116280d e x + 203490d e x +--R + +--R 9 24 12 10 23 11 11 22 10 12 21 9 +--R 293930d e x + 352716d e x + 352716d e x + 293930d e x +--R + +--R 13 20 8 14 19 7 15 18 6 16 17 5 +--R 203490d e x + 116280d e x + 54264d e x + 20349d e x +--R + +--R 17 16 4 18 15 3 19 14 2 20 13 21 12 +--R 5985d e x + 1330d e x + 210d e x + 21d e x + d e +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 11 11 +--R - 3879876B b e x +--R + +--R 10 9 11 10 10 10 +--R ((- 3527160A b - 35271600B a b )e - 3879876B b d e )x +--R + +--R 9 2 8 11 +--R (- 32332300A a b - 145495350B a b )e +--R + +--R 10 9 10 10 2 9 +--R (- 2939300A b - 29393000B a b )d e - 3233230B b d e +--R * +--R 9 +--R x +--R + +--R 2 8 3 7 11 +--R (- 134303400A a b - 358142400B a b )e +--R + +--R 9 2 8 10 +--R (- 22383900A a b - 100727550B a b )d e +--R + +--R 10 9 2 9 10 3 8 +--R (- 2034900A b - 20349000B a b )d e - 2238390B b d e +--R * +--R 8 +--R x +--R + +--R 3 7 4 6 11 +--R (- 332560800A a b - 581981400B a b )e +--R + +--R 2 8 3 7 10 +--R (- 76744800A a b - 204652800B a b )d e +--R + +--R 9 2 8 2 9 +--R (- 12790800A a b - 57558600B a b )d e +--R + +--R 10 9 3 8 10 4 7 +--R (- 1162800A b - 11628000B a b )d e - 1279080B b d e +--R * +--R 7 +--R x +--R + +--R 4 6 5 5 11 +--R (- 543182640A a b - 651819168B a b )e +--R + +--R 3 7 4 6 10 +--R (- 155195040A a b - 271591320B a b )d e +--R + +--R 2 8 3 7 2 9 +--R (- 35814240A a b - 95504640B a b )d e +--R + +--R 9 2 8 3 8 +--R (- 5969040A a b - 26860680B a b )d e +--R + +--R 10 9 4 7 10 5 6 +--R (- 542640A b - 5426400B a b )d e - 596904B b d e +--R * +--R 6 +--R x +--R + +--R 5 5 6 4 11 +--R (- 611080470A a b - 509233725B a b )e +--R + +--R 4 6 5 5 10 +--R (- 203693490A a b - 244432188B a b )d e +--R + +--R 3 7 4 6 2 9 +--R (- 58198140A a b - 101846745B a b )d e +--R + +--R 2 8 3 7 3 8 +--R (- 13430340A a b - 35814240B a b )d e +--R + +--R 9 2 8 4 7 +--R (- 2238390A a b - 10072755B a b )d e +--R + +--R 10 9 5 6 10 6 5 +--R (- 203490A b - 2034900B a b )d e - 223839B b d e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 11 +--R (- 479278800A a b - 273873600B a b )e +--R + +--R 5 5 6 4 10 +--R (- 179729550A a b - 149774625B a b )d e +--R + +--R 4 6 5 5 2 9 +--R (- 59909850A a b - 71891820B a b )d e +--R + +--R 3 7 4 6 3 8 +--R (- 17117100A a b - 29954925B a b )d e +--R + +--R 2 8 3 7 4 7 +--R (- 3950100A a b - 10533600B a b )d e +--R + +--R 9 2 8 5 6 +--R (- 658350A a b - 2962575B a b )d e +--R + +--R 10 9 6 5 10 7 4 +--R (- 59850A b - 598500B a b )d e - 65835B b d e +--R * +--R 4 +--R x +--R + +--R 7 3 8 2 11 +--R (- 258658400A a b - 96996900B a b )e +--R + +--R 6 4 7 3 10 +--R (- 106506400A a b - 60860800B a b )d e +--R + +--R 5 5 6 4 2 9 +--R (- 39939900A a b - 33283250B a b )d e +--R + +--R 4 6 5 5 3 8 +--R (- 13313300A a b - 15975960B a b )d e +--R + +--R 3 7 4 6 4 7 +--R (- 3803800A a b - 6656650B a b )d e +--R + +--R 2 8 3 7 5 6 +--R (- 877800A a b - 2340800B a b )d e +--R + +--R 9 2 8 6 5 +--R (- 146300A a b - 658350B a b )d e +--R + +--R 10 9 7 4 10 8 3 +--R (- 13300A b - 133000B a b )d e - 14630B b d e +--R * +--R 3 +--R x +--R + +--R 8 2 9 11 +--R (- 91891800A a b - 20420400B a b)e +--R + +--R 7 3 8 2 10 +--R (- 40840800A a b - 15315300B a b )d e +--R + +--R 6 4 7 3 2 9 +--R (- 16816800A a b - 9609600B a b )d e +--R + +--R 5 5 6 4 3 8 +--R (- 6306300A a b - 5255250B a b )d e +--R + +--R 4 6 5 5 4 7 +--R (- 2102100A a b - 2522520B a b )d e +--R + +--R 3 7 4 6 5 6 +--R (- 600600A a b - 1051050B a b )d e +--R + +--R 2 8 3 7 6 5 +--R (- 138600A a b - 369600B a b )d e +--R + +--R 9 2 8 7 4 10 9 8 3 +--R (- 23100A a b - 103950B a b )d e + (- 2100A b - 21000B a b )d e +--R + +--R 10 9 2 +--R - 2310B b d e +--R * +--R 2 +--R x +--R + +--R 9 10 11 +--R (- 19399380A a b - 1939938B a )e +--R + +--R 8 2 9 10 +--R (- 9189180A a b - 2042040B a b)d e +--R + +--R 7 3 8 2 2 9 +--R (- 4084080A a b - 1531530B a b )d e +--R + +--R 6 4 7 3 3 8 +--R (- 1681680A a b - 960960B a b )d e +--R + +--R 5 5 6 4 4 7 +--R (- 630630A a b - 525525B a b )d e +--R + +--R 4 6 5 5 5 6 +--R (- 210210A a b - 252252B a b )d e +--R + +--R 3 7 4 6 6 5 +--R (- 60060A a b - 105105B a b )d e +--R + +--R 2 8 3 7 7 4 9 2 8 8 3 +--R (- 13860A a b - 36960B a b )d e + (- 2310A a b - 10395B a b )d e +--R + +--R 10 9 9 2 10 10 +--R (- 210A b - 2100B a b )d e - 231B b d e +--R * +--R x +--R + +--R 10 11 9 10 10 +--R - 1847560A a e + (- 923780A a b - 92378B a )d e +--R + +--R 8 2 9 2 9 7 3 8 2 3 8 +--R (- 437580A a b - 97240B a b)d e + (- 194480A a b - 72930B a b )d e +--R + +--R 6 4 7 3 4 7 5 5 6 4 5 6 +--R (- 80080A a b - 45760B a b )d e + (- 30030A a b - 25025B a b )d e +--R + +--R 4 6 5 5 6 5 3 7 4 6 7 4 +--R (- 10010A a b - 12012B a b )d e + (- 2860A a b - 5005B a b )d e +--R + +--R 2 8 3 7 8 3 9 2 8 9 2 +--R (- 660A a b - 1760B a b )d e + (- 110A a b - 495B a b )d e +--R + +--R 10 9 10 10 11 +--R (- 10A b - 100B a b )d e - 11B b d +--R / +--R 33 21 32 20 2 31 19 +--R 38798760e x + 814773960d e x + 8147739600d e x +--R + +--R 3 30 18 4 29 17 5 28 16 +--R 51602350800d e x + 232210578600d e x + 789515967240d e x +--R + +--R 6 27 15 7 26 14 8 25 13 +--R 2105375912640d e x + 4511519812800d e x + 7895159672400d e x +--R + +--R 9 24 12 10 23 11 +--R 11404119526800d e x + 13684943432160d e x +--R + +--R 11 22 10 12 21 9 13 20 8 +--R 13684943432160d e x + 11404119526800d e x + 7895159672400d e x +--R + +--R 14 19 7 15 18 6 16 17 5 +--R 4511519812800d e x + 2105375912640d e x + 789515967240d e x +--R + +--R 17 16 4 18 15 3 19 14 2 +--R 232210578600d e x + 51602350800d e x + 8147739600d e x +--R + +--R 20 13 21 12 +--R 814773960d e x + 38798760d e +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x) +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^4*x/b^6+1/2*(A*b-a*B)*(b*d-a*e)^3*(d+e*x)^2/b^5+_ + 1/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^3/b^4+_ + 1/4*(A*b-a*B)*(b*d-a*e)*(d+e*x)^4/b^3+1/5*(A*b-a*B)*(d+e*x)^5/b^2+_ + 1/6*B*(d+e*x)^6/(b*e)+(A*b-a*B)*(b*d-a*e)^5*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (- 60A a b + 60B a )e + (300A a b - 300B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 600A a b + 600B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 +--R (- 300A a b + 300B a b )d e + (60A b - 60B a b )d e +--R * +--R log(b x + a) +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 10B b e x + ((12A b - 12B a b )e + 60B b d e )x +--R + +--R 5 2 4 6 6 5 5 6 2 4 4 +--R ((- 15A a b + 15B a b )e + (75A b - 75B a b )d e + 150B b d e )x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (20A a b - 20B a b )e + (- 100A a b + 100B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (200A b - 200B a b )d e + 200B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (- 30A a b + 30B a b )e + (150A a b - 150B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 6 4 2 +--R (- 300A a b + 300B a b )d e + (300A b - 300B a b )d e + 150B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (60A a b - 60B a b)e + (- 300A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (300A b - 300B a b )d e + 60B b d e +--R * +--R x +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 30A a b + 30B a b )d e + (110A a b - 110B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 145A a b + 145B a b )d e + (77A b - 77B a b )d e + 10B b d +--R / +--R 7 +--R 60b e +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 4 2 5 4 +--R (- 60A a b + 60B a )e + (300A a b - 300B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 600A a b + 600B a b )d e + (600A a b - 600B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 300A a b + 300B a b )d e + (60A b - 60B a b )d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 10B b e x + ((12A b - 12B a b )e + 60B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 15A a b + 15B a b )e + (75A b - 75B a b )d e + 150B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (20A a b - 20B a b )e + (- 100A a b + 100B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (200A b - 200B a b )d e + 200B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 30A a b + 30B a b )e + (150A a b - 150B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 300A a b + 300B a b )d e + (300A b - 300B a b )d e + 150B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (60A a b - 60B a b)e + (- 300A a b + 300B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 300B a b )d e + 60B b d +--R * +--R x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 4 2 2 3 3 3 +--R (30A a b - 30B a )d e + (- 110A a b + 110B a b)d e +--R + +--R 3 2 2 4 2 4 3 5 4 6 +--R (145A a b - 145B a b )d e + (- 77A b + 77B a b )d e - 10B b d +--R / +--R 5 +--R 60b e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x) +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^3*x/b^5+1/2*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^2/b^4+_ + 1/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^3/b^3+1/4*(A*b-a*B)*(d+e*x)^4/b^2+_ + 1/5*B*(d+e*x)^5/(b*e)+(A*b-a*B)*(b*d-a*e)^4*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 5 5 3 2 4 4 +--R (60A a b - 60B a )e + (- 240A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (360A a b - 360B a b )d e + (- 240A a b + 240B a b )d e +--R + +--R 5 4 4 +--R (60A b - 60B a b )d e +--R * +--R log(b x + a) +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 12B b e x + ((15A b - 15B a b )e + 60B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 3 +--R ((- 20A a b + 20B a b )e + (80A b - 80B a b )d e + 120B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 30B a b )e + (- 120A a b + 120B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 180B a b )d e + 120B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 60A a b + 60B a b)e + (240A a b - 240B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (- 360A a b + 360B a b )d e + (240A b - 240B a b )d e + 60B b d e +--R * +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (30A a b - 30B a b )d e + (- 80A a b + 80B a b )d e +--R + +--R 5 4 4 5 5 +--R (65A b - 65B a b )d e + 12B b d +--R / +--R 6 +--R 60b e +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 3 2 4 3 +--R (60A a b - 60B a )e + (- 240A a b + 240B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (360A a b - 360B a b )d e + (- 240A a b + 240B a b )d e +--R + +--R 5 4 4 +--R (60A b - 60B a b )d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 12B b e x + ((15A b - 15B a b )e + 60B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 20A a b + 20B a b )e + (80A b - 80B a b )d e + 120B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (30A a b - 30B a b )e + (- 120A a b + 120B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (180A b - 180B a b )d e + 120B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 60A a b + 60B a b)e + (240A a b - 240B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 360A a b + 360B a b )d e + (240A b - 240B a b )d e + 60B b d +--R * +--R x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 3 2 2 3 2 +--R (- 30A a b + 30B a )d e + (80A a b - 80B a b)d e +--R + +--R 3 2 4 3 5 +--R (- 65A b + 65B a b )d e - 12B b d +--R / +--R 4 +--R 60b e +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)^2*x/b^4+1/2*(A*b-a*B)*(b*d-a*e)*(d+e*x)^2/b^3+_ + 1/3*(A*b-a*B)*(d+e*x)^3/b^2+1/4*B*(d+e*x)^4/(b*e)+_ + (A*b-a*B)*(b*d-a*e)^3*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (36A b - 36B a b )d e + 12B b d e +--R * +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 6A a b + 6B a b )d e + (10A b - 10B a b )d e + 3B b d +--R / +--R 5 +--R 12b e +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 +--R (- 12A a b + 12B a )e + (36A a b - 36B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 36A a b + 36B a b )d e + (12A b - 12B a b )d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 3B b e x + ((4A b - 4B a b )e + 12B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 6B a b )e + (18A b - 18B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 12B a b)e + (- 36A a b + 36B a b )d e +--R + +--R 4 3 2 4 3 +--R (36A b - 36B a b )d e + 12B b d +--R * +--R x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1293 +m0:=a0-r0 +--R +--R +--R 2 2 2 2 3 2 4 +--R (6A a b - 6B a )d e + (- 10A b + 10B a b)d e - 3B b d +--R (4) -------------------------------------------------------- +--R 3 +--R 12b e +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1293 +r0:=(A*b-a*B)*e*(b*d-a*e)*x/b^3+1/2*(A*b-a*B)*(d+e*x)^2/b^2+_ + 1/3*B*(d+e*x)^3/(b*e)+(A*b-a*B)*(b*d-a*e)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (6A a b - 6B a )e + (- 12A a b + 12B a b)d e +--R + +--R 3 2 2 +--R (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d e)x +--R + +--R 3 2 2 3 3 +--R (3A b - 3B a b )d e + 2B b d +--R / +--R 4 +--R 6b e +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 3 2 2 +--R ((6A a b - 6B a )e + (- 12A a b + 12B a b)d e + (6A b - 6B a b )d ) +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R 2B b e x + ((3A b - 3B a b )e + 6B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (12A b - 12B a b )d e + 6B b d )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 +--R (- 3A b + 3B a)d e - 2B b d +--R (4) ---------------------------- +--R 2 +--R 6b e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x) +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1293 +r0:=B*(b*d-a*e)*x/b^2+1/2*e*(A+B*x)^2/(b*B)+(A*b-a*B)*(b*d-a*e)*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R ((- 2A B a b + 2B a )e + (2A B b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 2 2 2 2 +--R ((2A B b - 2B a b)e + 2B b d)x + A b e +--R / +--R 3 +--R 2B b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)log(b x + a) + B b e x +--R + +--R 2 2 +--R ((2A b - 2B a b)e + 2B b d)x +--R / +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R A e +--R (4) - ---- +--R 2B b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1293 +t0:=(A+B*x)/(a+b*x) +--R +--R +--R B x + A +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1293 +r0:=B*x/b+(A*b-a*B)*log(a+b*x)/b^2 +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (2) ------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (A b - B a)log(b x + a) + B b x +--R (3) ------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)) +--R +--R +--R B x + A +--R (1) --------------------------- +--R 2 +--R b e x + (a e + b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1293 +r0:=(A*b-a*B)*log(a+b*x)/(b*(b*d-a*e))+(B*d-A*e)*log(d+e*x)/(e*(b*d-a*e)) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (2) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (A b e - B b d)log(e x + d) + (- A b + B a)e log(b x + a) +--R (3) --------------------------------------------------------- +--R 2 2 +--R a b e - b d e +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^2) +--R +--R +--R B x + A +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (a e + 2b d e)x + (2a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1293 +r0:=(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x))+(A*b-a*B)*log(a+b*x)/(b*d-a*e)^2-_ + (A*b-a*B)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) +--R + +--R 2 2 +--R ((A b - B a)e x + (A b - B a)d e)log(b x + a) - A a e + (A b + B a)d e +--R + +--R 2 +--R - B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a e - 2a b d e + b d e )x + a d e - 2a b d e + b d e +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^3) +--R +--R +--R (1) +--R B x + A +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1293 +r0:=1/2*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^2)+(A*b-a*B)/((b*d-a*e)^2*(d+e*x))+_ + b*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^3-b*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((2A b - 2B a b)e x + (4A b - 4B a b)d e x + (2A b - 2B a b)d e) +--R * +--R log(e x + d) +--R + +--R 2 3 2 2 2 +--R (- 2A b + 2B a b)e x + (- 4A b + 4B a b)d e x +--R + +--R 2 2 +--R (- 2A b + 2B a b)d e +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 2 3 +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d e )x - A a e +--R + +--R 2 2 2 2 2 3 +--R (4A a b - B a )d e - 3A b d e + B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a e - 6a b d e + 6a b d e - 2b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a d e - 12a b d e + 12a b d e - 4b d e )x + 2a d e - 6a b d e +--R + +--R 2 4 2 3 5 +--R 6a b d e - 2b d e +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^4) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1293 +r0:=1/3*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^3)+_ + 1/2*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^2)+_ + b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x))+_ + b^2*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^4-b^2*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 2 3 2 +--R (- 6A b + 6B a b )e x + (- 18A b + 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (- 18A b + 18B a b )d e x + (- 6A b + 6B a b )d e +--R * +--R log(e x + d) +--R + +--R 3 2 4 3 3 2 3 2 +--R (6A b - 6B a b )e x + (18A b - 18B a b )d e x +--R + +--R 3 2 2 2 3 2 3 +--R (18A b - 18B a b )d e x + (6A b - 6B a b )d e +--R * +--R log(b x + a) +--R + +--R 2 2 4 3 2 3 2 +--R ((- 6A a b + 6B a b)e + (6A b - 6B a b )d e )x +--R + +--R 2 3 4 2 2 3 +--R (3A a b - 3B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 +--R (15A b - 15B a b )d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 2A a e + (9A a b - B a )d e + (- 18A a b + 6B a b)d e +--R + +--R 3 2 3 3 4 +--R (11A b - 3B a b )d e - 2B b d +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 3 +--R (6a e - 24a b d e + 36a b d e - 24a b d e + 6b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 4 5 3 2 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 4 6 2 4 3 5 +--R (18a d e - 72a b d e + 108a b d e - 72a b d e + 18b d e )x + 6a d e +--R + +--R 3 4 4 2 2 5 3 3 6 2 4 7 +--R - 24a b d e + 36a b d e - 24a b d e + 6b d e +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^5) +--R +--R +--R (1) +--R B x + A +--R / +--R 5 6 5 4 5 4 2 3 4 +--R b e x + (a e + 5b d e )x + (5a d e + 10b d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a d e + 10b d e )x + (10a d e + 5b d e)x + (5a d e + b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1293 +r0:=1/4*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^4)+_ + 1/3*(A*b-a*B)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*b*(A*b-a*B)/((b*d-a*e)^3*(d+e*x)^2)+_ + b^2*(A*b-a*B)/((b*d-a*e)^4*(d+e*x))+_ + b^3*(A*b-a*B)*log(a+b*x)/(b*d-a*e)^5-b^3*(A*b-a*B)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 5 4 4 3 4 3 +--R (12A b - 12B a b )e x + (48A b - 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (72A b - 72B a b )d e x + (48A b - 48B a b )d e x +--R + +--R 4 3 4 +--R (12A b - 12B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 3 4 3 +--R (- 12A b + 12B a b )e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (- 72A b + 72B a b )d e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 4 +--R (- 12A b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 5 4 3 4 3 +--R ((12A a b - 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b + 6B a b)e + (48A a b - 48B a b )d e +--R + +--R 4 3 2 3 +--R (- 42A b + 42B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b - 4B a )e + (- 24A a b + 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b - 72B a b )d e + (- 52A b + 52B a b )d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (16A a b - B a )d e + (- 36A a b + 6B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b - 18B a b )d e + (- 25A b + 10B a b )d e + 3B b d +--R / +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 5 5 5 +--R - 12b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 6 4 +--R - 48b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 6 4 +--R 72a d e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 5 7 3 +--R - 72b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 4 7 3 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 8 2 +--R - 48b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 4 8 2 5 9 +--R 12a d e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12b d e +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 4 4 3 4 3 +--R (12A b - 12B a b )e x + (48A b - 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (72A b - 72B a b )d e x + (48A b - 48B a b )d e x +--R + +--R 4 3 4 +--R (12A b - 12B a b )d e +--R * +--R log(e x + d) +--R + +--R 4 3 5 4 4 3 4 3 +--R (- 12A b + 12B a b )e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 2 3 2 4 3 3 2 +--R (- 72A b + 72B a b )d e x + (- 48A b + 48B a b )d e x +--R + +--R 4 3 4 +--R (- 12A b + 12B a b )d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 5 4 3 4 3 +--R ((12A a b - 12B a b )e + (- 12A b + 12B a b )d e )x +--R + +--R 2 2 3 5 3 2 2 4 +--R (- 6A a b + 6B a b)e + (48A a b - 48B a b )d e +--R + +--R 4 3 2 3 +--R (- 42A b + 42B a b )d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 3 4 +--R (4A a b - 4B a )e + (- 24A a b + 24B a b)d e +--R + +--R 3 2 2 2 3 4 3 3 2 +--R (72A a b - 72B a b )d e + (- 52A b + 52B a b )d e +--R * +--R x +--R + +--R 4 5 3 4 4 2 2 3 2 3 +--R - 3A a e + (16A a b - B a )d e + (- 36A a b + 6B a b)d e +--R + +--R 3 2 2 3 2 4 3 4 4 5 +--R (48A a b - 18B a b )d e + (- 25A b + 10B a b )d e + 3B b d +--R / +--R 5 10 4 9 3 2 2 8 2 3 3 7 4 4 6 +--R 12a e - 60a b d e + 120a b d e - 120a b d e + 60a b d e +--R + +--R 5 5 5 +--R - 12b d e +--R * +--R 4 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 4 5 5 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 6 4 +--R - 48b d e +--R * +--R 3 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 4 6 4 +--R 72a d e - 360a b d e + 720a b d e - 720a b d e + 360a b d e +--R + +--R 5 7 3 +--R - 72b d e +--R * +--R 2 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 4 7 3 +--R 48a d e - 240a b d e + 480a b d e - 480a b d e + 240a b d e +--R + +--R 5 8 2 +--R - 48b d e +--R * +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 4 8 2 5 9 +--R 12a d e - 60a b d e + 120a b d e - 120a b d e + 60a b d e - 12b d e +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x)^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1293 +r0:=5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*x/b^6-_ + (A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x))+_ + 5*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^2/b^7+_ + 5/3*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^3/b^7+_ + 1/4*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^4/b^7+_ + 1/5*B*e^5*(a+b*x)^5/b^7+(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 360B a b)e + (- 1200A a b + 1500B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 600B a b )d e + 60B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (300A a b - 360B a )e + (- 1200A a b + 1500B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 5 2 4 4 5 5 +--R (300A a b - 600B a b )d e + 60B a b d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 12B b e x + ((15A b - 18B a b )e + 75B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 25A a b + 30B a b )e + (100A b - 125B a b )d e + 200B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (50A a b - 60B a b )e + (- 200A a b + 250B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (300A b - 400B a b )d e + 300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 150A a b + 180B a b )e + (600A a b - 750B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 900A a b + 1200B a b )d e + (600A b - 900B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 25A a b - 78B a b)e + (400A a b - 125B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 900A a b + 800B a b )d e + (600A a b - 900B a b )d e +--R + +--R 5 4 +--R 300B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (275A a b - 438B a )e + (- 800A a b + 1375B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (900A a b - 1600B a b )d e + (- 600A a b + 900B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (300A a b - 300B a b )d e + (- 60A b + 60B a b )d +--R / +--R 8 7 +--R 60b x + 60a b +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 5 3 3 4 2 4 +--R (300A a b - 360B a b)e + (- 1200A a b + 1500B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 6 5 4 6 5 +--R (300A b - 600B a b )d e + 60B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (300A a b - 360B a )e + (- 1200A a b + 1500B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (1800A a b - 2400B a b )d e + (- 1200A a b + 1800B a b )d e +--R + +--R 5 2 4 4 5 5 +--R (300A a b - 600B a b )d e + 60B a b d +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 12B b e x + ((15A b - 18B a b )e + 75B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 25A a b + 30B a b )e + (100A b - 125B a b )d e + 200B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (50A a b - 60B a b )e + (- 200A a b + 250B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (300A b - 400B a b )d e + 300B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 150A a b + 180B a b )e + (600A a b - 750B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 6 4 +--R (- 900A a b + 1200B a b )d e + (600A b - 900B a b )d e + 300B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 300B a b)e + (900A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 1200A a b + 1800B a b )d e + (600A a b - 1200B a b )d e +--R + +--R 5 4 +--R 300B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (60A a b - 60B a )e + (- 300A a b + 300B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (600A a b - 600B a b )d e + (- 600A a b + 600B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (300A a b - 300B a b )d e + (- 60A b + 60B a b )d +--R / +--R 8 7 +--R 60b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 5 3 2 4 4 +--R (- 215A a b + 378B a )e + (500A a b - 1075B a b)d e +--R + +--R 2 3 3 2 2 3 2 3 3 2 +--R (- 300A a b + 1000B a b )d e - 300B a b d e +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x)^2 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1293 +r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-_ + (A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x))+_ + e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+_ + 1/4*B*e^4*(a+b*x)^4/b^6+(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (16A a b - 5B a b)e + (- 72A a b + 64B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 108B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 32A a b + 55B a )e + (72A a b - 128B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 108B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 4 2 3 3 2 3 +--R (- 48A a b + 60B a b)e + (144A a b - 192B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 144A a b + 216B a b )d e + (48A b - 96B a b )d e + 12B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 48A a b + 60B a )e + (144A a b - 192B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 4 4 +--R (- 144A a b + 216B a b )d e + (48A a b - 96B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 3B b e x + ((4A b - 5B a b )e + 16B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 8A a b + 10B a b )e + (24A b - 32B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (24A a b - 30B a b )e + (- 72A a b + 96B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (72A b - 108B a b )d e + 48B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (36A a b - 48B a b)e + (- 96A a b + 144B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 144B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 12A a b + 12B a )e + (48A a b - 48B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 72A a b + 72B a b )d e + (48A a b - 48B a b )d e +--R + +--R 5 4 4 +--R (- 12A b + 12B a b )d +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1293 +m0:=a0-r0 +--R +--R +--R 3 4 4 2 2 3 3 2 2 2 2 +--R (20A a b - 43B a )e + (- 24A a b + 80B a b)d e - 36B a b d e +--R (4) ---------------------------------------------------------------- +--R 6 +--R 12b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1293 +r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-_ + (A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x))+_ + 1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+_ + 1/3*B*e^3*(a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 9A a b + 8B a b)e + (18A a b - 27B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (9A a b - 16B a )e + (- 18A a b + 27B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 3 2 2 2 +--R (18A a b - 24B a b)e + (- 36A a b + 54B a b )d e +--R + +--R 4 3 2 4 3 +--R (18A b - 36B a b )d e + 6B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (18A a b - 24B a )e + (- 36A a b + 54B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (18A a b - 36B a b )d e + 6B a b d +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 2B b e x + ((3A b - 4B a b )e + 9B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 9A a b + 12B a b )e + (18A b - 27B a b )d e + 18B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 18B a b)e + (18A a b - 36B a b )d e + 18B a b d e)x +--R + +--R 3 4 3 2 2 3 2 +--R (6A a b - 6B a )e + (- 18A a b + 18B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (18A a b - 18B a b )d e + (- 6A b + 6B a b )d +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 3 2 2 +--R (- 3A a b + 10B a )e - 9B a b d e +--R (4) ----------------------------------- +--R 5 +--R 6b +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x)^2 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1293 +r0:=e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-_ + (A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*_ + (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 +--R ((- 4A a b + 6B a b)e + (4A b - 8B a b )d e + 2B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 4A a b + 6B a )e + (4A a b - 8B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R B b e x + ((2A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((2A a b - 4B a b)e + 4B a b d e)x + (- 2A a b + 2B a )e +--R + +--R 2 2 3 2 2 +--R (4A a b - 4B a b)d e + (- 2A b + 2B a b )d +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x)^2 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) --------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1293 +r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+_ + (b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (((A b - 2B a b)e + B b d)x + (A a b - 2B a )e + B a b d)log(b x + a) +--R + +--R 2 2 2 2 +--R B b e x + B a b e x + (A a b - B a )e + (- A b + B a b)d +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1293 +t0:=(A+B*x)/(a+b*x)^2 +--R +--R +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1293 +r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (2) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (B b x + B a)log(b x + a) - A b + B a +--R (3) ------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 3 2 2 2 2 +--R b e x + (2a b e + b d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1293 +r0:=(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-_ + (B*d-A*e)*log(d+e*x)/(b*d-a*e)^2 +--R +--R +--R (2) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R ((A b e - B b d)x + A a b e - B a b d)log(e x + d) +--R + +--R 2 2 2 +--R ((- A b e + B b d)x - A a b e + B a b d)log(b x + a) + (A a b - B a )e +--R + +--R 2 +--R (- A b + B a b)d +--R / +--R 2 2 2 3 4 2 3 2 2 2 3 2 +--R (a b e - 2a b d e + b d )x + a b e - 2a b d e + a b d +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1293 +r0:=(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+_ + (b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-_ + (b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R ((- 2A b + B a b)e + B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 2A a b + B a )e + (- 2A b + 2B a b)d e + B b d )x +--R + +--R 2 2 +--R (- 2A a b + B a )d e + B a b d +--R * +--R log(e x + d) +--R + +--R 2 2 2 2 +--R ((2A b - B a b)e - B b d e)x +--R + +--R 2 2 2 2 2 +--R ((2A a b - B a )e + (2A b - 2B a b)d e - B b d )x +--R + +--R 2 2 +--R (2A a b - B a )d e - B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 2A a b + B a )e + 2A b d e - B b d )x - A a e + 2B a d e +--R + +--R 2 2 +--R (A b - 2B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b e - 3a b d e + 3a b d e - b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a e - 2a b d e + 2a b d e - b d )x + a d e - 3a b d e + 3a b d e +--R + +--R 3 4 +--R - a b d +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1293 +r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/_ + ((b*d-a*e)^2*(d+e*x)^2)+(b*B*d-2*A*b*e+a*B*e)/_ + ((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*_ + log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((6A b - 4B a b )e - 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (12A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((12A a b - 8B a b)d e + (6A b - 8B a b )d e - 2B b d )x +--R + +--R 2 2 2 2 3 +--R (6A a b - 4B a b)d e - 2B a b d +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((- 6A b + 4B a b )e + 2B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 4B a b)e + (- 12A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((- 12A a b + 8B a b)d e + (- 6A b + 8B a b )d e + 2B b d )x +--R + +--R 2 2 2 2 3 +--R (- 6A a b + 4B a b)d e + 2B a b d +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((6A a b - 4B a b)e + (- 6A b + 2B a b )d e + 2B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b - 2B a )e + (6A a b - 5B a b)d e + (- 9A b + 4B a b )d e +--R + +--R 3 3 +--R 3B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - A a e + (6A a b - B a )d e + (- 3A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- 2A b + 5B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4b d e)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a d e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^4) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1293 +r0:=-b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x))+_ + 1/3*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^3)+_ + 1/2*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^2)+_ + b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x))+_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^5-_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 24A b + 18B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 18B a b )e + (- 72A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 4 3 2 2 +--R (- 72A a b + 54B a b )d e + (- 72A b + 72B a b )d e +--R + +--R 4 3 +--R 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((- 72A a b + 54B a b )d e + (- 24A b + 36B a b )d e + 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (- 24A a b + 18B a b )d e + 6B a b d +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 18B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 18B a b )e + (72A b - 60B a b )d e - 18B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((72A a b - 54B a b )d e + (72A b - 72B a b )d e - 18B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((72A a b - 54B a b )d e + (24A b - 36B a b )d e - 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (24A a b - 18B a b )d e - 6B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 18B a b )e + (24A b - 12B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 9B a b)e + (- 48A a b + 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (60A b - 33B a b )d e - 15B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b - 3B a )e + (- 36A a b + 26B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 12A a b + 18B a b )d e + (44A b - 30B a b )d e - 11B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (12A a b - B a )d e + (- 36A a b + 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (20A a b + 9B a b )d e + (6A b - 17B a b )d +--R / +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e )x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 5 5 3 6 6 2 +--R 84a b d e - 18b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 2 4 5 3 5 6 2 +--R 18a d e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 6 7 +--R - 18b d e +--R * +--R 2 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2 +--R 18a d e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 5 7 6 8 +--R 12a b d e - 6b d +--R * +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 5 8 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((- 24A b + 18B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 18B a b )e + (- 72A b + 60B a b )d e +--R + +--R 4 2 2 +--R 18B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 4 3 2 2 +--R (- 72A a b + 54B a b )d e + (- 72A b + 72B a b )d e +--R + +--R 4 3 +--R 18B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((- 72A a b + 54B a b )d e + (- 24A b + 36B a b )d e + 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (- 24A a b + 18B a b )d e + 6B a b d +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((24A b - 18B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 18B a b )e + (72A b - 60B a b )d e - 18B b d e )x +--R + +--R 3 2 2 3 4 3 2 2 4 3 2 +--R ((72A a b - 54B a b )d e + (72A b - 72B a b )d e - 18B b d e)x +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R ((72A a b - 54B a b )d e + (24A b - 36B a b )d e - 6B b d )x +--R + +--R 3 2 2 3 3 4 +--R (24A a b - 18B a b )d e - 6B a b d +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((- 24A a b + 18B a b )e + (24A b - 12B a b )d e - 6B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 9B a b)e + (- 48A a b + 39B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (60A b - 33B a b )d e - 15B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (4A a b - 3B a )e + (- 36A a b + 26B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 12A a b + 18B a b )d e + (44A b - 30B a b )d e - 11B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 2A a e + (12A a b - B a )d e + (- 36A a b + 9B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (20A a b + 9B a b )d e + (6A b - 17B a b )d +--R / +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 4 +--R (6a b e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6b d e )x +--R + +--R 6 8 5 7 4 2 2 6 3 3 3 5 2 4 4 4 +--R 6a e - 12a b d e - 30a b d e + 120a b d e - 150a b d e +--R + +--R 5 5 3 6 6 2 +--R 84a b d e - 18b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 2 6 4 2 3 5 2 4 5 3 5 6 2 +--R 18a d e - 72a b d e + 90a b d e - 90a b d e + 72a b d e +--R + +--R 6 7 +--R - 18b d e +--R * +--R 2 +--R x +--R + +--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2 +--R 18a d e - 84a b d e + 150a b d e - 120a b d e + 30a b d e +--R + +--R 5 7 6 8 +--R 12a b d e - 6b d +--R * +--R x +--R + +--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7 5 8 +--R 6a d e - 30a b d e + 60a b d e - 60a b d e + 30a b d e - 6a b d +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^5) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b e x + (2a b e + 5b d e )x + (a e + 10a b d e + 10b d e )x +--R + +--R 2 4 2 3 2 3 2 4 2 2 3 3 2 2 4 3 +--R (5a d e + 20a b d e + 10b d e )x + (10a d e + 20a b d e + 5b d e)x +--R + +--R 2 3 2 4 2 5 2 2 4 5 2 5 +--R (10a d e + 10a b d e + b d )x + (5a d e + 2a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1293 +r0:=-b^3*(A*b-a*B)/((b*d-a*e)^5*(a+b*x))+_ + 1/4*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^4)+_ + 1/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x)^3)+_ + 1/2*b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(d+e*x)^2)+_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(d+e*x))+_ + b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(a+b*x)/(b*d-a*e)^6-_ + b^3*(b*B*d-5*A*b*e+4*a*B*e)*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((60A b - 48B a b )e - 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (240A b - 204B a b )d e - 48B b d e )x +--R + +--R 4 2 3 4 5 4 2 3 +--R (240A a b - 192B a b )d e + (360A b - 336B a b )d e +--R + +--R 5 3 2 +--R - 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (360A a b - 288B a b )d e + (240A b - 264B a b )d e +--R + +--R 5 4 +--R - 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R ((240A a b - 192B a b )d e + (60A b - 96B a b )d e - 12B b d )x +--R + +--R 4 2 3 4 4 5 +--R (60A a b - 48B a b )d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((- 60A b + 48B a b )e + 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 60A a b + 48B a b )e + (- 240A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 240A a b + 192B a b )d e + (- 360A b + 336B a b )d e +--R + +--R 5 3 2 +--R 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 360A a b + 288B a b )d e + (- 240A b + 264B a b )d e +--R + +--R 5 4 +--R 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 240A a b + 192B a b )d e + (- 60A b + 96B a b )d e +--R + +--R 5 5 +--R 12B b d +--R * +--R x +--R + +--R 4 2 3 4 4 5 +--R (- 60A a b + 48B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (- 60A b + 36B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 24B a b )e + (180A a b - 150B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 210A b + 132B a b )d e + 42B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 10A a b + 8B a b)e + (120A a b - 94B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (150A a b - 144B a b )d e + (- 260A b + 178B a b )d e + 52B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 4B a )e + (- 40A a b + 31B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 136B a b )d e + (- 20A a b - 20B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 125A b + 104B a b )d e + 25B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 3A a e + (20A a b - B a )d e + (- 60A a b + 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (120A a b - 36B a b )d e + (- 65A a b - 8B a b )d e +--R + +--R 5 4 5 +--R (- 12A b + 37B a b )d +--R / +--R 6 10 5 2 9 4 3 2 8 3 4 3 7 2 5 4 6 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 6 5 5 7 6 4 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R 648a b d e - 276a b d e + 48b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R 48a d e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 2 5 6 4 6 7 3 7 8 2 +--R 792a b d e - 384a b d e + 72b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 3 4 6 4 +--R 72a d e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 2 5 7 3 6 8 2 7 9 +--R 288a b d e - 216a b d e + 48b d e +--R * +--R 2 +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 3 4 7 3 +--R 48a d e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 5 8 2 6 9 7 10 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 2 5 9 6 10 +--R - 72a b d e + 12a b d +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 +--R ((60A b - 48B a b )e - 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (240A b - 204B a b )d e - 48B b d e )x +--R + +--R 4 2 3 4 5 4 2 3 +--R (240A a b - 192B a b )d e + (360A b - 336B a b )d e +--R + +--R 5 3 2 +--R - 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (360A a b - 288B a b )d e + (240A b - 264B a b )d e +--R + +--R 5 4 +--R - 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 5 5 +--R ((240A a b - 192B a b )d e + (60A b - 96B a b )d e - 12B b d )x +--R + +--R 4 2 3 4 4 5 +--R (60A a b - 48B a b )d e - 12B a b d +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((- 60A b + 48B a b )e + 12B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 60A a b + 48B a b )e + (- 240A b + 204B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 4 +--R x +--R + +--R 4 2 3 4 5 4 2 3 +--R (- 240A a b + 192B a b )d e + (- 360A b + 336B a b )d e +--R + +--R 5 3 2 +--R 72B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (- 360A a b + 288B a b )d e + (- 240A b + 264B a b )d e +--R + +--R 5 4 +--R 48B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 3 3 2 5 4 4 +--R (- 240A a b + 192B a b )d e + (- 60A b + 96B a b )d e +--R + +--R 5 5 +--R 12B b d +--R * +--R x +--R + +--R 4 2 3 4 4 5 +--R (- 60A a b + 48B a b )d e + 12B a b d +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((60A a b - 48B a b )e + (- 60A b + 36B a b )d e + 12B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (30A a b - 24B a b )e + (180A a b - 150B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 210A b + 132B a b )d e + 42B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 10A a b + 8B a b)e + (120A a b - 94B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (150A a b - 144B a b )d e + (- 260A b + 178B a b )d e + 52B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 4B a )e + (- 40A a b + 31B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 136B a b )d e + (- 20A a b - 20B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 125A b + 104B a b )d e + 25B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 3A a e + (20A a b - B a )d e + (- 60A a b + 8B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (120A a b - 36B a b )d e + (- 65A a b - 8B a b )d e +--R + +--R 5 4 5 +--R (- 12A b + 37B a b )d +--R / +--R 6 10 5 2 9 4 3 2 8 3 4 3 7 2 5 4 6 +--R 12a b e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 6 5 5 7 6 4 +--R - 72a b d e + 12b d e +--R * +--R 5 +--R x +--R + +--R 7 10 6 9 5 2 2 8 4 3 3 7 3 4 4 6 +--R 12a e - 24a b d e - 108a b d e + 480a b d e - 780a b d e +--R + +--R 2 5 5 5 6 6 4 7 7 3 +--R 648a b d e - 276a b d e + 48b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 2 3 7 4 3 4 6 3 4 5 5 +--R 48a d e - 216a b d e + 288a b d e + 120a b d e - 720a b d e +--R + +--R 2 5 6 4 6 7 3 7 8 2 +--R 792a b d e - 384a b d e + 72b d e +--R * +--R 3 +--R x +--R + +--R 7 2 8 6 3 7 5 2 4 6 4 3 5 5 3 4 6 4 +--R 72a d e - 384a b d e + 792a b d e - 720a b d e + 120a b d e +--R + +--R 2 5 7 3 6 8 2 7 9 +--R 288a b d e - 216a b d e + 48b d e +--R * +--R 2 +--R x +--R + +--R 7 3 7 6 4 6 5 2 5 5 4 3 6 4 3 4 7 3 +--R 48a d e - 276a b d e + 648a b d e - 780a b d e + 480a b d e +--R + +--R 2 5 8 2 6 9 7 10 +--R - 108a b d e - 24a b d e + 12b d +--R * +--R x +--R + +--R 7 4 6 6 5 5 5 2 6 4 4 3 7 3 3 4 8 2 +--R 12a d e - 72a b d e + 180a b d e - 240a b d e + 180a b d e +--R + +--R 2 5 9 6 10 +--R - 72a b d e + 12a b d +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1293 +t0:=(A+B*x)*(d+e*x)^5/(a+b*x)^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R B e x + (A e + 5B d e )x + (5A d e + 10B d e )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10A d e + 10B d e )x + (10A d e + 5B d e)x + (5A d e + B d )x + A d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1293 +r0:=10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*x/b^6-_ + 1/2*(A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x)^2)-_ + (b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)/(b^7*(a+b*x))+_ + 5/2*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^2/b^7+_ + 1/3*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^3/b^7+_ + 1/4*B*e^5*(a+b*x)^4/b^7+5*e*(b*d-a*e)^3*_ + (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 120A a b + 180B a b )e + (360A a b - 600B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 360A a b + 720B a b )d e + (120A b - 360B a b )d e +--R + +--R 6 4 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 360B a b)e + (720A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 720A a b + 1440B a b )d e + (240A a b - 720B a b )d e +--R + +--R 5 4 +--R 120B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 120A a b + 180B a )e + (360A a b - 600B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 360A a b + 720B a b )d e + (120A a b - 360B a b )d e +--R + +--R 2 4 4 +--R 60B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 3B b e x + ((4A b - 6B a b )e + 20B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 10A a b + 15B a b )e + (30A b - 50B a b )d e + 60B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (40A a b - 60B a b )e + (- 120A a b + 200B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (120A b - 240B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (100A a b - 135B a b )e + (- 300A a b + 500B a b )d e +--R + +--R 5 2 4 2 3 5 3 2 +--R (240A a b - 600B a b )d e + 240B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 40A a b + 90B a b)e + (120A a b - 200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 240A a b + 240B a b )d e + (240A a b - 240B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 60A b + 120B a b )d e - 12B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 80A a b + 135B a )e + (240A a b - 400B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 480B a b )d e + (180A a b - 300B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b + 90B a b )d e + (- 6A b - 6B a b )d +--R / +--R 9 2 8 2 7 +--R 12b x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 120A a b + 180B a b )e + (360A a b - 600B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 360A a b + 720B a b )d e + (120A b - 360B a b )d e +--R + +--R 6 4 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (- 240A a b + 360B a b)e + (720A a b - 1200B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 720A a b + 1440B a b )d e + (240A a b - 720B a b )d e +--R + +--R 5 4 +--R 120B a b d e +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 120A a b + 180B a )e + (360A a b - 600B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 360A a b + 720B a b )d e + (120A a b - 360B a b )d e +--R + +--R 2 4 4 +--R 60B a b d e +--R * +--R log(b x + a) +--R + +--R 6 5 6 6 5 5 6 4 5 +--R 3B b e x + ((4A b - 6B a b )e + 20B b d e )x +--R + +--R 5 2 4 5 6 5 4 6 2 3 4 +--R ((- 10A a b + 15B a b )e + (30A b - 50B a b )d e + 60B b d e )x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (40A a b - 60B a b )e + (- 120A a b + 200B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (120A b - 240B a b )d e + 120B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (126A a b - 204B a b )e + (- 330A a b + 630B a b )d e +--R + +--R 5 2 4 2 3 5 3 2 +--R (240A a b - 660B a b )d e + 240B a b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (12A a b - 48B a b)e + (60A a b + 60B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (- 240A a b + 120B a b )d e + (240A a b - 240B a b )d e +--R + +--R 6 5 4 6 5 +--R (- 60A b + 120B a b )d e - 12B b d +--R * +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 54A a b + 66B a )e + (210A a b - 270B a b)d e +--R + +--R 3 3 4 2 2 3 2 4 3 3 3 2 +--R (- 300A a b + 420B a b )d e + (180A a b - 300B a b )d e +--R + +--R 5 2 4 4 6 5 5 +--R (- 30A a b + 90B a b )d e + (- 6A b - 6B a b )d +--R / +--R 9 2 8 2 7 +--R 12b x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1293 +m0:=a0-r0 +--R +--R +--R 3 4 5 2 2 3 4 2 2 2 3 +--R (26A a b - 69B a )e + (- 30A a b + 130B a b)d e - 60B a b d e +--R (4) ----------------------------------------------------------------- +--R 7 +--R 12b +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1293 +t0:=(A+B*x)*(d+e*x)^4/(a+b*x)^3 +--R +--R +--R (1) +--R 4 5 4 3 4 3 2 2 3 +--R B e x + (A e + 4B d e )x + (4A d e + 6B d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6A d e + 4B d e)x + (4A d e + B d )x + A d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1293 +r0:=2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*x/b^5-_ + 1/2*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)^2)-_ + (b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*(a+b*x))+_ + 1/2*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^2/b^6+_ + 1/3*B*e^4*(a+b*x)^3/b^6+2*e*(b*d-a*e)^2*_ + (2*b*B*d+3*A*b*e-5*a*B*e)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 30A a b + 50B a b )e + (48A a b - 120B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12A a b - 20B a b)e + (- 48A a b + 48B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (24A a b - 40B a )e + (- 60A a b + 96B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 4 4 2 3 3 +--R (36A a b - 60B a b )e + (- 72A a b + 144B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (36A b - 108B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (72A a b - 120B a b)e + (- 144A a b + 288B a b )d e +--R + +--R 4 2 3 2 2 4 3 +--R (72A a b - 216B a b )d e + 48B a b d e +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (36A a b - 60B a )e + (- 72A a b + 144B a b)d e +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (36A a b - 108B a b )d e + 24B a b d e +--R * +--R log(b x + a) +--R + +--R 5 4 5 5 4 4 5 3 4 +--R 2B b e x + ((3A b - 5B a b )e + 12B b d e )x +--R + +--R 4 2 3 4 5 4 3 5 2 2 3 +--R ((- 12A a b + 20B a b )e + (24A b - 48B a b )d e + 36B b d e )x +--R + +--R 2 3 3 2 4 4 2 3 3 4 2 2 2 +--R ((- 33A a b + 63B a b )e + (48A a b - 132B a b )d e + 72B a b d e )x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (6A a b + 6B a b)e + (- 48A a b + 24B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (72A a b - 72B a b )d e + (- 24A b + 48B a b )d e - 6B b d +--R * +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (21A a b - 27B a )e + (- 60A a b + 84B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (54A a b - 90B a b )d e + (- 12A a b + 36B a b )d e +--R + +--R 5 4 4 +--R (- 3A b - 3B a b )d +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1293 +m0:=a0-r0 +--R +--R +--R 2 3 4 2 3 +--R (- 3A a b + 13B a )e - 12B a b d e +--R (4) ------------------------------------ +--R 6 +--R 6b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1293 +t0:=(A+B*x)*(d+e*x)^3/(a+b*x)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x + A d +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1293 +r0:=e^2*(3*b*B*d+A*b*e-3*a*B*e)*x/b^4+1/2*B*e^3*x^2/b^3-_ + 1/2*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^2)-_ + (b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x))+_ + 3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 6A a b + 12B a b )e + (6A b - 18B a b )d e + 6B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 12A a b + 24B a b)e + (12A a b - 36B a b )d e + 12B a b d e)x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 6A a b + 12B a )e + (6A a b - 18B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 4 3 4 4 3 3 4 2 3 +--R B b e x + ((2A b - 4B a b )e + 6B b d e )x +--R + +--R 3 2 2 3 3 2 2 +--R ((4A a b - 11B a b )e + 12B a b d e )x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 4A a b + 2B a b)e + (12A a b - 12B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 6A b + 12B a b )d e - 2B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 3 2 2 2 +--R (- 5A a b + 7B a )e + (9A a b - 15B a b)d e + (- 3A a b + 9B a b )d e +--R + +--R 4 3 3 +--R (- A b - B a b )d +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1293 +t0:=(A+B*x)*(d+e*x)^2/(a+b*x)^3 +--R +--R +--R 2 3 2 2 2 2 +--R B e x + (A e + 2B d e)x + (2A d e + B d )x + A d +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1293 +r0:=B*e^2*x/b^3-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)^2)-_ + (b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)/(b^4*(a+b*x))+_ + e*(2*b*B*d+A*b*e-3*a*B*e)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 2 +--R ((2A b - 6B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((4A a b - 12B a b)e + 8B a b d e)x + (2A a b - 6B a )e + 4B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 2 2 +--R 2B b e x + 4B a b e x +--R + +--R 2 2 2 3 2 3 2 +--R ((4A a b - 4B a b)e + (- 4A b + 8B a b )d e - 2B b d )x +--R + +--R 2 3 2 2 2 3 2 2 +--R (3A a b - 5B a )e + (- 2A a b + 6B a b)d e + (- A b - B a b )d +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1293 +t0:=(A+B*x)*(d+e*x)/(a+b*x)^3 +--R +--R +--R 2 +--R B e x + (A e + B d)x + A d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1293 +r0:=-1/2*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^2)+_ + (-b*B*d-A*b*e+2*a*B*e)/(b^3*(a+b*x))+B*e*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2B b e x + 4B a b e x + 2B a e)log(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2A b + 4B a b)e - 2B b d)x + (- A a b + 3B a )e + (- A b - B a b)d +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1293 +t0:=(A+B*x)/(a+b*x)^3 +--R +--R +--R B x + A +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1293 +r0:=-1/2*(A+B*x)^2/((A*b-a*B)*(a+b*x)^2) +--R +--R +--R 1 2 2 1 2 +--R - - B x - A B x - - A +--R 2 2 +--R (2) ------------------------------------------------------ +--R 3 2 2 2 2 2 3 +--R (A b - B a b )x + (2A a b - 2B a b)x + A a b - B a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 1293 +a0:=integrate(t0,x) +--R +--R +--R - 2B b x - A b - B a +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1293 +m0:=a0-r0 +--R +--R +--R 2 +--R B +--R (4) --------------- +--R 3 2 +--R 2A b - 2B a b +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1293 +r0:=1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2)+(-B*d+A*e)/((b*d-a*e)^2*(a+b*x))-_ + e*(B*d-A*e)*log(a+b*x)/(b*d-a*e)^3+e*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^3 +--R +--R +--R (2) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 2 2 2 2 2 +--R (2A b e - 2B b d e)x + (4A a b e - 4B a b d e)x + 2A a b e +--R + +--R 2 +--R - 2B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 2 2 2 2 2 2 +--R (- 2A b e + 2B b d e)x + (- 4A a b e + 4B a b d e)x - 2A a b e +--R + +--R 2 +--R 2B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 3 2 2 3 2 +--R (2A a b e + (- 2A b - 2B a b )d e + 2B b d )x + (3A a b - B a )e +--R + +--R 2 3 2 2 +--R - 4A a b d e + (A b + B a b )d +--R / +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (2a b e - 6a b d e + 6a b d e - 2b d )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 3 4 2 2 +--R (4a b e - 12a b d e + 12a b d e - 4a b d )x + 2a b e - 6a b d e +--R + +--R 3 3 2 2 4 3 +--R 6a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^2) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 1293 +r0:=1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^2)+_ + (-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*(a+b*x))-_ + e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x))-_ + e*(2*b*B*d-3*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^4+_ + e*(2*b*B*d-3*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 +--R ((- 6A b + 2B a b )e + 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 12A a b + 4B a b)e + (- 6A b + 10B a b )d e + 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((- 6A a b + 2B a )e + (- 12A a b + 8B a b)d e + 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (- 6A a b + 2B a )d e + 4B a b d e +--R * +--R log(e x + d) +--R + +--R 3 2 3 3 2 3 +--R ((6A b - 2B a b )e - 4B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((12A a b - 4B a b)e + (6A b - 10B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 2 2 +--R ((6A a b - 2B a )e + (12A a b - 8B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 +--R (6A a b - 2B a )d e - 4B a b d e +--R * +--R log(b x + a) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 6A a b + 2B a b)e + (6A b + 2B a b )d e - 4B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (- 9A a b + 3B a )e + (6A a b + 4B a b)d e + (3A b - 5B a b )d e +--R + +--R 3 3 +--R - 2B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (- 3A a b + 5B a )d e + (6A a b - 4B a b)d e +--R + +--R 3 2 3 +--R (- A b - B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (2a b e - 8a b d e + 12a b d e - 8a b d e + 2b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 6 5 2 +--R (4a b e - 14a b d e + 16a b d e - 4a b d e - 4a b d e + 2b d )x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (2a e - 4a b d e - 4a b d e + 16a b d e - 14a b d e + 4a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 2a d e - 8a b d e + 12a b d e - 8a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^3) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a e + 9a b d e + 9a b d e + b d )x + (3a d e + 9a b d e + 3a b d )x +--R + +--R 3 2 2 3 3 3 +--R (3a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 1293 +r0:=-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^2)-_ + b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(a+b*x))-_ + 1/2*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^2)-_ + e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x))-_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^5+_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 +--R ((12A b - 6B a b )e - 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((24A a b - 12B a b )e + (24A b - 24B a b )d e - 12B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (12A a b - 6B a b)e + (48A a b - 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (12A b - 30B a b )d e - 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 3 3 +--R ((24A a b - 12B a b)d e + (24A a b - 24B a b )d e - 12B a b d e)x +--R + +--R 2 2 3 2 2 2 2 3 +--R (12A a b - 6B a b)d e - 6B a b d e +--R * +--R log(e x + d) +--R + +--R 4 3 4 4 3 4 +--R ((- 12A b + 6B a b )e + 6B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 24A a b + 12B a b )e + (- 24A b + 24B a b )d e +--R + +--R 4 2 2 +--R 12B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 12A a b + 6B a b)e + (- 48A a b + 30B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 12A b + 30B a b )d e + 6B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (- 24A a b + 12B a b)d e + (- 24A a b + 24B a b )d e +--R + +--R 3 3 +--R 12B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 12A a b + 6B a b)d e + 6B a b d e +--R * +--R log(b x + a) +--R + +--R 3 2 2 4 4 3 4 2 2 3 +--R ((12A a b - 6B a b )e - 12A b d e + 6B b d e )x +--R + +--R 2 2 3 4 2 2 3 4 3 2 2 +--R (18A a b - 9B a b)e - 9B a b d e + (- 18A b + 9B a b )d e +--R + +--R 4 3 +--R 9B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (4A a b - 2B a )e + (24A a b - 14B a b)d e - 24A a b d e +--R + +--R 4 3 3 4 4 +--R (- 4A b + 14B a b )d e + 2B b d +--R * +--R x +--R + +--R 4 4 3 4 3 3 2 2 3 2 2 3 +--R - A a e + (8A a b - B a )d e - 9B a b d e + (- 8A a b + 9B a b )d e +--R + +--R 4 3 4 +--R (A b + B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2b d e )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4b d e)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a e - 2a b d e - 18a b d e + 50a b d e - 50a b d e + 18a b d e +--R + +--R 6 6 7 7 +--R 2a b d e - 2b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a d e - 16a b d e + 20a b d e - 20a b d e + 16a b d e - 4a b d )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a d e - 10a b d e + 20a b d e - 20a b d e + 10a b d e - 2a b d +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^4) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 +--R b e x + (3a b e + 4b d e )x + (3a b e + 12a b d e + 6b d e )x +--R + +--R 3 4 2 3 2 2 2 3 3 4 +--R (a e + 12a b d e + 18a b d e + 4b d e)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 +--R (4a d e + 18a b d e + 12a b d e + b d )x +--R + +--R 3 2 2 2 3 2 4 2 3 3 2 4 3 4 +--R (6a d e + 12a b d e + 3a b d )x + (4a d e + 3a b d )x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 1293 +r0:=-1/2*b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x)^2)-_ + b^2*(b*B*d-4*A*b*e+3*a*B*e)/((b*d-a*e)^5*(a+b*x))-_ + 1/3*e*(B*d-A*e)/((b*d-a*e)^3*(d+e*x)^3)-_ + 1/2*e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(d+e*x)^2)-_ + 3*b*e*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^5*(d+e*x))-_ + 2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(a+b*x)/(b*d-a*e)^6+_ + 2*b^2*e*(2*b*B*d-5*A*b*e+3*a*B*e)*log(d+e*x)/(b*d-a*e)^6 +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((- 60A b + 36B a b )e + 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 120A a b + 72B a b )e + (- 180A b + 156B a b )d e +--R + +--R 5 2 3 +--R 72B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 60A a b + 36B a b )e + (- 360A a b + 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 180A b + 252B a b )d e + 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (- 180A a b + 108B a b )d e + (- 360A a b + 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (- 60A b + 180B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 180A a b + 108B a b )d e + (- 120A a b + 144B a b )d e +--R + +--R 4 4 +--R 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (- 60A a b + 36B a b )d e + 24B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 36B a b )e - 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((120A a b - 72B a b )e + (180A b - 156B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (60A a b - 36B a b )e + (360A a b - 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 252B a b )d e - 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (180A a b - 108B a b )d e + (360A a b - 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (60A b - 180B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 108B a b )d e + (120A a b - 144B a b )d e +--R + +--R 4 4 +--R - 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (60A a b - 36B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 36B a b )e + (60A b - 12B a b )d e - 24B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 90A a b + 54B a b )e + (- 60A a b + 72B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (150A b - 66B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 20A a b + 12B a b)e + (- 210A a b + 134B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b + 12B a b )d e + (110A b - 114B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 3B a )e + (- 60A a b + 34B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 120A a b + 96B a b )d e + (160A a b - 48B a b )d e +--R + +--R 5 4 4 5 5 +--R (15A b - 73B a b )d e - 6B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A a e + (15A a b - B a )d e + (- 60A a b + 12B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (20A a b + 36B a b )d e + (30A a b - 44B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - 3B a b )d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 +--R ((- 60A b + 36B a b )e + 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (- 120A a b + 72B a b )e + (- 180A b + 156B a b )d e +--R + +--R 5 2 3 +--R 72B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 60A a b + 36B a b )e + (- 360A a b + 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (- 180A b + 252B a b )d e + 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (- 180A a b + 108B a b )d e + (- 360A a b + 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (- 60A b + 180B a b )d e + 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 180A a b + 108B a b )d e + (- 120A a b + 144B a b )d e +--R + +--R 4 4 +--R 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (- 60A a b + 36B a b )d e + 24B a b d e +--R * +--R log(e x + d) +--R + +--R 5 4 5 5 4 5 +--R ((60A b - 36B a b )e - 24B b d e )x +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((120A a b - 72B a b )e + (180A b - 156B a b )d e - 72B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (60A a b - 36B a b )e + (360A a b - 240B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (180A b - 252B a b )d e - 72B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 4 4 2 3 2 3 +--R (180A a b - 108B a b )d e + (360A a b - 288B a b )d e +--R + +--R 5 4 3 2 5 4 +--R (60A b - 180B a b )d e - 24B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 108B a b )d e + (120A a b - 144B a b )d e +--R + +--R 4 4 +--R - 48B a b d e +--R * +--R x +--R + +--R 2 3 3 2 3 2 2 3 4 +--R (60A a b - 36B a b )d e - 24B a b d e +--R * +--R log(b x + a) +--R + +--R 4 2 3 5 5 4 4 5 2 3 4 +--R ((- 60A a b + 36B a b )e + (60A b - 12B a b )d e - 24B b d e )x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (- 90A a b + 54B a b )e + (- 60A a b + 72B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (150A b - 66B a b )d e - 60B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 20A a b + 12B a b)e + (- 210A a b + 134B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 5 4 +--R (120A a b + 12B a b )d e + (110A b - 114B a b )d e - 44B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (5A a b - 3B a )e + (- 60A a b + 34B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 120A a b + 96B a b )d e + (160A a b - 48B a b )d e +--R + +--R 5 4 4 5 5 +--R (15A b - 73B a b )d e - 6B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 2A a e + (15A a b - B a )d e + (- 60A a b + 12B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (20A a b + 36B a b )d e + (30A a b - 44B a b )d e +--R + +--R 5 4 5 +--R (- 3A b - 3B a b )d +--R / +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 6a b e - 36a b d e + 90a b d e - 120a b d e + 90a b d e +--R + +--R 7 5 4 8 6 3 +--R - 36a b d e + 6b d e +--R * +--R 5 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 12a b e - 54a b d e + 72a b d e + 30a b d e - 180a b d e +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 198a b d e - 96a b d e + 18b d e +--R * +--R 4 +--R x +--R + +--R 8 9 6 2 2 7 5 3 3 6 4 4 4 5 3 5 5 4 +--R 6a e - 108a b d e + 312a b d e - 360a b d e + 144a b d e +--R + +--R 2 6 6 3 7 7 2 8 8 +--R 60a b d e - 72a b d e + 18b d e +--R * +--R 3 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 5 3 4 5 4 4 5 4 +--R 18a d e - 72a b d e + 60a b d e + 144a b d e - 360a b d e +--R + +--R 3 5 6 3 2 6 7 2 8 9 +--R 312a b d e - 108a b d e + 6b d +--R * +--R 2 +--R x +--R + +--R 8 2 7 7 3 6 6 2 4 5 5 3 5 4 4 4 6 3 +--R 18a d e - 96a b d e + 198a b d e - 180a b d e + 30a b d e +--R + +--R 3 5 7 2 2 6 8 7 9 +--R 72a b d e - 54a b d e + 12a b d +--R * +--R x +--R + +--R 8 3 6 7 4 5 6 2 5 4 5 3 6 3 4 4 7 2 3 5 8 +--R 6a d e - 36a b d e + 90a b d e - 120a b d e + 90a b d e - 36a b d e +--R + +--R 2 6 9 +--R 6a b d +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 5 3 2 4 +--R B b e x + ((A b + B a)e + 3B b d e )x +--R + +--R 3 2 2 3 +--R (A a e + (3A b + 3B a)d e + 3B b d e)x +--R + +--R 2 2 3 2 2 3 +--R (3A a d e + (3A b + 3B a)d e + B b d )x + (3A a d e + (A b + B a)d )x +--R + +--R 3 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1293 +r0:=2/9*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(9/2)/e^3-_ + 2/11*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^3+2/13*b*B*(d+e*x)^(13/2)/e^3 +--R +--R +--R (2) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 6 5 5 +--R 198B b e x + ((234A b + 234B a)e + 720B b d e )x +--R + +--R 6 5 2 4 4 +--R (286A a e + (884A b + 884B a)d e + 916B b d e )x +--R + +--R 5 2 4 3 3 3 +--R (1144A a d e + (1196A b + 1196B a)d e + 424B b d e )x +--R + +--R 2 4 3 3 4 2 2 +--R (1716A a d e + (624A b + 624B a)d e + 6B b d e )x +--R + +--R 3 3 4 2 5 4 2 +--R (1144A a d e + (26A b + 26B a)d e - 8B b d e)x + 286A a d e +--R + +--R 5 6 +--R (- 52A b - 52B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 1287e +--R Type: Union(Expression(Integer),...) +--E 638 + +--S 639 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1293 +r0:=2/7*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(7/2)/e^3-_ + 2/9*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^3+2/11*b*B*(d+e*x)^(11/2)/e^3 +--R +--R +--R (2) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 4 +--R 126B b e x + ((154A b + 154B a)e + 322B b d e )x +--R + +--R 5 4 2 3 3 +--R (198A a e + (418A b + 418B a)d e + 226B b d e )x +--R + +--R 4 2 3 3 2 2 +--R (594A a d e + (330A b + 330B a)d e + 6B b d e )x +--R + +--R 2 3 3 2 4 3 2 +--R (594A a d e + (22A b + 22B a)d e - 8B b d e)x + 198A a d e +--R + +--R 4 5 +--R (- 44A b - 44B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 693e +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1293 +t0:=(a+b*x)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1293 +r0:=2/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(5/2)/e^3-_ + 2/7*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^3+2/9*b*B*(d+e*x)^(9/2)/e^3 +--R +--R +--R (2) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 3 +--R 70B b e x + ((90A b + 90B a)e + 100B b d e )x +--R + +--R 4 3 2 2 2 +--R (126A a e + (144A b + 144B a)d e + 6B b d e )x +--R + +--R 3 2 2 3 2 2 +--R (252A a d e + (18A b + 18B a)d e - 8B b d e)x + 126A a d e +--R + +--R 3 4 +--R (- 36A b - 36B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 648 + +--S 649 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +)clear all + +--S 651 of 1293 +t0:=(a+b*x)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 +-------+ +--R (1) (B b x + (A b + B a)x + A a)\|e x + d +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1293 +r0:=2/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(3/2)/e^3-_ + 2/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^3+2/7*b*B*(d+e*x)^(7/2)/e^3 +--R +--R +--R (2) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 2 +--R 30B b e x + ((42A b + 42B a)e + 6B b d e )x +--R + +--R 3 2 2 2 +--R (70A a e + (14A b + 14B a)d e - 8B b d e)x + 70A a d e +--R + +--R 2 3 +--R (- 28A b - 28B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 653 + +--S 654 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 655 + +)clear all + +--S 656 of 1293 +t0:=(a+b*x)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1293 +r0:=-2/3*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^3+_ + 2/5*b*B*(d+e*x)^(5/2)/e^3+2*(b*d-a*e)*(B*d-A*e)*sqrt(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((10A b + 10B a)e - 8B b d e)x + 30A a e +--R + +--R 2 +--R (- 20A b - 20B a)d e + 16B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15e +--R Type: Union(Expression(Integer),...) +--E 658 + +--S 659 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 660 + +)clear all + +--S 661 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1293 +r0:=2/3*b*B*(d+e*x)^(3/2)/e^3-2*(b*d-a*e)*(B*d-A*e)/(e^3*sqrt(d+e*x))-_ + 2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 2B b e x + ((6A b + 6B a)e - 8B b d e)x - 6A a e + (12A b + 12B a)d e +--R + +--R 2 +--R - 16B b d +--R / +--R 3 +-------+ +--R 3e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 663 + +--S 664 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 665 + +)clear all + +--S 666 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1293 +r0:=-2/3*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(3/2))+_ + 2*(2*b*B*d-A*b*e-a*B*e)/(e^3*sqrt(d+e*x))+2*b*B*sqrt(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R 6B b e x + ((- 6A b - 6B a)e + 24B b d e)x - 2A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e + 16B b d +--R / +--R 4 3 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 668 + +--S 669 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 670 + +)clear all + +--S 671 of 1293 +t0:=(a+b*x)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1293 +r0:=-2/5*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(5/2))+_ + 2/3*(2*b*B*d-A*b*e-a*B*e)/(e^3*(d+e*x)^(3/2))-2*b*B/(e^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R - 30B b e x + ((- 10A b - 10B a)e - 40B b d e)x - 6A a e +--R + +--R 2 +--R (- 4A b - 4B a)d e - 16B b d +--R / +--R 5 2 4 2 3 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 673 + +--S 674 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 675 + +)clear all + +--S 676 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (1) +--R 2 3 6 2 3 2 2 5 +--R B b e x + ((A b + 2B a b)e + 3B b d e )x +--R + +--R 2 3 2 2 2 2 4 +--R ((2A a b + B a )e + (3A b + 6B a b)d e + 3B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (A a e + (6A a b + 3B a )d e + (3A b + 6B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 3 2 +--R (3A a d e + (6A a b + 3B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 3 2 3 +--R (3A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1293 +r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+_ + 2/11*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-_ + 2/13*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^4+_ + 2/15*b^2*B*(d+e*x)^(15/2)/e^4 +--R +--R +--R (2) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 7 2 6 6 +--R 858B b e x + ((990A b + 1980B a b)e + 3036B b d e )x +--R + +--R 2 7 2 6 +--R (2340A a b + 1170B a )e + (3600A b + 7200B a b)d e +--R + +--R 2 2 5 +--R 3708B b d e +--R * +--R 5 +--R x +--R + +--R 2 7 2 6 +--R 1430A a e + (8840A a b + 4420B a )d e +--R + +--R 2 2 5 2 3 4 +--R (4580A b + 9160B a b)d e + 1600B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 2 5 +--R 5720A a d e + (11960A a b + 5980B a )d e +--R + +--R 2 3 4 2 4 3 +--R (2120A b + 4240B a b)d e + 10B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 5 2 3 4 2 4 3 +--R 8580A a d e + (6240A a b + 3120B a )d e + (30A b + 60B a b)d e +--R + +--R 2 5 2 +--R - 12B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 2 4 3 2 5 2 +--R 5720A a d e + (260A a b + 130B a )d e + (- 40A b - 80B a b)d e +--R + +--R 2 6 +--R 16B b d e +--R * +--R x +--R + +--R 2 4 3 2 5 2 2 6 +--R 1430A a d e + (- 520A a b - 260B a )d e + (80A b + 160B a b)d e +--R + +--R 2 7 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 6435e +--R Type: Union(Expression(Integer),...) +--E 678 + +--S 679 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 680 + +)clear all + +--S 681 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1293 +r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+_ + 2/9*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-_ + 2/11*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^4+_ + 2/13*b^2*B*(d+e*x)^(13/2)/e^4 +--R +--R +--R (2) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 6 2 5 5 +--R 1386B b e x + ((1638A b + 3276B a b)e + 3402B b d e )x +--R + +--R 2 6 2 5 +--R (4004A a b + 2002B a )e + (4186A b + 8372B a b)d e +--R + +--R 2 2 4 +--R 2226B b d e +--R * +--R 4 +--R x +--R + +--R 2 6 2 5 +--R 2574A a e + (10868A a b + 5434B a )d e +--R + +--R 2 2 4 2 3 3 +--R (2938A b + 5876B a b)d e + 30B b d e +--R * +--R 3 +--R x +--R + +--R 2 5 2 2 4 2 3 3 +--R 7722A a d e + (8580A a b + 4290B a )d e + (78A b + 156B a b)d e +--R + +--R 2 4 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 4 2 3 3 +--R 7722A a d e + (572A a b + 286B a )d e +--R + +--R 2 4 2 2 5 +--R (- 104A b - 208B a b)d e + 48B b d e +--R * +--R x +--R + +--R 2 3 3 2 4 2 2 5 +--R 2574A a d e + (- 1144A a b - 572B a )d e + (208A b + 416B a b)d e +--R + +--R 2 6 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 9009e +--R Type: Union(Expression(Integer),...) +--E 683 + +--S 684 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 685 + +)clear all + +--S 686 of 1293 +t0:=(a+b*x)^2*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1293 +r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-_ + 2/9*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^4+_ + 2/11*b^2*B*(d+e*x)^(11/2)/e^4 +--R +--R +--R (2) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 5 2 5 2 4 4 +--R 630B b e x + ((770A b + 1540B a b)e + 840B b d e )x +--R + +--R 2 5 2 4 2 2 3 3 +--R ((1980A a b + 990B a )e + (1100A b + 2200B a b)d e + 30B b d e )x +--R + +--R 2 5 2 4 2 2 3 +--R 1386A a e + (3168A a b + 1584B a )d e + (66A b + 132B a b)d e +--R + +--R 2 3 2 +--R - 36B b d e +--R * +--R 2 +--R x +--R + +--R 2 4 2 2 3 2 3 2 +--R 2772A a d e + (396A a b + 198B a )d e + (- 88A b - 176B a b)d e +--R + +--R 2 4 +--R 48B b d e +--R * +--R x +--R + +--R 2 2 3 2 3 2 2 4 +--R 1386A a d e + (- 792A a b - 396B a )d e + (176A b + 352B a b)d e +--R + +--R 2 5 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 688 + +--S 689 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 690 + +)clear all + +--S 691 of 1293 +t0:=(a+b*x)^2*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1293 +r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+_ + 2/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-_ + 2/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^4+_ + 2/9*b^2*B*(d+e*x)^(9/2)/e^4 +--R +--R +--R (2) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 2 4 2 3 3 +--R 70B b e x + ((90A b + 180B a b)e + 10B b d e )x +--R + +--R 2 4 2 3 2 2 2 2 +--R ((252A a b + 126B a )e + (18A b + 36B a b)d e - 12B b d e )x +--R + +--R 2 4 2 3 2 2 2 +--R 210A a e + (84A a b + 42B a )d e + (- 24A b - 48B a b)d e +--R + +--R 2 3 +--R 16B b d e +--R * +--R x +--R + +--R 2 3 2 2 2 2 3 +--R 210A a d e + (- 168A a b - 84B a )d e + (48A b + 96B a b)d e +--R + +--R 2 4 +--R - 32B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 693 + +--S 694 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 695 + +)clear all + +--S 696 of 1293 +t0:=(a+b*x)^2*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1293 +r0:=2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-_ + 2/5*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+_ + 2/7*b^2*B*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((42A b + 84B a b)e - 36B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((140A a b + 70B a )e + (- 56A b - 112B a b)d e + 48B b d e)x +--R + +--R 2 3 2 2 2 2 +--R 210A a e + (- 280A a b - 140B a )d e + (112A b + 224B a b)d e +--R + +--R 2 3 +--R - 96B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105e +--R Type: Union(Expression(Integer),...) +--E 698 + +--S 699 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1293 +r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+_ + 2/5*b^2*B*(d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((10A b + 20B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((60A a b + 30B a )e + (- 40A b - 80B a b)d e + 48B b d e)x - 30A a e +--R + +--R 2 2 2 2 2 3 +--R (120A a b + 60B a )d e + (- 80A b - 160B a b)d e + 96B b d +--R / +--R 4 +-------+ +--R 15e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1293 +r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+_ + 2/3*b^2*B*(d+e*x)^(3/2)/e^4-_ + 2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*sqrt(d+e*x))-_ + 2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 2B b e x + ((6A b + 12B a b)e - 12B b d e )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12A a b - 6B a )e + (24A b + 48B a b)d e - 48B b d e)x - 2A a e +--R + +--R 2 2 2 2 2 3 +--R (- 8A a b - 4B a )d e + (16A b + 32B a b)d e - 32B b d +--R / +--R 5 4 +-------+ +--R (3e x + 3d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1293 +t0:=(a+b*x)^2*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--R (1) ---------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1293 +r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-_ + 2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+_ + 2*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 2 2 +--R 30B b e x + ((- 30A b - 60B a b)e + 180B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 20A a b - 10B a )e + (- 40A b - 80B a b)d e + 240B b d e)x +--R + +--R 2 3 2 2 2 2 2 3 +--R - 6A a e + (- 8A a b - 4B a )d e + (- 16A b - 32B a b)d e + 96B b d +--R / +--R 6 2 5 2 4 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 713 + +--S 714 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +)clear all + +--S 716 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 3 7 3 2 3 3 2 6 +--R B b e x + ((A b + 3B a b )e + 3B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 5 +--R ((3A a b + 3B a b)e + (3A b + 9B a b )d e + 3B b d e)x +--R + +--R 2 3 3 2 2 2 3 2 2 +--R (3A a b + B a )e + (9A a b + 9B a b)d e + (3A b + 9B a b )d e +--R + +--R 3 3 +--R B b d +--R * +--R 4 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R A a e + (9A a b + 3B a )d e + (9A a b + 9B a b)d e +--R + +--R 3 2 3 +--R (A b + 3B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3A a d e + (9A a b + 3B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 2 3 3 3 3 +--R (3A a d e + (3A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1293 +r0:=2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)/e^5-_ + 2/11*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5+_ + 6/13*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(13/2)/e^5-_ + 2/15*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^5+_ + 2/17*b^3*B*(d+e*x)^(17/2)/e^5 +--R +--R +--R (2) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8 8 3 2 8 3 7 7 +--R 12870B b e x + ((14586A b + 43758B a b )e + 44616B b d e )x +--R + +--R 2 2 8 3 2 7 +--R (50490A a b + 50490B a b)e + (51612A b + 154836B a b )d e +--R + +--R 3 2 6 +--R 52932B b d e +--R * +--R 6 +--R x +--R + +--R 2 3 8 2 2 7 +--R (59670A a b + 19890B a )e + (183600A a b + 183600B a b)d e +--R + +--R 3 2 2 6 3 3 5 +--R (63036A b + 189108B a b )d e + 21816B b d e +--R * +--R 5 +--R x +--R + +--R 3 8 2 3 7 +--R 24310A a e + (225420A a b + 75140B a )d e +--R + +--R 2 2 2 6 3 2 3 5 +--R (233580A a b + 233580B a b)d e + (27200A b + 81600B a b )d e +--R + +--R 3 4 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 2 6 +--R 97240A a d e + (304980A a b + 101660B a )d e +--R + +--R 2 2 3 5 3 2 4 4 +--R (108120A a b + 108120B a b)d e + (170A b + 510B a b )d e +--R + +--R 3 5 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 6 2 3 3 5 +--R 145860A a d e + (159120A a b + 53040B a )d e +--R + +--R 2 2 4 4 3 2 5 3 +--R (1530A a b + 1530B a b)d e + (- 204A b - 612B a b )d e +--R + +--R 3 6 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 3 5 2 3 4 4 +--R 97240A a d e + (6630A a b + 2210B a )d e +--R + +--R 2 2 5 3 3 2 6 2 +--R (- 2040A a b - 2040B a b)d e + (272A b + 816B a b )d e +--R + +--R 3 7 +--R - 128B b d e +--R * +--R x +--R + +--R 3 4 4 2 3 5 3 +--R 24310A a d e + (- 13260A a b - 4420B a )d e +--R + +--R 2 2 6 2 3 2 7 3 8 +--R (4080A a b + 4080B a b)d e + (- 544A b - 1632B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 109395e +--R Type: Union(Expression(Integer),...) +--E 718 + +--S 719 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 720 + +)clear all + +--S 721 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 2 6 3 2 2 3 5 +--R B b e x + ((A b + 3B a b )e + 2B b d e)x +--R + +--R 2 2 2 3 2 3 2 4 +--R ((3A a b + 3B a b)e + (2A b + 6B a b )d e + B b d )x +--R + +--R 2 3 2 2 2 3 2 2 3 +--R ((3A a b + B a )e + (6A a b + 6B a b)d e + (A b + 3B a b )d )x +--R + +--R 3 2 2 3 2 2 2 2 +--R (A a e + (6A a b + 2B a )d e + (3A a b + 3B a b)d )x +--R + +--R 3 2 3 2 3 2 +--R (2A a d e + (3A a b + B a )d )x + A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1293 +r0:=2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)/e^5-_ + 2/9*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5+_ + 6/11*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)/e^5-_ + 2/13*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^5+_ + 2/15*b^3*B*(d+e*x)^(15/2)/e^5 +--R +--R +--R (2) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 7 3 2 7 3 6 6 +--R 6006B b e x + ((6930A b + 20790B a b )e + 14322B b d e )x +--R + +--R 2 2 7 3 2 6 +--R (24570A a b + 24570B a b)e + (17010A b + 51030B a b )d e +--R + +--R 3 2 5 +--R 8946B b d e +--R * +--R 5 +--R x +--R + +--R 2 3 7 2 2 6 +--R (30030A a b + 10010B a )e + (62790A a b + 62790B a b)d e +--R + +--R 3 2 2 5 3 3 4 +--R (11130A b + 33390B a b )d e + 70B b d e +--R * +--R 4 +--R x +--R + +--R 3 7 2 3 6 +--R 12870A a e + (81510A a b + 27170B a )d e +--R + +--R 2 2 2 5 3 2 3 4 +--R (44070A a b + 44070B a b)d e + (150A b + 450B a b )d e +--R + +--R 3 4 3 +--R - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 2 5 +--R 38610A a d e + (64350A a b + 21450B a )d e +--R + +--R 2 2 3 4 3 2 4 3 +--R (1170A a b + 1170B a b)d e + (- 180A b - 540B a b )d e +--R + +--R 3 5 2 +--R 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 5 2 3 3 4 +--R 38610A a d e + (4290A a b + 1430B a )d e +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 1560A a b - 1560B a b)d e + (240A b + 720B a b )d e +--R + +--R 3 6 +--R - 128B b d e +--R * +--R x +--R + +--R 3 3 4 2 3 4 3 +--R 12870A a d e + (- 8580A a b - 2860B a )d e +--R + +--R 2 2 5 2 3 2 6 3 7 +--R (3120A a b + 3120B a b)d e + (- 480A b - 1440B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 45045e +--R Type: Union(Expression(Integer),...) +--E 723 + +--S 724 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 725 + +)clear all + +--S 726 of 1293 +t0:=(a+b*x)^3*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 5 3 2 3 4 +--R B b e x + ((A b + 3B a b )e + B b d)x +--R + +--R 2 2 3 2 3 +--R ((3A a b + 3B a b)e + (A b + 3B a b )d)x +--R + +--R 2 3 2 2 2 3 2 3 +--R ((3A a b + B a )e + (3A a b + 3B a b)d)x + (A a e + (3A a b + B a )d)x +--R + +--R 3 +--R A a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1293 +r0:=2/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(5/2)/e^5-2/7*(b*d-a*e)^2*(4*b*B*d-_ + 3*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5+_ + 2/3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)/e^5-_ + 2/11*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^5+_ + 2/13*b^3*B*(d+e*x)^(13/2)/e^5 +--R +--R +--R (2) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 6 3 2 6 3 5 5 +--R 2310B b e x + ((2730A b + 8190B a b )e + 2940B b d e )x +--R + +--R 2 2 6 3 2 5 +--R (10010A a b + 10010B a b)e + (3640A b + 10920B a b )d e +--R + +--R 3 2 4 +--R 70B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 6 2 2 5 +--R (12870A a b + 4290B a )e + (14300A a b + 14300B a b)d e +--R + +--R 3 2 2 4 3 3 3 +--R (130A b + 390B a b )d e - 80B b d e +--R * +--R 3 +--R x +--R + +--R 3 6 2 3 5 +--R 6006A a e + (20592A a b + 6864B a )d e +--R + +--R 2 2 2 4 3 2 3 3 3 4 2 +--R (858A a b + 858B a b)d e + (- 156A b - 468B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 2 4 +--R 12012A a d e + (2574A a b + 858B a )d e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 1144A a b - 1144B a b)d e + (208A b + 624B a b )d e +--R + +--R 3 5 +--R - 128B b d e +--R * +--R x +--R + +--R 3 2 4 2 3 3 3 +--R 6006A a d e + (- 5148A a b - 1716B a )d e +--R + +--R 2 2 4 2 3 2 5 3 6 +--R (2288A a b + 2288B a b)d e + (- 416A b - 1248B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 15015e +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 1293 +t0:=(a+b*x)^3*(A+B*x)*sqrt(d+e*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x +--R + +--R 3 +--R A a +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1293 +r0:=2/3*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(3/2)/e^5-2/5*(b*d-a*e)^2*(4*b*B*d-_ + 3*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5+_ + 6/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)/e^5-_ + 2/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^5+_ + 2/11*b^3*B*(d+e*x)^(11/2)/e^5 +--R +--R +--R (2) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 5 3 2 5 3 4 4 +--R 630B b e x + ((770A b + 2310B a b )e + 70B b d e )x +--R + +--R 2 2 5 3 2 4 3 2 3 3 +--R ((2970A a b + 2970B a b)e + (110A b + 330B a b )d e - 80B b d e )x +--R + +--R 2 3 5 2 2 4 +--R (4158A a b + 1386B a )e + (594A a b + 594B a b)d e +--R + +--R 3 2 2 3 3 3 2 +--R (- 132A b - 396B a b )d e + 96B b d e +--R * +--R 2 +--R x +--R + +--R 3 5 2 3 4 +--R 2310A a e + (1386A a b + 462B a )d e +--R + +--R 2 2 2 3 3 2 3 2 3 4 +--R (- 792A a b - 792B a b)d e + (176A b + 528B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 2 3 +--R 2310A a d e + (- 2772A a b - 924B a )d e +--R + +--R 2 2 3 2 3 2 4 3 5 +--R (1584A a b + 1584B a b)d e + (- 352A b - 1056B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 3465e +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 1293 +t0:=(a+b*x)^3*(A+B*x)/sqrt(d+e*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1293 +r0:=-2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5+_ + 6/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)/e^5-_ + 2/7*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^5+_ + 2/9*b^3*B*(d+e*x)^(9/2)/e^5+2*(b*d-a*e)^3*(B*d-A*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 70B b e x + ((90A b + 270B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((378A a b + 378B a b)e + (- 108A b - 324B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (630A a b + 210B a )e + (- 504A a b - 504B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (144A b + 432B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R 630A a e + (- 1260A a b - 420B a )d e + (1008A a b + 1008B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 288A b - 864B a b )d e + 256B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315e +--R Type: Union(Expression(Integer),...) +--E 738 + +--S 739 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 740 + +)clear all + +--S 741 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1293 +r0:=2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5-_ + 2/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^5+_ + 2/7*b^3*B*(d+e*x)^(7/2)/e^5-2*(b*d-a*e)^3*(B*d-A*e)/(e^5*sqrt(d+e*x))-_ + 2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((14A b + 42B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((70A a b + 70B a b)e + (- 28A b - 84B a b )d e + 32B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (210A a b + 70B a )e + (- 280A a b - 280B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (112A b + 336B a b )d e - 128B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 70A a e + (420A a b + 140B a )d e + (- 560A a b - 560B a b)d e +--R + +--R 3 2 3 3 4 +--R (224A b + 672B a b )d e - 256B b d +--R / +--R 5 +-------+ +--R 35e \|e x + d +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1293 +r0:=-2/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(3/2))-_ + 2/3*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^5+_ + 2/5*b^3*B*(d+e*x)^(5/2)/e^5+2*(b*d-a*e)^2*_ + (4*b*B*d-3*A*b*e-a*B*e)/(e^5*sqrt(d+e*x))+6*b*(b*d-a*e)*_ + (2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 6B b e x + ((10A b + 30B a b )e - 16B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((90A a b + 90B a b)e + (- 60A b - 180B a b )d e + 96B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 90A a b - 30B a )e + (360A a b + 360B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 240A b - 720B a b )d e + 384B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 10A a e + (- 60A a b - 20B a )d e + (240A a b + 240B a b)d e +--R + +--R 3 2 3 3 4 +--R (- 160A b - 480B a b )d e + 256B b d +--R / +--R 6 5 +-------+ +--R (15e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 748 + +--S 749 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1293 +t0:=(a+b*x)^3*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 3 +--R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x + A a +--R ---------------------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1293 +r0:=-2/5*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(5/2))+_ + 2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)/(e^5*(d+e*x)^(3/2))+_ + 2/3*b^3*B*(d+e*x)^(3/2)/e^5-6*b*(b*d-a*e)*_ + (2*b*B*d-A*b*e-a*B*e)/(e^5*sqrt(d+e*x))-_ + 2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/e^5 +--R +--R +--R (2) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 2 4 3 3 3 +--R 10B b e x + ((30A b + 90B a b )e - 80B b d e )x +--R + +--R 2 2 4 3 2 3 3 2 2 2 +--R ((- 90A a b - 90B a b)e + (180A b + 540B a b )d e - 480B b d e )x +--R + +--R 2 3 4 2 2 3 +--R (- 30A a b - 10B a )e + (- 120A a b - 120B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (240A b + 720B a b )d e - 640B b d e +--R * +--R x +--R + +--R 3 4 2 3 3 2 2 2 2 +--R - 6A a e + (- 12A a b - 4B a )d e + (- 48A a b - 48B a b)d e +--R + +--R 3 2 3 3 4 +--R (96A b + 288B a b )d e - 256B b d +--R / +--R 7 2 6 2 5 +-------+ +--R (15e x + 30d e x + 15d e )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1293 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1293 +r0:=2/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^(3/2)/b^4+_ + 2/5*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(5/2)/b^3+_ + 2/7*(A*b-a*B)*(d+e*x)^(7/2)/b^2+2/9*B*(d+e*x)^(9/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(7/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+2*(A*b-a*B)*_ + (b*d-a*e)^3*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (630A a b - 630B a )e + (- 1890A a b + 1890B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1890A a b - 1890B a b )d e + (- 630A b + 630B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e + 70B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 +-+ +--R 315b e\|b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 4 4 2 2 3 3 +--R (- 315A a b + 315B a )e + (945A a b - 945B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 945A a b + 945B a b )d e + (315A b - 315B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e +--R + +--R 4 4 +--R 70B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315b e +--R , +--R +--R 3 4 4 2 2 3 3 +--R (630A a b - 630B a )e + (- 1890A a b + 1890B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1890A a b - 1890B a b )d e + (- 630A b + 630B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 70B b e x + ((90A b - 90B a b )e + 280B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 126A a b + 126B a b )e + (396A b - 396B a b )d e +--R + +--R 4 2 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (210A a b - 210B a b)e + (- 672A a b + 672B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (732A b - 732B a b )d e + 280B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 630A a b + 630B a )e + (2100A a b - 2100B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2436A a b + 2436B a b )d e + (1056A b - 1056B a b )d e +--R + +--R 4 4 +--R 70B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 +--R 315b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 758 + +--S 759 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 3 4 3 2 2 3 2 +--R (- A a b + B a )e + (3A a b - 3B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 3A a b + 3B a b )d e + (A b - B a b )d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 4 3 2 2 3 2 +--R (- 2A a b + 2B a )e + (6A a b - 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A a b + 6B a b )d e + (2A b - 2B a b )d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 3 4 3 2 2 3 2 +--R (- 2A a b + 2B a )e + (6A a b - 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 6A a b + 6B a b )d e + (2A b - 2B a b )d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 4 3 2 2 3 2 +--R (2A a b - 2B a )e + (- 6A a b + 6B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (6A a b - 6B a b )d e + (- 2A b + 2B a b )d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1293 +r0:=2/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(3/2)/b^3+_ + 2/5*(A*b-a*B)*(d+e*x)^(5/2)/b^2+2/7*B*(d+e*x)^(7/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(5/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+2*(A*b-a*B)*_ + (b*d-a*e)^2*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 +-+ +--R 105b e\|b +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 3 2 2 2 +--R (- 105A a b + 105B a )e + (210A a b - 210B a b)d e +--R + +--R 3 2 2 +--R (- 105A b + 105B a b )d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R , +--R +--R 2 3 3 2 2 2 +--R (- 210A a b + 210B a )e + (420A a b - 420B a b)d e +--R + +--R 3 2 2 +--R (- 210A b + 210B a b )d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 30B b e x + ((42A b - 42B a b )e + 90B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 70A a b + 70B a b)e + (154A b - 154B a b )d e + 90B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (210A a b - 210B a )e + (- 490A a b + 490B a b)d e +--R + +--R 3 2 2 3 3 +--R (322A b - 322B a b )d e + 30B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 +--R 105b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 765 + +--S 766 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 3 2 2 +--R ((- A a b + B a )e + (2A a b - 2B a b)d e + (- A b + B a b )d ) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 3 2 2 +--R ((2A a b - 2B a )e + (- 4A a b + 4B a b)d e + (2A b - 2B a b )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 3 2 2 +--R ((2A a b - 2B a )e + (- 4A a b + 4B a b)d e + (2A b - 2B a b )d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 3 2 2 +--R ((- 2A a b + 2B a )e + (4A a b - 4B a b)d e + (- 2A b + 2B a b )d ) +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 769 + +)clear all + +--S 770 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1293 +r0:=2/3*(A*b-a*B)*(d+e*x)^(3/2)/b^2+2/5*B*(d+e*x)^(5/2)/(b*e)-_ + 2*(A*b-a*B)*(b*d-a*e)^(3/2)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(A*b-a*B)*(b*d-a*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +-----------+ +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 3 +-+ +--R 15b e\|b +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- a e + b d +--R ((- 15A a b + 15B a )e + (15A b - 15B a b)d e) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R , +--R +--R +---------+ +--R 2 2 2 |a e - b d +--R ((30A a b - 30B a )e + (- 30A b + 30B a b)d e) |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 +--R 6B b e x + ((10A b - 10B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 30A a b + 30B a )e + (40A b - 40B a b)d e + 6B b d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 +--R 15b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 772 + +--S 773 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 |- a e + b d +-+ +--R ((- A a b + B a )e + (A b - B a b)d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 +-----------+ +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 +-----------+ +--R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 2 +-+ |a e - b d \|e x + d +--R ((2A a b - 2B a )e + (- 2A b + 2B a b)d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 776 + +)clear all + +--S 777 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R b x + a +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1293 +r0:=2/3*B*(d+e*x)^(3/2)/(b*e)-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(5/2)+2*(A*b-a*B)*sqrt(d+e*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (- 6A b + 6B a)e\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-+ +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|b \|e x + d +--R / +--R 2 +-+ +--R 3b e\|b +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R |- a e + b d +--R (3A b - 3B a)e |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R , +--R +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R (- 6A b + 6B a)e |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R +-------+ +--R (2B b e x + (6A b - 6B a)e + 2B b d)\|e x + d +--R / +--R 2 +--R 3b e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 779 + +--S 780 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R (A b - B a) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (2A b - 2B a)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R (2A b - 2B a)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R (- 2A b + 2B a)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 783 + +)clear all + +--S 784 of 1293 +t0:=(A+B*x)/((a+b*x)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1293 +r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ + sqrt(b*d-a*e))+2*B*sqrt(d+e*x)/(b*e) +--R +--R +--R (2) +--R +-+ +-------+ +--R \|b \|e x + d +-----------+ +-+ +-------+ +--R (- 2A b + 2B a)e atanh(--------------) + 2B\|- a e + b d \|b \|e x + d +--R +-----------+ +--R \|- a e + b d +--R ----------------------------------------------------------------------- +--R +-----------+ +-+ +--R b e\|- a e + b d \|b +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (A b - B a)e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R 2B\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R | 2 +--R b e\|- a b e + b d +--R , +--R +-----------+ +--R | 2 +-------+ +-----------+ +--R \|a b e - b d \|e x + d | 2 +-------+ +--R (2A b - 2B a)e atan(------------------------) + 2B\|a b e - b d \|e x + d +--R a e - b d +--R --------------------------------------------------------------------------] +--R +-----------+ +--R | 2 +--R b e\|a b e - b d +--R Type: Union(List(Expression(Integer)),...) +--E 786 + +--S 787 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R (A b - B a)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (2A b - 2B a)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R b\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (2A b - 2B a)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R (2A b - 2B a)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R b\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (1) --------------------------------------- +--R 2 +-------+ +--R (b e x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1293 +r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(3/2)*sqrt(b))-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R (2A b - 2B a)e\|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (- 2A e + 2B d)\|- a e + b d \|b +--R / +--R 2 +-----------+ +-+ +-------+ +--R (a e - b d e)\|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R (A b - B a)e\|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +--R (- 2A e + 2B d)\|- a b e + b d +--R / +--R +-------------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|- a b e + b d \|e x + d +--R , +--R +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)e\|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (- 2A e + 2B d)\|a b e - b d +--R / +--R +-----------+ +--R 2 | 2 +-------+ +--R (a e - b d e)\|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 793 + +--S 794 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R (A b - B a)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (- 2A b + 2B a)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R | 2 +-----------+ +-+ +--R (a e - b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R (- 2A b + 2B a)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R (- 2A b + 2B a)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R +-----------+ +-+ | 2 +--R (a e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(5/2)) +--R +--R +--R B x + A +--R (1) ---------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|e x + d +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1293 +r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(3/2))-2*(A*b-a*B)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/_ + (b*d-a*e)^(5/2)+2*(A*b-a*B)/((b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 +-+ +-------+ +--R ((- 6A b + 6B a)e x + (- 6A b + 6B a)d e)\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 +-----------+ +--R ((6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d )\|- a e + b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e) +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 | b +-------+ +--R ((3A b - 3B a)e x + (3A b - 3B a)d e) |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R , +--R +--R +---------+ +--R 2 | b +-------+ +--R ((6A b - 6B a)e x + (6A b - 6B a)d e) |--------- \|e x + d +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 +--R (6A b - 6B a)e x - 2A a e + (8A b - 4B a)d e - 2B b d +--R / +--R 2 4 3 2 2 2 2 3 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e )x + 3a d e - 6a b d e + 3b d e)\|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 800 + +--S 801 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R (A b - B a)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R (2A b - 2B a)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R (2A b - 2B a)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-----------+ | b b\|e x + d +--R (2A b - 2B a)\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 2 2 2 2 +-----------+ +--R (a e - 2a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 804 + +)clear all + +--S 805 of 1293 +t0:=(A+B*x)/((a+b*x)*(d+e*x)^(7/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1293 +r0:=-2/5*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/3*(A*b-a*B)/_ + ((b*d-a*e)^2*(d+e*x)^(3/2))-2*b^(3/2)*(A*b-a*B)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+_ + 2*b*(A*b-a*B)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R (30A b - 30B a b)e x + (60A b - 60B a b)d e x +--R + +--R 2 2 +--R (30A b - 30B a b)d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 +--R (15A b - 15B a b)e x + (30A b - 30B a b)d e x +--R + +--R 2 2 +--R (15A b - 15B a b)d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 3 2 2 2 +--R (- 30A b + 30B a b)e x + (- 60A b + 60B a b)d e x +--R + +--R 2 2 +--R (- 30A b + 30B a b)d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 3 2 +--R (- 30A b + 30B a b)e x +--R + +--R 2 3 2 2 2 3 +--R ((10A a b - 10B a )e + (- 70A b + 70B a b)d e )x - 6A a e +--R + +--R 2 2 2 2 2 3 +--R (22A a b - 4B a )d e + (- 46A b + 28B a b)d e + 6B b d +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 +--R (30a d e - 90a b d e + 90a b d e - 30b d e )x + 15a d e +--R + +--R 2 3 3 2 4 2 3 5 +--R - 45a b d e + 45a b d e - 15b d e +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 807 + +--S 808 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R (A b - B a b)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R (- 2A b + 2B a b)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R (- 2A b + 2B a b)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-----------+ | b b\|e x + d +--R (- 2A b + 2B a b)\|- a e + b d |--------- atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 811 + +)clear all + +--S 812 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^2 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1293 +r0:=1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+_ + 1/7*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x))-_ + (b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*_ + (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +--R (105b x + 105a b )\|b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 3 3 2 2 2 +--R (735A a b - 945B a b)e + (- 1470A a b + 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (735A b - 1365B a b )d e + 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1470A a b + 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (735A a b - 1365B a b )d e + 210B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 60B b e x + ((84A b - 108B a b )e + 264B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 196A a b + 252B a b )e + (448A b - 632B a b )d e +--R + +--R 4 2 +--R 488B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (980A a b - 1260B a b)e + (- 2352A a b + 3304B a b )d e +--R + +--R 4 3 2 4 3 +--R (1624A b - 2760B a b )d e + 704B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (1470A a b - 1890B a )e + (- 3430A a b + 4830B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (2254A a b - 3878B a b )d e + (- 210A b + 914B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 210b x + 210a b +--R , +--R +--R 2 2 3 3 3 2 2 2 +--R (- 735A a b + 945B a b)e + (1470A a b - 2100B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 735A b + 1365B a b )d e - 210B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 735A a b + 945B a )e + (1470A a b - 2100B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (- 735A a b + 1365B a b )d e - 210B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 30B b e x + ((42A b - 54B a b )e + 132B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 98A a b + 126B a b )e + (224A b - 316B a b )d e +--R + +--R 4 2 +--R 244B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (490A a b - 630B a b)e + (- 1176A a b + 1652B a b )d e +--R + +--R 4 3 2 4 3 +--R (812A b - 1380B a b )d e + 352B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (735A a b - 945B a )e + (- 1715A a b + 2415B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (1127A a b - 1939B a b )d e + (- 105A b + 457B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 5 +--R 105b x + 105a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 814 + +--S 815 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 18B a )e + (- 28A a b + 40B a b)d e +--R + +--R 3 2 2 3 3 +--R (14A b - 26B a b )d e + 4B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 3 2 2 2 +--R (7A a b - 9B a )e + (- 14A a b + 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (7A b - 13B a b )d e + 2B b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 3 2 2 2 +--R (- 7A a b + 9B a )e + (14A a b - 20B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 7A b + 13B a b )d e - 2B b d +--R * +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R \|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1293 +r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+_ + 1/5*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x))-_ + (b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+_ + (b*d-a*e)*(2*b*B*d+5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 12B b e x + ((20A b - 28B a b )e + 44B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 100A a b + 140B a b)e + (140A b - 236B a b )d e + 92B b d )x +--R + +--R 2 3 2 2 2 +--R (- 150A a b + 210B a )e + (200A a b - 340B a b)d e +--R + +--R 3 2 2 +--R (- 30A b + 122B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 +--R ((75A a b - 105B a b)e + (- 75A b + 135B a b )d e - 30B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (75A a b - 105B a )e + (- 75A a b + 135B a b)d e - 30B a b d +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((10A b - 14B a b )e + 22B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 50A a b + 70B a b)e + (70A b - 118B a b )d e + 46B b d )x +--R + +--R 2 3 2 2 2 +--R (- 75A a b + 105B a )e + (100A a b - 170B a b)d e +--R + +--R 3 2 2 +--R (- 15A b + 61B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 821 + +--S 822 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 2 |- a e + b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R +-+ \| b +--R \|b log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 +--R ((- 10A a b + 14B a )e + (10A b - 18B a b)d e + 4B b d ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2 2 2 +-----------+ +--R ((- 5A a b + 7B a )e + (5A b - 9B a b)d e + 2B b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 2 2 +-+ |a e - b d +--R ((5A a b - 7B a )e + (- 5A b + 9B a b)d e - 2B b d )\|b |--------- +--R \| b +--R * +--R +-------+ +--R \|e x + d +--R atan(------------) +--R +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^2 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1293 +r0:=1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-_ + (A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-_ + (2*b*B*d+3*A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+_ + (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((9A b - 15B a b)e + 6B b d)x + (9A a b - 15B a )e + 6B a b d) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 2 2 +--R 4B b e x + ((12A b - 20B a b)e + 16B b d)x + (18A a b - 30B a )e +--R + +--R 2 +--R (- 6A b + 22B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R 2 2 2 +--R (((- 9A b + 15B a b)e - 6B b d)x + (- 9A a b + 15B a )e - 6B a b d) +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((6A b - 10B a b)e + 8B b d)x + (9A a b - 15B a )e +--R + +--R 2 +--R (- 3A b + 11B a b)d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 828 + +--S 829 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a e + b d +-+ +--R ((3A b - 5B a)e + 2B b d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R - 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((6A b - 10B a)e + 4B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R ((3A b - 5B a)e + 2B b d)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R +-+ |a e - b d \|e x + d +--R ((- 3A b + 5B a)e - 2B b d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^2 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1293 +r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-_ + (2*b*B*d+A*b*e-3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+(2*b*B*d+A*b*e-3*a*B*e)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b + 3B a b)e - 2B b d)x + (- A a b + 3B a )e - 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (2B b x - A b + 3B a)\|- a e + b d \|b \|e x + d +--R / +--R 3 2 +-----------+ +-+ +--R (b x + a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (4B b x - 2A b + 6B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 3 2 | 2 +--R (2b x + 2a b )\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b - 3B a b)e + 2B b d)x + (A a b - 3B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (2B b x - A b + 3B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 3 2 | 2 +--R (b x + a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 835 + +--S 836 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b - 6B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R 2b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b - 3B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 839 + +)clear all + +--S 840 of 1293 +t0:=(A+B*x)/((a+b*x)^2*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1293 +r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + (b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 +--R (((- A b - B a b)e + 2B b d)x + (- A a b - B a )e + 2B a b d) +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +-------+ +--R (A b - B a)\|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 2 +-----------+ +-+ +--R ((a b e - b d)x + a b e - a b d)\|- a e + b d \|b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +--R | 2 +-------+ +--R (2A b - 2B a)\|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 2 3 2 2 | 2 +--R ((2a b e - 2b d)x + 2a b e - 2a b d)\|- a b e + b d +--R , +--R +--R 2 2 2 +--R (((A b + B a b)e - 2B b d)x + (A a b + B a )e - 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R (A b - B a)\|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 2 3 2 2 | 2 +--R ((a b e - b d)x + a b e - a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 842 + +--S 843 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((2A b + 2B a)e - 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 | 2 +-----------+ +-+ +--R (2a b e - 2b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((A b + B a)e - 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + B a)e - 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 +-----------+ +-+ | 2 +--R (a b e - b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 846 + +)clear all + +--S 847 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1293 +r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ + ((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/_ + (b*(b*d-a*e)^2*sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 +-------+ +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d)\|e x + d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +-+ +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|- a e + b d \|b +--R / +--R 2 2 2 3 2 3 2 2 2 2 +-----------+ +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|- a e + b d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (((3A b - B a b)e - 2B b d)x + (3A a b - B a )e - 2B a b d) +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R (((- 6A b + 2B a)e + 4B b d)x - 4A a e + (- 2A b + 6B a)d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 2 2 2 3 2 3 2 2 2 2 +--R ((2a b e - 4a b d e + 2b d )x + 2a e - 4a b d e + 2a b d ) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 2 2 2 +--R (((- 3A b + B a b)e + 2B b d)x + (- 3A a b + B a )e + 2B a b d) +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R +-----------+ +--R | 2 +--R (((- 3A b + B a)e + 2B b d)x - 2A a e + (- A b + 3B a)d)\|a b e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 3 2 2 2 2 | 2 +--R ((a b e - 2a b d e + b d )x + a e - 2a b d e + a b d )\|a b e - b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 849 + +--S 850 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +-+ +--R ((3A b - B a)e - 2B b d)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 6A b + 2B a)e + 4B b d)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 2 | 2 +-----------+ +-+ +--R (2a e - 4a b d e + 2b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R | 2 \|b \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R +-----------+ +-+ \|a b e - b d \|e x + d +--R ((- 3A b + B a)e + 2B b d)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 2 +-----------+ +-+ | 2 +--R (a e - 2a b d e + b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 853 + +)clear all + +--S 854 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1293 +r0:=1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-_ + (2*b*B*d-5*A*b*e+3*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*_ + sqrt(b)/(b*d-a*e)^(7/2)+(2*b*B*d-5*A*b*e+3*a*B*e)/_ + ((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 15A b + 9B a b)e + 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 15A a b + 9B a )e + (- 15A b + 15B a b)d e + 6B b d )x +--R + +--R 2 2 +--R (- 15A a b + 9B a )d e + 6B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((30A b - 18B a b)e - 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((20A a b - 12B a )e + (40A b - 32B a b)d e - 16B b d )x - 4A a e +--R + +--R 2 2 2 +--R (28A a b - 8B a )d e + (6A b - 22B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b e - 18a b d e + 18a b d e - 6b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (6a e - 12a b d e + 12a b d e - 6b d )x + 6a d e - 18a b d e +--R + +--R 2 2 3 3 4 +--R 18a b d e - 6a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 +--R ((15A a b - 9B a )e + (15A b - 15B a b)d e - 6B b d )x +--R + +--R 2 2 +--R (15A a b - 9B a )d e - 6B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 2 2 2 2 +--R ((15A b - 9B a b)e - 6B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((10A a b - 6B a )e + (20A b - 16B a b)d e - 8B b d )x - 2A a e +--R + +--R 2 2 2 +--R (14A a b - 4B a )d e + (3A b - 11B a b)d +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d e)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (3a e - 6a b d e + 6a b d e - 3b d )x + 3a d e - 9a b d e +--R + +--R 2 2 3 3 4 +--R 9a b d e - 3a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 856 + +--S 857 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((10A b - 6B a)e - 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (2a e - 6a b d e + 6a b d e - 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ \|b \|e x + d +--R ((5A b - 3B a)e - 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R +-----------+ | b +--R ((5A b - 3B a)e - 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (a e - 3a b d e + 3a b d e - b d )\|- a e + b d +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1293 +t0:=(A+B*x)/((a+b*x)^2*(d+e*x)^(7/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1293 +r0:=1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + (-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+_ + 1/3*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-_ + b^(3/2)*(2*b*B*d-7*A*b*e+5*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+_ + b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e +--R + +--R 3 2 +--R 70B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 75B a b )e - 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((105A a b - 75B a b)e + (210A b - 180B a b )d e - 60B b d e)x +--R + +--R 2 2 2 3 2 2 3 3 +--R ((210A a b - 150B a b)d e + (105A b - 135B a b )d e - 30B b d )x +--R + +--R 2 2 2 2 3 +--R (105A a b - 75B a b)d e - 30B a b d +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((- 210A b + 150B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 140A a b + 100B a b)e + (- 490A b + 390B a b )d e +--R + +--R 3 2 +--R 140B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (28A a b - 20B a )e + (- 336A a b + 232B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 322A b + 326B a b )d e + 92B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 12A a e + (64A a b - 8B a )d e + (- 232A a b + 96B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 122B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (30a b e - 120a b d e + 180a b d e - 120a b d e + 30b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 30a e - 60a b d e - 60a b d e + 240a b d e - 210a b d e +--R + +--R 5 5 +--R 60b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 60a d e - 210a b d e + 240a b d e - 60a b d e - 60a b d e +--R + +--R 5 6 +--R 30b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 30a d e - 120a b d e + 180a b d e - 120a b d e + 30a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 105A a b + 75B a b)e + (- 210A b + 180B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 +--R (- 210A a b + 150B a b)d e + (- 105A b + 135B a b )d e +--R + +--R 3 3 +--R 30B b d +--R * +--R x +--R + +--R 2 2 2 2 3 +--R (- 105A a b + 75B a b)d e + 30B a b d +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((- 105A b + 75B a b )e + 30B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 70A a b + 50B a b)e + (- 245A b + 195B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (14A a b - 10B a )e + (- 168A a b + 116B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 161A b + 163B a b )d e + 46B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (32A a b - 4B a )d e + (- 116A a b + 48B a b)d e +--R + +--R 3 2 3 +--R (- 15A b + 61B a b )d +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (15a b e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 15a e - 30a b d e - 30a b d e + 120a b d e - 105a b d e +--R + +--R 5 5 +--R 30b d e +--R * +--R 2 +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R 30a d e - 105a b d e + 120a b d e - 30a b d e - 30a b d e +--R + +--R 5 6 +--R 15b d +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 863 + +--S 864 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +--R ((7A b - 5B a b)e - 2B b d)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 14A b + 10B a b)e + 4B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (2a e - 8a b d e + 12a b d e - 8a b d e + 2b d )\|- a e + b d +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ \|b \|e x + d +--R ((- 7A b + 5B a b)e + 2B b d)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 +-----------+ | b +--R ((- 7A b + 5B a b)e + 2B b d)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (a e - 4a b d e + 6a b d e - 4a b d e + b d )\|- a e + b d +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^3 +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1293 +r0:=7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ + 7/20*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e))-_ + 1/4*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 7/4*e*(b*d-a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+_ + 7/4*e*(b*d-a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 7 2 6 2 5 +-+ +--R (60b x + 120a b x + 60a b )\|b +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 4 3 2 +--R (- 525A a b + 945B a b )e + (525A b - 1365B a b )d e +--R + +--R 4 2 +--R 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1050A a b + 1890B a b)e + (1050A a b - 2730B a b )d e +--R + +--R 3 2 +--R 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (- 525A a b + 945B a )e + (525A a b - 1365B a b)d e + 420B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 48B b e x + ((80A b - 144B a b )e + 256B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 560A a b + 1008B a b )e + (800A b - 1888B a b )d e +--R + +--R 4 2 +--R 928B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 1750A a b + 3150B a b)e + (2380A a b - 5684B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 390A b + 2606B a b )d e - 120B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 1050A a b + 1890B a )e + (1400A a b - 3360B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 210A a b + 1498B a b )d e + (- 60A b - 60B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 120b x + 240a b x + 120a b +--R , +--R +--R 3 2 2 3 4 3 2 +--R (525A a b - 945B a b )e + (- 525A b + 1365B a b )d e +--R + +--R 4 2 +--R - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (1050A a b - 1890B a b)e + (- 1050A a b + 2730B a b )d e +--R + +--R 3 2 +--R - 840B a b d e +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 2 2 2 +--R (525A a b - 945B a )e + (- 525A a b + 1365B a b)d e - 420B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 24B b e x + ((40A b - 72B a b )e + 128B b d e )x +--R + +--R 3 2 2 3 4 3 2 +--R (- 280A a b + 504B a b )e + (400A b - 944B a b )d e +--R + +--R 4 2 +--R 464B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 875A a b + 1575B a b)e + (1190A a b - 2842B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 195A b + 1303B a b )d e - 60B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 525A a b + 945B a )e + (700A a b - 1680B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 105A a b + 749B a b )d e + (- 30A b - 30B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 7 2 6 2 5 +--R 60b x + 120a b x + 60a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 870 + +--S 871 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 +--R ((- 35A a b + 63B a )e + (35A b - 91B a b)d e + 28B b d e) +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ - 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d +-+ \| b +--R |----------- \|b log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 +--R ((- 70A a b + 126B a )e + (70A b - 182B a b)d e + 56B b d e) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R 2 3 2 2 2 2 +--R ((- 35A a b + 63B a )e + (35A b - 91B a b)d e + 28B b d e) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 3 2 2 2 2 +-+ +--R ((35A a b - 63B a )e + (- 35A b + 91B a b)d e - 28B b d e)\|b +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 874 + +)clear all + +--S 875 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^3 +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1293 +r0:=5/12*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e))-_ + 1/4*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(9/2)+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*_ + sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x + (- 45A a b + 105B a )e +--R + +--R 2 +--R - 60B a b d e +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|e x + d +--R \|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 2 5 2 4 +-+ +--R (12b x + 24a b x + 12a b )\|b +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R +-----------+ 2b |----------- \|e x + d + b e x - a e + 2b d +--R |- a e + b d \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 3 2 2 3 2 +--R 16B b e x + ((48A b - 112B a b )e + 112B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((150A a b - 350B a b)e + (- 54A b + 326B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (90A a b - 210B a )e + (- 30A a b + 190B a b)d e +--R + +--R 3 2 2 +--R (- 12A b - 12B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 24b x + 48a b x + 24a b +--R , +--R +--R 3 2 2 3 2 +--R ((- 45A b + 105B a b )e - 60B b d e)x +--R + +--R 2 2 2 2 +--R ((- 90A a b + 210B a b)e - 120B a b d e)x +--R + +--R 2 3 2 2 +--R (- 45A a b + 105B a )e - 60B a b d e +--R * +--R +---------+ +-------+ +--R |a e - b d \|e x + d +--R |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((24A b - 56B a b )e + 56B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((75A a b - 175B a b)e + (- 27A b + 163B a b )d e - 12B b d )x +--R + +--R 2 3 2 2 2 +--R (45A a b - 105B a )e + (- 15A a b + 95B a b)d e +--R + +--R 3 2 2 +--R (- 6A b - 6B a b )d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 6 2 5 2 4 +--R 12b x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 877 + +--S 878 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a e + b d +-+ +--R ((- 15A b + 35B a)e - 20B b d e) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a e + b d +-------+ +--R 2b |----------- \|e x + d + b e x - a e + 2b d +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R ((30A b - 70B a)e + 40B b d e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|e x + d +--R ((15A b - 35B a)e + 20B b d e)\|- a e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +-------+ +--R 2 +-+ |a e - b d \|e x + d +--R ((- 15A b + 35B a)e - 20B b d e)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a e - b d +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 881 + +)clear all + +--S 882 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^3 +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1293 +r0:=-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x))-_ + 1/2*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/_ + sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e))+3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*_ + sqrt(d+e*x)/(b^3*(b*d-a*e)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b + 15B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b + 30B a b)e - 24B a b d e)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 5 2 4 2 3 +-----------+ +-+ +--R (4b x + 8a b x + 4a b )\|- a e + b d \|b +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R 16B b e x + ((- 10A b + 50B a b)e - 8B b d)x +--R + +--R 2 2 +--R (- 6A a b + 30B a )e + (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R +-------------+ +--R 5 2 4 2 3 | 2 +--R (8b x + 16a b x + 8a b )\|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b - 15B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((6A a b - 30B a b)e + 24B a b d e)x + (3A a b - 15B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 2 +--R 8B b e x + ((- 5A b + 25B a b)e - 4B b d)x + (- 3A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 5 2 4 2 3 | 2 +--R (4b x + 8a b x + 4a b )\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 884 + +--S 885 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R ((3A b - 15B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((6A b - 30B a)e + 24B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 | 2 +-----------+ +-+ +--R 8b \|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((3A b - 15B a)e + 12B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 +-----------+ +-+ +--R ((3A b - 15B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 +-----------+ +-+ | 2 +--R 4b \|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^3 +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1293 +r0:=-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2))-_ + 1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- A b - 3B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2A a b - 6B a b)e + 8B a b d e)x + (- A a b - 3B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e + (2A b + 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +-----------+ +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|- a e + b d +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((2A b - 10B a b)e + 8B b d)x + (- 2A a b - 6B a )e +--R + +--R 2 +--R (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 4 5 2 2 3 4 3 2 2 3 +--R ((8a b e - 8b d)x + (16a b e - 16a b d)x + 8a b e - 8a b d) +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((A b + 3B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2A a b + 6B a b)e - 8B a b d e)x + (A a b + 3B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((A b - 5B a b)e + 4B b d)x + (- A a b - 3B a )e +--R + +--R 2 +--R (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R +-----------+ +--R 4 5 2 2 3 4 3 2 2 3 | 2 +--R ((4a b e - 4b d)x + (8a b e - 8a b d)x + 4a b e - 4a b d)\|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 891 + +--S 892 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R ((A b + 3B a)e - 4B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((2A b + 6B a)e - 8B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 3 | 2 +-----------+ +-+ +--R (8a b e - 8b d)\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((A b + 3B a)e - 4B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((A b + 3B a)e - 4B b d e)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 3 +-----------+ +-+ | 2 +--R (4a b e - 4b d)\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1293 +t0:=(A+B*x)/((a+b*x)^3*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (b x + 3a b x + 3a b x + a )\|e x + d +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1293 +r0:=1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2))-_ + 1/2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^2)-_ + 1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((- 3A b - B a b )e + 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6A a b - 2B a b)e + 8B a b d e)x + (- 3A a b - B a )e +--R + +--R 2 +--R 4B a b d e +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R (((3A b + B a b)e - 4B b d)x + (5A a b - B a )e + (- 2A b - 2B a b)d) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +--R ((6A b + 2B a b)e - 8B b d)x + (10A a b - 2B a )e +--R + +--R 2 +--R (- 4A b - 4B a b)d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (8a b e - 16a b d e + 8b d )x + (16a b e - 32a b d e + 16a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 8a b e - 16a b d e + 8a b d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R , +--R +--R 3 2 2 3 2 +--R ((3A b + B a b )e - 4B b d e)x +--R + +--R 2 2 2 2 2 3 2 2 +--R ((6A a b + 2B a b)e - 8B a b d e)x + (3A a b + B a )e - 4B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 +--R ((3A b + B a b)e - 4B b d)x + (5A a b - B a )e +--R + +--R 2 +--R (- 2A b - 2B a b)d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (4a b e - 8a b d e + 4b d )x + (8a b e - 16a b d e + 8a b d )x +--R + +--R 4 2 3 2 2 3 2 +--R 4a b e - 8a b d e + 4a b d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 898 + +--S 899 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R ((3A b + B a)e - 4B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2a b e - 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(----------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((6A b + 2B a)e - 8B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 2 2 2 3 2 | 2 +-----------+ +-+ +--R (8a b e - 16a b d e + 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((3A b + B a)e - 4B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +-----------+ +--R | 2 +-------+ +--R 2 +-----------+ +-+ \|a b e - b d \|e x + d +--R ((3A b + B a)e - 4B b d e)\|- a e + b d \|b atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 2 2 2 3 2 +-----------+ +-+ | 2 +--R (4a b e - 8a b d e + 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 4 2 3 3 2 2 2 3 2 3 +--R (b e x + (3a b e + b d)x + (3a b e + 3a b d)x + (a e + 3a b d)x + a d) +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1293 +r0:=3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(b))-_ + 3/4*e*(4*b*B*d-5*A*b*e+a*B*e)/(b*(b*d-a*e)^3*sqrt(d+e*x))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*sqrt(d+e*x))+_ + 1/4*(-4*b*B*d+5*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-+ +-------+ +--R +-------+ \|b \|e x + d +--R \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x - 8A a e +--R + +--R 2 2 2 +--R (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +-+ +--R \|- a e + b d \|b +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +-+ +-------+ +--R \|- a e + b d \|b \|e x + d +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 2 +--R ((15A b - 3B a b )e - 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((30A a b - 6B a b)e - 24B a b d e)x + (15A a b - 3B a )e +--R + +--R 2 +--R - 12B a b d e +--R * +--R +-------+ +--R \|e x + d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +--R ((- 30A b + 6B a b)e + 24B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 50A a b + 10B a )e + (- 10A b + 42B a b)d e + 8B b d )x +--R + +--R 2 2 2 2 2 +--R - 16A a e + (- 18A a b + 26B a )d e + (4A b + 4B a b)d +--R * +--R +-------------+ +--R | 2 +--R \|- a b e + b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (8a b e - 24a b d e + 24a b d e - 8b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (16a b e - 48a b d e + 48a b d e - 16a b d )x + 8a e - 24a b d e +--R + +--R 3 2 2 2 3 3 +--R 24a b d e - 8a b d +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- a b e + b d \|e x + d +--R , +--R +--R 3 2 2 3 2 +--R ((- 15A b + 3B a b )e + 12B b d e)x +--R + +--R 2 2 2 2 2 3 2 +--R ((- 30A a b + 6B a b)e + 24B a b d e)x + (- 15A a b + 3B a )e +--R + +--R 2 +--R 12B a b d e +--R * +--R +-----------+ +--R | 2 +-------+ +--R +-------+ \|a b e - b d \|e x + d +--R \|e x + d atan(------------------------) +--R a e - b d +--R + +--R 2 2 2 2 +--R ((- 15A b + 3B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 +--R ((- 25A a b + 5B a )e + (- 5A b + 21B a b)d e + 4B b d )x +--R + +--R 2 2 2 2 2 +--R - 8A a e + (- 9A a b + 13B a )d e + (2A b + 2B a b)d +--R * +--R +-----------+ +--R | 2 +--R \|a b e - b d +--R / +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (4a b e - 12a b d e + 12a b d e - 4b d )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (8a b e - 24a b d e + 24a b d e - 8a b d )x + 4a e - 12a b d e +--R + +--R 3 2 2 2 3 3 +--R 12a b d e - 4a b d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 905 + +--S 906 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----------+ +-+ +--R ((15A b - 3B a)e - 12B b d e)\|- a e + b d \|b +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (- 2a b e + 2b d)\|e x + d + (b e x - a e + 2b d)\|- a b e + b d +--R log(------------------------------------------------------------------) +--R b x + a +--R + +--R +-------------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((- 30A b + 6B a)e + 24B b d e)\|- a b e + b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R +-------------+ +--R 3 3 2 2 2 2 3 3 | 2 +-----------+ +-+ +--R (8a e - 24a b d e + 24a b d e - 8b d )\|- a b e + b d \|- a e + b d \|b +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +-+ +-------+ +--R 2 | 2 \|b \|e x + d +--R ((- 15A b + 3B a)e + 12B b d e)\|a b e - b d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 2 +-----------+ +-+ +--R ((- 15A b + 3B a)e + 12B b d e)\|- a e + b d \|b +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|a b e - b d \|e x + d +--R atan(------------------------) +--R a e - b d +--R / +--R +-----------+ +--R 3 3 2 2 2 2 3 3 +-----------+ +-+ | 2 +--R (4a e - 12a b d e + 12a b d e - 4b d )\|- a e + b d \|b \|a b e - b d +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b e x + (3a b e + 2b d e)x + (3a b e + 6a b d e + b d )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a e + 6a b d e + 3a b d )x + (2a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1293 +r0:=-5/12*e*(4*b*B*d-7*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(3/2))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(3/2))+_ + 1/4*(-4*b*B*d+7*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))+_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*atanh(sqrt(b)*_ + sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(9/2)-_ + 5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 105A b + 45B a b )e + 60B b d e )x +--R + +--R 2 2 3 3 2 2 +--R (- 210A a b + 90B a b)e + (- 105A b + 165B a b )d e +--R + +--R 3 2 +--R 60B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- 105A a b + 45B a )e + (- 210A a b + 150B a b)d e +--R + +--R 2 2 +--R 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (- 105A a b + 45B a )d e + 60B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 +--R (12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e + 24a b d )x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 3 2 3 3 2 3 +--R ((210A b - 90B a b )e - 120B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((350A a b - 150B a b)e + (280A b - 320B a b )d e - 160B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (112A a b - 48B a )e + (476A a b - 268B a b)d e +--R + +--R 3 2 2 3 3 +--R (42A b - 290B a b )d e - 24B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 16A a e + (160A a b - 32B a )d e + (78A a b - 166B a b)d e +--R + +--R 3 2 3 +--R (- 12A b - 12B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (24a b e - 96a b d e + 144a b d e - 96a b d e + 24b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 48a b e - 168a b d e + 192a b d e - 48a b d e - 48a b d e +--R + +--R 6 5 +--R 24b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 24a e - 48a b d e - 48a b d e + 192a b d e - 168a b d e +--R + +--R 5 5 +--R 48a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 24a d e - 96a b d e + 144a b d e - 96a b d e + 24a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((210A a b - 90B a b)e + (105A b - 165B a b )d e - 60B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (105A a b - 45B a )e + (210A a b - 150B a b)d e +--R + +--R 2 2 +--R - 120B a b d e +--R * +--R x +--R + +--R 2 3 2 2 2 +--R (105A a b - 45B a )d e - 60B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 3 2 3 3 2 3 +--R ((105A b - 45B a b )e - 60B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((175A a b - 75B a b)e + (140A b - 160B a b )d e - 80B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (56A a b - 24B a )e + (238A a b - 134B a b)d e +--R + +--R 3 2 2 3 3 +--R (21A b - 145B a b )d e - 12B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 8A a e + (80A a b - 16B a )d e + (39A a b - 83B a b)d e +--R + +--R 3 2 3 +--R (- 6A b - 6B a b )d +--R / +--R 4 2 5 3 3 4 2 4 2 3 5 3 2 6 4 3 +--R (12a b e - 48a b d e + 72a b d e - 48a b d e + 12b d e)x +--R + +--R 5 5 4 2 4 3 3 2 3 2 4 3 2 5 4 +--R 24a b e - 84a b d e + 96a b d e - 24a b d e - 24a b d e +--R + +--R 6 5 +--R 12b d +--R * +--R 2 +--R x +--R + +--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 +--R 12a e - 24a b d e - 24a b d e + 96a b d e - 84a b d e +--R + +--R 5 5 +--R 24a b d +--R * +--R x +--R + +--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +--R 12a d e - 48a b d e + 72a b d e - 48a b d e + 12a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 912 + +--S 913 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 +-----------+ | b +--R ((35A b - 15B a)e - 20B b d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (2a e - 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R ((70A b - 30B a)e - 40B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (8a e - 32a b d e + 48a b d e - 32a b d e + 8b d )\|- a e + b d +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-+ \|b \|e x + d +--R ((35A b - 15B a)e - 20B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 +-----------+ | b +--R ((35A b - 15B a)e - 20B b d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (4a e - 16a b d e + 24a b d e - 16a b d e + 4b d )\|- a e + b d +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 916 + +)clear all + +--S 917 of 1293 +t0:=(A+B*x)/((a+b*x)^3*(d+e*x)^(7/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b e x + (3a b e + 3b d e )x + (3a b e + 9a b d e + 3b d e)x +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a e + 9a b d e + 9a b d e + b d )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (3a d e + 9a b d e + 3a b d )x + (3a d e + 3a b d )x + a d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1293 +r0:=-7/20*e*(4*b*B*d-9*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))+_ + 1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^2*(d+e*x)^(5/2))+_ + 1/4*(-4*b*B*d+9*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))-_ + 7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^4*(d+e*x)^(3/2))+_ + 7/4*b^(3/2)*e*(4*b*B*d-9*A*b*e+5*a*B*e)*_ + atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)-_ + 7/4*b*e*(4*b*B*d-9*A*b*e+5*a*B*e)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|b \|e x + d +--R \|b \|e x + d atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R * +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-----------+ +-------+ +--R \|- a e + b d \|e x + d +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 4 4 3 4 +--R ((945A b - 525B a b )e - 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1890A a b - 1050B a b )e + (1890A b - 1890B a b )d e +--R + +--R 4 2 2 +--R - 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (945A a b - 525B a b)e + (3780A a b - 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (945A b - 2205B a b )d e - 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 3 2 2 2 2 +--R (1890A a b - 1050B a b)d e + (1890A a b - 1890B a b )d e +--R + +--R 3 3 +--R - 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (945A a b - 525B a b)d e - 420B a b d e +--R * +--R +-----------+ +--R | b +-------+ +--R |- --------- \|e x + d +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 4 3 4 4 3 4 +--R ((- 1890A b + 1050B a b )e + 840B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 3150A a b + 1750B a b )e + (- 4410A b + 3850B a b )d e +--R + +--R 4 2 2 +--R 1960B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 1008A a b + 560B a b)e + (- 7434A a b + 4578B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2898A b + 4914B a b )d e + 1288B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (144A a b - 80B a )e + (- 2448A a b + 1296B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 4986A a b + 3858B a b )d e + (- 270A b + 2366B a b )d e +--R + +--R 4 4 +--R 120B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 48A a e + (336A a b - 32B a )d e + (- 1728A a b + 544B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 510A a b + 1318B a b )d e + (60A b + 60B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 120a b e - 600a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 4 3 7 5 2 +--R 600a b d e - 120b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 +--R 240a b e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 6 5 2 7 6 +--R 960a b d e - 240b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 +--R 120a e - 120a b d e - 1080a b d e + 3000a b d e +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R - 3000a b d e + 1080a b d e + 120a b d e - 120b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 +--R 240a d e - 960a b d e + 1200a b d e - 1200a b d e +--R + +--R 2 5 6 6 7 +--R 960a b d e - 240a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 120a d e - 600a b d e + 1200a b d e - 1200a b d e + 600a b d e +--R + +--R 2 5 7 +--R - 120a b d +--R * +--R +-------+ +--R \|e x + d +--R , +--R +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1890A a b + 1050B a b )e + (- 1890A b + 1890B a b )d e +--R + +--R 4 2 2 +--R 840B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 945A a b + 525B a b)e + (- 3780A a b + 2520B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 945A b + 2205B a b )d e + 420B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 3 +--R (- 1890A a b + 1050B a b)d e +--R + +--R 3 2 2 2 2 3 3 +--R (- 1890A a b + 1890B a b )d e + 840B a b d e +--R * +--R x +--R + +--R 2 2 3 2 2 2 2 3 +--R (- 945A a b + 525B a b)d e + 420B a b d e +--R * +--R +---------+ +-------+ +--R | b +-------+ b\|e x + d +--R |--------- \|e x + d atan(-----------------------) +--R \|a e - b d +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R + +--R 4 3 4 4 3 4 +--R ((- 945A b + 525B a b )e + 420B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 1575A a b + 875B a b )e + (- 2205A b + 1925B a b )d e +--R + +--R 4 2 2 +--R 980B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 504A a b + 280B a b)e + (- 3717A a b + 2289B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 1449A b + 2457B a b )d e + 644B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (72A a b - 40B a )e + (- 1224A a b + 648B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 2493A a b + 1929B a b )d e + (- 135A b + 1183B a b )d e +--R + +--R 4 4 +--R 60B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 24A a e + (168A a b - 16B a )d e + (- 864A a b + 272B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 255A a b + 659B a b )d e + (30A b + 30B a b )d +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 60a b e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 7 5 2 +--R - 60b d e +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 120a b e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 7 6 +--R - 120b d e +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 60a e - 60a b d e - 540a b d e + 1500a b d e - 1500a b d e +--R + +--R 2 5 5 2 6 6 7 7 +--R 540a b d e + 60a b d e - 60b d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 120a d e - 480a b d e + 600a b d e - 600a b d e + 480a b d e +--R + +--R 6 7 +--R - 120a b d +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 +--R 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--R + +--R 2 5 7 +--R - 60a b d +--R * +--R +-------+ +--R \|e x + d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 919 + +--S 920 of 1293 +m0:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 +-----------+ | b +--R ((63A b - 35B a b)e - 28B b d e)\|- a e + b d |- --------- +--R \| a e - b d +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a e + 2b d) |- --------- \|e x + d + b e x - a e + 2b d +--R \| a e - b d +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 +-+ \|b \|e x + d +--R ((- 126A b + 70B a b)e + 56B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (8a e - 40a b d e + 80a b d e - 80a b d e + 40a b d e - 8b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1293 +m0:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 +-+ \|b \|e x + d +--R ((- 63A b + 35B a b)e + 28B b d e)\|b atanh(--------------) +--R +-----------+ +--R \|- a e + b d +--R + +--R +---------+ +--R 2 2 2 +-----------+ | b +--R ((- 63A b + 35B a b)e + 28B b d e)\|- a e + b d |--------- +--R \|a e - b d +--R * +--R +-------+ +--R b\|e x + d +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a e - b d) |--------- +--R \|a e - b d +--R / +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (4a e - 20a b d e + 40a b d e - 40a b d e + 20a b d e - 4b d ) +--R * +--R +-----------+ +--R \|- a e + b d +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1293 +d0:=D(m0,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 923 + +)clear all + +--S 924 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1293 +r0:=-1/48*(b*d-a*e)*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + (d+e*x)^(3/2)/(b^3*e)-1/40*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + (a+b*x)^(3/2)*(d+e*x)^(5/2)/(b^2*e)+1/5*B*(a+b*x)^(3/2)*_ + (d+e*x)^(7/2)/(b*e)+1/128*(b*d-a*e)^4*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(5/2))-_ + 1/64*(b*d-a*e)^2*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b^4*e)-1/128*(b*d-a*e)^3*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^2) +--R +--R +--R (2) +--R 4 5 5 3 2 4 4 +--R (- 150A a b + 105B a )e + (600A a b - 375B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 900A a b + 450B a b )d e + (600A a b - 150B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 150A b - 75B a b )d e + 45B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 384B b e x + ((480A b + 48B a b )e + 1008B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (80A a b - 56B a b )e + (1360A b + 176B a b )d e +--R + +--R 4 2 2 +--R 744B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 100A a b + 70B a b)e + (360A a b - 222B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (1180A b + 218B a b )d e + 30B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (150A a b - 105B a )e + (- 550A a b + 340B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (730A a b - 346B a b )d e + (150A b + 60B a b )d e - 45B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 2 +-+ +-+ +--R 1920b e \|b \|e +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1293 +--a0:=integrate(t0,x) +--E 926 + +--S 927 of 1293 +--m0:=a0-r0 +--E 927 + +--S 928 of 1293 +--d0:=D(m0,x) +--E 928 + +)clear all + +--S 929 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) (B e x + (A e + B d)x + A d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1293 +r0:=-1/24*(3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/4*B*(a+b*x)^(3/2)*(d+e*x)^(5/2)/(b*e)+1/64*(b*d-a*e)^3*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(5/2))-1/32*(b*d-a*e)*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e)-_ + 1/64*(b*d-a*e)^2*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^3*e^2) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (24A a b - 15B a )e + (- 72A a b + 36B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (72A a b - 18B a b )d e + (- 24A b - 12B a b )d e + 9B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 8B a b )e + 72B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((16A a b - 10B a b)e + (112A b + 20B a b )d e + 6B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (- 24A a b + 15B a )e + (64A a b - 31B a b)d e +--R + +--R 3 2 2 3 3 +--R (24A b + 9B a b )d e - 9B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 2 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1293 +--a0:=integrate(t0,x) +--E 931 + +--S 932 of 1293 +--m0:=a0-r0 +--E 932 + +--S 933 of 1293 +--d0:=D(m0,x) +--E 933 + +)clear all + +--S 934 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)*sqrt(d+e*x) +--R +--R +--R +-------+ +-------+ +--R (1) (B x + A)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1293 +r0:=1/3*B*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b*e)-1/8*(b*d-a*e)^2*_ + (2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(5/2))+1/4*(2*A*b*e-B*(b*d+a*e))*_ + (a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e)+1/8*(b*d-a*e)*_ + (2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^2) +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (- 6A a b + 3B a )e + (12A a b - 3B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 6A b - 3B a b )d e + 3B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 2 2 +--R 8B b e x + ((12A b + 2B a b)e + 2B b d e)x + (6A a b - 3B a )e +--R + +--R 2 2 2 +--R (6A b + 2B a b)d e - 3B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 2 +-+ +-+ +--R 24b e \|b \|e +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1293 +--a0:=integrate(t0,x) +--E 936 + +--S 937 of 1293 +--m0:=a0-r0 +--E 937 + +--S 938 of 1293 +--d0:=D(m0,x) +--E 938 + +)clear all + +--S 939 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/sqrt(d+e*x) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1293 +r0:=1/4*(b*d-a*e)*(3*b*B*d-4*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(5/2))+1/2*B*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b*e)-1/4*(3*b*B*d-4*A*b*e+a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b*e^2) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((4A a b - B a )e + (- 4A b - 2B a b)d e + 3B b d ) +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2B b e x + (4A b + B a)e - 3B b d)\|b \|e \|b x + a \|e x + d +--R / +--R 2 +-+ +-+ +--R 4b e \|b \|e +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1293 +--a0:=integrate(t0,x) +--E 941 + +--S 942 of 1293 +--m0:=a0-r0 +--E 942 + +--S 943 of 1293 +--d0:=D(m0,x) +--E 943 + +)clear all + +--S 944 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1293 +r0:=-(3*b*B*d-2*A*b*e-a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(e^(5/2)*sqrt(b))-2*(B*d-A*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)*sqrt(d+e*x))+(3*b*B*d-2*A*b*e-a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(e^2*(b*d-a*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R ((2A b + B a)e - 3B b d)\|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (B e x - 2A e + 3B d)\|b \|e \|b x + a +--R / +--R 2 +-+ +-+ +-------+ +--R e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1293 +--a0:=integrate(t0,x) +--E 946 + +--S 947 of 1293 +--m0:=a0-r0 +--E 947 + +--S 948 of 1293 +--d0:=D(m0,x) +--E 948 + +)clear all + +--S 949 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(5/2)-_ + 2*B*sqrt(a+b*x)/(e^2*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 +-+ +-------+ +--R ((6B a e - 6B b d e)x + 6B a d e - 6B b d )\|b \|e x + d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 +-+ +--R (((- 2A b - 6B a)e + 8B b d e)x - 2A a e - 4B a d e + 6B b d )\|e +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 3 3 2 2 +-+ +-------+ +--R ((3a e - 3b d e )x + 3a d e - 3b d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1293 +--a0:=integrate(t0,x) +--E 951 + +--S 952 of 1293 +--m0:=a0-r0 +--E 952 + +--S 953 of 1293 +--d0:=D(m0,x) +--E 953 + +)clear all + +--S 954 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(7/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ + 2/15*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 2 2 2 +--R ((4A b - 10B a b)e + 6B b d)x +--R + +--R 2 2 2 +--R ((- 2A a b - 10B a )e + (10A b + 2B a b)d)x - 6A a e +--R + +--R 2 +--R (10A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (15a e - 30a b d e + 15b d e )x + (30a d e - 60a b d e + 30b d e)x +--R + +--R 2 2 2 3 2 4 +--R 15a d e - 30a b d e + 15b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 +--R ((4A b - 10B a b)d e + 6B b d )x +--R + +--R 2 3 2 4 2 3 +--R ((- 2A a b - 10B a )d e + (10A b + 2B a b)d )x - 6A a d e +--R + +--R 2 4 +--R (10A a b - 4B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 4 2 2 2 3 3 3 +--R ((- 3A a d - 3A a )e + ((5A a b - 2B a )d + (5A a b - 2B a )d)e )x +--R + +--R 2 2 3 3 +--R (- 9A a d - 9A a d)e +--R + +--R 2 3 2 3 2 2 +--R ((15A a b - 6B a )d + (15A a b - 6B a )d )e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R ((- 9A a d - 9A a d )e + ((15A a b - 6B a )d + (15A a b - 6B a )d )e)x +--R + +--R 2 4 3 3 2 5 2 3 4 +--R (- 3A a d - 3A a d )e + (5A a b - 2B a )d + (5A a b - 2B a )d +--R / +--R 2 3 5 4 4 2 5 3 3 +--R (15a d e - 30a b d e + 15b d e )x +--R + +--R 2 4 4 5 3 2 6 2 2 2 5 3 6 2 2 7 +--R (45a d e - 90a b d e + 45b d e )x + (45a d e - 90a b d e + 45b d e)x +--R + +--R 2 6 2 7 2 8 +--R 15a d e - 30a b d e + 15b d +--R Type: Union(Expression(Integer),...) +--E 956 + +--S 957 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 3 2 2 2 3 +--R (- 3A a d - 3A a )e + (5A a b - 2B a )d + (5A a b - 2B a )d +--R (4) ------------------------------------------------------------ +--R 2 3 2 4 2 5 +--R 15a d e - 30a b d e + 15b d +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +)clear all + +--S 959 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(9/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(3*b*B*d+4*A*b*e-7*a*B*e)*(a+b*x)^(3/2)/_ + (e*(b*d-a*e)^2*(d+e*x)^(5/2))+4/105*b*(3*b*B*d+4*A*b*e-7*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 3 2 2 3 3 +--R ((- 16A b + 28B a b )e - 12B b d e)x +--R + +--R 2 2 2 3 2 3 2 2 +--R ((8A a b - 14B a b)e + (- 56A b + 104B a b )d e - 42B b d )x +--R + +--R 2 3 2 2 2 +--R (- 6A a b - 42B a )e + (28A a b + 104B a b)d e +--R + +--R 3 2 2 +--R (- 70A b - 14B a b )d +--R * +--R x +--R + +--R 3 2 2 3 2 2 2 +--R - 30A a e + (84A a b - 12B a )d e + (- 70A a b + 28B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 6 2 5 2 2 4 3 3 3 3 +--R (105a e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 2 +--R (315a d e - 945a b d e + 945a b d e - 315b d e )x +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 3 3 3 +--R (315a d e - 945a b d e + 945a b d e - 315b d e)x + 105a d e +--R + +--R 2 4 2 2 5 3 6 +--R - 315a b d e + 315a b d e - 105b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 3 5 3 +--R ((- 16A b + 28B a b )d e - 12B b d e)x +--R + +--R 2 2 4 2 3 2 5 3 6 2 +--R ((8A a b - 14B a b)d e + (- 56A b + 104B a b )d e - 42B b d )x +--R + +--R 2 3 4 2 2 2 5 +--R (- 6A a b - 42B a )d e + (28A a b + 104B a b)d e +--R + +--R 3 2 6 +--R (- 70A b - 14B a b )d +--R * +--R x +--R + +--R 3 4 2 2 3 5 2 2 6 +--R - 30A a d e + (84A a b - 12B a )d e + (- 70A a b + 28B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 6 +--R (15A a d + 15A a )e +--R + +--R 2 3 2 3 4 5 +--R ((- 42A a b + 6B a )d + (- 42A a b + 6B a )d)e +--R + +--R 2 2 3 2 2 3 2 4 +--R ((35A a b - 14B a b)d + (35A a b - 14B a b)d )e +--R * +--R 4 +--R x +--R + +--R 3 2 4 5 +--R (60A a d + 60A a d)e +--R + +--R 2 3 3 3 4 2 4 +--R ((- 168A a b + 24B a )d + (- 168A a b + 24B a )d )e +--R + +--R 2 2 4 2 2 3 3 3 +--R ((140A a b - 56B a b)d + (140A a b - 56B a b)d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 4 +--R (90A a d + 90A a d )e +--R + +--R 2 3 4 3 4 3 3 +--R ((- 252A a b + 36B a )d + (- 252A a b + 36B a )d )e +--R + +--R 2 2 5 2 2 3 4 2 +--R ((210A a b - 84B a b)d + (210A a b - 84B a b)d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 3 +--R (60A a d + 60A a d )e +--R + +--R 2 3 5 3 4 4 2 +--R ((- 168A a b + 24B a )d + (- 168A a b + 24B a )d )e +--R + +--R 2 2 6 2 2 3 5 +--R ((140A a b - 56B a b)d + (140A a b - 56B a b)d )e +--R * +--R x +--R + +--R 3 5 4 4 2 +--R (15A a d + 15A a d )e +--R + +--R 2 3 6 3 4 5 2 2 7 +--R ((- 42A a b + 6B a )d + (- 42A a b + 6B a )d )e + (35A a b - 14B a b)d +--R + +--R 2 2 3 6 +--R (35A a b - 14B a b)d +--R / +--R 3 4 7 2 5 6 2 6 5 3 7 4 4 +--R (105a d e - 315a b d e + 315a b d e - 105b d e )x +--R + +--R 3 5 6 2 6 5 2 7 4 3 8 3 3 +--R (420a d e - 1260a b d e + 1260a b d e - 420b d e )x +--R + +--R 3 6 5 2 7 4 2 8 3 3 9 2 2 +--R (630a d e - 1890a b d e + 1890a b d e - 630b d e )x +--R + +--R 3 7 4 2 8 3 2 9 2 3 10 3 8 3 +--R (420a d e - 1260a b d e + 1260a b d e - 420b d e)x + 105a d e +--R + +--R 2 9 2 2 10 3 11 +--R - 315a b d e + 315a b d e - 105b d +--R Type: Union(Expression(Integer),...) +--E 961 + +--S 962 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 2 2 3 2 3 4 +--R (15A a d + 15A a )e + ((- 42A a b + 6B a )d + (- 42A a b + 6B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R (35A a b - 14B a b)d + (35A a b - 14B a b)d +--R / +--R 3 4 3 2 5 2 2 6 3 7 +--R 105a d e - 315a b d e + 315a b d e - 105b d +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(11/2) +--R +--R +--R +-------+ +--R (B x + A)\|b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1293 +r0:=-2/9*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/21*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/_ + (e*(b*d-a*e)^2*(d+e*x)^(7/2))+8/105*b*(b*B*d+2*A*b*e-3*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(5/2))+16/315*b^2*_ + (b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 4 3 3 4 2 4 +--R ((32A b - 48B a b )e + 16B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 3 +--R ((- 16A a b + 24B a b )e + (144A b - 224B a b )d e + 72B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (12A a b - 18B a b)e + (- 72A a b + 114B a b )d e +--R + +--R 4 3 2 4 3 +--R (252A b - 414B a b )d e + 126B b d +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 10A a b - 90B a )e + (54A a b + 334B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 126A a b - 414B a b )d e + (210A b + 42B a b )d +--R * +--R x +--R + +--R 4 3 3 4 2 2 2 3 2 +--R - 70A a e + (270A a b - 20B a )d e + (- 378A a b + 72B a b)d e +--R + +--R 3 2 2 3 +--R (210A a b - 84B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 8 3 7 2 2 2 6 3 3 5 4 4 4 4 +--R (315a e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d e )x +--R + +--R 4 7 3 2 6 2 2 3 5 3 4 4 +--R 1260a d e - 5040a b d e + 7560a b d e - 5040a b d e +--R + +--R 4 5 3 +--R 1260b d e +--R * +--R 3 +--R x +--R + +--R 4 2 6 3 3 5 2 2 4 4 3 5 3 +--R 1890a d e - 7560a b d e + 11340a b d e - 7560a b d e +--R + +--R 4 6 2 +--R 1890b d e +--R * +--R 2 +--R x +--R + +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 4 7 +--R (1260a d e - 5040a b d e + 7560a b d e - 5040a b d e + 1260b d e)x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 +--R 315a d e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 3 4 6 2 4 +--R ((96A b - 144B a b )d e + 48B b d e )x +--R + +--R 3 2 2 5 3 4 3 6 2 +--R (- 48A a b + 72B a b )d e + (432A b - 672B a b )d e +--R + +--R 4 7 +--R 216B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 3 3 2 2 6 2 +--R (36A a b - 54B a b)d e + (- 216A a b + 342B a b )d e +--R + +--R 4 3 7 4 8 +--R (756A b - 1242B a b )d e + 378B b d +--R * +--R 2 +--R x +--R + +--R 3 4 5 3 2 2 3 6 2 +--R (- 30A a b - 270B a )d e + (162A a b + 1002B a b)d e +--R + +--R 3 2 2 7 4 3 8 +--R (- 378A a b - 1242B a b )d e + (630A b + 126B a b )d +--R * +--R x +--R + +--R 4 5 3 3 4 6 2 +--R - 210A a d e + (810A a b - 60B a )d e +--R + +--R 2 2 3 7 3 2 2 8 +--R (- 1134A a b + 216B a b)d e + (630A a b - 252B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 8 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 7 +--R ((135A a b - 10B a )d + (1215A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 6 +--R ((- 189A a b + 36B a b)d + (- 1701A a b + 324B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 5 +--R ((105A a b - 42B a b )d + (945A a b - 378B a b )d )e +--R * +--R 5 +--R x +--R + +--R 4 2 5 7 +--R (- 175A a d - 1575A a d)e +--R + +--R 3 4 3 4 5 2 6 +--R ((675A a b - 50B a )d + (6075A a b - 450B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 5 +--R ((- 945A a b + 180B a b)d + (- 8505A a b + 1620B a b)d )e +--R + +--R 3 2 2 5 2 3 3 2 4 4 +--R ((525A a b - 210B a b )d + (4725A a b - 1890B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 6 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 4 4 5 3 5 +--R ((1350A a b - 100B a )d + (12150A a b - 900B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 4 +--R ((- 1890A a b + 360B a b)d + (- 17010A a b + 3240B a b)d )e +--R + +--R 3 2 2 6 2 3 3 2 5 3 +--R ((1050A a b - 420B a b )d + (9450A a b - 3780B a b )d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 5 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 5 4 5 4 4 +--R ((1350A a b - 100B a )d + (12150A a b - 900B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 3 +--R ((- 1890A a b + 360B a b)d + (- 17010A a b + 3240B a b)d )e +--R + +--R 3 2 2 7 2 3 3 2 6 2 +--R ((1050A a b - 420B a b )d + (9450A a b - 3780B a b )d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 4 +--R (- 175A a d - 1575A a d )e +--R + +--R 3 4 6 4 5 5 3 +--R ((675A a b - 50B a )d + (6075A a b - 450B a )d )e +--R + +--R 2 2 3 7 3 2 4 6 2 +--R ((- 945A a b + 180B a b)d + (- 8505A a b + 1620B a b)d )e +--R + +--R 3 2 2 8 2 3 3 2 7 +--R ((525A a b - 210B a b )d + (4725A a b - 1890B a b )d )e +--R * +--R x +--R + +--R 4 6 5 5 3 +--R (- 35A a d - 315A a d )e +--R + +--R 3 4 7 4 5 6 2 +--R ((135A a b - 10B a )d + (1215A a b - 90B a )d )e +--R + +--R 2 2 3 8 3 2 4 7 +--R ((- 189A a b + 36B a b)d + (- 1701A a b + 324B a b)d )e +--R + +--R 3 2 2 9 2 3 3 2 8 +--R (105A a b - 42B a b )d + (945A a b - 378B a b )d +--R / +--R 4 5 9 3 6 8 2 2 7 7 3 8 6 4 9 5 5 +--R (945a d e - 3780a b d e + 5670a b d e - 3780a b d e + 945b d e )x +--R + +--R 4 6 8 3 7 7 2 2 8 6 3 9 5 +--R 4725a d e - 18900a b d e + 28350a b d e - 18900a b d e +--R + +--R 4 10 4 +--R 4725b d e +--R * +--R 4 +--R x +--R + +--R 4 7 7 3 8 6 2 2 9 5 3 10 4 +--R 9450a d e - 37800a b d e + 56700a b d e - 37800a b d e +--R + +--R 4 11 3 +--R 9450b d e +--R * +--R 3 +--R x +--R + +--R 4 8 6 3 9 5 2 2 10 4 3 11 3 +--R 9450a d e - 37800a b d e + 56700a b d e - 37800a b d e +--R + +--R 4 12 2 +--R 9450b d e +--R * +--R 2 +--R x +--R + +--R 4 9 5 3 10 4 2 2 11 3 3 12 2 +--R 4725a d e - 18900a b d e + 28350a b d e - 18900a b d e +--R + +--R 4 13 +--R 4725b d e +--R * +--R x +--R + +--R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 +--R 945a d e - 3780a b d e + 5670a b d e - 3780a b d e + 945b d +--R Type: Union(Expression(Integer),...) +--E 966 + +--S 967 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 3 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 2 +--R ((135A a b - 10B a )d + (1215A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 +--R ((- 189A a b + 36B a b)d + (- 1701A a b + 324B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R (105A a b - 42B a b )d + (945A a b - 378B a b )d +--R / +--R 4 5 4 3 6 3 2 2 7 2 3 8 4 9 +--R 945a d e - 3780a b d e + 5670a b d e - 3780a b d e + 945b d +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 968 + +)clear all + +--S 969 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R +-------+ +--R (B x + A)\|b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1293 +r0:=-2/11*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ + 2/99*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(9/2))+4/231*b*(3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(7/2))+16/1155*b^2*_ + (3*b*B*d+8*A*b*e-11*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(5/2))+32/3465*b^3*(3*b*B*d+8*A*b*e-11*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^5*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 5 4 4 5 3 5 +--R ((- 256A b + 352B a b )e - 96B b d e )x +--R + +--R 4 2 3 4 5 4 3 +--R (128A a b - 176B a b )e + (- 1408A b + 1984B a b )d e +--R + +--R 5 2 2 +--R - 528B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 96A a b + 132B a b )e + (704A a b - 1004B a b )d e +--R + +--R 5 4 2 2 5 3 +--R (- 3168A b + 4620B a b )d e - 1188B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (80A a b - 110B a b)e + (- 528A a b + 756B a b )d e +--R + +--R 4 2 3 2 2 5 4 3 +--R (1584A a b - 2376B a b )d e + (- 3696A b + 5676B a b )d e +--R + +--R 5 4 +--R - 1386B b d +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 2 4 3 +--R (- 70A a b - 770B a )e + (440A a b + 3700B a b)d e +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 1188A a b - 6864B a b )d e + (1848A a b + 5676B a b )d e +--R + +--R 5 4 4 +--R (- 2310A b - 462B a b )d +--R * +--R x +--R + +--R 5 4 4 5 3 3 2 4 2 2 +--R - 630A a e + (3080A a b - 140B a )d e + (- 5940A a b + 660B a b)d e +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (5544A a b - 1188B a b )d e + (- 2310A a b + 924B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 10 4 9 3 2 2 8 2 3 3 7 +--R 3465a e - 17325a b d e + 34650a b d e - 34650a b d e +--R + +--R 4 4 6 5 5 5 +--R 17325a b d e - 3465b d e +--R * +--R 5 +--R x +--R + +--R 5 9 4 2 8 3 2 3 7 2 3 4 6 +--R 17325a d e - 86625a b d e + 173250a b d e - 173250a b d e +--R + +--R 4 5 5 5 6 4 +--R 86625a b d e - 17325b d e +--R * +--R 4 +--R x +--R + +--R 5 2 8 4 3 7 3 2 4 6 2 3 5 5 +--R 34650a d e - 173250a b d e + 346500a b d e - 346500a b d e +--R + +--R 4 6 4 5 7 3 +--R 173250a b d e - 34650b d e +--R * +--R 3 +--R x +--R + +--R 5 3 7 4 4 6 3 2 5 5 2 3 6 4 +--R 34650a d e - 173250a b d e + 346500a b d e - 346500a b d e +--R + +--R 4 7 3 5 8 2 +--R 173250a b d e - 34650b d e +--R * +--R 2 +--R x +--R + +--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3 +--R 17325a d e - 86625a b d e + 173250a b d e - 173250a b d e +--R + +--R 4 8 2 5 9 +--R 86625a b d e - 17325b d e +--R * +--R x +--R + +--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2 +--R 3465a d e - 17325a b d e + 34650a b d e - 34650a b d e +--R + +--R 4 9 5 10 +--R 17325a b d e - 3465b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 6 4 5 7 3 5 +--R ((- 256A b + 352B a b )d e - 96B b d e )x +--R + +--R 4 2 3 6 4 5 4 7 3 +--R (128A a b - 176B a b )d e + (- 1408A b + 1984B a b )d e +--R + +--R 5 8 2 +--R - 528B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 4 4 2 3 7 3 +--R (- 96A a b + 132B a b )d e + (704A a b - 1004B a b )d e +--R + +--R 5 4 8 2 5 9 +--R (- 3168A b + 4620B a b )d e - 1188B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 4 2 3 3 2 7 3 +--R (80A a b - 110B a b)d e + (- 528A a b + 756B a b )d e +--R + +--R 4 2 3 8 2 5 4 9 +--R (1584A a b - 2376B a b )d e + (- 3696A b + 5676B a b )d e +--R + +--R 5 10 +--R - 1386B b d +--R * +--R 2 +--R x +--R + +--R 4 5 6 4 3 2 4 7 3 +--R (- 70A a b - 770B a )d e + (440A a b + 3700B a b)d e +--R + +--R 2 3 3 2 8 2 4 2 3 9 +--R (- 1188A a b - 6864B a b )d e + (1848A a b + 5676B a b )d e +--R + +--R 5 4 10 +--R (- 2310A b - 462B a b )d +--R * +--R x +--R + +--R 5 6 4 4 5 7 3 +--R - 630A a d e + (3080A a b - 140B a )d e +--R + +--R 3 2 4 8 2 2 3 3 2 9 +--R (- 5940A a b + 660B a b)d e + (5544A a b - 1188B a b )d e +--R + +--R 4 2 3 10 +--R (- 2310A a b + 924B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 6 10 +--R (315A a d + 315A a )e +--R + +--R 4 5 2 5 6 9 +--R ((- 1540A a b + 70B a )d + (- 1540A a b + 70B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 8 +--R ((2970A a b - 330B a b)d + (2970A a b - 330B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 7 +--R ((- 2772A a b + 594B a b )d + (- 2772A a b + 594B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 6 +--R ((1155A a b - 462B a b )d + (1155A a b - 462B a b )d )e +--R * +--R 6 +--R x +--R + +--R 5 2 6 9 +--R (1890A a d + 1890A a d)e +--R + +--R 4 5 3 5 6 2 8 +--R ((- 9240A a b + 420B a )d + (- 9240A a b + 420B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 7 +--R ((17820A a b - 1980B a b)d + (17820A a b - 1980B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 6 +--R ((- 16632A a b + 3564B a b )d + (- 16632A a b + 3564B a b )d )e +--R + +--R 4 2 3 6 2 4 3 3 5 5 +--R ((6930A a b - 2772B a b )d + (6930A a b - 2772B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 3 6 2 8 +--R (4725A a d + 4725A a d )e +--R + +--R 4 5 4 5 6 3 7 +--R ((- 23100A a b + 1050B a )d + (- 23100A a b + 1050B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 6 +--R ((44550A a b - 4950B a b)d + (44550A a b - 4950B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 5 +--R ((- 41580A a b + 8910B a b )d + (- 41580A a b + 8910B a b )d )e +--R + +--R 4 2 3 7 2 4 3 3 6 4 +--R ((17325A a b - 6930B a b )d + (17325A a b - 6930B a b )d )e +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 7 +--R (6300A a d + 6300A a d )e +--R + +--R 4 5 5 5 6 4 6 +--R ((- 30800A a b + 1400B a )d + (- 30800A a b + 1400B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 5 +--R ((59400A a b - 6600B a b)d + (59400A a b - 6600B a b)d )e +--R + +--R 2 3 3 2 7 3 3 4 2 6 4 +--R ((- 55440A a b + 11880B a b )d + (- 55440A a b + 11880B a b )d )e +--R + +--R 4 2 3 8 2 4 3 3 7 3 +--R ((23100A a b - 9240B a b )d + (23100A a b - 9240B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 5 6 4 6 +--R (4725A a d + 4725A a d )e +--R + +--R 4 5 6 5 6 5 5 +--R ((- 23100A a b + 1050B a )d + (- 23100A a b + 1050B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 4 +--R ((44550A a b - 4950B a b)d + (44550A a b - 4950B a b)d )e +--R + +--R 2 3 3 2 8 3 3 4 2 7 3 +--R ((- 41580A a b + 8910B a b )d + (- 41580A a b + 8910B a b )d )e +--R + +--R 4 2 3 9 2 4 3 3 8 2 +--R ((17325A a b - 6930B a b )d + (17325A a b - 6930B a b )d )e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 5 +--R (1890A a d + 1890A a d )e +--R + +--R 4 5 7 5 6 6 4 +--R ((- 9240A a b + 420B a )d + (- 9240A a b + 420B a )d )e +--R + +--R 3 2 4 8 4 2 5 7 3 +--R ((17820A a b - 1980B a b)d + (17820A a b - 1980B a b)d )e +--R + +--R 2 3 3 2 9 3 3 4 2 8 2 +--R ((- 16632A a b + 3564B a b )d + (- 16632A a b + 3564B a b )d )e +--R + +--R 4 2 3 10 2 4 3 3 9 +--R ((6930A a b - 2772B a b )d + (6930A a b - 2772B a b )d )e +--R * +--R x +--R + +--R 5 7 6 6 4 +--R (315A a d + 315A a d )e +--R + +--R 4 5 8 5 6 7 3 +--R ((- 1540A a b + 70B a )d + (- 1540A a b + 70B a )d )e +--R + +--R 3 2 4 9 4 2 5 8 2 +--R ((2970A a b - 330B a b)d + (2970A a b - 330B a b)d )e +--R + +--R 2 3 3 2 10 3 3 4 2 9 +--R ((- 2772A a b + 594B a b )d + (- 2772A a b + 594B a b )d )e +--R + +--R 4 2 3 11 2 4 3 3 10 +--R (1155A a b - 462B a b )d + (1155A a b - 462B a b )d +--R / +--R 5 6 11 4 7 10 3 2 8 9 2 3 9 8 +--R 3465a d e - 17325a b d e + 34650a b d e - 34650a b d e +--R + +--R 4 10 7 5 11 6 +--R 17325a b d e - 3465b d e +--R * +--R 6 +--R x +--R + +--R 5 7 10 4 8 9 3 2 9 8 2 3 10 7 +--R 20790a d e - 103950a b d e + 207900a b d e - 207900a b d e +--R + +--R 4 11 6 5 12 5 +--R 103950a b d e - 20790b d e +--R * +--R 5 +--R x +--R + +--R 5 8 9 4 9 8 3 2 10 7 2 3 11 6 +--R 51975a d e - 259875a b d e + 519750a b d e - 519750a b d e +--R + +--R 4 12 5 5 13 4 +--R 259875a b d e - 51975b d e +--R * +--R 4 +--R x +--R + +--R 5 9 8 4 10 7 3 2 11 6 2 3 12 5 +--R 69300a d e - 346500a b d e + 693000a b d e - 693000a b d e +--R + +--R 4 13 4 5 14 3 +--R 346500a b d e - 69300b d e +--R * +--R 3 +--R x +--R + +--R 5 10 7 4 11 6 3 2 12 5 2 3 13 4 +--R 51975a d e - 259875a b d e + 519750a b d e - 519750a b d e +--R + +--R 4 14 3 5 15 2 +--R 259875a b d e - 51975b d e +--R * +--R 2 +--R x +--R + +--R 5 11 6 4 12 5 3 2 13 4 2 3 14 3 +--R 20790a d e - 103950a b d e + 207900a b d e - 207900a b d e +--R + +--R 4 15 2 5 16 +--R 103950a b d e - 20790b d e +--R * +--R x +--R + +--R 5 12 5 4 13 4 3 2 14 3 2 3 15 2 +--R 3465a d e - 17325a b d e + 34650a b d e - 34650a b d e +--R + +--R 4 16 5 17 +--R 17325a b d e - 3465b d +--R Type: Union(Expression(Integer),...) +--E 971 + +--S 972 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 4 +--R (315A a d + 315A a )e +--R + +--R 4 5 2 5 6 3 +--R ((- 1540A a b + 70B a )d + (- 1540A a b + 70B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 2 +--R ((2970A a b - 330B a b)d + (2970A a b - 330B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 +--R ((- 2772A a b + 594B a b )d + (- 2772A a b + 594B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 +--R (1155A a b - 462B a b )d + (1155A a b - 462B a b )d +--R / +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 3465a d e - 17325a b d e + 34650a b d e - 34650a b d e +--R + +--R 4 10 5 11 +--R 17325a b d e - 3465b d +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 973 + +)clear all + +--S 974 of 1293 +t0:=(A+B*x)*sqrt(a+b*x)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R +-------+ +--R (B x + A)\|b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1293 +r0:=-2/13*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ + 2/143*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(11/2))+16/1287*b*(3*b*B*d+10*A*b*e-13*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+32/3003*b^2*_ + (3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(7/2))+128/15015*b^3*(3*b*B*d+10*A*b*e-13*a*B*e)*_ + (a+b*x)^(3/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2))+_ + 256/45045*b^4*(3*b*B*d+10*A*b*e-13*a*B*e)*(a+b*x)^(3/2)/_ + (e*(b*d-a*e)^6*(d+e*x)^(3/2)) +--R +--R +--R (2) +--R 6 5 5 6 4 6 +--R ((2560A b - 3328B a b )e + 768B b d e )x +--R + +--R 5 2 4 5 6 5 4 +--R (- 1280A a b + 1664B a b )e + (16640A b - 22016B a b )d e +--R + +--R 6 2 3 +--R 4992B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 5 5 2 4 4 +--R (960A a b - 1248B a b )e + (- 8320A a b + 11104B a b )d e +--R + +--R 6 5 2 3 6 3 2 +--R (45760A b - 61984B a b )d e + 13728B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 5 2 4 3 3 4 +--R (- 800A a b + 1040B a b )e + (6240A a b - 8352B a b )d e +--R + +--R 5 2 4 2 3 6 5 3 2 +--R (- 22880A a b + 31616B a b )d e + (68640A b - 96096B a b )d e +--R + +--R 6 4 +--R 20592B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 3 3 4 2 4 +--R (700A a b - 910B a b)e + (- 5200A a b + 6970B a b )d e +--R + +--R 2 4 3 3 2 3 5 2 4 3 2 +--R (17160A a b - 23868B a b )d e + (- 34320A a b + 49764B a b )d e +--R + +--R 6 5 4 6 5 +--R (60060A b - 88374B a b )d e + 18018B b d +--R * +--R 2 +--R x +--R + +--R 5 6 5 4 2 5 4 +--R (- 630A a b - 8190B a )e + (4550A a b + 47950B a b)d e +--R + +--R 3 3 4 2 2 3 +--R (- 14300A a b - 115180B a b )d e +--R + +--R 2 4 3 3 3 2 5 2 4 4 +--R (25740A a b + 142428B a b )d e + (- 30030A a b - 88374B a b )d e +--R + +--R 6 5 5 +--R (30030A b + 6006B a b )d +--R * +--R x +--R + +--R 6 5 5 6 4 +--R - 6930A a e + (40950A a b - 1260B a )d e +--R + +--R 4 2 5 2 3 3 3 4 2 3 2 +--R (- 100100A a b + 7280B a b)d e + (128700A a b - 17160B a b )d e +--R + +--R 2 4 3 3 4 5 2 4 5 +--R (- 90090A a b + 20592B a b )d e + (30030A a b - 12012B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 12 5 11 4 2 2 10 3 3 3 9 +--R 45045a e - 270270a b d e + 675675a b d e - 900900a b d e +--R + +--R 2 4 4 8 5 5 7 6 6 6 +--R 675675a b d e - 270270a b d e + 45045b d e +--R * +--R 6 +--R x +--R + +--R 6 11 5 2 10 4 2 3 9 +--R 270270a d e - 1621620a b d e + 4054050a b d e +--R + +--R 3 3 4 8 2 4 5 7 5 6 6 6 7 5 +--R - 5405400a b d e + 4054050a b d e - 1621620a b d e + 270270b d e +--R * +--R 5 +--R x +--R + +--R 6 2 10 5 3 9 4 2 4 8 +--R 675675a d e - 4054050a b d e + 10135125a b d e +--R + +--R 3 3 5 7 2 4 6 6 5 7 5 +--R - 13513500a b d e + 10135125a b d e - 4054050a b d e +--R + +--R 6 8 4 +--R 675675b d e +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 2 5 7 +--R 900900a d e - 5405400a b d e + 13513500a b d e +--R + +--R 3 3 6 6 2 4 7 5 5 8 4 +--R - 18018000a b d e + 13513500a b d e - 5405400a b d e +--R + +--R 6 9 3 +--R 900900b d e +--R * +--R 3 +--R x +--R + +--R 6 4 8 5 5 7 4 2 6 6 +--R 675675a d e - 4054050a b d e + 10135125a b d e +--R + +--R 3 3 7 5 2 4 8 4 5 9 3 +--R - 13513500a b d e + 10135125a b d e - 4054050a b d e +--R + +--R 6 10 2 +--R 675675b d e +--R * +--R 2 +--R x +--R + +--R 6 5 7 5 6 6 4 2 7 5 3 3 8 4 +--R 270270a d e - 1621620a b d e + 4054050a b d e - 5405400a b d e +--R + +--R 2 4 9 3 5 10 2 6 11 +--R 4054050a b d e - 1621620a b d e + 270270b d e +--R * +--R x +--R + +--R 6 6 6 5 7 5 4 2 8 4 3 3 9 3 +--R 45045a d e - 270270a b d e + 675675a b d e - 900900a b d e +--R + +--R 2 4 10 2 5 11 6 12 +--R 675675a b d e - 270270a b d e + 45045b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 7 5 6 8 4 6 +--R ((10240A b - 13312B a b )d e + 3072B b d e )x +--R + +--R 5 2 4 7 5 6 5 8 4 +--R (- 5120A a b + 6656B a b )d e + (66560A b - 88064B a b )d e +--R + +--R 6 9 3 +--R 19968B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 5 5 2 4 8 4 +--R (3840A a b - 4992B a b )d e + (- 33280A a b + 44416B a b )d e +--R + +--R 6 5 9 3 6 10 2 +--R (183040A b - 247936B a b )d e + 54912B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 5 2 4 3 3 8 4 +--R (- 3200A a b + 4160B a b )d e + (24960A a b - 33408B a b )d e +--R + +--R 5 2 4 9 3 +--R (- 91520A a b + 126464B a b )d e +--R + +--R 6 5 10 2 6 11 +--R (274560A b - 384384B a b )d e + 82368B b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 5 3 3 4 2 8 4 +--R (2800A a b - 3640B a b)d e + (- 20800A a b + 27880B a b )d e +--R + +--R 2 4 3 3 9 3 +--R (68640A a b - 95472B a b )d e +--R + +--R 5 2 4 10 2 +--R (- 137280A a b + 199056B a b )d e +--R + +--R 6 5 11 6 12 +--R (240240A b - 353496B a b )d e + 72072B b d +--R * +--R 2 +--R x +--R + +--R 5 6 7 5 4 2 5 8 4 +--R (- 2520A a b - 32760B a )d e + (18200A a b + 191800B a b)d e +--R + +--R 3 3 4 2 9 3 +--R (- 57200A a b - 460720B a b )d e +--R + +--R 2 4 3 3 10 2 +--R (102960A a b + 569712B a b )d e +--R + +--R 5 2 4 11 6 5 12 +--R (- 120120A a b - 353496B a b )d e + (120120A b + 24024B a b )d +--R * +--R x +--R + +--R 6 7 5 5 6 8 4 +--R - 27720A a d e + (163800A a b - 5040B a )d e +--R + +--R 4 2 5 9 3 3 3 4 2 10 2 +--R (- 400400A a b + 29120B a b)d e + (514800A a b - 68640B a b )d e +--R + +--R 2 4 3 3 11 5 2 4 12 +--R (- 360360A a b + 82368B a b )d e + (120120A a b - 48048B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 6 7 12 +--R (- 3465A a d - 55440A a )e +--R + +--R 5 6 2 6 7 11 +--R ((20475A a b - 630B a )d + (327600A a b - 10080B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 10 +--R ((- 50050A a b + 3640B a b)d + (- 800800A a b + 58240B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 9 +--R ((64350A a b - 8580B a b )d + (1029600A a b - 137280B a b )d )e +--R + +--R 2 4 3 3 5 +--R (- 45045A a b + 10296B a b )d +--R + +--R 3 4 4 3 4 +--R (- 720720A a b + 164736B a b )d +--R * +--R 8 +--R e +--R + +--R 5 2 4 6 2 5 3 4 5 7 +--R ((15015A a b - 6006B a b )d + (240240A a b - 96096B a b )d )e +--R * +--R 7 +--R x +--R + +--R 6 2 7 11 +--R (- 24255A a d - 388080A a d)e +--R + +--R 5 6 3 6 7 2 10 +--R ((143325A a b - 4410B a )d + (2293200A a b - 70560B a )d )e +--R + +--R 4 2 5 4 +--R (- 350350A a b + 25480B a b)d +--R + +--R 5 2 6 3 +--R (- 5605600A a b + 407680B a b)d +--R * +--R 9 +--R e +--R + +--R 3 3 4 2 5 4 3 5 2 4 8 +--R ((450450A a b - 60060B a b )d + (7207200A a b - 960960B a b )d )e +--R + +--R 2 4 3 3 6 +--R (- 315315A a b + 72072B a b )d +--R + +--R 3 4 4 3 5 +--R (- 5045040A a b + 1153152B a b )d +--R * +--R 7 +--R e +--R + +--R 5 2 4 7 2 5 3 4 6 6 +--R ((105105A a b - 42042B a b )d + (1681680A a b - 672672B a b )d )e +--R * +--R 6 +--R x +--R + +--R 6 3 7 2 10 +--R (- 72765A a d - 1164240A a d )e +--R + +--R 5 6 4 6 7 3 9 +--R ((429975A a b - 13230B a )d + (6879600A a b - 211680B a )d )e +--R + +--R 4 2 5 5 +--R (- 1051050A a b + 76440B a b)d +--R + +--R 5 2 6 4 +--R (- 16816800A a b + 1223040B a b)d +--R * +--R 8 +--R e +--R + +--R 3 3 4 2 6 +--R (1351350A a b - 180180B a b )d +--R + +--R 4 3 5 2 5 +--R (21621600A a b - 2882880B a b )d +--R * +--R 7 +--R e +--R + +--R 2 4 3 3 7 +--R (- 945945A a b + 216216B a b )d +--R + +--R 3 4 4 3 6 +--R (- 15135120A a b + 3459456B a b )d +--R * +--R 6 +--R e +--R + +--R 5 2 4 8 2 5 3 4 7 5 +--R ((315315A a b - 126126B a b )d + (5045040A a b - 2018016B a b )d )e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 9 +--R (- 121275A a d - 1940400A a d )e +--R + +--R 5 6 5 6 7 4 8 +--R ((716625A a b - 22050B a )d + (11466000A a b - 352800B a )d )e +--R + +--R 4 2 5 6 +--R (- 1751750A a b + 127400B a b)d +--R + +--R 5 2 6 5 +--R (- 28028000A a b + 2038400B a b)d +--R * +--R 7 +--R e +--R + +--R 3 3 4 2 7 +--R (2252250A a b - 300300B a b )d +--R + +--R 4 3 5 2 6 +--R (36036000A a b - 4804800B a b )d +--R * +--R 6 +--R e +--R + +--R 2 4 3 3 8 +--R (- 1576575A a b + 360360B a b )d +--R + +--R 3 4 4 3 7 +--R (- 25225200A a b + 5765760B a b )d +--R * +--R 5 +--R e +--R + +--R 5 2 4 9 2 5 3 4 8 4 +--R ((525525A a b - 210210B a b )d + (8408400A a b - 3363360B a b )d )e +--R * +--R 4 +--R x +--R + +--R 6 5 7 4 8 +--R (- 121275A a d - 1940400A a d )e +--R + +--R 5 6 6 6 7 5 7 +--R ((716625A a b - 22050B a )d + (11466000A a b - 352800B a )d )e +--R + +--R 4 2 5 7 +--R (- 1751750A a b + 127400B a b)d +--R + +--R 5 2 6 6 +--R (- 28028000A a b + 2038400B a b)d +--R * +--R 6 +--R e +--R + +--R 3 3 4 2 8 +--R (2252250A a b - 300300B a b )d +--R + +--R 4 3 5 2 7 +--R (36036000A a b - 4804800B a b )d +--R * +--R 5 +--R e +--R + +--R 2 4 3 3 9 +--R (- 1576575A a b + 360360B a b )d +--R + +--R 3 4 4 3 8 +--R (- 25225200A a b + 5765760B a b )d +--R * +--R 4 +--R e +--R + +--R 5 2 4 10 +--R (525525A a b - 210210B a b )d +--R + +--R 2 5 3 4 9 +--R (8408400A a b - 3363360B a b )d +--R * +--R 3 +--R e +--R * +--R 3 +--R x +--R + +--R 6 6 7 5 7 +--R (- 72765A a d - 1164240A a d )e +--R + +--R 5 6 7 6 7 6 6 +--R ((429975A a b - 13230B a )d + (6879600A a b - 211680B a )d )e +--R + +--R 4 2 5 8 +--R (- 1051050A a b + 76440B a b)d +--R + +--R 5 2 6 7 +--R (- 16816800A a b + 1223040B a b)d +--R * +--R 5 +--R e +--R + +--R 3 3 4 2 9 +--R (1351350A a b - 180180B a b )d +--R + +--R 4 3 5 2 8 +--R (21621600A a b - 2882880B a b )d +--R * +--R 4 +--R e +--R + +--R 2 4 3 3 10 +--R (- 945945A a b + 216216B a b )d +--R + +--R 3 4 4 3 9 +--R (- 15135120A a b + 3459456B a b )d +--R * +--R 3 +--R e +--R + +--R 5 2 4 11 +--R (315315A a b - 126126B a b )d +--R + +--R 2 5 3 4 10 +--R (5045040A a b - 2018016B a b )d +--R * +--R 2 +--R e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 6 +--R (- 24255A a d - 388080A a d )e +--R + +--R 5 6 8 6 7 7 5 +--R ((143325A a b - 4410B a )d + (2293200A a b - 70560B a )d )e +--R + +--R 4 2 5 9 +--R (- 350350A a b + 25480B a b)d +--R + +--R 5 2 6 8 +--R (- 5605600A a b + 407680B a b)d +--R * +--R 4 +--R e +--R + +--R 3 3 4 2 10 +--R (450450A a b - 60060B a b )d +--R + +--R 4 3 5 2 9 +--R (7207200A a b - 960960B a b )d +--R * +--R 3 +--R e +--R + +--R 2 4 3 3 11 +--R (- 315315A a b + 72072B a b )d +--R + +--R 3 4 4 3 10 +--R (- 5045040A a b + 1153152B a b )d +--R * +--R 2 +--R e +--R + +--R 5 2 4 12 2 5 3 4 11 +--R ((105105A a b - 42042B a b )d + (1681680A a b - 672672B a b )d )e +--R * +--R x +--R + +--R 6 8 7 7 5 +--R (- 3465A a d - 55440A a d )e +--R + +--R 5 6 9 6 7 8 4 +--R ((20475A a b - 630B a )d + (327600A a b - 10080B a )d )e +--R + +--R 4 2 5 10 5 2 6 9 3 +--R ((- 50050A a b + 3640B a b)d + (- 800800A a b + 58240B a b)d )e +--R + +--R 3 3 4 2 11 4 3 5 2 10 2 +--R ((64350A a b - 8580B a b )d + (1029600A a b - 137280B a b )d )e +--R + +--R 2 4 3 3 12 3 4 4 3 11 +--R ((- 45045A a b + 10296B a b )d + (- 720720A a b + 164736B a b )d )e +--R + +--R 5 2 4 13 2 5 3 4 12 +--R (15015A a b - 6006B a b )d + (240240A a b - 96096B a b )d +--R / +--R 6 7 13 5 8 12 4 2 9 11 +--R 180180a d e - 1081080a b d e + 2702700a b d e +--R + +--R 3 3 10 10 2 4 11 9 5 12 8 +--R - 3603600a b d e + 2702700a b d e - 1081080a b d e +--R + +--R 6 13 7 +--R 180180b d e +--R * +--R 7 +--R x +--R + +--R 6 8 12 5 9 11 4 2 10 10 +--R 1261260a d e - 7567560a b d e + 18918900a b d e +--R + +--R 3 3 11 9 2 4 12 8 5 13 7 +--R - 25225200a b d e + 18918900a b d e - 7567560a b d e +--R + +--R 6 14 6 +--R 1261260b d e +--R * +--R 6 +--R x +--R + +--R 6 9 11 5 10 10 4 2 11 9 +--R 3783780a d e - 22702680a b d e + 56756700a b d e +--R + +--R 3 3 12 8 2 4 13 7 5 14 6 +--R - 75675600a b d e + 56756700a b d e - 22702680a b d e +--R + +--R 6 15 5 +--R 3783780b d e +--R * +--R 5 +--R x +--R + +--R 6 10 10 5 11 9 4 2 12 8 +--R 6306300a d e - 37837800a b d e + 94594500a b d e +--R + +--R 3 3 13 7 2 4 14 6 5 15 5 +--R - 126126000a b d e + 94594500a b d e - 37837800a b d e +--R + +--R 6 16 4 +--R 6306300b d e +--R * +--R 4 +--R x +--R + +--R 6 11 9 5 12 8 4 2 13 7 +--R 6306300a d e - 37837800a b d e + 94594500a b d e +--R + +--R 3 3 14 6 2 4 15 5 5 16 4 +--R - 126126000a b d e + 94594500a b d e - 37837800a b d e +--R + +--R 6 17 3 +--R 6306300b d e +--R * +--R 3 +--R x +--R + +--R 6 12 8 5 13 7 4 2 14 6 +--R 3783780a d e - 22702680a b d e + 56756700a b d e +--R + +--R 3 3 15 5 2 4 16 4 5 17 3 +--R - 75675600a b d e + 56756700a b d e - 22702680a b d e +--R + +--R 6 18 2 +--R 3783780b d e +--R * +--R 2 +--R x +--R + +--R 6 13 7 5 14 6 4 2 15 5 +--R 1261260a d e - 7567560a b d e + 18918900a b d e +--R + +--R 3 3 16 4 2 4 17 3 5 18 2 +--R - 25225200a b d e + 18918900a b d e - 7567560a b d e +--R + +--R 6 19 +--R 1261260b d e +--R * +--R x +--R + +--R 6 14 6 5 15 5 4 2 16 4 3 3 17 3 +--R 180180a d e - 1081080a b d e + 2702700a b d e - 3603600a b d e +--R + +--R 2 4 18 2 5 19 6 20 +--R 2702700a b d e - 1081080a b d e + 180180b d +--R Type: Union(Expression(Integer),...) +--E 976 + +--S 977 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 5 +--R (- 3465A a d - 55440A a )e +--R + +--R 5 6 2 6 7 4 +--R ((20475A a b - 630B a )d + (327600A a b - 10080B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 3 +--R ((- 50050A a b + 3640B a b)d + (- 800800A a b + 58240B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 2 +--R ((64350A a b - 8580B a b )d + (1029600A a b - 137280B a b )d )e +--R + +--R 2 4 3 3 5 3 4 4 3 4 +--R ((- 45045A a b + 10296B a b )d + (- 720720A a b + 164736B a b )d )e +--R + +--R 5 2 4 6 2 5 3 4 5 +--R (15015A a b - 6006B a b )d + (240240A a b - 96096B a b )d +--R / +--R 6 7 6 5 8 5 4 2 9 4 3 3 10 3 +--R 180180a d e - 1081080a b d e + 2702700a b d e - 3603600a b d e +--R + +--R 2 4 11 2 5 12 6 13 +--R 2702700a b d e - 1081080a b d e + 180180b d +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 978 + +)clear all + +--S 979 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1) +--R 2 4 2 3 +--R B b e x + ((A b + B a)e + 2B b d e)x +--R + +--R 2 2 2 2 +--R (A a e + (2A b + 2B a)d e + B b d )x + (2A a d e + (A b + B a)d )x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1293 +r0:=-1/96*(b*d-a*e)*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ + (d+e*x)^(3/2)/(b^3*e)-1/60*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ + (d+e*x)^(5/2)/(b^2*e)+1/6*B*(a+b*x)^(5/2)*(d+e*x)^(7/2)/(b*e)-_ + 1/512*(b*d-a*e)^5*(5*b*B*d-12*A*b*e+7*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(7/2))-_ + 1/768*(b*d-a*e)^3*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ + sqrt(d+e*x)/(b^4*e^2)-1/192*(b*d-a*e)^2*(5*b*B*d-_ + 12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^4*e)+_ + 1/512*(b*d-a*e)^4*(5*b*B*d-12*A*b*e+7*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^4*e^3) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (- 180A a b + 105B a )e + (900A a b - 450B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (- 1800A a b + 675B a b )d e + (1800A a b - 300B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 900A a b - 225B a b )d e + (180A b + 270B a b )d e - 75B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 1280B b e x + ((1536A b + 1664B a b )e + 3200B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (2112A a b + 48B a b )e + (4032A b + 4448B a b )d e +--R + +--R 5 2 3 +--R 2160B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (96A a b - 56B a b )e + (6144A a b + 216B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (2976A b + 3384B a b )d e + 40B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 120A a b + 70B a b)e + (552A a b - 272B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (5592A a b + 348B a b )d e + (120A b + 160B a b )d e +--R + +--R 5 4 +--R - 50B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (180A a b - 105B a )e + (- 840A a b + 415B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (1536A a b - 546B a b )d e + (840A a b + 150B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 180A b - 245B a b )d e + 75B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 3 +-+ +-+ +--R 7680b e \|b \|e +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1293 +--a0:=integrate(t0,x) +--E 981 + +--S 982 of 1293 +--m0:=a0-r0 +--E 982 + +--S 983 of 1293 +--d0:=D(m0,x) +--E 983 + +)clear all + +--S 984 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1) +--R 3 2 +--R (B b e x + ((A b + B a)e + B b d)x + (A a e + (A b + B a)d)x + A a d) +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1293 +r0:=1/8*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/5*B*(a+b*x)^(5/2)*(d+e*x)^(5/2)/(b*e)+3/128*(b*d-a*e)^4*_ + (2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))/(b^(7/2)*e^(7/2))+1/64*(b*d-a*e)^2*(2*A*b*e-_ + B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^2)+1/16*(b*d-a*e)*_ + (2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^3*e)-_ + 3/128*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^3) +--R +--R +--R (2) +--R 4 5 5 3 2 4 4 +--R (30A a b - 15B a )e + (- 120A a b + 45B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (180A a b - 30B a b )d e + (- 120A a b - 30B a b )d e +--R + +--R 5 4 4 5 5 +--R (30A b + 45B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 128B b e x + ((160A b + 176B a b )e + 176B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 2 +--R ((240A a b + 8B a b )e + (240A b + 272B a b )d e + 8B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (20A a b - 10B a b)e + (440A a b + 26B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (20A b + 26B a b )d e - 10B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (- 30A a b + 15B a )e + (110A a b - 40B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (110A a b + 18B a b )d e + (- 30A b - 40B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 3 +-+ +-+ +--R 640b e \|b \|e +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1293 +--a0:=integrate(t0,x) +--E 986 + +--S 987 of 1293 +--m0:=a0-r0 +--E 987 + +--S 988 of 1293 +--d0:=D(m0,x) +--E 988 + +)clear all + +--S 989 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) (B b x + (A b + B a)x + A a)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1293 +r0:=1/4*B*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b*e)-1/64*(b*d-a*e)^3*_ + (5*b*B*d-8*A*b*e+3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(7/2))-1/96*(b*d-a*e)*_ + (5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^2)-_ + 1/24*(5*b*B*d-8*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b^2*e)+_ + 1/64*(b*d-a*e)^2*(5*b*B*d-8*A*b*e+3*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^2*e^3) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 24A a b + 9B a )e + (72A a b - 12B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 72A a b - 18B a b )d e + (24A b + 36B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 72B a b )e + 8B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((112A a b + 6B a b)e + (16A b + 20B a b )d e - 10B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (24A a b - 9B a )e + (64A a b + 9B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 24A b - 31B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 3 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1293 +--a0:=integrate(t0,x) +--E 991 + +--S 992 of 1293 +--m0:=a0-r0 +--E 992 + +--S 993 of 1293 +--d0:=D(m0,x) +--E 993 + +)clear all + +--S 994 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) --------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1293 +r0:=-1/8*(b*d-a*e)^2*(5*b*B*d-6*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(7/2))-1/12*(5*b*B*d-6*A*b*e+a*B*e)*_ + (a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^2)+1/3*B*(a+b*x)^(5/2)*_ + sqrt(d+e*x)/(b*e)+1/8*(b*d-a*e)*(5*b*B*d-6*A*b*e+a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b*e^3) +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (18A a b - 3B a )e + (- 36A a b - 9B a b)d e +--R + +--R 3 2 2 3 3 +--R (18A b + 27B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 2 2 +--R 8B b e x + ((12A b + 14B a b)e - 10B b d e)x + (30A a b + 3B a )e +--R + +--R 2 2 2 +--R (- 18A b - 22B a b)d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 +-+ +-+ +--R 24b e \|b \|e +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1293 +--a0:=integrate(t0,x) +--E 996 + +--S 997 of 1293 +--m0:=a0-r0 +--E 997 + +--S 998 of 1293 +--d0:=D(m0,x) +--E 998 + +)clear all + +--S 999 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) --------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1293 +r0:=3/4*(b*d-a*e)*(5*b*B*d-4*A*b*e-a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(7/2)*sqrt(b))-_ + 2*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*sqrt(d+e*x))+_ + 1/2*(5*b*B*d-4*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))-_ + 3/4*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +-------+ +--R ((12A a b + 3B a )e + (- 12A b - 18B a b)d e + 15B b d )\|e x + d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +--R 2B b e x + ((4A b + 5B a)e - 5B b d e)x - 8A a e +--R + +--R 2 +--R (12A b + 13B a)d e - 15B b d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|b x + a +--R / +--R 3 +-+ +-+ +-------+ +--R 4e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1293 +--a0:=integrate(t0,x) +--E 1001 + +--S 1002 of 1293 +--m0:=a0-r0 +--E 1002 + +--S 1003 of 1293 +--d0:=D(m0,x) +--E 1003 + +)clear all + +--S 1004 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) --------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))-_ + (5*b*B*d-2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(7/2)-2/3*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + (a+b*x)^(3/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+b*(5*b*B*d-2*A*b*e-3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(e^3*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 +-+ +--R (((6A b + 9B a)e - 15B b d e)x + (6A b + 9B a)d e - 15B b d )\|b +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +--R 3B b e x + ((- 8A b - 6B a)e + 20B b d e)x - 2A a e +--R + +--R 2 +--R (- 6A b - 4B a)d e + 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 4 3 +-+ +-------+ +--R (3e x + 3d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1293 +--a0:=integrate(t0,x) +--E 1006 + +--S 1007 of 1293 +--m0:=a0-r0 +--E 1007 + +--S 1008 of 1293 +--d0:=D(m0,x) +--E 1008 + +)clear all + +--S 1009 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ + 2/3*B*(a+b*x)^(3/2)/(e^2*(d+e*x)^(3/2))+2*b^(3/2)*_ + B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(7/2)-_ + 2*b*B*sqrt(a+b*x)/(e^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 2 2 2 2 2 +--R (30B a b e - 30B b d e )x + (60B a b d e - 60B b d e)x +--R + +--R 2 2 3 +--R 30B a b d e - 30B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 2 2 2 +--R ((- 6A b - 40B a b)e + 46B b d e )x +--R + +--R 2 3 2 2 2 2 3 +--R ((- 12A a b - 10B a )e - 48B a b d e + 70B b d e)x - 6A a e +--R + +--R 2 2 2 2 3 +--R - 4B a d e - 20B a b d e + 30B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 6 5 2 5 2 4 2 4 3 3 +--R ((15a e - 15b d e )x + (30a d e - 30b d e )x + 15a d e - 15b d e ) +--R * +--R +-+ +-------+ +--R \|e \|e x + d +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1293 +--a0:=integrate(t0,x) +--E 1011 + +--S 1012 of 1293 +--m0:=a0-r0 +--E 1012 + +--S 1013 of 1293 +--d0:=D(m0,x) +--E 1013 + +)clear all + +--S 1014 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(9/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) -------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 3 2 3 3 +--R ((4A b - 14B a b )e + 10B b d)x +--R + +--R 2 2 3 2 2 +--R ((- 2A a b - 28B a b)e + (14A b + 16B a b )d)x +--R + +--R 2 3 2 2 3 +--R ((- 16A a b - 14B a )e + (28A a b + 2B a b)d)x - 10A a e +--R + +--R 2 3 +--R (14A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 5 4 2 2 3 3 +--R (35a e - 70a b d e + 35b d e )x +--R + +--R 2 4 2 3 2 3 2 2 +--R (105a d e - 210a b d e + 105b d e )x +--R + +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +--R (105a d e - 210a b d e + 105b d e)x + 35a d e - 70a b d e + 35b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 5 3 +--R ((8A b - 28B a b )d e + 20B b d )x +--R + +--R 2 2 4 3 2 5 2 +--R ((- 4A a b - 56B a b)d e + (28A b + 32B a b )d )x +--R + +--R 2 3 4 2 2 5 3 4 +--R ((- 32A a b - 28B a )d e + (56A a b + 4B a b)d )x - 20A a d e +--R + +--R 2 3 5 +--R (28A a b - 8B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 5 2 3 2 3 4 4 4 +--R ((- 5A a d - 20A a )e + ((7A a b - 2B a )d + (28A a b - 8B a )d)e )x +--R + +--R 3 2 4 4 +--R (- 20A a d - 80A a d)e +--R + +--R 2 3 3 3 4 2 3 +--R ((28A a b - 8B a )d + (112A a b - 32B a )d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 3 +--R (- 30A a d - 120A a d )e +--R + +--R 2 3 4 3 4 3 2 +--R ((42A a b - 12B a )d + (168A a b - 48B a )d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 2 +--R (- 20A a d - 80A a d )e +--R + +--R 2 3 5 3 4 4 +--R ((28A a b - 8B a )d + (112A a b - 32B a )d )e +--R * +--R x +--R + +--R 3 5 4 4 2 3 6 3 4 5 +--R (- 5A a d - 20A a d )e + (7A a b - 2B a )d + (28A a b - 8B a )d +--R / +--R 2 4 6 5 5 2 6 4 4 +--R (70a d e - 140a b d e + 70b d e )x +--R + +--R 2 5 5 6 4 2 7 3 3 +--R (280a d e - 560a b d e + 280b d e )x +--R + +--R 2 6 4 7 3 2 8 2 2 +--R (420a d e - 840a b d e + 420b d e )x +--R + +--R 2 7 3 8 2 2 9 2 8 2 9 2 10 +--R (280a d e - 560a b d e + 280b d e)x + 70a d e - 140a b d e + 70b d +--R Type: Union(Expression(Integer),...) +--E 1016 + +--S 1017 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 3 4 2 3 2 3 4 +--R (- 5A a d - 20A a )e + (7A a b - 2B a )d + (28A a b - 8B a )d +--R (4) -------------------------------------------------------------- +--R 2 4 2 5 2 6 +--R 70a d e - 140a b d e + 70b d +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1018 + +)clear all + +--S 1019 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(11/2) +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R (1) -------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1293 +r0:=-2/9*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(7/2))+4/315*b*(5*b*B*d+4*A*b*e-9*a*B*e)*(a+b*x)^(5/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 4 3 2 4 4 +--R ((- 16A b + 36B a b )e - 20B b d e)x +--R + +--R 3 2 2 2 4 3 4 2 3 +--R ((8A a b - 18B a b )e + (- 72A b + 172B a b )d e - 90B b d )x +--R + +--R 2 2 3 2 3 2 2 +--R (- 6A a b - 144B a b)e + (36A a b + 384B a b )d e +--R + +--R 4 3 2 +--R (- 126A b - 144B a b )d +--R * +--R 2 +--R x +--R + +--R 3 4 2 2 2 3 +--R (- 100A a b - 90B a )e + (288A a b + 172B a b)d e +--R + +--R 3 2 2 2 +--R (- 252A a b - 18B a b )d +--R * +--R x +--R + +--R 4 2 3 4 2 2 3 2 +--R - 70A a e + (180A a b - 20B a )d e + (- 126A a b + 36B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 7 2 6 2 2 5 3 3 4 4 +--R (315a e - 945a b d e + 945a b d e - 315b d e )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 +--R (1260a d e - 3780a b d e + 3780a b d e - 1260b d e )x +--R + +--R 3 2 5 2 3 4 2 4 3 3 5 2 2 +--R (1890a d e - 5670a b d e + 5670a b d e - 1890b d e )x +--R + +--R 3 3 4 2 4 3 2 5 2 3 6 3 4 3 +--R (1260a d e - 3780a b d e + 3780a b d e - 1260b d e)x + 315a d e +--R + +--R 2 5 2 2 6 3 7 +--R - 945a b d e + 945a b d e - 315b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 2 4 6 4 +--R ((- 32A b + 72B a b )d e - 40B b d e)x +--R + +--R 3 2 2 5 2 4 3 6 +--R (16A a b - 36B a b )d e + (- 144A b + 344B a b )d e +--R + +--R 4 7 +--R - 180B b d +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 2 3 2 2 6 +--R (- 12A a b - 288B a b)d e + (72A a b + 768B a b )d e +--R + +--R 4 3 7 +--R (- 252A b - 288B a b )d +--R * +--R 2 +--R x +--R + +--R 3 4 5 2 2 2 3 6 +--R (- 200A a b - 180B a )d e + (576A a b + 344B a b)d e +--R + +--R 3 2 2 7 +--R (- 504A a b - 36B a b )d +--R * +--R x +--R + +--R 4 5 2 3 4 6 2 2 3 7 +--R - 140A a d e + (360A a b - 40B a )d e + (- 252A a b + 72B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 7 +--R (- 35A a d - 140A a )e +--R + +--R 3 4 2 4 5 6 +--R ((90A a b - 10B a )d + (360A a b - 40B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 5 +--R ((- 63A a b + 18B a b)d + (- 252A a b + 72B a b)d )e +--R * +--R 5 +--R x +--R + +--R 4 2 5 6 +--R (- 175A a d - 700A a d)e +--R + +--R 3 4 3 4 5 2 5 +--R ((450A a b - 50B a )d + (1800A a b - 200B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 4 +--R ((- 315A a b + 90B a b)d + (- 1260A a b + 360B a b)d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 5 +--R (- 350A a d - 1400A a d )e +--R + +--R 3 4 4 4 5 3 4 +--R ((900A a b - 100B a )d + (3600A a b - 400B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 3 +--R ((- 630A a b + 180B a b)d + (- 2520A a b + 720B a b)d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 4 +--R (- 350A a d - 1400A a d )e +--R + +--R 3 4 5 4 5 4 3 +--R ((900A a b - 100B a )d + (3600A a b - 400B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 2 +--R ((- 630A a b + 180B a b)d + (- 2520A a b + 720B a b)d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 3 +--R (- 175A a d - 700A a d )e +--R + +--R 3 4 6 4 5 5 2 +--R ((450A a b - 50B a )d + (1800A a b - 200B a )d )e +--R + +--R 2 2 3 7 3 2 4 6 +--R ((- 315A a b + 90B a b)d + (- 1260A a b + 360B a b)d )e +--R * +--R x +--R + +--R 4 6 5 5 2 +--R (- 35A a d - 140A a d )e +--R + +--R 3 4 7 4 5 6 +--R ((90A a b - 10B a )d + (360A a b - 40B a )d )e +--R + +--R 2 2 3 8 3 2 4 7 +--R (- 63A a b + 18B a b)d + (- 252A a b + 72B a b)d +--R / +--R 3 5 8 2 6 7 2 7 6 3 8 5 5 +--R (630a d e - 1890a b d e + 1890a b d e - 630b d e )x +--R + +--R 3 6 7 2 7 6 2 8 5 3 9 4 4 +--R (3150a d e - 9450a b d e + 9450a b d e - 3150b d e )x +--R + +--R 3 7 6 2 8 5 2 9 4 3 10 3 3 +--R (6300a d e - 18900a b d e + 18900a b d e - 6300b d e )x +--R + +--R 3 8 5 2 9 4 2 10 3 3 11 2 2 +--R (6300a d e - 18900a b d e + 18900a b d e - 6300b d e )x +--R + +--R 3 9 4 2 10 3 2 11 2 3 12 3 10 3 +--R (3150a d e - 9450a b d e + 9450a b d e - 3150b d e)x + 630a d e +--R + +--R 2 11 2 2 12 3 13 +--R - 1890a b d e + 1890a b d e - 630b d +--R Type: Union(Expression(Integer),...) +--E 1021 + +--S 1022 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 2 3 4 2 4 5 +--R (- 35A a d - 140A a )e + ((90A a b - 10B a )d + (360A a b - 40B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 +--R (- 63A a b + 18B a b)d + (- 252A a b + 72B a b)d +--R / +--R 3 5 3 2 6 2 2 7 3 8 +--R 630a d e - 1890a b d e + 1890a b d e - 630b d +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1293 +r0:=-2/11*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ + 2/99*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(9/2))+8/693*b*(5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(7/2))+16/3465*b^2*_ + (5*b*B*d+6*A*b*e-11*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 5 4 3 5 2 5 +--R ((96A b - 176B a b )e + 80B b d e )x +--R + +--R 4 2 3 3 5 4 2 5 2 4 +--R ((- 48A a b + 88B a b )e + (528A b - 1008B a b )d e + 440B b d e)x +--R + +--R 2 3 3 2 3 4 2 3 2 +--R (36A a b - 66B a b )e + (- 264A a b + 514B a b )d e +--R + +--R 5 4 2 5 3 +--R (1188A b - 2398B a b )d e + 990B b d +--R * +--R 3 +--R x +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 30A a b - 1100B a b)e + (198A a b + 4232B a b )d e +--R + +--R 4 2 3 2 5 4 3 +--R (- 594A a b - 5676B a b )d e + (1386A b + 1584B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 3 2 4 2 +--R (- 840A a b - 770B a )e + (3300A a b + 2490B a b)d e +--R + +--R 2 3 3 2 2 4 2 3 3 +--R (- 4752A a b - 2398B a b )d e + (2772A a b + 198B a b )d +--R * +--R x +--R + +--R 5 3 4 5 2 3 2 4 2 +--R - 630A a e + (2310A a b - 140B a )d e + (- 2970A a b + 440B a b)d e +--R + +--R 2 3 3 2 3 +--R (1386A a b - 396B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 9 3 8 2 2 2 7 3 3 6 +--R 3465a e - 13860a b d e + 20790a b d e - 13860a b d e +--R + +--R 4 4 5 +--R 3465b d e +--R * +--R 5 +--R x +--R + +--R 4 8 3 2 7 2 2 3 6 3 4 5 +--R 17325a d e - 69300a b d e + 103950a b d e - 69300a b d e +--R + +--R 4 5 4 +--R 17325b d e +--R * +--R 4 +--R x +--R + +--R 4 2 7 3 3 6 2 2 4 5 3 5 4 +--R 34650a d e - 138600a b d e + 207900a b d e - 138600a b d e +--R + +--R 4 6 3 +--R 34650b d e +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 5 2 2 5 4 3 6 3 +--R 34650a d e - 138600a b d e + 207900a b d e - 138600a b d e +--R + +--R 4 7 2 +--R 34650b d e +--R * +--R 2 +--R x +--R + +--R 4 4 5 3 5 4 2 2 6 3 3 7 2 +--R 17325a d e - 69300a b d e + 103950a b d e - 69300a b d e +--R + +--R 4 8 +--R 17325b d e +--R * +--R x +--R + +--R 4 5 4 3 6 3 2 2 7 2 3 8 4 9 +--R 3465a d e - 13860a b d e + 20790a b d e - 13860a b d e + 3465b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 6 3 5 7 2 5 +--R ((192A b - 352B a b )d e + 160B b d e )x +--R + +--R 4 2 3 6 3 5 4 7 2 +--R (- 96A a b + 176B a b )d e + (1056A b - 2016B a b )d e +--R + +--R 5 8 +--R 880B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 3 4 2 3 7 2 +--R (72A a b - 132B a b )d e + (- 528A a b + 1028B a b )d e +--R + +--R 5 4 8 5 9 +--R (2376A b - 4796B a b )d e + 1980B b d +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 3 2 3 3 2 7 2 +--R (- 60A a b - 2200B a b)d e + (396A a b + 8464B a b )d e +--R + +--R 4 2 3 8 5 4 9 +--R (- 1188A a b - 11352B a b )d e + (2772A b + 3168B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 6 3 3 2 4 7 2 +--R (- 1680A a b - 1540B a )d e + (6600A a b + 4980B a b)d e +--R + +--R 2 3 3 2 8 4 2 3 9 +--R (- 9504A a b - 4796B a b )d e + (5544A a b + 396B a b )d +--R * +--R x +--R + +--R 5 6 3 4 5 7 2 +--R - 1260A a d e + (4620A a b - 280B a )d e +--R + +--R 3 2 4 8 2 3 3 2 9 +--R (- 5940A a b + 880B a b)d e + (2772A a b - 792B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 6 9 +--R (315A a d + 1260A a )e +--R + +--R 4 5 2 5 6 8 +--R ((- 1155A a b + 70B a )d + (- 4620A a b + 280B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 7 +--R ((1485A a b - 220B a b)d + (5940A a b - 880B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 6 +--R ((- 693A a b + 198B a b )d + (- 2772A a b + 792B a b )d )e +--R * +--R 6 +--R x +--R + +--R 5 2 6 8 +--R (1890A a d + 7560A a d)e +--R + +--R 4 5 3 5 6 2 7 +--R ((- 6930A a b + 420B a )d + (- 27720A a b + 1680B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 6 +--R ((8910A a b - 1320B a b)d + (35640A a b - 5280B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 5 +--R ((- 4158A a b + 1188B a b )d + (- 16632A a b + 4752B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 3 6 2 7 +--R (4725A a d + 18900A a d )e +--R + +--R 4 5 4 5 6 3 6 +--R ((- 17325A a b + 1050B a )d + (- 69300A a b + 4200B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 5 +--R ((22275A a b - 3300B a b)d + (89100A a b - 13200B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 4 +--R ((- 10395A a b + 2970B a b )d + (- 41580A a b + 11880B a b )d )e +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 6 +--R (6300A a d + 25200A a d )e +--R + +--R 4 5 5 5 6 4 5 +--R ((- 23100A a b + 1400B a )d + (- 92400A a b + 5600B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 4 +--R ((29700A a b - 4400B a b)d + (118800A a b - 17600B a b)d )e +--R + +--R 2 3 3 2 7 3 3 4 2 6 3 +--R ((- 13860A a b + 3960B a b )d + (- 55440A a b + 15840B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 5 6 4 5 +--R (4725A a d + 18900A a d )e +--R + +--R 4 5 6 5 6 5 4 +--R ((- 17325A a b + 1050B a )d + (- 69300A a b + 4200B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 3 +--R ((22275A a b - 3300B a b)d + (89100A a b - 13200B a b)d )e +--R + +--R 2 3 3 2 8 3 3 4 2 7 2 +--R ((- 10395A a b + 2970B a b )d + (- 41580A a b + 11880B a b )d )e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 4 +--R (1890A a d + 7560A a d )e +--R + +--R 4 5 7 5 6 6 3 +--R ((- 6930A a b + 420B a )d + (- 27720A a b + 1680B a )d )e +--R + +--R 3 2 4 8 4 2 5 7 2 +--R ((8910A a b - 1320B a b)d + (35640A a b - 5280B a b)d )e +--R + +--R 2 3 3 2 9 3 3 4 2 8 +--R ((- 4158A a b + 1188B a b )d + (- 16632A a b + 4752B a b )d )e +--R * +--R x +--R + +--R 5 7 6 6 3 +--R (315A a d + 1260A a d )e +--R + +--R 4 5 8 5 6 7 2 +--R ((- 1155A a b + 70B a )d + (- 4620A a b + 280B a )d )e +--R + +--R 3 2 4 9 4 2 5 8 +--R ((1485A a b - 220B a b)d + (5940A a b - 880B a b)d )e +--R + +--R 2 3 3 2 10 3 3 4 2 9 +--R (- 693A a b + 198B a b )d + (- 2772A a b + 792B a b )d +--R / +--R 4 6 10 3 7 9 2 2 8 8 3 9 7 +--R 6930a d e - 27720a b d e + 41580a b d e - 27720a b d e +--R + +--R 4 10 6 +--R 6930b d e +--R * +--R 6 +--R x +--R + +--R 4 7 9 3 8 8 2 2 9 7 3 10 6 +--R 41580a d e - 166320a b d e + 249480a b d e - 166320a b d e +--R + +--R 4 11 5 +--R 41580b d e +--R * +--R 5 +--R x +--R + +--R 4 8 8 3 9 7 2 2 10 6 3 11 5 +--R 103950a d e - 415800a b d e + 623700a b d e - 415800a b d e +--R + +--R 4 12 4 +--R 103950b d e +--R * +--R 4 +--R x +--R + +--R 4 9 7 3 10 6 2 2 11 5 3 12 4 +--R 138600a d e - 554400a b d e + 831600a b d e - 554400a b d e +--R + +--R 4 13 3 +--R 138600b d e +--R * +--R 3 +--R x +--R + +--R 4 10 6 3 11 5 2 2 12 4 3 13 3 +--R 103950a d e - 415800a b d e + 623700a b d e - 415800a b d e +--R + +--R 4 14 2 +--R 103950b d e +--R * +--R 2 +--R x +--R + +--R 4 11 5 3 12 4 2 2 13 3 3 14 2 +--R 41580a d e - 166320a b d e + 249480a b d e - 166320a b d e +--R + +--R 4 15 +--R 41580b d e +--R * +--R x +--R + +--R 4 12 4 3 13 3 2 2 14 2 3 15 4 16 +--R 6930a d e - 27720a b d e + 41580a b d e - 27720a b d e + 6930b d +--R Type: Union(Expression(Integer),...) +--E 1026 + +--S 1027 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 3 +--R (315A a d + 1260A a )e +--R + +--R 4 5 2 5 6 2 +--R ((- 1155A a b + 70B a )d + (- 4620A a b + 280B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 +--R ((1485A a b - 220B a b)d + (5940A a b - 880B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 +--R (- 693A a b + 198B a b )d + (- 2772A a b + 792B a b )d +--R / +--R 4 6 4 3 7 3 2 2 8 2 3 9 4 10 +--R 6930a d e - 27720a b d e + 41580a b d e - 27720a b d e + 6930b d +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1028 + +)clear all + +--S 1029 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1293 +r0:=-2/13*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ + 2/143*(5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*_ + (b*d-a*e)^2*(d+e*x)^(11/2))+4/429*b*(5*b*B*d+8*A*b*e-13*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/3003*b^2*_ + (5*b*B*d+8*A*b*e-13*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(7/2))+32/15015*b^3*(5*b*B*d+8*A*b*e-13*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 6 5 4 6 3 6 +--R ((- 256A b + 416B a b )e - 160B b d e )x +--R + +--R 5 2 4 4 6 5 3 +--R (128A a b - 208B a b )e + (- 1664A b + 2784B a b )d e +--R + +--R 6 2 2 +--R - 1040B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 4 5 2 4 3 +--R (- 96A a b + 156B a b )e + (832A a b - 1412B a b )d e +--R + +--R 6 5 2 2 6 3 +--R (- 4576A b + 7956B a b )d e - 2860B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 4 2 4 3 3 3 +--R (80A a b - 130B a b )e + (- 624A a b + 1064B a b )d e +--R + +--R 5 2 4 2 2 6 5 3 +--R (2288A a b - 4108B a b )d e + (- 6864A b + 12584B a b )d e +--R + +--R 6 4 +--R - 4290B b d +--R * +--R 3 +--R x +--R + +--R 4 2 5 4 3 3 4 2 3 +--R (- 70A a b - 3640B a b)e + (520A a b + 17880B a b )d e +--R + +--R 2 4 3 3 2 2 5 2 4 3 +--R (- 1716A a b - 34424B a b )d e + (3432A a b + 30888B a b )d e +--R + +--R 6 5 4 +--R (- 6006A b - 6864B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 4 4 2 5 3 +--R (- 2940A a b - 2730B a )e + (14560A a b + 12040B a b)d e +--R + +--R 3 3 4 2 2 2 2 4 3 3 3 +--R (- 28600A a b - 19500B a b )d e + (27456A a b + 12584B a b )d e +--R + +--R 5 2 4 4 +--R (- 12012A a b - 858B a b )d +--R * +--R x +--R + +--R 6 4 5 6 3 +--R - 2310A a e + (10920A a b - 420B a )d e +--R + +--R 4 2 5 2 2 3 3 4 2 3 +--R (- 20020A a b + 1820B a b)d e + (17160A a b - 2860B a b )d e +--R + +--R 2 4 3 3 4 +--R (- 6006A a b + 1716B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 11 4 10 3 2 2 9 2 3 3 8 +--R 15015a e - 75075a b d e + 150150a b d e - 150150a b d e +--R + +--R 4 4 7 5 5 6 +--R 75075a b d e - 15015b d e +--R * +--R 6 +--R x +--R + +--R 5 10 4 2 9 3 2 3 8 2 3 4 7 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 5 6 5 6 5 +--R 450450a b d e - 90090b d e +--R * +--R 5 +--R x +--R + +--R 5 2 9 4 3 8 3 2 4 7 2 3 5 6 +--R 225225a d e - 1126125a b d e + 2252250a b d e - 2252250a b d e +--R + +--R 4 6 5 5 7 4 +--R 1126125a b d e - 225225b d e +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 2 5 6 2 3 6 5 +--R 300300a d e - 1501500a b d e + 3003000a b d e - 3003000a b d e +--R + +--R 4 7 4 5 8 3 +--R 1501500a b d e - 300300b d e +--R * +--R 3 +--R x +--R + +--R 5 4 7 4 5 6 3 2 6 5 2 3 7 4 +--R 225225a d e - 1126125a b d e + 2252250a b d e - 2252250a b d e +--R + +--R 4 8 3 5 9 2 +--R 1126125a b d e - 225225b d e +--R * +--R 2 +--R x +--R + +--R 5 5 6 4 6 5 3 2 7 4 2 3 8 3 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 9 2 5 10 +--R 450450a b d e - 90090b d e +--R * +--R x +--R + +--R 5 6 5 4 7 4 3 2 8 3 2 3 9 2 +--R 15015a d e - 75075a b d e + 150150a b d e - 150150a b d e +--R + +--R 4 10 5 11 +--R 75075a b d e - 15015b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 7 4 6 8 3 6 +--R ((- 1024A b + 1664B a b )d e - 640B b d e )x +--R + +--R 5 2 4 7 4 6 5 8 3 +--R (512A a b - 832B a b )d e + (- 6656A b + 11136B a b )d e +--R + +--R 6 9 2 +--R - 4160B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 4 5 2 4 8 3 +--R (- 384A a b + 624B a b )d e + (3328A a b - 5648B a b )d e +--R + +--R 6 5 9 2 6 10 +--R (- 18304A b + 31824B a b )d e - 11440B b d e +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 4 2 4 3 3 8 3 +--R (320A a b - 520B a b )d e + (- 2496A a b + 4256B a b )d e +--R + +--R 5 2 4 9 2 6 5 10 +--R (9152A a b - 16432B a b )d e + (- 27456A b + 50336B a b )d e +--R + +--R 6 11 +--R - 17160B b d +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 4 3 3 4 2 8 3 +--R (- 280A a b - 14560B a b)d e + (2080A a b + 71520B a b )d e +--R + +--R 2 4 3 3 9 2 +--R (- 6864A a b - 137696B a b )d e +--R + +--R 5 2 4 10 6 5 11 +--R (13728A a b + 123552B a b )d e + (- 24024A b - 27456B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 7 4 4 2 5 8 3 +--R (- 11760A a b - 10920B a )d e + (58240A a b + 48160B a b)d e +--R + +--R 3 3 4 2 9 2 +--R (- 114400A a b - 78000B a b )d e +--R + +--R 2 4 3 3 10 5 2 4 11 +--R (109824A a b + 50336B a b )d e + (- 48048A a b - 3432B a b )d +--R * +--R x +--R + +--R 6 7 4 5 6 8 3 +--R - 9240A a d e + (43680A a b - 1680B a )d e +--R + +--R 4 2 5 9 2 3 3 4 2 10 +--R (- 80080A a b + 7280B a b)d e + (68640A a b - 11440B a b )d e +--R + +--R 2 4 3 3 11 +--R (- 24024A a b + 6864B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 6 7 11 +--R (1155A a d + 18480A a )e +--R + +--R 5 6 2 6 7 10 +--R ((- 5460A a b + 210B a )d + (- 87360A a b + 3360B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 9 +--R ((10010A a b - 910B a b)d + (160160A a b - 14560B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 8 +--R ((- 8580A a b + 1430B a b )d + (- 137280A a b + 22880B a b )d )e +--R + +--R 2 4 3 3 5 3 4 4 3 4 7 +--R ((3003A a b - 858B a b )d + (48048A a b - 13728B a b )d )e +--R * +--R 7 +--R x +--R + +--R 6 2 7 10 +--R (8085A a d + 129360A a d)e +--R + +--R 5 6 3 6 7 2 9 +--R ((- 38220A a b + 1470B a )d + (- 611520A a b + 23520B a )d )e +--R + +--R 4 2 5 4 5 2 6 3 8 +--R ((70070A a b - 6370B a b)d + (1121120A a b - 101920B a b)d )e +--R + +--R 3 3 4 2 5 +--R (- 60060A a b + 10010B a b )d +--R + +--R 4 3 5 2 4 +--R (- 960960A a b + 160160B a b )d +--R * +--R 7 +--R e +--R + +--R 2 4 3 3 6 3 4 4 3 5 6 +--R ((21021A a b - 6006B a b )d + (336336A a b - 96096B a b )d )e +--R * +--R 6 +--R x +--R + +--R 6 3 7 2 9 +--R (24255A a d + 388080A a d )e +--R + +--R 5 6 4 6 7 3 8 +--R ((- 114660A a b + 4410B a )d + (- 1834560A a b + 70560B a )d )e +--R + +--R 4 2 5 5 5 2 6 4 7 +--R ((210210A a b - 19110B a b)d + (3363360A a b - 305760B a b)d )e +--R + +--R 3 3 4 2 6 +--R (- 180180A a b + 30030B a b )d +--R + +--R 4 3 5 2 5 +--R (- 2882880A a b + 480480B a b )d +--R * +--R 6 +--R e +--R + +--R 2 4 3 3 7 3 4 4 3 6 5 +--R ((63063A a b - 18018B a b )d + (1009008A a b - 288288B a b )d )e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 8 +--R (40425A a d + 646800A a d )e +--R + +--R 5 6 5 6 7 4 7 +--R ((- 191100A a b + 7350B a )d + (- 3057600A a b + 117600B a )d )e +--R + +--R 4 2 5 6 5 2 6 5 6 +--R ((350350A a b - 31850B a b)d + (5605600A a b - 509600B a b)d )e +--R + +--R 3 3 4 2 7 +--R (- 300300A a b + 50050B a b )d +--R + +--R 4 3 5 2 6 +--R (- 4804800A a b + 800800B a b )d +--R * +--R 5 +--R e +--R + +--R 2 4 3 3 8 3 4 4 3 7 4 +--R ((105105A a b - 30030B a b )d + (1681680A a b - 480480B a b )d )e +--R * +--R 4 +--R x +--R + +--R 6 5 7 4 7 +--R (40425A a d + 646800A a d )e +--R + +--R 5 6 6 6 7 5 6 +--R ((- 191100A a b + 7350B a )d + (- 3057600A a b + 117600B a )d )e +--R + +--R 4 2 5 7 5 2 6 6 5 +--R ((350350A a b - 31850B a b)d + (5605600A a b - 509600B a b)d )e +--R + +--R 3 3 4 2 8 +--R (- 300300A a b + 50050B a b )d +--R + +--R 4 3 5 2 7 +--R (- 4804800A a b + 800800B a b )d +--R * +--R 4 +--R e +--R + +--R 2 4 3 3 9 3 4 4 3 8 3 +--R ((105105A a b - 30030B a b )d + (1681680A a b - 480480B a b )d )e +--R * +--R 3 +--R x +--R + +--R 6 6 7 5 6 +--R (24255A a d + 388080A a d )e +--R + +--R 5 6 7 6 7 6 5 +--R ((- 114660A a b + 4410B a )d + (- 1834560A a b + 70560B a )d )e +--R + +--R 4 2 5 8 5 2 6 7 4 +--R ((210210A a b - 19110B a b)d + (3363360A a b - 305760B a b)d )e +--R + +--R 3 3 4 2 9 +--R (- 180180A a b + 30030B a b )d +--R + +--R 4 3 5 2 8 +--R (- 2882880A a b + 480480B a b )d +--R * +--R 3 +--R e +--R + +--R 2 4 3 3 10 3 4 4 3 9 2 +--R ((63063A a b - 18018B a b )d + (1009008A a b - 288288B a b )d )e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 5 +--R (8085A a d + 129360A a d )e +--R + +--R 5 6 8 6 7 7 4 +--R ((- 38220A a b + 1470B a )d + (- 611520A a b + 23520B a )d )e +--R + +--R 4 2 5 9 5 2 6 8 3 +--R ((70070A a b - 6370B a b)d + (1121120A a b - 101920B a b)d )e +--R + +--R 3 3 4 2 10 +--R (- 60060A a b + 10010B a b )d +--R + +--R 4 3 5 2 9 +--R (- 960960A a b + 160160B a b )d +--R * +--R 2 +--R e +--R + +--R 2 4 3 3 11 3 4 4 3 10 +--R ((21021A a b - 6006B a b )d + (336336A a b - 96096B a b )d )e +--R * +--R x +--R + +--R 6 8 7 7 4 +--R (1155A a d + 18480A a d )e +--R + +--R 5 6 9 6 7 8 3 +--R ((- 5460A a b + 210B a )d + (- 87360A a b + 3360B a )d )e +--R + +--R 4 2 5 10 5 2 6 9 2 +--R ((10010A a b - 910B a b)d + (160160A a b - 14560B a b)d )e +--R + +--R 3 3 4 2 11 4 3 5 2 10 +--R ((- 8580A a b + 1430B a b )d + (- 137280A a b + 22880B a b )d )e +--R + +--R 2 4 3 3 12 3 4 4 3 11 +--R (3003A a b - 858B a b )d + (48048A a b - 13728B a b )d +--R / +--R 5 7 12 4 8 11 3 2 9 10 2 3 10 9 +--R 60060a d e - 300300a b d e + 600600a b d e - 600600a b d e +--R + +--R 4 11 8 5 12 7 +--R 300300a b d e - 60060b d e +--R * +--R 7 +--R x +--R + +--R 5 8 11 4 9 10 3 2 10 9 +--R 420420a d e - 2102100a b d e + 4204200a b d e +--R + +--R 2 3 11 8 4 12 7 5 13 6 +--R - 4204200a b d e + 2102100a b d e - 420420b d e +--R * +--R 6 +--R x +--R + +--R 5 9 10 4 10 9 3 2 11 8 +--R 1261260a d e - 6306300a b d e + 12612600a b d e +--R + +--R 2 3 12 7 4 13 6 5 14 5 +--R - 12612600a b d e + 6306300a b d e - 1261260b d e +--R * +--R 5 +--R x +--R + +--R 5 10 9 4 11 8 3 2 12 7 +--R 2102100a d e - 10510500a b d e + 21021000a b d e +--R + +--R 2 3 13 6 4 14 5 5 15 4 +--R - 21021000a b d e + 10510500a b d e - 2102100b d e +--R * +--R 4 +--R x +--R + +--R 5 11 8 4 12 7 3 2 13 6 +--R 2102100a d e - 10510500a b d e + 21021000a b d e +--R + +--R 2 3 14 5 4 15 4 5 16 3 +--R - 21021000a b d e + 10510500a b d e - 2102100b d e +--R * +--R 3 +--R x +--R + +--R 5 12 7 4 13 6 3 2 14 5 +--R 1261260a d e - 6306300a b d e + 12612600a b d e +--R + +--R 2 3 15 4 4 16 3 5 17 2 +--R - 12612600a b d e + 6306300a b d e - 1261260b d e +--R * +--R 2 +--R x +--R + +--R 5 13 6 4 14 5 3 2 15 4 +--R 420420a d e - 2102100a b d e + 4204200a b d e +--R + +--R 2 3 16 3 4 17 2 5 18 +--R - 4204200a b d e + 2102100a b d e - 420420b d e +--R * +--R x +--R + +--R 5 14 5 4 15 4 3 2 16 3 2 3 17 2 +--R 60060a d e - 300300a b d e + 600600a b d e - 600600a b d e +--R + +--R 4 18 5 19 +--R 300300a b d e - 60060b d +--R Type: Union(Expression(Integer),...) +--E 1031 + +--S 1032 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 4 +--R (1155A a d + 18480A a )e +--R + +--R 5 6 2 6 7 3 +--R ((- 5460A a b + 210B a )d + (- 87360A a b + 3360B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 2 +--R ((10010A a b - 910B a b)d + (160160A a b - 14560B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 +--R ((- 8580A a b + 1430B a b )d + (- 137280A a b + 22880B a b )d )e +--R + +--R 2 4 3 3 5 3 4 4 3 4 +--R (3003A a b - 858B a b )d + (48048A a b - 13728B a b )d +--R / +--R 5 7 5 4 8 4 3 2 9 3 2 3 10 2 +--R 60060a d e - 300300a b d e + 600600a b d e - 600600a b d e +--R + +--R 4 11 5 12 +--R 300300a b d e - 60060b d +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1033 + +)clear all + +--S 1034 of 1293 +t0:=(a+b*x)^(3/2)*(A+B*x)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|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 e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1293 +r0:=-2/15*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ + 2/39*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(13/2))+16/429*b*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(11/2))+32/1287*b^2*(b*B*d+2*A*b*e-3*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^4*(d+e*x)^(9/2))+_ + 128/9009*b^3*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)^5*_ + (d+e*x)^(7/2))+256/45045*b^4*(b*B*d+2*A*b*e-3*a*B*e)*_ + (a+b*x)^(5/2)/(e*(b*d-a*e)^6*(d+e*x)^(5/2)) +--R +--R +--R (2) +--R 7 6 5 7 4 7 +--R ((512A b - 768B a b )e + 256B b d e )x +--R + +--R 6 2 5 5 7 6 4 +--R (- 256A a b + 384B a b )e + (3840A b - 5888B a b )d e +--R + +--R 7 2 3 +--R 1920B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 5 6 2 5 4 +--R (192A a b - 288B a b )e + (- 1920A a b + 2976B a b )d e +--R + +--R 7 6 2 3 7 3 2 +--R (12480A b - 19680B a b )d e + 6240B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 5 2 5 3 4 4 +--R (- 160A a b + 240B a b )e + (1440A a b - 2240B a b )d e +--R + +--R 6 2 5 2 3 7 6 3 2 +--R (- 6240A a b + 10080B a b )d e + (22880A b - 37440B a b )d e +--R + +--R 7 4 +--R 11440B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 5 3 4 4 3 4 +--R (140A a b - 210B a b )e + (- 1200A a b + 1870B a b )d e +--R + +--R 2 5 3 4 2 3 6 2 5 3 2 +--R (4680A a b - 7620B a b )d e + (- 11440A a b + 19500B a b )d e +--R + +--R 7 6 4 7 5 +--R (25740A b - 44330B a b )d e + 12870B b d +--R * +--R 3 +--R x +--R + +--R 5 2 6 5 4 3 5 2 4 +--R (- 126A a b - 8820B a b)e + (1050A a b + 52416B a b )d e +--R + +--R 3 4 4 3 2 3 2 5 3 4 3 2 +--R (- 3900A a b - 128760B a b )d e + (8580A a b + 165360B a b )d e +--R + +--R 6 2 5 4 7 6 5 +--R (- 12870A a b - 111540B a b )d e + (18018A b + 20592B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 5 5 2 6 4 +--R (- 7392A a b - 6930B a )e + (44100A a b + 38262B a b)d e +--R + +--R 4 3 5 2 2 3 +--R (- 109200A a b - 84420B a b )d e +--R + +--R 3 4 4 3 3 2 +--R (143000A a b + 91260B a b )d e +--R + +--R 2 5 3 4 4 6 2 5 5 +--R (- 102960A a b - 44330B a b )d e + (36036A a b + 2574B a b )d +--R * +--R x +--R + +--R 7 5 6 7 4 +--R - 6006A a e + (34650A a b - 924B a )d e +--R + +--R 5 2 6 2 3 4 3 5 2 3 2 +--R (- 81900A a b + 5040B a b)d e + (100100A a b - 10920B a b )d e +--R + +--R 3 4 4 3 4 2 5 3 4 5 +--R (- 64350A a b + 11440B a b )d e + (18018A a b - 5148B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 13 5 12 4 2 2 11 3 3 3 10 +--R 45045a e - 270270a b d e + 675675a b d e - 900900a b d e +--R + +--R 2 4 4 9 5 5 8 6 6 7 +--R 675675a b d e - 270270a b d e + 45045b d e +--R * +--R 7 +--R x +--R + +--R 6 12 5 2 11 4 2 3 10 +--R 315315a d e - 1891890a b d e + 4729725a b d e +--R + +--R 3 3 4 9 2 4 5 8 5 6 7 6 7 6 +--R - 6306300a b d e + 4729725a b d e - 1891890a b d e + 315315b d e +--R * +--R 6 +--R x +--R + +--R 6 2 11 5 3 10 4 2 4 9 +--R 945945a d e - 5675670a b d e + 14189175a b d e +--R + +--R 3 3 5 8 2 4 6 7 5 7 6 +--R - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R + +--R 6 8 5 +--R 945945b d e +--R * +--R 5 +--R x +--R + +--R 6 3 10 5 4 9 4 2 5 8 +--R 1576575a d e - 9459450a b d e + 23648625a b d e +--R + +--R 3 3 6 7 2 4 7 6 5 8 5 +--R - 31531500a b d e + 23648625a b d e - 9459450a b d e +--R + +--R 6 9 4 +--R 1576575b d e +--R * +--R 4 +--R x +--R + +--R 6 4 9 5 5 8 4 2 6 7 +--R 1576575a d e - 9459450a b d e + 23648625a b d e +--R + +--R 3 3 7 6 2 4 8 5 5 9 4 +--R - 31531500a b d e + 23648625a b d e - 9459450a b d e +--R + +--R 6 10 3 +--R 1576575b d e +--R * +--R 3 +--R x +--R + +--R 6 5 8 5 6 7 4 2 7 6 +--R 945945a d e - 5675670a b d e + 14189175a b d e +--R + +--R 3 3 8 5 2 4 9 4 5 10 3 +--R - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R + +--R 6 11 2 +--R 945945b d e +--R * +--R 2 +--R x +--R + +--R 6 6 7 5 7 6 4 2 8 5 3 3 9 4 +--R 315315a d e - 1891890a b d e + 4729725a b d e - 6306300a b d e +--R + +--R 2 4 10 3 5 11 2 6 12 +--R 4729725a b d e - 1891890a b d e + 315315b d e +--R * +--R x +--R + +--R 6 7 6 5 8 5 4 2 9 4 3 3 10 3 +--R 45045a d e - 270270a b d e + 675675a b d e - 900900a b d e +--R + +--R 2 4 11 2 5 12 6 13 +--R 675675a b d e - 270270a b d e + 45045b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 8 5 7 9 4 7 +--R ((2048A b - 3072B a b )d e + 1024B b d e )x +--R + +--R 6 2 5 8 5 7 6 9 4 +--R (- 1024A a b + 1536B a b )d e + (15360A b - 23552B a b )d e +--R + +--R 7 10 3 +--R 7680B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 8 5 6 2 5 9 4 +--R (768A a b - 1152B a b )d e + (- 7680A a b + 11904B a b )d e +--R + +--R 7 6 10 3 7 11 2 +--R (49920A b - 78720B a b )d e + 24960B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 8 5 2 5 3 4 9 4 +--R (- 640A a b + 960B a b )d e + (5760A a b - 8960B a b )d e +--R + +--R 6 2 5 10 3 +--R (- 24960A a b + 40320B a b )d e +--R + +--R 7 6 11 2 7 12 +--R (91520A b - 149760B a b )d e + 45760B b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 5 3 4 4 3 9 4 +--R (560A a b - 840B a b )d e + (- 4800A a b + 7480B a b )d e +--R + +--R 2 5 3 4 10 3 +--R (18720A a b - 30480B a b )d e +--R + +--R 6 2 5 11 2 +--R (- 45760A a b + 78000B a b )d e +--R + +--R 7 6 12 7 13 +--R (102960A b - 177320B a b )d e + 51480B b d +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 5 4 3 5 2 9 4 +--R (- 504A a b - 35280B a b)d e + (4200A a b + 209664B a b )d e +--R + +--R 3 4 4 3 10 3 +--R (- 15600A a b - 515040B a b )d e +--R + +--R 2 5 3 4 11 2 +--R (34320A a b + 661440B a b )d e +--R + +--R 6 2 5 12 7 6 13 +--R (- 51480A a b - 446160B a b )d e + (72072A b + 82368B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 8 5 5 2 6 9 4 +--R (- 29568A a b - 27720B a )d e + (176400A a b + 153048B a b)d e +--R + +--R 4 3 5 2 10 3 +--R (- 436800A a b - 337680B a b )d e +--R + +--R 3 4 4 3 11 2 +--R (572000A a b + 365040B a b )d e +--R + +--R 2 5 3 4 12 +--R (- 411840A a b - 177320B a b )d e +--R + +--R 6 2 5 13 +--R (144144A a b + 10296B a b )d +--R * +--R x +--R + +--R 7 8 5 6 7 9 4 +--R - 24024A a d e + (138600A a b - 3696B a )d e +--R + +--R 5 2 6 10 3 +--R (- 327600A a b + 20160B a b)d e +--R + +--R 4 3 5 2 11 2 +--R (400400A a b - 43680B a b )d e +--R + +--R 3 4 4 3 12 2 5 3 4 13 +--R (- 257400A a b + 45760B a b )d e + (72072A a b - 20592B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 7 8 13 +--R (3003A a d + 48048A a )e +--R + +--R 6 7 2 7 8 12 +--R ((- 17325A a b + 462B a )d + (- 277200A a b + 7392B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 11 +--R ((40950A a b - 2520B a b)d + (655200A a b - 40320B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 +--R ((- 50050A a b + 5460B a b )d + (- 800800A a b + 87360B a b )d ) +--R * +--R 10 +--R e +--R + +--R 3 4 4 3 5 4 4 5 3 4 9 +--R ((32175A a b - 5720B a b )d + (514800A a b - 91520B a b )d )e +--R + +--R 2 5 3 4 6 3 5 4 4 5 8 +--R ((- 9009A a b + 2574B a b )d + (- 144144A a b + 41184B a b )d )e +--R * +--R 8 +--R x +--R + +--R 7 2 8 12 +--R (24024A a d + 384384A a d)e +--R + +--R 6 7 3 7 8 2 11 +--R ((- 138600A a b + 3696B a )d + (- 2217600A a b + 59136B a )d )e +--R + +--R 5 2 6 4 6 2 7 3 10 +--R ((327600A a b - 20160B a b)d + (5241600A a b - 322560B a b)d )e +--R + +--R 4 3 5 2 5 +--R (- 400400A a b + 43680B a b )d +--R + +--R 5 3 6 2 4 +--R (- 6406400A a b + 698880B a b )d +--R * +--R 9 +--R e +--R + +--R 3 4 4 3 6 4 4 5 3 5 8 +--R ((257400A a b - 45760B a b )d + (4118400A a b - 732160B a b )d )e +--R + +--R 2 5 3 4 7 +--R (- 72072A a b + 20592B a b )d +--R + +--R 3 5 4 4 6 +--R (- 1153152A a b + 329472B a b )d +--R * +--R 7 +--R e +--R * +--R 7 +--R x +--R + +--R 7 3 8 2 11 +--R (84084A a d + 1345344A a d )e +--R + +--R 6 7 4 7 8 3 10 +--R ((- 485100A a b + 12936B a )d + (- 7761600A a b + 206976B a )d )e +--R + +--R 5 2 6 5 +--R (1146600A a b - 70560B a b)d +--R + +--R 6 2 7 4 +--R (18345600A a b - 1128960B a b)d +--R * +--R 9 +--R e +--R + +--R 4 3 5 2 6 +--R (- 1401400A a b + 152880B a b )d +--R + +--R 5 3 6 2 5 +--R (- 22422400A a b + 2446080B a b )d +--R * +--R 8 +--R e +--R + +--R 3 4 4 3 7 +--R (900900A a b - 160160B a b )d +--R + +--R 4 4 5 3 6 +--R 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(- 2802800A a b + 305760B a b )d +--R + +--R 5 3 6 2 8 +--R (- 44844800A a b + 4892160B a b )d +--R * +--R 5 +--R e +--R + +--R 3 4 4 3 10 +--R (1801800A a b - 320320B a b )d +--R + +--R 4 4 5 3 9 +--R (28828800A a b - 5125120B a b )d +--R * +--R 4 +--R e +--R + +--R 2 5 3 4 11 +--R (- 504504A a b + 144144B a b )d +--R + +--R 3 5 4 4 10 +--R (- 8072064A a b + 2306304B a b )d +--R * +--R 3 +--R e +--R * +--R 3 +--R x +--R + +--R 7 7 8 6 7 +--R (84084A a d + 1345344A a d )e +--R + +--R 6 7 8 7 8 7 6 +--R ((- 485100A a b + 12936B a )d + (- 7761600A a b + 206976B a )d )e +--R + +--R 5 2 6 9 +--R (1146600A a b - 70560B a b)d +--R + +--R 6 2 7 8 +--R (18345600A a b - 1128960B a b)d +--R * +--R 5 +--R e +--R + +--R 4 3 5 2 10 +--R (- 1401400A a b + 152880B a b )d +--R + +--R 5 3 6 2 9 +--R (- 22422400A a b + 2446080B a b )d +--R * +--R 4 +--R e +--R + +--R 3 4 4 3 11 +--R (900900A a b - 160160B a b )d +--R + +--R 4 4 5 3 10 +--R (14414400A a b - 2562560B a b )d +--R * +--R 3 +--R e +--R + +--R 2 5 3 4 12 +--R (- 252252A a b + 72072B a b )d +--R + +--R 3 5 4 4 11 +--R (- 4036032A a b + 1153152B a b )d +--R * +--R 2 +--R e +--R * +--R 2 +--R x +--R + +--R 7 8 8 7 6 +--R (24024A a d + 384384A a d )e +--R + +--R 6 7 9 7 8 8 5 +--R ((- 138600A a b + 3696B a )d + (- 2217600A a b + 59136B a )d )e +--R + +--R 5 2 6 10 6 2 7 9 4 +--R ((327600A a b - 20160B a b)d + (5241600A a b - 322560B a b)d )e +--R + +--R 4 3 5 2 11 +--R (- 400400A a b + 43680B a b )d +--R + +--R 5 3 6 2 10 +--R (- 6406400A a b + 698880B a b )d +--R * +--R 3 +--R e +--R + +--R 3 4 4 3 12 +--R (257400A a b - 45760B a b )d +--R + +--R 4 4 5 3 11 +--R (4118400A a b - 732160B a b )d +--R * +--R 2 +--R e +--R + +--R 2 5 3 4 13 +--R (- 72072A a b + 20592B a b )d +--R + +--R 3 5 4 4 12 +--R (- 1153152A a b + 329472B a b )d +--R * +--R e +--R * +--R x +--R + +--R 7 9 8 8 5 +--R (3003A a d + 48048A a d )e +--R + +--R 6 7 10 7 8 9 4 +--R ((- 17325A a b + 462B a )d + (- 277200A a b + 7392B a )d )e +--R + +--R 5 2 6 11 6 2 7 10 3 +--R ((40950A a b - 2520B a b)d + (655200A a b - 40320B a b)d )e +--R + +--R 4 3 5 2 12 5 3 6 2 11 2 +--R ((- 50050A a b + 5460B a b )d + (- 800800A a b + 87360B a b )d )e +--R + +--R 3 4 4 3 13 4 4 5 3 12 +--R ((32175A a b - 5720B a b )d + (514800A a b - 91520B a b )d )e +--R + +--R 2 5 3 4 14 3 5 4 4 13 +--R (- 9009A a b + 2574B a b )d + (- 144144A a b + 41184B a b )d +--R / +--R 6 8 14 5 9 13 4 2 10 12 +--R 180180a d e - 1081080a b d e + 2702700a b d e +--R + +--R 3 3 11 11 2 4 12 10 5 13 9 +--R - 3603600a b d e + 2702700a b d e - 1081080a b d e +--R + +--R 6 14 8 +--R 180180b d e +--R * +--R 8 +--R x +--R + +--R 6 9 13 5 10 12 4 2 11 11 +--R 1441440a d e - 8648640a b d e + 21621600a b d e +--R + +--R 3 3 12 10 2 4 13 9 5 14 8 +--R - 28828800a b d e + 21621600a b d e - 8648640a b d e +--R + +--R 6 15 7 +--R 1441440b d e +--R * +--R 7 +--R x +--R + +--R 6 10 12 5 11 11 4 2 12 10 +--R 5045040a d e - 30270240a b d e + 75675600a b d e +--R + +--R 3 3 13 9 2 4 14 8 5 15 7 +--R - 100900800a b d e + 75675600a b d e - 30270240a b d e +--R + +--R 6 16 6 +--R 5045040b d e +--R * +--R 6 +--R x +--R + +--R 6 11 11 5 12 10 4 2 13 9 +--R 10090080a d e - 60540480a b d e + 151351200a b d e +--R + +--R 3 3 14 8 2 4 15 7 5 16 6 +--R - 201801600a b d e + 151351200a b d e - 60540480a b d e +--R + +--R 6 17 5 +--R 10090080b d e +--R * +--R 5 +--R x +--R + +--R 6 12 10 5 13 9 4 2 14 8 +--R 12612600a d e - 75675600a b d e + 189189000a b d e +--R + +--R 3 3 15 7 2 4 16 6 5 17 5 +--R - 252252000a b d e + 189189000a b d e - 75675600a b d e +--R + +--R 6 18 4 +--R 12612600b d e +--R * +--R 4 +--R x +--R + +--R 6 13 9 5 14 8 4 2 15 7 +--R 10090080a d e - 60540480a b d e + 151351200a b d e +--R + +--R 3 3 16 6 2 4 17 5 5 18 4 +--R - 201801600a b d e + 151351200a b d e - 60540480a b d e +--R + +--R 6 19 3 +--R 10090080b d e +--R * +--R 3 +--R x +--R + +--R 6 14 8 5 15 7 4 2 16 6 +--R 5045040a d e - 30270240a b d e + 75675600a b d e +--R + +--R 3 3 17 5 2 4 18 4 5 19 3 +--R - 100900800a b d e + 75675600a b d e - 30270240a b d e +--R + +--R 6 20 2 +--R 5045040b d e +--R * +--R 2 +--R x +--R + +--R 6 15 7 5 16 6 4 2 17 5 +--R 1441440a d e - 8648640a b d e + 21621600a b d e +--R + +--R 3 3 18 4 2 4 19 3 5 20 2 +--R - 28828800a b d e + 21621600a b d e - 8648640a b d e +--R + +--R 6 21 +--R 1441440b d e +--R * +--R x +--R + +--R 6 16 6 5 17 5 4 2 18 4 3 3 19 3 +--R 180180a d e - 1081080a b d e + 2702700a b d e - 3603600a b d e +--R + +--R 2 4 20 2 5 21 6 22 +--R 2702700a b d e - 1081080a b d e + 180180b d +--R Type: Union(Expression(Integer),...) +--E 1036 + +--S 1037 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 5 +--R (3003A a d + 48048A a )e +--R + +--R 6 7 2 7 8 4 +--R ((- 17325A a b + 462B a )d + (- 277200A a b + 7392B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 3 +--R ((40950A a b - 2520B a b)d + (655200A a b - 40320B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 2 +--R ((- 50050A a b + 5460B a b )d + (- 800800A a b + 87360B a b )d )e +--R + +--R 3 4 4 3 5 4 4 5 3 4 +--R ((32175A a b - 5720B a b )d + (514800A a b - 91520B a b )d )e +--R + +--R 2 5 3 4 6 3 5 4 4 5 +--R (- 9009A a b + 2574B a b )d + (- 144144A a b + 41184B a b )d +--R / +--R 6 8 6 5 9 5 4 2 10 4 3 3 11 3 +--R 180180a d e - 1081080a b d e + 2702700a b d e - 3603600a b d e +--R + +--R 2 4 12 2 5 13 6 14 +--R 2702700a b d e - 1081080a b d e + 180180b d +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1038 + +)clear all + +--S 1039 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(5/2) +--R +--R +--R (1) +--R 2 2 5 2 2 2 4 +--R B b e x + ((A b + 2B a b)e + 2B b d e)x +--R + +--R 2 2 2 2 2 3 +--R ((2A a b + B a )e + (2A b + 4B a b)d e + B b d )x +--R + +--R 2 2 2 2 2 2 +--R (A a e + (4A a b + 2B a )d e + (A b + 2B a b)d )x +--R + +--R 2 2 2 2 2 +--R (2A a d e + (2A a b + B a )d )x + A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1293 +r0:=1/24*(b*d-a*e)*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(3/2)/_ + (b^3*e)+1/12*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*(d+e*x)^(5/2)/_ + (b^2*e)+1/7*B*(a+b*x)^(7/2)*(d+e*x)^(7/2)/(b*e)-5/1024*(b*d-a*e)^6*_ + (2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(9/2))-5/1536*(b*d-a*e)^4*_ + (2*A*b*e-B*(b*d+a*e))*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^4*e^3)+_ + 1/384*(b*d-a*e)^3*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(5/2)*sqrt(d+e*x)/_ + (b^4*e^2)+1/64*(b*d-a*e)^2*(2*A*b*e-B*(b*d+a*e))*(a+b*x)^(7/2)*_ + sqrt(d+e*x)/(b^4*e)+5/1024*(b*d-a*e)^5*(2*A*b*e-B*(b*d+a*e))*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^4) +--R +--R +--R (2) +--R 6 7 7 5 2 6 6 +--R (- 210A a b + 105B a )e + (1260A a b - 525B a b)d e +--R + +--R 4 3 5 2 2 5 3 4 4 3 3 4 +--R (- 3150A a b + 945B a b )d e + (4200A a b - 525B a b )d e +--R + +--R 2 5 3 4 4 3 6 2 5 5 2 +--R (- 3150A a b - 525B a b )d e + (1260A a b + 945B a b )d e +--R + +--R 7 6 6 7 7 +--R (- 210A b - 525B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 6 6 6 6 5 6 6 5 5 +--R 3072B b e x + ((3584A b + 7424B a b )e + 7424B b d e )x +--R + +--R 5 2 4 6 6 5 5 +--R (8960A a b + 4736B a b )e + (8960A b + 18688B a b )d e +--R + +--R 6 2 4 +--R 4736B b d e +--R * +--R 4 +--R x +--R + +--R 2 4 3 3 6 5 2 4 5 +--R (6048A a b + 48B a b )e + (23744A a b + 12752B a b )d e +--R + +--R 6 5 2 4 6 3 3 +--R (6048A b + 12752B a b )d e + 48B b d e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 6 2 4 3 3 5 +--R (112A a b - 56B a b )e + (17808A a b + 256B a b )d e +--R + +--R 5 2 4 2 4 6 5 3 3 +--R (17808A a b + 9840B a b )d e + (112A b + 256B a b )d e +--R + +--R 6 4 2 +--R - 56B b d e +--R * +--R 2 +--R x +--R + +--R 4 2 5 6 3 3 4 2 5 +--R (- 140A a b + 70B a b)e + (784A a b - 322B a b )d e +--R + +--R 2 4 3 3 2 4 5 2 4 3 3 +--R (16632A a b + 508B a b )d e + (784A a b + 508B a b )d e +--R + +--R 6 5 4 2 6 5 +--R (- 140A b - 322B a b )d e + 70B b d e +--R * +--R x +--R + +--R 5 6 6 4 2 5 5 +--R (210A a b - 105B a )e + (- 1190A a b + 490B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (2772A a b - 791B a b )d e + (2772A a b + 300B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (- 1190A a b - 791B a b )d e + (210A b + 490B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 4 +-+ +-+ +--R 21504b e \|b \|e +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1293 +--a0:=integrate(t0,x) +--E 1041 + +--S 1042 of 1293 +--m0:=a0-r0 +--E 1042 + +--S 1043 of 1293 +--d0:=D(m0,x) +--E 1043 + +)clear all + +--S 1044 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*(d+e*x)^(3/2) +--R +--R +--R (1) +--R 2 4 2 2 3 +--R B b e x + ((A b + 2B a b)e + B b d)x +--R + +--R 2 2 2 2 2 +--R ((2A a b + B a )e + (A b + 2B a b)d)x + (A a e + (2A a b + B a )d)x +--R + +--R 2 +--R A a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1293 +r0:=-1/60*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b^2*e)+_ + 1/6*B*(a+b*x)^(7/2)*(d+e*x)^(5/2)/(b*e)+1/512*(b*d-a*e)^5*(7*b*B*d-_ + 12*A*b*e+5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))/(b^(7/2)*e^(9/2))+1/768*(b*d-a*e)^3*(7*b*B*d-_ + 12*A*b*e+5*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^3*e^3)-_ + 1/960*(b*d-a*e)^2*(7*b*B*d-12*A*b*e+5*a*B*e)*(a+b*x)^(5/2)*_ + sqrt(d+e*x)/(b^3*e^2)-1/160*(b*d-a*e)*(7*b*B*d-12*A*b*e+5*a*B*e)*_ + (a+b*x)^(7/2)*sqrt(d+e*x)/(b^3*e)-1/512*(b*d-a*e)^4*_ + (7*b*B*d-12*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e^4) +--R +--R +--R (2) +--R 5 6 6 4 2 5 5 +--R (180A a b - 75B a )e + (- 900A a b + 270B a b)d e +--R + +--R 3 3 4 2 2 4 2 4 3 3 3 3 +--R (1800A a b - 225B a b )d e + (- 1800A a b - 300B a b )d e +--R + +--R 5 2 4 4 2 6 5 5 6 6 +--R (900A a b + 675B a b )d e + (- 180A b - 450B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 5 5 5 5 4 5 5 4 4 +--R 1280B b e x + ((1536A b + 3200B a b )e + 1664B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (4032A a b + 2160B a b )e + (2112A b + 4448B a b )d e +--R + +--R 5 2 3 +--R 48B b d e +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (2976A a b + 40B a b )e + (6144A a b + 3384B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (96A b + 216B a b )d e - 56B b d e +--R * +--R 2 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (120A a b - 50B a b)e + (5592A a b + 160B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (552A a b + 348B a b )d e + (- 120A b - 272B a b )d e +--R + +--R 5 4 +--R 70B b d e +--R * +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (- 180A a b + 75B a )e + (840A a b - 245B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (1536A a b + 150B a b )d e + (- 840A a b - 546B a b )d e +--R + +--R 5 4 4 5 5 +--R (180A b + 415B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 4 +-+ +-+ +--R 7680b e \|b \|e +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1293 +--a0:=integrate(t0,x) +--E 1046 + +--S 1047 of 1293 +--m0:=a0-r0 +--E 1047 + +--S 1048 of 1293 +--d0:=D(m0,x) +--E 1048 + +)clear all + +--S 1049 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)*sqrt(d+e*x) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1293 +r0:=1/5*B*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b*e)+1/128*(b*d-a*e)^4*_ + (7*b*B*d-10*A*b*e+3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(9/2))+1/192*(b*d-a*e)^2*_ + (7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b^2*e^3)-_ + 1/240*(b*d-a*e)*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/_ + (b^2*e^2)-1/40*(7*b*B*d-10*A*b*e+3*a*B*e)*(a+b*x)^(7/2)*_ + sqrt(d+e*x)/(b^2*e)-1/128*(b*d-a*e)^3*(7*b*B*d-10*A*b*e+3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^4) +--R +--R +--R (2) +--R 4 5 5 3 2 4 4 +--R (- 150A a b + 45B a )e + (600A a b - 75B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (- 900A a b - 150B a b )d e + (600A a b + 450B a b )d e +--R + +--R 5 4 4 5 5 +--R (- 150A b - 375B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 4 4 4 3 4 4 3 3 +--R 384B b e x + ((480A b + 1008B a b )e + 48B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (1360A a b + 744B a b )e + (80A b + 176B a b )d e +--R + +--R 4 2 2 +--R - 56B b d e +--R * +--R 2 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (1180A a b + 30B a b)e + (360A a b + 218B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 100A b - 222B a b )d e + 70B b d e +--R * +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (150A a b - 45B a )e + (730A a b + 60B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 550A a b - 346B a b )d e + (150A b + 340B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 2 4 +-+ +-+ +--R 1920b e \|b \|e +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1293 +--a0:=integrate(t0,x) +--E 1051 + +--S 1052 of 1293 +--m0:=a0-r0 +--E 1052 + +--S 1053 of 1293 +--d0:=D(m0,x) +--E 1053 + +)clear all + +--S 1054 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/sqrt(d+e*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1293 +r0:=5/64*(b*d-a*e)^3*(7*b*B*d-8*A*b*e+a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(3/2)*e^(9/2))+5/96*(b*d-a*e)*_ + (7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(b*e^3)-_ + 1/24*(7*b*B*d-8*A*b*e+a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(b*e^2)+_ + 1/4*B*(a+b*x)^(7/2)*sqrt(d+e*x)/(b*e)-5/64*(b*d-a*e)^2*_ + (7*b*B*d-8*A*b*e+a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b*e^4) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (120A a b - 15B a )e + (- 360A a b - 60B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (360A a b + 270B a b )d e + (- 120A b - 300B a b )d e + 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b + 136B a b )e - 56B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((208A a b + 118B a b)e + (- 80A b - 172B a b )d e + 70B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (264A a b + 15B a )e + (- 320A a b - 191B a b)d e +--R + +--R 3 2 2 3 3 +--R (120A b + 265B a b )d e - 105B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 +-+ +-+ +--R 192b e \|b \|e +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1293 +--a0:=integrate(t0,x) +--E 1056 + +--S 1057 of 1293 +--m0:=a0-r0 +--E 1057 + +--S 1058 of 1293 +--d0:=D(m0,x) +--E 1058 + +)clear all + +--S 1059 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R +-------+ +--R (e x + d)\|e x + d +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1293 +r0:=-5/8*(b*d-a*e)^2*(7*b*B*d-6*A*b*e-a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(9/2)*sqrt(b))-_ + 2*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*sqrt(d+e*x))-_ + 5/12*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/e^3+_ + 1/3*(7*b*B*d-6*A*b*e-a*B*e)*(a+b*x)^(5/2)*sqrt(d+e*x)/(e^2*(b*d-a*e))+_ + 5/8*(b*d-a*e)*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (90A a b + 15B a )e + (- 180A a b - 135B a b)d e +--R + +--R 3 2 2 3 3 +--R (90A b + 225B a b )d e - 105B b d +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 8B b e x + ((12A b + 26B a b)e - 14B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((54A a b + 33B a )e + (- 30A b - 68B a b)d e + 35B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 48A a e + (150A a b + 81B a )d e + (- 90A b - 190B a b)d e +--R + +--R 2 3 +--R 105B b d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|b x + a +--R / +--R 4 +-+ +-+ +-------+ +--R 24e \|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1293 +--a0:=integrate(t0,x) +--E 1061 + +--S 1062 of 1293 +--m0:=a0-r0 +--E 1062 + +--S 1063 of 1293 +--d0:=D(m0,x) +--E 1063 + +)clear all + +--S 1064 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (e x + 2d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1293 +r0:=-2/3*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 5/4*(b*d-a*e)*(7*b*B*d-4*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(b)/e^(9/2)-2/3*(7*b*B*d-4*A*b*e-3*a*B*e)*_ + (a+b*x)^(5/2)/(e^2*(b*d-a*e)*sqrt(d+e*x))+5/6*b*_ + (7*b*B*d-4*A*b*e-3*a*B*e)*(a+b*x)^(3/2)*sqrt(d+e*x)/(e^3*(b*d-a*e))-_ + 5/4*b*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/e^4 +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((60A a b + 45B a )e + (- 60A b - 150B a b)d e + 105B b d e)x +--R + +--R 2 2 2 2 2 3 +--R (60A a b + 45B a )d e + (- 60A b - 150B a b)d e + 105B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 6B b e x + ((12A b + 27B a b)e - 21B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 56A a b - 24B a )e + (80A b + 158B a b)d e - 140B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 8A a e + (- 40A a b - 16B a )d e + (60A b + 115B a b)d e +--R + +--R 2 3 +--R - 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 5 4 +-+ +-------+ +--R (12e x + 12d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1293 +--a0:=integrate(t0,x) +--E 1066 + +--S 1067 of 1293 +--m0:=a0-r0 +--E 1067 + +--S 1068 of 1293 +--d0:=D(m0,x) +--E 1068 + +)clear all + +--S 1069 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(7/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +--R (e x + 3d e x + 3d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1293 +r0:=-2/5*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ + 2/15*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(5/2)/(e^2*(b*d-a*e)*_ + (d+e*x)^(3/2))-b^(3/2)*(7*b*B*d-2*A*b*e-5*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/e^(9/2)-_ + 2/3*b*(7*b*B*d-2*A*b*e-5*a*B*e)*(a+b*x)^(3/2)/(e^3*(b*d-a*e)*_ + sqrt(d+e*x))+b^2*(7*b*B*d-2*A*b*e-5*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(e^4*(b*d-a*e)) +--R +--R +--R (2) +--R 2 3 2 2 2 +--R ((30A b + 75B a b)e - 105B b d e )x +--R + +--R 2 2 2 2 2 2 +--R ((60A b + 150B a b)d e - 210B b d e)x + (30A b + 75B a b)d e +--R + +--R 2 3 +--R - 105B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 3 3 2 3 2 2 2 +--R 15B b e x + ((- 46A b - 70B a b)e + 161B b d e )x +--R + +--R 2 3 2 2 2 2 +--R ((- 22A a b - 10B a )e + (- 70A b - 98B a b)d e + 245B b d e)x +--R + +--R 2 3 2 2 2 2 +--R - 6A a e + (- 10A a b - 4B a )d e + (- 30A b - 40B a b)d e +--R + +--R 2 3 +--R 105B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 6 2 5 2 4 +-+ +-------+ +--R (15e x + 30d e x + 15d e )\|e \|e x + d +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1293 +--a0:=integrate(t0,x) +--E 1071 + +--S 1072 of 1293 +--m0:=a0-r0 +--E 1072 + +--S 1073 of 1293 +--d0:=D(m0,x) +--E 1073 + +)clear all + +--S 1074 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(9/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1293 +r0:=-2/7*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))-_ + 2/5*B*(a+b*x)^(5/2)/(e^2*(d+e*x)^(5/2))-2/3*b*B*(a+b*x)^(3/2)/_ + (e^3*(d+e*x)^(3/2))+2*b^(5/2)*B*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/e^(9/2)-2*b^2*B*sqrt(a+b*x)/(e^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 4 3 3 3 2 3 3 2 2 2 +--R (210B a b e - 210B b d e )x + (630B a b d e - 630B b d e )x +--R + +--R 2 2 2 3 3 2 3 3 4 +--R (630B a b d e - 630B b d e)x + 210B a b d e - 210B b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|b \|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 4 3 3 3 +--R ((- 30A b - 322B a b )e + 352B b d e )x +--R + +--R 2 2 4 2 3 3 2 2 2 +--R ((- 90A a b - 154B a b)e - 568B a b d e + 812B b d e )x +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 90A a b - 42B a )e - 92B a b d e - 476B a b d e + 700B b d e)x +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 +--R - 30A a e - 12B a d e - 28B a b d e - 140B a b d e + 210B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R / +--R 8 7 3 7 2 6 2 +--R (105a e - 105b d e )x + (315a d e - 315b d e )x +--R + +--R 2 6 3 5 3 5 4 4 +--R (315a d e - 315b d e )x + 105a d e - 105b d e +--R * +--R +-+ +-------+ +--R \|e \|e x + d +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1293 +--a0:=integrate(t0,x) +--E 1076 + +--S 1077 of 1293 +--m0:=a0-r0 +--E 1077 + +--S 1078 of 1293 +--d0:=D(m0,x) +--E 1078 + +)clear all + +--S 1079 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(11/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R (1) ---------------------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1293 +r0:=-2/9*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(7*b*B*d+2*A*b*e-9*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*(d+e*x)^(7/2)) +--R +--R +--R (2) +--R 4 3 4 4 +--R ((4A b - 18B a b )e + 14B b d)x +--R + +--R 3 2 2 4 3 3 +--R ((- 2A a b - 54B a b )e + (18A b + 38B a b )d)x +--R + +--R 2 2 3 3 2 2 2 +--R ((- 30A a b - 54B a b)e + (54A a b + 30B a b )d)x +--R + +--R 3 4 2 2 3 4 +--R ((- 38A a b - 18B a )e + (54A a b + 2B a b)d)x - 14A a e +--R + +--R 3 4 +--R (18A a b - 4B a )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 6 5 2 2 4 4 +--R (63a e - 126a b d e + 63b d e )x +--R + +--R 2 5 2 4 2 3 3 3 +--R (252a d e - 504a b d e + 252b d e )x +--R + +--R 2 2 4 3 3 2 4 2 2 +--R (378a d e - 756a b d e + 378b d e )x +--R + +--R 2 3 3 4 2 2 5 2 4 2 5 2 6 +--R (252a d e - 504a b d e + 252b d e)x + 63a d e - 126a b d e + 63b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 4 6 4 +--R ((16A b - 72B a b )d e + 56B b d )x +--R + +--R 3 2 2 5 4 3 6 3 +--R ((- 8A a b - 216B a b )d e + (72A b + 152B a b )d )x +--R + +--R 2 2 3 5 3 2 2 6 2 +--R ((- 120A a b - 216B a b)d e + (216A a b + 120B a b )d )x +--R + +--R 3 4 5 2 2 3 6 4 5 +--R ((- 152A a b - 72B a )d e + (216A a b + 8B a b)d )x - 56A a d e +--R + +--R 3 4 6 +--R (72A a b - 16B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 6 +--R (7A a d + 112A a )e +--R + +--R 3 4 2 4 5 5 +--R ((- 9A a b + 2B a )d + (- 144A a b + 32B a )d)e +--R * +--R 5 +--R x +--R + +--R 4 2 5 5 +--R (35A a d + 560A a d)e +--R + +--R 3 4 3 4 5 2 4 +--R ((- 45A a b + 10B a )d + (- 720A a b + 160B a )d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 4 +--R (70A a d + 1120A a d )e +--R + +--R 3 4 4 4 5 3 3 +--R ((- 90A a b + 20B a )d + (- 1440A a b + 320B a )d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 3 +--R (70A a d + 1120A a d )e +--R + +--R 3 4 5 4 5 4 2 +--R ((- 90A a b + 20B a )d + (- 1440A a b + 320B a )d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 2 +--R (35A a d + 560A a d )e +--R + +--R 3 4 6 4 5 5 +--R ((- 45A a b + 10B a )d + (- 720A a b + 160B a )d )e +--R * +--R x +--R + +--R 4 6 5 5 3 4 7 4 5 6 +--R (7A a d + 112A a d )e + (- 9A a b + 2B a )d + (- 144A a b + 32B a )d +--R / +--R 2 5 7 6 6 2 7 5 5 +--R (252a d e - 504a b d e + 252b d e )x +--R + +--R 2 6 6 7 5 2 8 4 4 +--R (1260a d e - 2520a b d e + 1260b d e )x +--R + +--R 2 7 5 8 4 2 9 3 3 +--R (2520a d e - 5040a b d e + 2520b d e )x +--R + +--R 2 8 4 9 3 2 10 2 2 +--R (2520a d e - 5040a b d e + 2520b d e )x +--R + +--R 2 9 3 10 2 2 11 2 10 2 11 +--R (1260a d e - 2520a b d e + 1260b d e)x + 252a d e - 504a b d e +--R + +--R 2 12 +--R 252b d +--R Type: Union(Expression(Integer),...) +--E 1081 + +--S 1082 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 5 3 4 2 4 5 +--R (7A a d + 112A a )e + (- 9A a b + 2B a )d + (- 144A a b + 32B a )d +--R (4) ------------------------------------------------------------------- +--R 2 5 2 6 2 7 +--R 252a d e - 504a b d e + 252b d +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1083 + +)clear all + +--S 1084 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(13/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R ------------------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +-------+ +--R (e x + 6d e x + 15d e x + 20d e x + 15d e x + 6d e x + d )\|e x + d +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1293 +r0:=-2/11*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ + 2/99*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(9/2))+4/693*b*(7*b*B*d+4*A*b*e-11*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(7/2)) +--R +--R +--R (2) +--R 5 4 2 5 5 +--R ((- 16A b + 44B a b )e - 28B b d e)x +--R + +--R 4 2 3 2 5 4 5 2 4 +--R ((8A a b - 22B a b )e + (- 88A b + 256B a b )d e - 154B b d )x +--R + +--R 2 3 3 2 2 4 2 3 +--R (- 6A a b - 330B a b )e + (44A a b + 908B a b )d e +--R + +--R 5 4 2 +--R (- 198A b - 418B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 226A a b - 418B a b)e + (660A a b + 908B a b )d e +--R + +--R 4 2 3 2 +--R (- 594A a b - 330B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 2 4 +--R (- 322A a b - 154B a )e + (836A a b + 256B a b)d e +--R + +--R 2 3 3 2 2 +--R (- 594A a b - 22B a b )d +--R * +--R x +--R + +--R 5 2 4 5 3 2 4 2 +--R - 126A a e + (308A a b - 28B a )d e + (- 198A a b + 44B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 8 2 7 2 2 6 3 3 5 5 +--R (693a e - 2079a b d e + 2079a b d e - 693b d e )x +--R + +--R 3 7 2 2 6 2 3 5 3 4 4 4 +--R (3465a d e - 10395a b d e + 10395a b d e - 3465b d e )x +--R + +--R 3 2 6 2 3 5 2 4 4 3 5 3 3 +--R (6930a d e - 20790a b d e + 20790a b d e - 6930b d e )x +--R + +--R 3 3 5 2 4 4 2 5 3 3 6 2 2 +--R (6930a d e - 20790a b d e + 20790a b d e - 6930b d e )x +--R + +--R 3 4 4 2 5 3 2 6 2 3 7 3 5 3 +--R (3465a d e - 10395a b d e + 10395a b d e - 3465b d e)x + 693a d e +--R + +--R 2 6 2 2 7 3 8 +--R - 2079a b d e + 2079a b d e - 693b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 6 2 5 7 5 +--R ((- 32A b + 88B a b )d e - 56B b d e)x +--R + +--R 4 2 3 6 2 5 4 7 +--R (16A a b - 44B a b )d e + (- 176A b + 512B a b )d e +--R + +--R 5 8 +--R - 308B b d +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 6 2 4 2 3 7 +--R (- 12A a b - 660B a b )d e + (88A a b + 1816B a b )d e +--R + +--R 5 4 8 +--R (- 396A b - 836B a b )d +--R * +--R 3 +--R x +--R + +--R 3 2 4 6 2 2 3 3 2 7 +--R (- 452A a b - 836B a b)d e + (1320A a b + 1816B a b )d e +--R + +--R 4 2 3 8 +--R (- 1188A a b - 660B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 6 2 3 2 4 7 +--R (- 644A a b - 308B a )d e + (1672A a b + 512B a b)d e +--R + +--R 2 3 3 2 8 +--R (- 1188A a b - 44B a b )d +--R * +--R x +--R + +--R 5 6 2 4 5 7 3 2 4 8 +--R - 252A a d e + (616A a b - 56B a )d e + (- 396A a b + 88B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 6 8 +--R (63A a d + 252A a )e +--R + +--R 4 5 2 5 6 7 +--R ((- 154A a b + 14B a )d + (- 616A a b + 56B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 6 +--R ((99A a b - 22B a b)d + (396A a b - 88B a b)d )e +--R * +--R 6 +--R x +--R + +--R 5 2 6 7 +--R (378A a d + 1512A a d)e +--R + +--R 4 5 3 5 6 2 6 +--R ((- 924A a b + 84B a )d + (- 3696A a b + 336B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 5 +--R ((594A a b - 132B a b)d + (2376A a b - 528B a b)d )e +--R * +--R 5 +--R x +--R + +--R 5 3 6 2 6 +--R (945A a d + 3780A a d )e +--R + +--R 4 5 4 5 6 3 5 +--R ((- 2310A a b + 210B a )d + (- 9240A a b + 840B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 4 +--R ((1485A a b - 330B a b)d + (5940A a b - 1320B a b)d )e +--R * +--R 4 +--R x +--R + +--R 5 4 6 3 5 +--R (1260A a d + 5040A a d )e +--R + +--R 4 5 5 5 6 4 4 +--R ((- 3080A a b + 280B a )d + (- 12320A a b + 1120B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 3 +--R ((1980A a b - 440B a b)d + (7920A a b - 1760B a b)d )e +--R * +--R 3 +--R x +--R + +--R 5 5 6 4 4 +--R (945A a d + 3780A a d )e +--R + +--R 4 5 6 5 6 5 3 +--R ((- 2310A a b + 210B a )d + (- 9240A a b + 840B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 2 +--R ((1485A a b - 330B a b)d + (5940A a b - 1320B a b)d )e +--R * +--R 2 +--R x +--R + +--R 5 6 6 5 3 +--R (378A a d + 1512A a d )e +--R + +--R 4 5 7 5 6 6 2 +--R ((- 924A a b + 84B a )d + (- 3696A a b + 336B a )d )e +--R + +--R 3 2 4 8 4 2 5 7 +--R ((594A a b - 132B a b)d + (2376A a b - 528B a b)d )e +--R * +--R x +--R + +--R 5 7 6 6 2 +--R (63A a d + 252A a d )e +--R + +--R 4 5 8 5 6 7 +--R ((- 154A a b + 14B a )d + (- 616A a b + 56B a )d )e +--R + +--R 3 2 4 9 4 2 5 8 +--R (99A a b - 22B a b)d + (396A a b - 88B a b)d +--R / +--R 3 6 9 2 7 8 2 8 7 3 9 6 6 +--R (1386a d e - 4158a b d e + 4158a b d e - 1386b d e )x +--R + +--R 3 7 8 2 8 7 2 9 6 3 10 5 5 +--R (8316a d e - 24948a b d e + 24948a b d e - 8316b d e )x +--R + +--R 3 8 7 2 9 6 2 10 5 3 11 4 4 +--R (20790a d e - 62370a b d e + 62370a b d e - 20790b d e )x +--R + +--R 3 9 6 2 10 5 2 11 4 3 12 3 3 +--R (27720a d e - 83160a b d e + 83160a b d e - 27720b d e )x +--R + +--R 3 10 5 2 11 4 2 12 3 3 13 2 2 +--R (20790a d e - 62370a b d e + 62370a b d e - 20790b d e )x +--R + +--R 3 11 4 2 12 3 2 13 2 3 14 +--R (8316a d e - 24948a b d e + 24948a b d e - 8316b d e)x +--R + +--R 3 12 3 2 13 2 2 14 3 15 +--R 1386a d e - 4158a b d e + 4158a b d e - 1386b d +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 2 +--R (63A a d + 252A a )e +--R + +--R 4 5 2 5 6 +--R ((- 154A a b + 14B a )d + (- 616A a b + 56B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 +--R (99A a b - 22B a b)d + (396A a b - 88B a b)d +--R / +--R 3 6 3 2 7 2 2 8 3 9 +--R 1386a d e - 4158a b d e + 4158a b d e - 1386b d +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1088 + +)clear all + +--S 1089 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(15/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|b x + a +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R e x + 7d e x + 21d e x + 35d e x + 35d e x + 21d e x + 7d e x +--R + +--R 7 +--R d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1293 +r0:=-2/13*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ + 2/143*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(11/2))+8/1287*b*(7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(9/2))+16/9009*b^2*_ + (7*b*B*d+6*A*b*e-13*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*(d+e*x)^(7/2)) +--R +--R +--R (2) +--R 6 5 3 6 2 6 +--R ((96A b - 208B a b )e + 112B b d e )x +--R + +--R 5 2 4 3 6 5 2 +--R (- 48A a b + 104B a b )e + (624A b - 1408B a b )d e +--R + +--R 6 2 +--R 728B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 3 5 2 4 2 +--R (36A a b - 78B a b )e + (- 312A a b + 718B a b )d e +--R + +--R 6 5 2 6 3 +--R (1716A b - 4082B a b )d e + 2002B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 3 2 4 3 3 2 +--R (- 30A a b - 2938B a b )e + (234A a b + 11470B a b )d e +--R + +--R 5 2 4 2 6 5 3 +--R (- 858A a b - 15886B a b )d e + (2574A b + 5434B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 3 3 4 2 2 +--R (- 2226A a b - 4186B a b)e + (8814A a b + 14342B a b )d e +--R + +--R 2 4 3 3 2 5 2 4 3 +--R (- 12870A a b - 15886B a b )d e + (7722A a b + 4290B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 2 5 2 +--R (- 3402A a b - 1638B a )e + (12558A a b + 4858B a b)d e +--R + +--R 3 3 4 2 2 2 4 3 3 3 +--R (- 16302A a b - 4082B a b )d e + (7722A a b + 286B a b )d +--R * +--R x +--R + +--R 6 3 5 6 2 4 2 5 2 +--R - 1386A a e + (4914A a b - 252B a )d e + (- 6006A a b + 728B a b)d e +--R + +--R 3 3 4 2 3 +--R (2574A a b - 572B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 10 3 9 2 2 2 8 3 3 7 +--R 9009a e - 36036a b d e + 54054a b d e - 36036a b d e +--R + +--R 4 4 6 +--R 9009b d e +--R * +--R 6 +--R x +--R + +--R 4 9 3 2 8 2 2 3 7 3 4 6 +--R 54054a d e - 216216a b d e + 324324a b d e - 216216a b d e +--R + +--R 4 5 5 +--R 54054b d e +--R * +--R 5 +--R x +--R + +--R 4 2 8 3 3 7 2 2 4 6 3 5 5 +--R 135135a d e - 540540a b d e + 810810a b d e - 540540a b d e +--R + +--R 4 6 4 +--R 135135b d e +--R * +--R 4 +--R x +--R + +--R 4 3 7 3 4 6 2 2 5 5 3 6 4 +--R 180180a d e - 720720a b d e + 1081080a b d e - 720720a b d e +--R + +--R 4 7 3 +--R 180180b d e +--R * +--R 3 +--R x +--R + +--R 4 4 6 3 5 5 2 2 6 4 3 7 3 +--R 135135a d e - 540540a b d e + 810810a b d e - 540540a b d e +--R + +--R 4 8 2 +--R 135135b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 6 4 2 2 7 3 3 8 2 +--R 54054a d e - 216216a b d e + 324324a b d e - 216216a b d e +--R + +--R 4 9 +--R 54054b d e +--R * +--R x +--R + +--R 4 6 4 3 7 3 2 2 8 2 3 9 4 10 +--R 9009a d e - 36036a b d e + 54054a b d e - 36036a b d e + 9009b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 7 3 6 8 2 6 +--R ((192A b - 416B a b )d e + 224B b d e )x +--R + +--R 5 2 4 7 3 6 5 8 2 +--R (- 96A a b + 208B a b )d e + (1248A b - 2816B a b )d e +--R + +--R 6 9 +--R 1456B b d e +--R * +--R 5 +--R x +--R + +--R 2 4 3 3 7 3 5 2 4 8 2 +--R (72A a b - 156B a b )d e + (- 624A a b + 1436B a b )d e +--R + +--R 6 5 9 6 10 +--R (3432A b - 8164B a b )d e + 4004B b d +--R * +--R 4 +--R x +--R + +--R 3 3 4 2 7 3 2 4 3 3 8 2 +--R (- 60A a b - 5876B a b )d e + (468A a b + 22940B a b )d e +--R + +--R 5 2 4 9 6 5 10 +--R (- 1716A a b - 31772B a b )d e + (5148A b + 10868B a b )d +--R * +--R 3 +--R x +--R + +--R 4 2 5 7 3 3 3 4 2 8 2 +--R (- 4452A a b - 8372B a b)d e + (17628A a b + 28684B a b )d e +--R + +--R 2 4 3 3 9 5 2 4 10 +--R (- 25740A a b - 31772B a b )d e + (15444A a b + 8580B a b )d +--R * +--R 2 +--R x +--R + +--R 5 6 7 3 4 2 5 8 2 +--R (- 6804A a b - 3276B a )d e + (25116A a b + 9716B a b)d e +--R + +--R 3 3 4 2 9 2 4 3 3 10 +--R (- 32604A a b - 8164B a b )d e + (15444A a b + 572B a b )d +--R * +--R x +--R + +--R 6 7 3 5 6 8 2 +--R - 2772A a d e + (9828A a b - 504B a )d e +--R + +--R 4 2 5 9 3 3 4 2 10 +--R (- 12012A a b + 1456B a b)d e + (5148A a b - 1144B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 6 7 10 +--R (- 693A a d - 2772A a )e +--R + +--R 5 6 2 6 7 9 +--R ((2457A a b - 126B a )d + (9828A a b - 504B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 8 +--R ((- 3003A a b + 364B a b)d + (- 12012A a b + 1456B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 7 +--R ((1287A a b - 286B a b )d + (5148A a b - 1144B a b )d )e +--R * +--R 7 +--R x +--R + +--R 6 2 7 9 +--R (- 4851A a d - 19404A a d)e +--R + +--R 5 6 3 6 7 2 8 +--R ((17199A a b - 882B a )d + (68796A a b - 3528B a )d )e +--R + +--R 4 2 5 4 5 2 6 3 7 +--R ((- 21021A a b + 2548B a b)d + (- 84084A a b + 10192B a b)d )e +--R + +--R 3 3 4 2 5 4 3 5 2 4 6 +--R ((9009A a b - 2002B a b )d + (36036A a b - 8008B a b )d )e +--R * +--R 6 +--R x +--R + +--R 6 3 7 2 8 +--R (- 14553A a d - 58212A a d )e +--R + +--R 5 6 4 6 7 3 7 +--R ((51597A a b - 2646B a )d + (206388A a b - 10584B a )d )e +--R + +--R 4 2 5 5 5 2 6 4 6 +--R ((- 63063A a b + 7644B a b)d + (- 252252A a b + 30576B a b)d )e +--R + +--R 3 3 4 2 6 4 3 5 2 5 5 +--R ((27027A a b - 6006B a b )d + (108108A a b - 24024B a b )d )e +--R * +--R 5 +--R x +--R + +--R 6 4 7 3 7 +--R (- 24255A a d - 97020A a d )e +--R + +--R 5 6 5 6 7 4 6 +--R ((85995A a b - 4410B a )d + (343980A a b - 17640B a )d )e +--R + +--R 4 2 5 6 5 2 6 5 5 +--R ((- 105105A a b + 12740B a b)d + (- 420420A a b + 50960B a b)d )e +--R + +--R 3 3 4 2 7 4 3 5 2 6 4 +--R ((45045A a b - 10010B a b )d + (180180A a b - 40040B a b )d )e +--R * +--R 4 +--R x +--R + +--R 6 5 7 4 6 +--R (- 24255A a d - 97020A a d )e +--R + +--R 5 6 6 6 7 5 5 +--R ((85995A a b - 4410B a )d + (343980A a b - 17640B a )d )e +--R + +--R 4 2 5 7 5 2 6 6 4 +--R ((- 105105A a b + 12740B a b)d + (- 420420A a b + 50960B a b)d )e +--R + +--R 3 3 4 2 8 4 3 5 2 7 3 +--R ((45045A a b - 10010B a b )d + (180180A a b - 40040B a b )d )e +--R * +--R 3 +--R x +--R + +--R 6 6 7 5 5 +--R (- 14553A a d - 58212A a d )e +--R + +--R 5 6 7 6 7 6 4 +--R ((51597A a b - 2646B a )d + (206388A a b - 10584B a )d )e +--R + +--R 4 2 5 8 5 2 6 7 3 +--R ((- 63063A a b + 7644B a b)d + (- 252252A a b + 30576B a b)d )e +--R + +--R 3 3 4 2 9 4 3 5 2 8 2 +--R ((27027A a b - 6006B a b )d + (108108A a b - 24024B a b )d )e +--R * +--R 2 +--R x +--R + +--R 6 7 7 6 4 +--R (- 4851A a d - 19404A a d )e +--R + +--R 5 6 8 6 7 7 3 +--R ((17199A a b - 882B a )d + (68796A a b - 3528B a )d )e +--R + +--R 4 2 5 9 5 2 6 8 2 +--R ((- 21021A a b + 2548B a b)d + (- 84084A a b + 10192B a b)d )e +--R + +--R 3 3 4 2 10 4 3 5 2 9 +--R ((9009A a b - 2002B a b )d + (36036A a b - 8008B a b )d )e +--R * +--R x +--R + +--R 6 8 7 7 3 +--R (- 693A a d - 2772A a d )e +--R + +--R 5 6 9 6 7 8 2 +--R ((2457A a b - 126B a )d + (9828A a b - 504B a )d )e +--R + +--R 4 2 5 10 5 2 6 9 +--R ((- 3003A a b + 364B a b)d + (- 12012A a b + 1456B a b)d )e +--R + +--R 3 3 4 2 11 4 3 5 2 10 +--R (1287A a b - 286B a b )d + (5148A a b - 1144B a b )d +--R / +--R 4 7 11 3 8 10 2 2 9 9 3 10 8 +--R 18018a d e - 72072a b d e + 108108a b d e - 72072a b d e +--R + +--R 4 11 7 +--R 18018b d e +--R * +--R 7 +--R x +--R + +--R 4 8 10 3 9 9 2 2 10 8 3 11 7 +--R 126126a d e - 504504a b d e + 756756a b d e - 504504a b d e +--R + +--R 4 12 6 +--R 126126b d e +--R * +--R 6 +--R x +--R + +--R 4 9 9 3 10 8 2 2 11 7 3 12 6 +--R 378378a d e - 1513512a b d e + 2270268a b d e - 1513512a b d e +--R + +--R 4 13 5 +--R 378378b d e +--R * +--R 5 +--R x +--R + +--R 4 10 8 3 11 7 2 2 12 6 +--R 630630a d e - 2522520a b d e + 3783780a b d e +--R + +--R 3 13 5 4 14 4 +--R - 2522520a b d e + 630630b d e +--R * +--R 4 +--R x +--R + +--R 4 11 7 3 12 6 2 2 13 5 +--R 630630a d e - 2522520a b d e + 3783780a b d e +--R + +--R 3 14 4 4 15 3 +--R - 2522520a b d e + 630630b d e +--R * +--R 3 +--R x +--R + +--R 4 12 6 3 13 5 2 2 14 4 +--R 378378a d e - 1513512a b d e + 2270268a b d e +--R + +--R 3 15 3 4 16 2 +--R - 1513512a b d e + 378378b d e +--R * +--R 2 +--R x +--R + +--R 4 13 5 3 14 4 2 2 15 3 3 16 2 +--R 126126a d e - 504504a b d e + 756756a b d e - 504504a b d e +--R + +--R 4 17 +--R 126126b d e +--R * +--R x +--R + +--R 4 14 4 3 15 3 2 2 16 2 3 17 +--R 18018a d e - 72072a b d e + 108108a b d e - 72072a b d e +--R + +--R 4 18 +--R 18018b d +--R Type: Union(Expression(Integer),...) +--E 1091 + +--S 1092 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 6 7 3 +--R (- 693A a d - 2772A a )e +--R + +--R 5 6 2 6 7 2 +--R ((2457A a b - 126B a )d + (9828A a b - 504B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 +--R ((- 3003A a b + 364B a b)d + (- 12012A a b + 1456B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 +--R (1287A a b - 286B a b )d + (5148A a b - 1144B a b )d +--R / +--R 4 7 4 3 8 3 2 2 9 2 3 10 4 11 +--R 18018a d e - 72072a b d e + 108108a b d e - 72072a b d e + 18018b d +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1093 + +)clear all + +--S 1094 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(17/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|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 e x + 8d e x + 28d e x + 56d e x + 70d e x + 56d e x + 28d e x +--R + +--R 7 8 +--R 8d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1293 +r0:=-2/15*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ + 2/195*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(13/2))+4/715*b*(7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(11/2))+16/6435*b^2*_ + (7*b*B*d+8*A*b*e-15*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(9/2))+32/45045*b^3*(7*b*B*d+8*A*b*e-15*a*B*e)*_ + (a+b*x)^(7/2)/(e*(b*d-a*e)^5*(d+e*x)^(7/2)) +--R +--R +--R (2) +--R 7 6 4 7 3 7 +--R ((- 256A b + 480B a b )e - 224B b d e )x +--R + +--R 6 2 5 4 7 6 3 +--R (128A a b - 240B a b )e + (- 1920A b + 3712B a b )d e +--R + +--R 7 2 2 +--R - 1680B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 4 6 2 5 3 +--R (- 96A a b + 180B a b )e + (960A a b - 1884B a b )d e +--R + +--R 7 6 2 2 7 3 +--R (- 6240A b + 12540B a b )d e - 5460B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 4 2 5 3 4 3 +--R (80A a b - 150B a b )e + (- 720A a b + 1420B a b )d e +--R + +--R 6 2 5 2 2 7 6 3 +--R (3120A a b - 6480B a b )d e + (- 11440A b + 24180B a b )d e +--R + +--R 7 4 +--R - 10010B b d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 4 3 4 4 3 3 +--R (- 70A a b - 11130B a b )e + (600A a b + 55120B a b )d e +--R + +--R 2 5 3 4 2 2 6 2 5 3 +--R (- 2340A a b - 107700B a b )d e + (5720A a b + 99840B a b )d e +--R + +--R 7 6 4 +--R (- 12870A b - 27170B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 4 3 5 2 3 +--R (- 8946A a b - 17010B a b)e + (44520A a b + 77616B a b )d e +--R + +--R 3 4 4 3 2 2 2 5 3 4 3 +--R (- 88140A a b - 133620B a b )d e + (85800A a b + 99840B a b )d e +--R + +--R 6 2 5 4 +--R (- 38610A a b - 21450B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 4 5 2 6 3 +--R (- 14322A a b - 6930B a )e + (68040A a b + 28812B a b)d e +--R + +--R 4 3 5 2 2 2 +--R (- 125580A a b - 42840B a b )d e +--R + +--R 3 4 4 3 3 2 5 3 4 4 +--R (108680A a b + 24180B a b )d e + (- 38610A a b - 1430B a b )d +--R * +--R x +--R + +--R 7 4 6 7 3 +--R - 6006A a e + (27720A a b - 924B a )d e +--R + +--R 5 2 6 2 2 4 3 5 2 3 +--R (- 49140A a b + 3780B a b)d e + (40040A a b - 5460B a b )d e +--R + +--R 3 4 4 3 4 +--R (- 12870A a b + 2860B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 12 4 11 3 2 2 10 2 3 3 9 +--R 45045a e - 225225a b d e + 450450a b d e - 450450a b d e +--R + +--R 4 4 8 5 5 7 +--R 225225a b d e - 45045b d e +--R * +--R 7 +--R x +--R + +--R 5 11 4 2 10 3 2 3 9 +--R 315315a d e - 1576575a b d e + 3153150a b d e +--R + +--R 2 3 4 8 4 5 7 5 6 6 +--R - 3153150a b d e + 1576575a b d e - 315315b d e +--R * +--R 6 +--R x +--R + +--R 5 2 10 4 3 9 3 2 4 8 2 3 5 7 +--R 945945a d e - 4729725a b d e + 9459450a b d e - 9459450a b d e +--R + +--R 4 6 6 5 7 5 +--R 4729725a b d e - 945945b d e +--R * +--R 5 +--R x +--R + +--R 5 3 9 4 4 8 3 2 5 7 +--R 1576575a d e - 7882875a b d e + 15765750a b d e +--R + +--R 2 3 6 6 4 7 5 5 8 4 +--R - 15765750a b d e + 7882875a b d e - 1576575b d e +--R * +--R 4 +--R x +--R + +--R 5 4 8 4 5 7 3 2 6 6 +--R 1576575a d e - 7882875a b d e + 15765750a b d e +--R + +--R 2 3 7 5 4 8 4 5 9 3 +--R - 15765750a b d e + 7882875a b d e - 1576575b d e +--R * +--R 3 +--R x +--R + +--R 5 5 7 4 6 6 3 2 7 5 2 3 8 4 +--R 945945a d e - 4729725a b d e + 9459450a b d e - 9459450a b d e +--R + +--R 4 9 3 5 10 2 +--R 4729725a b d e - 945945b d e +--R * +--R 2 +--R x +--R + +--R 5 6 6 4 7 5 3 2 8 4 2 3 9 3 +--R 315315a d e - 1576575a b d e + 3153150a b d e - 3153150a b d e +--R + +--R 4 10 2 5 11 +--R 1576575a b d e - 315315b d e +--R * +--R x +--R + +--R 5 7 5 4 8 4 3 2 9 3 2 3 10 2 +--R 45045a d e - 225225a b d e + 450450a b d e - 450450a b d e +--R + +--R 4 11 5 12 +--R 225225a b d e - 45045b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 8 4 7 9 3 7 +--R ((- 512A b + 960B a b )d e - 448B b d e )x +--R + +--R 6 2 5 8 4 7 6 9 3 +--R (256A a b - 480B a b )d e + (- 3840A b + 7424B a b )d e +--R + +--R 7 10 2 +--R - 3360B b d e +--R * +--R 6 +--R x +--R + +--R 2 5 3 4 8 4 6 2 5 9 3 +--R (- 192A a b + 360B a b )d e + (1920A a b - 3768B a b )d e +--R + +--R 7 6 10 2 7 11 +--R (- 12480A b + 25080B a b )d e - 10920B b d e +--R * +--R 5 +--R x +--R + +--R 3 4 4 3 8 4 2 5 3 4 9 3 +--R (160A a b - 300B a b )d e + (- 1440A a b + 2840B a b )d e +--R + +--R 6 2 5 10 2 7 6 11 +--R (6240A a b - 12960B a b )d e + (- 22880A b + 48360B a b )d e +--R + +--R 7 12 +--R - 20020B b d +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 8 4 3 4 4 3 9 3 +--R (- 140A a b - 22260B a b )d e + (1200A a b + 110240B a b )d e +--R + +--R 2 5 3 4 10 2 +--R (- 4680A a b - 215400B a b )d e +--R + +--R 6 2 5 11 7 6 12 +--R (11440A a b + 199680B a b )d e + (- 25740A b - 54340B a b )d +--R * +--R 3 +--R x +--R + +--R 5 2 6 8 4 +--R (- 17892A a b - 34020B a b)d e +--R + +--R 4 3 5 2 9 3 +--R (89040A a b + 155232B a b )d e +--R + +--R 3 4 4 3 10 2 +--R (- 176280A a b - 267240B a b )d e +--R + +--R 2 5 3 4 11 +--R (171600A a b + 199680B a b )d e +--R + +--R 6 2 5 12 +--R (- 77220A a b - 42900B a b )d +--R * +--R 2 +--R x +--R + +--R 6 7 8 4 5 2 6 9 3 +--R (- 28644A a b - 13860B a )d e + (136080A a b + 57624B a b)d e +--R + +--R 4 3 5 2 10 2 +--R (- 251160A a b - 85680B a b )d e +--R + +--R 3 4 4 3 11 2 5 3 4 12 +--R (217360A a b + 48360B a b )d e + (- 77220A a b - 2860B a b )d +--R * +--R x +--R + +--R 7 8 4 6 7 9 3 +--R - 12012A a d e + (55440A a b - 1848B a )d e +--R + +--R 5 2 6 10 2 4 3 5 2 11 +--R (- 98280A a b + 7560B a b)d e + (80080A a b - 10920B a b )d e +--R + +--R 3 4 4 3 12 +--R (- 25740A a b + 5720B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 7 8 12 +--R (3003A a d + 12012A a )e +--R + +--R 6 7 2 7 8 11 +--R ((- 13860A a b + 462B a )d + (- 55440A a b + 1848B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 10 +--R ((24570A a b - 1890B a b)d + (98280A a b - 7560B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 9 +--R ((- 20020A a b + 2730B a b )d + (- 80080A a b + 10920B a b )d )e +--R + +--R 3 4 4 3 5 4 4 5 3 4 8 +--R ((6435A a b - 1430B a b )d + (25740A a b - 5720B a b )d )e +--R * +--R 8 +--R x +--R + +--R 7 2 8 11 +--R (24024A a d + 96096A a d)e +--R + +--R 6 7 3 7 8 2 10 +--R ((- 110880A a b + 3696B a )d + (- 443520A a b + 14784B a )d )e +--R + +--R 5 2 6 4 6 2 7 3 9 +--R ((196560A a b - 15120B a b)d + (786240A a b - 60480B a b)d )e +--R + +--R 4 3 5 2 5 +--R (- 160160A a b + 21840B a b )d +--R + +--R 5 3 6 2 4 +--R (- 640640A a b + 87360B a b )d +--R * +--R 8 +--R e +--R + +--R 3 4 4 3 6 4 4 5 3 5 7 +--R ((51480A a b - 11440B a b )d + (205920A a b - 45760B a b )d )e +--R * +--R 7 +--R x +--R + +--R 7 3 8 2 10 +--R (84084A a d + 336336A a d )e +--R + +--R 6 7 4 7 8 3 9 +--R ((- 388080A a b + 12936B a )d + (- 1552320A a b + 51744B a )d )e +--R + +--R 5 2 6 5 6 2 7 4 8 +--R ((687960A a b - 52920B a b)d + (2751840A a b - 211680B a b)d )e +--R + +--R 4 3 5 2 6 +--R (- 560560A a b + 76440B a b )d +--R + +--R 5 3 6 2 5 +--R (- 2242240A a b + 305760B a b )d +--R * +--R 7 +--R e +--R + +--R 3 4 4 3 7 4 4 5 3 6 6 +--R ((180180A a b - 40040B a b )d + (720720A a b - 160160B a b )d )e +--R * +--R 6 +--R x +--R + +--R 7 4 8 3 9 +--R (168168A a d + 672672A a d )e +--R + +--R 6 7 5 7 8 4 8 +--R ((- 776160A a b + 25872B a )d + (- 3104640A a b + 103488B a )d )e +--R + +--R 5 2 6 6 6 2 7 5 7 +--R ((1375920A a b - 105840B a b)d + (5503680A a b - 423360B a b)d )e +--R + +--R 4 3 5 2 7 +--R (- 1121120A a b + 152880B a b )d +--R + +--R 5 3 6 2 6 +--R (- 4484480A a b + 611520B a b )d +--R * +--R 6 +--R e +--R + +--R 3 4 4 3 8 4 4 5 3 7 5 +--R ((360360A a b - 80080B a b )d + (1441440A a b - 320320B a b )d )e +--R * +--R 5 +--R x +--R + +--R 7 5 8 4 8 +--R (210210A a d + 840840A a d )e +--R + +--R 6 7 6 7 8 5 7 +--R ((- 970200A a b + 32340B a )d + (- 3880800A a b + 129360B a )d )e +--R + +--R 5 2 6 7 6 2 7 6 6 +--R ((1719900A a b - 132300B a b)d + (6879600A a b - 529200B a b)d )e +--R + +--R 4 3 5 2 8 +--R (- 1401400A a b + 191100B a b )d +--R + +--R 5 3 6 2 7 +--R (- 5605600A a b + 764400B a b )d +--R * +--R 5 +--R e +--R + +--R 3 4 4 3 9 4 4 5 3 8 4 +--R ((450450A a b - 100100B a b )d + (1801800A a b - 400400B a b )d )e +--R * +--R 4 +--R x +--R + +--R 7 6 8 5 7 +--R (168168A a d + 672672A a d )e +--R + +--R 6 7 7 7 8 6 6 +--R ((- 776160A a b + 25872B a )d + (- 3104640A a b + 103488B a )d )e +--R + +--R 5 2 6 8 6 2 7 7 5 +--R ((1375920A a b - 105840B a b)d + (5503680A a b - 423360B a b)d )e +--R + +--R 4 3 5 2 9 +--R (- 1121120A a b + 152880B a b )d +--R + +--R 5 3 6 2 8 +--R (- 4484480A a b + 611520B a b )d +--R * +--R 4 +--R e +--R + +--R 3 4 4 3 10 4 4 5 3 9 3 +--R ((360360A a b - 80080B a b )d + (1441440A a b - 320320B a b )d )e +--R * +--R 3 +--R x +--R + +--R 7 7 8 6 6 +--R (84084A a d + 336336A a d )e +--R + +--R 6 7 8 7 8 7 5 +--R ((- 388080A a b + 12936B a )d + (- 1552320A a b + 51744B a )d )e +--R + +--R 5 2 6 9 6 2 7 8 4 +--R ((687960A a b - 52920B a b)d + (2751840A a b - 211680B a b)d )e +--R + +--R 4 3 5 2 10 +--R (- 560560A a b + 76440B a b )d +--R + +--R 5 3 6 2 9 +--R (- 2242240A a b + 305760B a b )d +--R * +--R 3 +--R e +--R + +--R 3 4 4 3 11 4 4 5 3 10 2 +--R ((180180A a b - 40040B a b )d + (720720A a b - 160160B a b )d )e +--R * +--R 2 +--R x +--R + +--R 7 8 8 7 5 +--R (24024A a d + 96096A a d )e +--R + +--R 6 7 9 7 8 8 4 +--R ((- 110880A a b + 3696B a )d + (- 443520A a b + 14784B a )d )e +--R + +--R 5 2 6 10 6 2 7 9 3 +--R ((196560A a b - 15120B a b)d + (786240A a b - 60480B a b)d )e +--R + +--R 4 3 5 2 11 +--R (- 160160A a b + 21840B a b )d +--R + +--R 5 3 6 2 10 +--R (- 640640A a b + 87360B a b )d +--R * +--R 2 +--R e +--R + +--R 3 4 4 3 12 4 4 5 3 11 +--R ((51480A a b - 11440B a b )d + (205920A a b - 45760B a b )d )e +--R * +--R x +--R + +--R 7 9 8 8 4 +--R (3003A a d + 12012A a d )e +--R + +--R 6 7 10 7 8 9 3 +--R ((- 13860A a b + 462B a )d + (- 55440A a b + 1848B a )d )e +--R + +--R 5 2 6 11 6 2 7 10 2 +--R ((24570A a b - 1890B a b)d + (98280A a b - 7560B a b)d )e +--R + +--R 4 3 5 2 12 5 3 6 2 11 +--R ((- 20020A a b + 2730B a b )d + (- 80080A a b + 10920B a b )d )e +--R + +--R 3 4 4 3 13 4 4 5 3 12 +--R (6435A a b - 1430B a b )d + (25740A a b - 5720B a b )d +--R / +--R 5 8 13 4 9 12 3 2 10 11 2 3 11 10 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 12 9 5 13 8 +--R 450450a b d e - 90090b d e +--R * +--R 8 +--R x +--R + +--R 5 9 12 4 10 11 3 2 11 10 +--R 720720a d e - 3603600a b d e + 7207200a b d e +--R + +--R 2 3 12 9 4 13 8 5 14 7 +--R - 7207200a b d e + 3603600a b d e - 720720b d e +--R * +--R 7 +--R x +--R + +--R 5 10 11 4 11 10 3 2 12 9 +--R 2522520a d e - 12612600a b d e + 25225200a b d e +--R + +--R 2 3 13 8 4 14 7 5 15 6 +--R - 25225200a b d e + 12612600a b d e - 2522520b d e +--R * +--R 6 +--R x +--R + +--R 5 11 10 4 12 9 3 2 13 8 +--R 5045040a d e - 25225200a b d e + 50450400a b d e +--R + +--R 2 3 14 7 4 15 6 5 16 5 +--R - 50450400a b d e + 25225200a b d e - 5045040b d e +--R * +--R 5 +--R x +--R + +--R 5 12 9 4 13 8 3 2 14 7 +--R 6306300a d e - 31531500a b d e + 63063000a b d e +--R + +--R 2 3 15 6 4 16 5 5 17 4 +--R - 63063000a b d e + 31531500a b d e - 6306300b d e +--R * +--R 4 +--R x +--R + +--R 5 13 8 4 14 7 3 2 15 6 +--R 5045040a d e - 25225200a b d e + 50450400a b d e +--R + +--R 2 3 16 5 4 17 4 5 18 3 +--R - 50450400a b d e + 25225200a b d e - 5045040b d e +--R * +--R 3 +--R x +--R + +--R 5 14 7 4 15 6 3 2 16 5 +--R 2522520a d e - 12612600a b d e + 25225200a b d e +--R + +--R 2 3 17 4 4 18 3 5 19 2 +--R - 25225200a b d e + 12612600a b d e - 2522520b d e +--R * +--R 2 +--R x +--R + +--R 5 15 6 4 16 5 3 2 17 4 +--R 720720a d e - 3603600a b d e + 7207200a b d e +--R + +--R 2 3 18 3 4 19 2 5 20 +--R - 7207200a b d e + 3603600a b d e - 720720b d e +--R * +--R x +--R + +--R 5 16 5 4 17 4 3 2 18 3 2 3 19 2 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 20 5 21 +--R 450450a b d e - 90090b d +--R Type: Union(Expression(Integer),...) +--E 1096 + +--S 1097 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 7 8 4 +--R (3003A a d + 12012A a )e +--R + +--R 6 7 2 7 8 3 +--R ((- 13860A a b + 462B a )d + (- 55440A a b + 1848B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 2 +--R ((24570A a b - 1890B a b)d + (98280A a b - 7560B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 +--R ((- 20020A a b + 2730B a b )d + (- 80080A a b + 10920B a b )d )e +--R + +--R 3 4 4 3 5 4 4 5 3 4 +--R (6435A a b - 1430B a b )d + (25740A a b - 5720B a b )d +--R / +--R 5 8 5 4 9 4 3 2 10 3 2 3 11 2 +--R 90090a d e - 450450a b d e + 900900a b d e - 900900a b d e +--R + +--R 4 12 5 13 +--R 450450a b d e - 90090b d +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1098 + +)clear all + +--S 1099 of 1293 +t0:=(a+b*x)^(5/2)*(A+B*x)/(d+e*x)^(19/2) +--R +--R +--R (1) +--R 2 3 2 2 2 2 +-------+ +--R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|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 e x + 9d e x + 36d e x + 84d e x + 126d e x + 126d e x + 84d e x +--R + +--R 7 2 2 8 9 +--R 36d e x + 9d e x + d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1293 +r0:=-2/17*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(17/2))+_ + 2/255*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^2*_ + (d+e*x)^(15/2))+16/3315*b*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^3*(d+e*x)^(13/2))+32/12155*b^2*_ + (7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)^4*_ + (d+e*x)^(11/2))+128/109395*b^3*(7*b*B*d+10*A*b*e-17*a*B*e)*_ + (a+b*x)^(7/2)/(e*(b*d-a*e)^5*(d+e*x)^(9/2))+_ + 256/765765*b^4*(7*b*B*d+10*A*b*e-17*a*B*e)*(a+b*x)^(7/2)/_ + (e*(b*d-a*e)^6*(d+e*x)^(7/2)) +--R +--R +--R (2) +--R 8 7 5 8 4 8 +--R ((2560A b - 4352B a b )e + 1792B b d e )x +--R + +--R 7 2 6 5 8 7 4 +--R (- 1280A a b + 2176B a b )e + (21760A b - 37888B a b )d e +--R + +--R 8 2 3 +--R 15232B b d e +--R * +--R 7 +--R x +--R + +--R 2 6 3 5 5 7 2 6 4 +--R (960A a b - 1632B a b )e + (- 10880A a b + 19168B a b )d e +--R + +--R 8 7 2 3 8 3 2 +--R (81600A b - 146336B a b )d e + 57120B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 5 2 6 3 5 4 +--R (- 800A a b + 1360B a b )e + (8160A a b - 14432B a b )d e +--R + +--R 7 2 6 2 3 8 7 3 2 +--R (- 40800A a b + 75072B a b )d e + (176800A b - 329120B a b )d e +--R + +--R 8 4 +--R 123760B b d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 5 3 5 4 4 4 +--R (700A a b - 1190B a b )e + (- 6800A a b + 12050B a b )d e +--R + +--R 2 6 3 5 2 3 +--R (30600A a b - 56780B a b )d e +--R + +--R 7 2 6 3 2 8 7 4 +--R (- 88400A a b + 171700B a b )d e + (243100A b - 475150B a b )d e +--R + +--R 8 5 +--R 170170B b d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 5 4 4 5 3 4 +--R (- 630A a b - 152082B a b )e + (5950A a b + 908362B a b )d e +--R + +--R 3 5 4 4 2 3 +--R (- 25500A a b - 2249780B a b )d e +--R + +--R 2 6 3 5 3 2 +--R (66300A a b + 2932500B a b )d e +--R + +--R 7 2 6 4 8 7 5 +--R (- 121550A a b - 2044250B a b )d e + (218790A b + 461890B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 5 +--R (- 127050A a b - 243474B a b)e +--R + +--R 5 3 6 2 4 +--R (760410A a b + 1375122B a b )d e +--R + +--R 4 4 5 3 2 3 +--R (- 1892100A a b - 3143028B a b )d e +--R + +--R 3 5 4 4 3 2 +--R (2497300A a b + 3619300B a b )d e +--R + +--R 2 6 3 5 4 +--R (- 1823250A a b - 2044250B a b )d e +--R + +--R 7 2 6 5 +--R (656370A a b + 364650B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 5 6 2 7 4 +--R (- 210210A a b - 102102B a )e + (1217370A a b + 540078B a b)d e +--R + +--R 5 3 6 2 2 3 +--R (- 2891700A a b - 1123836B a b )d e +--R + +--R 4 4 5 3 3 2 +--R (3558100A a b + 1116220B a b )d e +--R + +--R 3 5 4 4 4 2 6 3 5 5 +--R (- 2309450A a b - 475150B a b )d e + (656370A a b + 24310B a b )d +--R * +--R x +--R + +--R 8 5 7 8 4 +--R - 90090A a e + (510510A a b - 12012B a )d e +--R + +--R 6 2 7 2 3 5 3 6 2 3 2 +--R (- 1178100A a b + 62832B a b)d e + (1392300A a b - 128520B a b )d e +--R + +--R 4 4 5 3 4 3 5 4 4 5 +--R (- 850850A a b + 123760B a b )d e + (218790A a b - 48620B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 6 14 5 13 4 2 2 12 +--R 765765a e - 4594590a b d e + 11486475a b d e +--R + +--R 3 3 3 11 2 4 4 10 5 5 9 +--R - 15315300a b d e + 11486475a b d e - 4594590a b d e +--R + +--R 6 6 8 +--R 765765b d e +--R * +--R 8 +--R x +--R + +--R 6 13 5 2 12 4 2 3 11 +--R 6126120a d e - 36756720a b d e + 91891800a b d e +--R + +--R 3 3 4 10 2 4 5 9 5 6 8 +--R - 122522400a b d e + 91891800a b d e - 36756720a b d e +--R + +--R 6 7 7 +--R 6126120b d e +--R * +--R 7 +--R x +--R + +--R 6 2 12 5 3 11 4 2 4 10 +--R 21441420a d e - 128648520a b d e + 321621300a b d e +--R + +--R 3 3 5 9 2 4 6 8 5 7 7 +--R - 428828400a b d e + 321621300a b d e - 128648520a b d e +--R + +--R 6 8 6 +--R 21441420b d e +--R * +--R 6 +--R x +--R + +--R 6 3 11 5 4 10 4 2 5 9 +--R 42882840a d e - 257297040a b d e + 643242600a b d e +--R + +--R 3 3 6 8 2 4 7 7 5 8 6 +--R - 857656800a b d e + 643242600a b d e - 257297040a b d e +--R + +--R 6 9 5 +--R 42882840b d e +--R * +--R 5 +--R x +--R + +--R 6 4 10 5 5 9 4 2 6 8 +--R 53603550a d e - 321621300a b d e + 804053250a b d e +--R + +--R 3 3 7 7 2 4 8 6 5 9 5 +--R - 1072071000a b d e + 804053250a b d e - 321621300a b d e +--R + +--R 6 10 4 +--R 53603550b d e +--R * +--R 4 +--R x +--R + +--R 6 5 9 5 6 8 4 2 7 7 +--R 42882840a d e - 257297040a b d e + 643242600a b d e +--R + +--R 3 3 8 6 2 4 9 5 5 10 4 +--R - 857656800a b d e + 643242600a b d e - 257297040a b d e +--R + +--R 6 11 3 +--R 42882840b d e +--R * +--R 3 +--R x +--R + +--R 6 6 8 5 7 7 4 2 8 6 +--R 21441420a d e - 128648520a b d e + 321621300a b d e +--R + +--R 3 3 9 5 2 4 10 4 5 11 3 +--R - 428828400a b d e + 321621300a b d e - 128648520a b d e +--R + +--R 6 12 2 +--R 21441420b d e +--R * +--R 2 +--R x +--R + +--R 6 7 7 5 8 6 4 2 9 5 +--R 6126120a d e - 36756720a b d e + 91891800a b d e +--R + +--R 3 3 10 4 2 4 11 3 5 12 2 +--R - 122522400a b d e + 91891800a b d e - 36756720a b d e +--R + +--R 6 13 +--R 6126120b d e +--R * +--R x +--R + +--R 6 8 6 5 9 5 4 2 10 4 3 3 11 3 +--R 765765a d e - 4594590a b d e + 11486475a b d e - 15315300a b d e +--R + +--R 2 4 12 2 5 13 6 14 +--R 11486475a b d e - 4594590a b d e + 765765b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 9 5 8 10 4 8 +--R ((7680A b - 13056B a b )d e + 5376B b d e )x +--R + +--R 7 2 6 9 5 8 7 10 4 +--R (- 3840A a b + 6528B a b )d e + (65280A b - 113664B a b )d e +--R + +--R 8 11 3 +--R 45696B b d e +--R * +--R 7 +--R x +--R + +--R 2 6 3 5 9 5 +--R (2880A a b - 4896B a b )d e +--R + +--R 7 2 6 10 4 +--R (- 32640A a b + 57504B a b )d e +--R + +--R 8 7 11 3 8 12 2 +--R (244800A b - 439008B a b )d e + 171360B b d e +--R * +--R 6 +--R x +--R + +--R 3 5 4 4 9 5 +--R (- 2400A a b + 4080B a b )d e +--R + +--R 2 6 3 5 10 4 +--R (24480A a b - 43296B a b )d e +--R + +--R 7 2 6 11 3 +--R (- 122400A a b + 225216B a b )d e +--R + +--R 8 7 12 2 8 13 +--R (530400A b - 987360B a b )d e + 371280B b d e +--R * +--R 5 +--R x +--R + +--R 4 4 5 3 9 5 +--R (2100A a b - 3570B a b )d e +--R + +--R 3 5 4 4 10 4 +--R (- 20400A a b + 36150B a b )d e +--R + +--R 2 6 3 5 11 3 +--R (91800A a b - 170340B a b )d e +--R + +--R 7 2 6 12 2 +--R (- 265200A a b + 515100B a b )d e +--R + +--R 8 7 13 8 14 +--R (729300A b - 1425450B a b )d e + 510510B b d +--R * +--R 4 +--R x +--R + +--R 5 3 6 2 9 5 +--R (- 1890A a b - 456246B a b )d e +--R + +--R 4 4 5 3 10 4 +--R (17850A a b + 2725086B a b )d e +--R + +--R 3 5 4 4 11 3 +--R (- 76500A a b - 6749340B a b )d e +--R + +--R 2 6 3 5 12 2 +--R (198900A a b + 8797500B a b )d e +--R + +--R 7 2 6 13 +--R (- 364650A a b - 6132750B a b )d e +--R + +--R 8 7 14 +--R (656370A b + 1385670B a b )d +--R * +--R 3 +--R x +--R + +--R 6 2 7 9 5 +--R (- 381150A a b - 730422B a b)d e +--R + +--R 5 3 6 2 10 4 +--R (2281230A a b + 4125366B a b )d e +--R + +--R 4 4 5 3 11 3 +--R (- 5676300A a b - 9429084B a b )d e +--R + +--R 3 5 4 4 12 2 +--R (7491900A a b + 10857900B a b )d e +--R + +--R 2 6 3 5 13 +--R (- 5469750A a b - 6132750B a b )d e +--R + +--R 7 2 6 14 +--R (1969110A a b + 1093950B a b )d +--R * +--R 2 +--R x +--R + +--R 7 8 9 5 +--R (- 630630A a b - 306306B a )d e +--R + +--R 6 2 7 10 4 +--R (3652110A a b + 1620234B a b)d e +--R + +--R 5 3 6 2 11 3 +--R (- 8675100A a b - 3371508B a b )d e +--R + +--R 4 4 5 3 12 2 +--R (10674300A a b + 3348660B a b )d e +--R + +--R 3 5 4 4 13 +--R (- 6928350A a b - 1425450B a b )d e +--R + +--R 2 6 3 5 14 +--R (1969110A a b + 72930B a b )d +--R * +--R x +--R + +--R 8 9 5 7 8 10 4 +--R - 270270A a d e + (1531530A a b - 36036B a )d e +--R + +--R 6 2 7 11 3 +--R (- 3534300A a b + 188496B a b)d e +--R + +--R 5 3 6 2 12 2 +--R (4176900A a b - 385560B a b )d e +--R + +--R 4 4 5 3 13 3 5 4 4 14 +--R (- 2552550A a b + 371280B a b )d e + (656370A a b - 145860B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 8 9 14 +--R (45045A a d + 405405A a )e +--R + +--R 7 8 2 8 9 13 +--R ((- 255255A a b + 6006B a )d + (- 2297295A a b + 54054B a )d)e +--R + +--R 6 2 7 3 7 2 8 2 12 +--R ((589050A a b - 31416B a b)d + (5301450A a b - 282744B a b)d )e +--R + +--R 5 3 6 2 4 +--R (- 696150A a b + 64260B a b )d +--R + +--R 6 3 7 2 3 +--R (- 6265350A a b + 578340B a b )d +--R * +--R 11 +--R e +--R + +--R 4 4 5 3 5 5 4 6 3 4 +--R ((425425A a b - 61880B a b )d + (3828825A a b - 556920B a b )d ) +--R * +--R 10 +--R e +--R + +--R 3 5 4 4 6 +--R (- 109395A a b + 24310B a b )d +--R + +--R 4 5 5 4 5 +--R (- 984555A a b + 218790B a b )d +--R * +--R 9 +--R e +--R * +--R 9 +--R x +--R + +--R 8 2 9 13 +--R (405405A a d + 3648645A a d)e +--R + +--R 7 8 3 8 9 2 +--R ((- 2297295A a b + 54054B a )d + (- 20675655A a b + 486486B a )d ) +--R * +--R 12 +--R e +--R + +--R 6 2 7 4 +--R (5301450A a b - 282744B a b)d +--R + +--R 7 2 8 3 +--R (47713050A a b - 2544696B a b)d +--R * +--R 11 +--R e +--R + +--R 5 3 6 2 5 +--R (- 6265350A a b + 578340B a b )d +--R + +--R 6 3 7 2 4 +--R (- 56388150A a b + 5205060B a b )d +--R * +--R 10 +--R e +--R + +--R 4 4 5 3 6 +--R (3828825A a b - 556920B a b )d +--R + +--R 5 4 6 3 5 +--R (34459425A a b - 5012280B a b )d +--R * +--R 9 +--R e +--R + +--R 3 5 4 4 7 +--R (- 984555A a b + 218790B a b )d +--R + +--R 4 5 5 4 6 +--R (- 8860995A a b + 1969110B a b )d +--R * +--R 8 +--R e +--R * +--R 8 +--R x +--R + +--R 8 3 9 2 12 +--R (1621620A a d + 14594580A a d )e +--R + +--R 7 8 4 +--R (- 9189180A a b + 216216B a )d +--R + +--R 8 9 3 +--R (- 82702620A a b + 1945944B a )d +--R * +--R 11 +--R e +--R + +--R 6 2 7 5 +--R (21205800A a b - 1130976B a b)d +--R + +--R 7 2 8 4 +--R (190852200A a b - 10178784B a b)d +--R * +--R 10 +--R e +--R + +--R 5 3 6 2 6 +--R (- 25061400A a b + 2313360B a b )d +--R + +--R 6 3 7 2 5 +--R (- 225552600A a b + 20820240B a b )d +--R * +--R 9 +--R e +--R + +--R 4 4 5 3 7 +--R (15315300A a b - 2227680B a b )d +--R + +--R 5 4 6 3 6 +--R (137837700A a b - 20049120B a b )d +--R * +--R 8 +--R e +--R + +--R 3 5 4 4 8 +--R (- 3938220A a b + 875160B a b )d +--R + +--R 4 5 5 4 7 +--R (- 35443980A a b + 7876440B a b )d +--R * +--R 7 +--R e +--R * +--R 7 +--R x +--R + +--R 8 4 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(74220300A a b - 3958416B a b)d +--R + +--R 7 2 8 6 +--R (667982700A a b - 35625744B a b)d +--R * +--R 8 +--R e +--R + +--R 5 3 6 2 8 +--R (- 87714900A a b + 8096760B a b )d +--R + +--R 6 3 7 2 7 +--R (- 789434100A a b + 72870840B a b )d +--R * +--R 7 +--R e +--R + +--R 4 4 5 3 9 +--R (53603550A a b - 7796880B a b )d +--R + +--R 5 4 6 3 8 +--R (482431950A a b - 70171920B a b )d +--R * +--R 6 +--R e +--R + +--R 3 5 4 4 10 +--R (- 13783770A a b + 3063060B a b )d +--R + +--R 4 5 5 4 9 +--R (- 124053930A a b + 27567540B a b )d +--R * +--R 5 +--R e +--R * +--R 5 +--R x +--R + +--R 8 6 9 5 9 +--R (5675670A a d + 51081030A a d )e +--R + +--R 7 8 7 +--R (- 32162130A a b + 756756B a )d +--R + +--R 8 9 6 +--R (- 289459170A a b + 6810804B a )d +--R * +--R 8 +--R e +--R + +--R 6 2 7 8 +--R (74220300A a b - 3958416B a b)d +--R + +--R 7 2 8 7 +--R (667982700A a b - 35625744B a b)d +--R * +--R 7 +--R e +--R + +--R 5 3 6 2 9 +--R (- 87714900A a b + 8096760B a b )d +--R + +--R 6 3 7 2 8 +--R (- 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+--R 3 5 4 4 12 +--R (- 9189180A a b + 2042040B a b )d +--R + +--R 4 5 5 4 11 +--R (- 82702620A a b + 18378360B a b )d +--R * +--R 3 +--R e +--R * +--R 3 +--R x +--R + +--R 8 8 9 7 7 +--R (1621620A a d + 14594580A a d )e +--R + +--R 7 8 9 +--R (- 9189180A a b + 216216B a )d +--R + +--R 8 9 8 +--R (- 82702620A a b + 1945944B a )d +--R * +--R 6 +--R e +--R + +--R 6 2 7 10 +--R (21205800A a b - 1130976B a b)d +--R + +--R 7 2 8 9 +--R (190852200A a b - 10178784B a b)d +--R * +--R 5 +--R e +--R + +--R 5 3 6 2 11 +--R (- 25061400A a b + 2313360B a b )d +--R + +--R 6 3 7 2 10 +--R (- 225552600A a b + 20820240B a b )d +--R * +--R 4 +--R e +--R + +--R 4 4 5 3 12 +--R (15315300A a b - 2227680B a b )d +--R + +--R 5 4 6 3 11 +--R (137837700A a b - 20049120B a b )d +--R * +--R 3 +--R e +--R + +--R 3 5 4 4 13 +--R (- 3938220A a b + 875160B a b )d +--R + +--R 4 5 5 4 12 +--R (- 35443980A a b + 7876440B a b )d +--R * +--R 2 +--R e +--R * +--R 2 +--R x +--R + +--R 8 9 9 8 6 +--R (405405A a d + 3648645A a d )e +--R + +--R 7 8 10 +--R (- 2297295A a b + 54054B a )d +--R + +--R 8 9 9 +--R (- 20675655A a b + 486486B a )d +--R * +--R 5 +--R e +--R + +--R 6 2 7 11 +--R (5301450A a b - 282744B a b)d +--R + +--R 7 2 8 10 +--R (47713050A a b - 2544696B a b)d +--R * +--R 4 +--R e +--R + +--R 5 3 6 2 12 +--R (- 6265350A a b + 578340B a b )d +--R + +--R 6 3 7 2 11 +--R (- 56388150A a b + 5205060B a b )d +--R * +--R 3 +--R e +--R + +--R 4 4 5 3 13 +--R (3828825A a b - 556920B a b )d +--R + +--R 5 4 6 3 12 +--R (34459425A a b - 5012280B a b )d +--R * +--R 2 +--R e +--R + +--R 3 5 4 4 14 +--R (- 984555A a b + 218790B a b )d +--R + +--R 4 5 5 4 13 +--R (- 8860995A a b + 1969110B a b )d +--R * +--R e +--R * +--R x +--R + +--R 8 10 9 9 5 +--R (45045A a d + 405405A a d )e +--R + +--R 7 8 11 8 9 10 4 +--R ((- 255255A a b + 6006B a )d + (- 2297295A a b + 54054B a )d )e +--R + +--R 6 2 7 12 7 2 8 11 3 +--R ((589050A a b - 31416B a b)d + (5301450A a b - 282744B a b)d )e +--R + +--R 5 3 6 2 13 +--R (- 696150A a b + 64260B a b )d +--R + +--R 6 3 7 2 12 +--R (- 6265350A a b + 578340B a b )d +--R * +--R 2 +--R e +--R + +--R 4 4 5 3 14 5 4 6 3 13 +--R ((425425A a b - 61880B a b )d + (3828825A a b - 556920B a b )d )e +--R + +--R 3 5 4 4 15 4 5 5 4 14 +--R (- 109395A a b + 24310B a b )d + (- 984555A a b + 218790B a b )d +--R / +--R 6 9 15 5 10 14 4 2 11 13 +--R 2297295a d e - 13783770a b d e + 34459425a b d e +--R + +--R 3 3 12 12 2 4 13 11 5 14 10 +--R - 45945900a b d e + 34459425a b d e - 13783770a b d e +--R + +--R 6 15 9 +--R 2297295b d e +--R * +--R 9 +--R x +--R + +--R 6 10 14 5 11 13 4 2 12 12 +--R 20675655a d e - 124053930a b d e + 310134825a b d e +--R + +--R 3 3 13 11 2 4 14 10 5 15 9 +--R - 413513100a b d e + 310134825a b d e - 124053930a b d e +--R + +--R 6 16 8 +--R 20675655b d e +--R * +--R 8 +--R x +--R + +--R 6 11 13 5 12 12 4 2 13 11 +--R 82702620a d e - 496215720a b d e + 1240539300a b d e +--R + +--R 3 3 14 10 2 4 15 9 5 16 8 +--R - 1654052400a b d e + 1240539300a b d e - 496215720a b d e +--R + +--R 6 17 7 +--R 82702620b d e +--R * +--R 7 +--R x +--R + +--R 6 12 12 5 13 11 4 2 14 10 +--R 192972780a d e - 1157836680a b d e + 2894591700a b d e +--R + +--R 3 3 15 9 2 4 16 8 5 17 7 +--R - 3859455600a b d e + 2894591700a b d e - 1157836680a b d e +--R + +--R 6 18 6 +--R 192972780b d e +--R * +--R 6 +--R x +--R + +--R 6 13 11 5 14 10 4 2 15 9 +--R 289459170a d e - 1736755020a b d e + 4341887550a b d e +--R + +--R 3 3 16 8 2 4 17 7 5 18 6 +--R - 5789183400a b d e + 4341887550a b d e - 1736755020a b d e +--R + +--R 6 19 5 +--R 289459170b d e +--R * +--R 5 +--R x +--R + +--R 6 14 10 5 15 9 4 2 16 8 +--R 289459170a d e - 1736755020a b d e + 4341887550a b d e +--R + +--R 3 3 17 7 2 4 18 6 5 19 5 +--R - 5789183400a b d e + 4341887550a b d e - 1736755020a b d e +--R + +--R 6 20 4 +--R 289459170b d e +--R * +--R 4 +--R x +--R + +--R 6 15 9 5 16 8 4 2 17 7 +--R 192972780a d e - 1157836680a b d e + 2894591700a b d e +--R + +--R 3 3 18 6 2 4 19 5 5 20 4 +--R - 3859455600a b d e + 2894591700a b d e - 1157836680a b d e +--R + +--R 6 21 3 +--R 192972780b d e +--R * +--R 3 +--R x +--R + +--R 6 16 8 5 17 7 4 2 18 6 +--R 82702620a d e - 496215720a b d e + 1240539300a b d e +--R + +--R 3 3 19 5 2 4 20 4 5 21 3 +--R - 1654052400a b d e + 1240539300a b d e - 496215720a b d e +--R + +--R 6 22 2 +--R 82702620b d e +--R * +--R 2 +--R x +--R + +--R 6 17 7 5 18 6 4 2 19 5 +--R 20675655a d e - 124053930a b d e + 310134825a b d e +--R + +--R 3 3 20 4 2 4 21 3 5 22 2 +--R - 413513100a b d e + 310134825a b d e - 124053930a b d e +--R + +--R 6 23 +--R 20675655b d e +--R * +--R x +--R + +--R 6 18 6 5 19 5 4 2 20 4 +--R 2297295a d e - 13783770a b d e + 34459425a b d e +--R + +--R 3 3 21 3 2 4 22 2 5 23 6 24 +--R - 45945900a b d e + 34459425a b d e - 13783770a b d e + 2297295b d +--R Type: Union(Expression(Integer),...) +--E 1101 + +--S 1102 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 8 9 5 +--R (45045A a d + 405405A a )e +--R + +--R 7 8 2 8 9 4 +--R ((- 255255A a b + 6006B a )d + (- 2297295A a b + 54054B a )d)e +--R + +--R 6 2 7 3 7 2 8 2 3 +--R ((589050A a b - 31416B a b)d + (5301450A a b - 282744B a b)d )e +--R + +--R 5 3 6 2 4 6 3 7 2 3 2 +--R ((- 696150A a b + 64260B a b )d + (- 6265350A a b + 578340B a b )d )e +--R + +--R 4 4 5 3 5 5 4 6 3 4 +--R ((425425A a b - 61880B a b )d + (3828825A a b - 556920B a b )d )e +--R + +--R 3 5 4 4 6 4 5 5 4 5 +--R (- 109395A a b + 24310B a b )d + (- 984555A a b + 218790B a b )d +--R / +--R 6 9 6 5 10 5 4 2 11 4 3 3 12 3 +--R 2297295a d e - 13783770a b d e + 34459425a b d e - 45945900a b d e +--R + +--R 2 4 13 2 5 14 6 15 +--R 34459425a b d e - 13783770a b d e + 2297295b d +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1103 + +)clear all + +--S 1104 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/sqrt(a+b*x) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1293 +r0:=-5/64*(b*d-a*e)^3*(b*B*d-8*A*b*e+7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*e^(3/2))-_ + 5/96*(b*d-a*e)*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a+b*x)/(b^3*e)-1/24*(b*B*d-8*A*b*e+7*a*B*e)*(d+e*x)^(5/2)*_ + sqrt(a+b*x)/(b^2*e)+1/4*B*(d+e*x)^(7/2)*sqrt(a+b*x)/(b*e)-_ + 5/64*(b*d-a*e)^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e) +--R +--R +--R (2) +--R 3 4 4 2 2 3 3 +--R (- 120A a b + 105B a )e + (360A a b - 300B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 360A a b + 270B a b )d e + (120A b - 60B a b )d e - 15B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 3 3 3 2 3 3 2 2 +--R 48B b e x + ((64A b - 56B a b )e + 136B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 80A a b + 70B a b)e + (208A b - 172B a b )d e + 118B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (120A a b - 105B a )e + (- 320A a b + 265B a b)d e +--R + +--R 3 2 2 3 3 +--R (264A b - 191B a b )d e + 15B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 4 +-+ +-+ +--R 192b e\|b \|e +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1293 +--a0:=integrate(t0,x) +--E 1106 + +--S 1107 of 1293 +--m0:=a0-r0 +--E 1107 + +--S 1108 of 1293 +--d0:=D(m0,x) +--E 1108 + +)clear all + +--S 1109 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/sqrt(a+b*x) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1293 +r0:=-1/8*(b*d-a*e)^2*(b*B*d-6*A*b*e+5*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*e^(3/2))-_ + 1/12*(b*B*d-6*A*b*e+5*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^2*e)+_ + 1/3*B*(d+e*x)^(5/2)*sqrt(a+b*x)/(b*e)-1/8*(b*d-a*e)*_ + (b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/(b^3*e) +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (18A a b - 15B a )e + (- 36A a b + 27B a b)d e +--R + +--R 3 2 2 3 3 +--R (18A b - 9B a b )d e - 3B b d +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 2 +--R 8B b e x + ((12A b - 10B a b)e + 14B b d e)x +--R + +--R 2 2 2 2 2 +--R (- 18A a b + 15B a )e + (30A b - 22B a b)d e + 3B b d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|e \|b x + a \|e x + d +--R / +--R 3 +-+ +-+ +--R 24b e\|b \|e +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1293 +--a0:=integrate(t0,x) +--E 1111 + +--S 1112 of 1293 +--m0:=a0-r0 +--E 1112 + +--S 1113 of 1293 +--d0:=D(m0,x) +--E 1113 + +)clear all + +--S 1114 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/sqrt(a+b*x) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1293 +r0:=-1/4*(b*d-a*e)*(b*B*d-4*A*b*e+3*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*e^(3/2))+_ + 1/2*B*(d+e*x)^(3/2)*sqrt(a+b*x)/(b*e)-1/4*(b*B*d-4*A*b*e+3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R ((- 4A a b + 3B a )e + (4A b - 2B a b)d e - B b d ) +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2B b e x + (4A b - 3B a)e + B b d)\|b \|e \|b x + a \|e x + d +--R / +--R 2 +-+ +-+ +--R 4b e\|b \|e +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1293 +--a0:=integrate(t0,x) +--E 1116 + +--S 1117 of 1293 +--m0:=a0-r0 +--E 1117 + +--S 1118 of 1293 +--d0:=D(m0,x) +--E 1118 + +)clear all + +--S 1119 of 1293 +t0:=(A+B*x)/(sqrt(a+b*x)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1293 +r0:=(2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ + (b^(3/2)*e^(3/2))+B*sqrt(a+b*x)*sqrt(d+e*x)/(b*e) +--R +--R +--R (2) +--R +-+ +-------+ +--R \|e \|b x + a +-+ +-+ +-------+ +-------+ +--R ((2A b - B a)e - B b d)atanh(--------------) + B\|b \|e \|b x + a \|e x + d +--R +-+ +-------+ +--R \|b \|e x + d +--R ---------------------------------------------------------------------------- +--R +-+ +-+ +--R b e\|b \|e +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1293 +--a0:=integrate(t0,x) +--E 1121 + +--S 1122 of 1293 +--m0:=a0-r0 +--E 1122 + +--S 1123 of 1293 +--d0:=D(m0,x) +--E 1123 + +)clear all + +--S 1124 of 1293 +t0:=(A+B*x)/((d+e*x)^(3/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (e x + d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1293 +r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(3/2)*sqrt(b))-_ + 2*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R (2B a e - 2B b d)\|e x + d atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (- 2A e + 2B d)\|b \|e \|b x + a +--R / +--R 2 +-+ +-+ +-------+ +--R (a e - b d e)\|b \|e \|e x + d +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1293 +--a0:=integrate(t0,x) +--E 1126 + +--S 1127 of 1293 +--m0:=a0-r0 +--E 1127 + +--S 1128 of 1293 +--d0:=D(m0,x) +--E 1128 + +)clear all + +--S 1129 of 1293 +t0:=(A+B*x)/((d+e*x)^(5/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (e x + 2d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1293 +r0:=-2/3*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ + 2/3*(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*sqrt(d+e*x)) +--R +--R +--R +-------+ +--R (((4A b - 6B a)e + 2B b d)x - 2A a e + (6A b - 4B a)d)\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +-------+ +--R ((3a e - 6a b d e + 3b d e)x + 3a d e - 6a b d e + 3b d )\|e x + d +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 3 +-------+ +--R (((4A b - 6B a)d e + 2B b d )x - 2A a d e + (6A b - 4B a)d )\|b x + a +--R * +--R +-------+ +--R \|e x + d +--R + +--R 2 3 2 2 2 2 +--R ((A a d + A a )e + ((- 3A b + 2B a)d + (- 3A a b + 2B a )d)e )x +--R + +--R 2 2 2 3 2 2 +--R ((2A a d + 2A a d)e + ((- 6A b + 4B a)d + (- 6A a b + 4B a )d )e)x +--R + +--R 3 2 2 4 2 3 +--R (A a d + A a d )e + (- 3A b + 2B a)d + (- 3A a b + 2B a )d +--R / +--R 2 2 4 3 3 2 4 2 2 2 3 3 4 2 2 5 +--R (3a d e - 6a b d e + 3b d e )x + (6a d e - 12a b d e + 6b d e)x +--R + +--R 2 4 2 5 2 6 +--R 3a d e - 6a b d e + 3b d +--R Type: Union(Expression(Integer),...) +--E 1131 + +--S 1132 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (A a d + A a )e + (- 3A b + 2B a)d + (- 3A a b + 2B a )d +--R (4) --------------------------------------------------------- +--R 2 2 2 3 2 4 +--R 3a d e - 6a b d e + 3b d +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1133 + +)clear all + +--S 1134 of 1293 +t0:=(A+B*x)/((d+e*x)^(7/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1) -------------------------------------------------- +--R 3 3 2 2 2 3 +-------+ +-------+ +--R (e x + 3d e x + 3d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1293 +r0:=-2/5*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ + 2/15*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + 4/15*b*(b*B*d+4*A*b*e-5*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 16A b + 20B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((8A a b - 10B a )e + (- 40A b + 52B a b)d e - 10B b d )x - 6A a e +--R + +--R 2 2 2 +--R (20A a b - 4B a )d e + (- 30A b + 20B a b)d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (15a e - 45a b d e + 45a b d e - 15b d e )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (30a d e - 90a b d e + 90a b d e - 30b d e)x + 15a d e - 45a b d e +--R + +--R 2 4 3 5 +--R 45a b d e - 15b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 4 2 +--R ((- 64A b + 80B a b)d e - 16B b d e)x +--R + +--R 2 3 2 2 4 2 5 +--R ((32A a b - 40B a )d e + (- 160A b + 208B a b)d e - 40B b d )x +--R + +--R 2 3 2 2 4 2 5 +--R - 24A a d e + (80A a b - 16B a )d e + (- 120A b + 80B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 5 +--R (3A a d + 48A a )e +--R + +--R 2 2 2 3 4 +--R ((- 10A a b + 2B a )d + (- 160A a b + 32B a )d)e +--R + +--R 2 3 2 2 2 3 +--R ((15A b - 10B a b)d + (240A a b - 160B a b)d )e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 +--R (9A a d + 144A a d)e +--R + +--R 2 3 2 3 2 3 +--R ((- 30A a b + 6B a )d + (- 480A a b + 96B a )d )e +--R + +--R 2 4 2 2 3 2 +--R ((45A b - 30B a b)d + (720A a b - 480B a b)d )e +--R * +--R 2 +--R x +--R + +--R 2 3 3 2 3 +--R (9A a d + 144A a d )e +--R + +--R 2 4 2 3 3 2 +--R ((- 30A a b + 6B a )d + (- 480A a b + 96B a )d )e +--R + +--R 2 5 2 2 4 +--R ((45A b - 30B a b)d + (720A a b - 480B a b)d )e +--R * +--R x +--R + +--R 2 4 3 3 2 +--R (3A a d + 48A a d )e +--R + +--R 2 5 2 3 4 2 6 +--R ((- 10A a b + 2B a )d + (- 160A a b + 32B a )d )e + (15A b - 10B a b)d +--R + +--R 2 2 5 +--R (240A a b - 160B a b)d +--R / +--R 3 3 6 2 4 5 2 5 4 3 6 3 3 +--R (60a d e - 180a b d e + 180a b d e - 60b d e )x +--R + +--R 3 4 5 2 5 4 2 6 3 3 7 2 2 +--R (180a d e - 540a b d e + 540a b d e - 180b d e )x +--R + +--R 3 5 4 2 6 3 2 7 2 3 8 3 6 3 +--R (180a d e - 540a b d e + 540a b d e - 180b d e)x + 60a d e +--R + +--R 2 7 2 2 8 3 9 +--R - 180a b d e + 180a b d e - 60b d +--R Type: Union(Expression(Integer),...) +--E 1136 + +--S 1137 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 3 +--R (3A a d + 48A a )e + ((- 10A a b + 2B a )d + (- 160A a b + 32B a )d)e +--R + +--R 2 3 2 2 2 +--R (15A b - 10B a b)d + (240A a b - 160B a b)d +--R / +--R 3 3 3 2 4 2 2 5 3 6 +--R 60a d e - 180a b d e + 180a b d e - 60b d +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1138 + +)clear all + +--S 1139 of 1293 +t0:=(A+B*x)/((d+e*x)^(9/2)*sqrt(a+b*x)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +-------+ +-------+ +--R (e x + 4d e x + 6d e x + 4d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1293 +r0:=-2/7*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ + 2/35*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + 8/105*b*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^3*_ + (d+e*x)^(3/2))+16/105*b^2*(b*B*d+6*A*b*e-7*a*B*e)*_ + sqrt(a+b*x)/(e*(b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((96A b - 112B a b )e + 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 48A a b + 56B a b)e + (336A b - 400B a b )d e + 56B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (36A a b - 42B a )e + (- 168A a b + 202B a b)d e +--R + +--R 3 2 2 3 3 +--R (420A b - 518B a b )d e + 70B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 30A a e + (126A a b - 12B a )d e + (- 210A a b + 56B a b)d e +--R + +--R 3 2 3 +--R (210A b - 140B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 4 7 3 6 2 2 2 5 3 3 4 4 4 3 3 +--R (105a e - 420a b d e + 630a b d e - 420a b d e + 105b d e )x +--R + +--R 4 6 3 2 5 2 2 3 4 3 4 3 4 5 2 2 +--R (315a d e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d e )x +--R + +--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4 6 +--R (315a d e - 1260a b d e + 1890a b d e - 1260a b d e + 315b d e)x +--R + +--R 4 3 4 3 4 3 2 2 5 2 3 6 4 7 +--R 105a d e - 420a b d e + 630a b d e - 420a b d e + 105b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 3 5 2 3 +--R ((96A b - 112B a b )d e + 16B b d e )x +--R + +--R 2 2 4 3 3 2 5 2 +--R (- 48A a b + 56B a b)d e + (336A b - 400B a b )d e +--R + +--R 3 6 +--R 56B b d e +--R * +--R 2 +--R x +--R + +--R 2 3 4 3 2 2 5 2 +--R (36A a b - 42B a )d e + (- 168A a b + 202B a b)d e +--R + +--R 3 2 6 3 7 +--R (420A b - 518B a b )d e + 70B b d +--R * +--R x +--R + +--R 3 4 3 2 3 5 2 2 2 6 +--R - 30A a d e + (126A a b - 12B a )d e + (- 210A a b + 56B a b)d e +--R + +--R 3 2 7 +--R (210A b - 140B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 7 2 3 2 3 4 6 +--R (- 15A a d - 15A a )e + ((63A a b - 6B a )d + (63A a b - 6B a )d)e +--R + +--R 2 2 3 2 2 3 2 5 +--R ((- 105A a b + 28B a b)d + (- 105A a b + 28B a b)d )e +--R + +--R 3 2 4 3 2 2 3 4 +--R ((105A b - 70B a b )d + (105A a b - 70B a b )d )e +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 +--R (- 60A a d - 60A a d)e +--R + +--R 2 3 3 3 4 2 5 +--R ((252A a b - 24B a )d + (252A a b - 24B a )d )e +--R + +--R 2 2 4 2 2 3 3 4 +--R ((- 420A a b + 112B a b)d + (- 420A a b + 112B a b)d )e +--R + +--R 3 2 5 3 2 2 4 3 +--R ((420A b - 280B a b )d + (420A a b - 280B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 3 4 2 5 +--R (- 90A a d - 90A a d )e +--R + +--R 2 3 4 3 4 3 4 +--R ((378A a b - 36B a )d + (378A a b - 36B a )d )e +--R + +--R 2 2 5 2 2 3 4 3 +--R ((- 630A a b + 168B a b)d + (- 630A a b + 168B a b)d )e +--R + +--R 3 2 6 3 2 2 5 2 +--R ((630A b - 420B a b )d + (630A a b - 420B a b )d )e +--R * +--R 2 +--R x +--R + +--R 3 4 4 3 4 +--R (- 60A a d - 60A a d )e +--R + +--R 2 3 5 3 4 4 3 +--R ((252A a b - 24B a )d + (252A a b - 24B a )d )e +--R + +--R 2 2 6 2 2 3 5 2 +--R ((- 420A a b + 112B a b)d + (- 420A a b + 112B a b)d )e +--R + +--R 3 2 7 3 2 2 6 +--R ((420A b - 280B a b )d + (420A a b - 280B a b )d )e +--R * +--R x +--R + +--R 3 5 4 4 3 2 3 6 3 4 5 2 +--R (- 15A a d - 15A a d )e + ((63A a b - 6B a )d + (63A a b - 6B a )d )e +--R + +--R 2 2 7 2 2 3 6 +--R ((- 105A a b + 28B a b)d + (- 105A a b + 28B a b)d )e +--R + +--R 3 2 8 3 2 2 7 +--R (105A b - 70B a b )d + (105A a b - 70B a b )d +--R / +--R 4 4 8 3 5 7 2 2 6 6 3 7 5 4 8 4 4 +--R (105a d e - 420a b d e + 630a b d e - 420a b d e + 105b d e )x +--R + +--R 4 5 7 3 6 6 2 2 7 5 3 8 4 4 9 3 3 +--R (420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--R + +--R 4 6 6 3 7 5 2 2 8 4 3 9 3 4 10 2 2 +--R (630a d e - 2520a b d e + 3780a b d e - 2520a b d e + 630b d e )x +--R + +--R 4 7 5 3 8 4 2 2 9 3 3 10 2 4 11 +--R (420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e)x +--R + +--R 4 8 4 3 9 3 2 2 10 2 3 11 4 12 +--R 105a d e - 420a b d e + 630a b d e - 420a b d e + 105b d +--R Type: Union(Expression(Integer),...) +--E 1141 + +--S 1142 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 3 2 3 4 2 +--R (- 15A a d - 15A a )e + ((63A a b - 6B a )d + (63A a b - 6B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((- 105A a b + 28B a b)d + (- 105A a b + 28B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (105A b - 70B a b )d + (105A a b - 70B a b )d +--R / +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 8 +--R 105a d e - 420a b d e + 630a b d e - 420a b d e + 105b d +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1143 + +)clear all + +--S 1144 of 1293 +t0:=(A+B*x)/((d+e*x)^(11/2)*sqrt(a+b*x)) +--R +--R +--R (1) +--R B x + A +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +-------+ +--R (e x + 5d e x + 10d e x + 10d e x + 5d e x + d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1293 +r0:=-2/9*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ + 2/63*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^2*(d+e*x)^(7/2))+_ + 4/105*b*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/_ + (e*(b*d-a*e)^3*(d+e*x)^(5/2))+16/315*b^2*(b*B*d+8*A*b*e-9*a*B*e)*_ + sqrt(a+b*x)/(e*(b*d-a*e)^4*(d+e*x)^(3/2))+_ + 32/315*b^3*(b*B*d+8*A*b*e-9*a*B*e)*sqrt(a+b*x)/(e*(b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 256A b + 288B a b )e - 32B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (128A a b - 144B a b )e + (- 1152A b + 1312B a b )d e +--R + +--R 4 2 2 +--R - 144B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 96A a b + 108B a b)e + (576A a b - 660B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 2016A b + 2340B a b )d e - 252B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (80A a b - 90B a )e + (- 432A a b + 496B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 +--R (1008A a b - 1188B a b )d e + (- 1680A b + 2016B a b )d e +--R + +--R 4 4 +--R - 210B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 70A a e + (360A a b - 20B a )d e + (- 756A a b + 108B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (840A a b - 252B a b )d e + (- 630A b + 420B a b )d +--R * +--R +-------+ +--R \|b x + a +--R / +--R 5 9 4 8 3 2 2 7 2 3 3 6 4 4 5 +--R 315a e - 1575a b d e + 3150a b d e - 3150a b d e + 1575a b d e +--R + +--R 5 5 4 +--R - 315b d e +--R * +--R 4 +--R x +--R + +--R 5 8 4 2 7 3 2 3 6 2 3 4 5 +--R 1260a d e - 6300a b d e + 12600a b d e - 12600a b d e +--R + +--R 4 5 4 5 6 3 +--R 6300a b d e - 1260b d e +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 2 4 5 2 3 5 4 +--R 1890a d e - 9450a b d e + 18900a b d e - 18900a b d e +--R + +--R 4 6 3 5 7 2 +--R 9450a b d e - 1890b d e +--R * +--R 2 +--R x +--R + +--R 5 3 6 4 4 5 3 2 5 4 2 3 6 3 +--R 1260a d e - 6300a b d e + 12600a b d e - 12600a b d e +--R + +--R 4 7 2 5 8 +--R 6300a b d e - 1260b d e +--R * +--R x +--R + +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 4 8 +--R 315a d e - 1575a b d e + 3150a b d e - 3150a b d e + 1575a b d e +--R + +--R 5 9 +--R - 315b d +--R * +--R +-------+ +--R \|e x + d +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 5 4 4 6 3 4 +--R ((- 768A b + 864B a b )d e - 96B b d e )x +--R + +--R 3 2 2 5 4 4 3 6 3 +--R (384A a b - 432B a b )d e + (- 3456A b + 3936B a b )d e +--R + +--R 4 7 2 +--R - 432B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 5 4 3 2 2 6 3 +--R (- 288A a b + 324B a b)d e + (1728A a b - 1980B a b )d e +--R + +--R 4 3 7 2 4 8 +--R (- 6048A b + 7020B a b )d e - 756B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 5 4 2 2 3 6 3 +--R (240A a b - 270B a )d e + (- 1296A a b + 1488B a b)d e +--R + +--R 3 2 2 7 2 4 3 8 +--R (3024A a b - 3564B a b )d e + (- 5040A b + 6048B a b )d e +--R + +--R 4 9 +--R - 630B b d +--R * +--R x +--R + +--R 4 5 4 3 4 6 3 +--R - 210A a d e + (1080A a b - 60B a )d e +--R + +--R 2 2 3 7 2 3 2 2 8 +--R (- 2268A a b + 324B a b)d e + (2520A a b - 756B a b )d e +--R + +--R 4 3 9 +--R (- 1890A b + 1260B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 9 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 8 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 7 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 6 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 5 4 2 3 4 5 +--R ((- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d )e +--R * +--R 5 +--R x +--R + +--R 4 2 5 8 +--R (- 175A a d - 1575A a d)e +--R + +--R 3 4 3 4 5 2 7 +--R ((900A a b - 50B a )d + (8100A a b - 450B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 6 +--R ((- 1890A a b + 270B a b)d + (- 17010A a b + 2430B a b)d )e +--R + +--R 3 2 2 5 2 3 3 2 4 5 +--R ((2100A a b - 630B a b )d + (18900A a b - 5670B a b )d )e +--R + +--R 4 3 6 4 2 3 5 4 +--R ((- 1575A b + 1050B a b )d + (- 14175A a b + 9450B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 7 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 4 4 5 3 6 +--R ((1800A a b - 100B a )d + (16200A a b - 900B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 5 +--R ((- 3780A a b + 540B a b)d + (- 34020A a b + 4860B a b)d )e +--R + +--R 3 2 2 6 2 3 3 2 5 4 +--R ((4200A a b - 1260B a b )d + (37800A a b - 11340B a b )d )e +--R + +--R 4 3 7 4 2 3 6 3 +--R ((- 3150A b + 2100B a b )d + (- 28350A a b + 18900B a b )d )e +--R * +--R 3 +--R x +--R + +--R 4 4 5 3 6 +--R (- 350A a d - 3150A a d )e +--R + +--R 3 4 5 4 5 4 5 +--R ((1800A a b - 100B a )d + (16200A a b - 900B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 4 +--R ((- 3780A a b + 540B a b)d + (- 34020A a b + 4860B a b)d )e +--R + +--R 3 2 2 7 2 3 3 2 6 3 +--R ((4200A a b - 1260B a b )d + (37800A a b - 11340B a b )d )e +--R + +--R 4 3 8 4 2 3 7 2 +--R ((- 3150A b + 2100B a b )d + (- 28350A a b + 18900B a b )d )e +--R * +--R 2 +--R x +--R + +--R 4 5 5 4 5 +--R (- 175A a d - 1575A a d )e +--R + +--R 3 4 6 4 5 5 4 +--R ((900A a b - 50B a )d + (8100A a b - 450B a )d )e +--R + +--R 2 2 3 7 3 2 4 6 3 +--R ((- 1890A a b + 270B a b)d + (- 17010A a b + 2430B a b)d )e +--R + +--R 3 2 2 8 2 3 3 2 7 2 +--R ((2100A a b - 630B a b )d + (18900A a b - 5670B a b )d )e +--R + +--R 4 3 9 4 2 3 8 +--R ((- 1575A b + 1050B a b )d + (- 14175A a b + 9450B a b )d )e +--R * +--R x +--R + +--R 4 6 5 5 4 +--R (- 35A a d - 315A a d )e +--R + +--R 3 4 7 4 5 6 3 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d )e +--R + +--R 2 2 3 8 3 2 4 7 2 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 9 2 3 3 2 8 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 10 4 2 3 9 +--R (- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d +--R / +--R 5 5 10 4 6 9 3 2 7 8 2 3 8 7 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e +--R + +--R 4 9 6 5 10 5 +--R 4725a b d e - 945b d e +--R * +--R 5 +--R x +--R + +--R 5 6 9 4 7 8 3 2 8 7 2 3 9 6 +--R 4725a d e - 23625a b d e + 47250a b d e - 47250a b d e +--R + +--R 4 10 5 5 11 4 +--R 23625a b d e - 4725b d e +--R * +--R 4 +--R x +--R + +--R 5 7 8 4 8 7 3 2 9 6 2 3 10 5 +--R 9450a d e - 47250a b d e + 94500a b d e - 94500a b d e +--R + +--R 4 11 4 5 12 3 +--R 47250a b d e - 9450b d e +--R * +--R 3 +--R x +--R + +--R 5 8 7 4 9 6 3 2 10 5 2 3 11 4 +--R 9450a d e - 47250a b d e + 94500a b d e - 94500a b d e +--R + +--R 4 12 3 5 13 2 +--R 47250a b d e - 9450b d e +--R * +--R 2 +--R x +--R + +--R 5 9 6 4 10 5 3 2 11 4 2 3 12 3 +--R 4725a d e - 23625a b d e + 47250a b d e - 47250a b d e +--R + +--R 4 13 2 5 14 +--R 23625a b d e - 4725b d e +--R * +--R x +--R + +--R 5 10 5 4 11 4 3 2 12 3 2 3 13 2 4 14 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e + 4725a b d e +--R + +--R 5 15 +--R - 945b d +--R Type: Union(Expression(Integer),...) +--E 1146 + +--S 1147 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 +--R (- 35A a d - 315A a )e +--R + +--R 3 4 2 4 5 3 +--R ((180A a b - 10B a )d + (1620A a b - 90B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((- 378A a b + 54B a b)d + (- 3402A a b + 486B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((420A a b - 126B a b )d + (3780A a b - 1134B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (- 315A b + 210B a b )d + (- 2835A a b + 1890B a b )d +--R / +--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2 4 9 +--R 945a d e - 4725a b d e + 9450a b d e - 9450a b d e + 4725a b d e +--R + +--R 5 10 +--R - 945b d +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1148 + +)clear all + +--S 1149 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1293 +r0:=5/8*(b*d-a*e)^2*(b*B*d+6*A*b*e-7*a*B*e)*_ + atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(b^(9/2)*sqrt(e))-_ + 2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*sqrt(a+b*x))+_ + 5/12*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^3+_ + 1/3*(b*B*d+6*A*b*e-7*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/(b^2*(b*d-a*e))+_ + 5/8*(b*d-a*e)*(b*B*d+6*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 +--R (90A a b - 105B a )e + (- 180A a b + 225B a b)d e +--R + +--R 3 2 2 3 3 +--R (90A b - 135B a b )d e + 15B b d +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 3 3 2 2 3 2 +--R 8B b e x + ((12A b - 14B a b )e + 26B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((- 30A a b + 35B a b)e + (54A b - 68B a b )d e + 33B b d )x +--R + +--R 2 3 2 2 2 +--R (- 90A a b + 105B a )e + (150A a b - 190B a b)d e +--R + +--R 3 2 2 +--R (- 48A b + 81B a b )d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|e x + d +--R / +--R 4 +-+ +-+ +-------+ +--R 24b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1293 +--a0:=integrate(t0,x) +--E 1151 + +--S 1152 of 1293 +--m0:=a0-r0 +--E 1152 + +--S 1153 of 1293 +--d0:=D(m0,x) +--E 1153 + +)clear all + +--S 1154 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1293 +r0:=3/4*(b*d-a*e)*(b*B*d+4*A*b*e-5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(7/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(5/2)/_ + (b*(b*d-a*e)*sqrt(a+b*x))+1/2*(b*B*d+4*A*b*e-5*a*B*e)*(d+e*x)^(3/2)*_ + sqrt(a+b*x)/(b^2*(b*d-a*e))+3/4*(b*B*d+4*A*b*e-5*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +-------+ +--R ((- 12A a b + 15B a )e + (12A b - 18B a b)d e + 3B b d )\|b x + a +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 +--R 2B b e x + ((4A b - 5B a b)e + 5B b d)x + (12A a b - 15B a )e +--R + +--R 2 +--R (- 8A b + 13B a b)d +--R * +--R +-+ +-+ +-------+ +--R \|b \|e \|e x + d +--R / +--R 3 +-+ +-+ +-------+ +--R 4b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1293 +--a0:=integrate(t0,x) +--E 1156 + +--S 1157 of 1293 +--m0:=a0-r0 +--E 1157 + +--S 1158 of 1293 +--d0:=D(m0,x) +--E 1158 + +)clear all + +--S 1159 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^(3/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1293 +r0:=(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))/(b^(5/2)*sqrt(e))-2*(A*b-a*B)*(d+e*x)^(3/2)/_ + (b*(b*d-a*e)*sqrt(a+b*x))+(b*B*d+2*A*b*e-3*a*B*e)*sqrt(a+b*x)*_ + sqrt(d+e*x)/(b^2*(b*d-a*e)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R ((2A b - 3B a)e + B b d)\|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (B b x - 2A b + 3B a)\|b \|e \|e x + d +--R / +--R 2 +-+ +-+ +-------+ +--R b \|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1293 +--a0:=integrate(t0,x) +--E 1161 + +--S 1162 of 1293 +--m0:=a0-r0 +--E 1162 + +--S 1163 of 1293 +--d0:=D(m0,x) +--E 1163 + +)clear all + +--S 1164 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (b x + a)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1293 +r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ + (b^(3/2)*sqrt(e))-2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*sqrt(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R (2B a e - 2B b d)\|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R +-+ +-+ +-------+ +--R (2A b - 2B a)\|b \|e \|e x + d +--R / +--R 2 +-+ +-+ +-------+ +--R (a b e - b d)\|b \|e \|b x + a +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1293 +--a0:=integrate(t0,x) +--E 1166 + +--S 1167 of 1293 +--m0:=a0-r0 +--E 1167 + +--S 1168 of 1293 +--d0:=D(m0,x) +--E 1168 + +)clear all + +--S 1169 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(3/2)) +--R +--R +--R B x + A +--R (1) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b e x + (a e + b d)x + a d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1293 +r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*sqrt(a+b*x)*sqrt(d+e*x))+_ + 2*(b*B*d-2*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*sqrt(a+b*x)) +--R +--R +--R ((- 4A b + 2B a)e + 2B b d)x - 2A a e + (- 2A b + 4B a)d +--R (2) -------------------------------------------------------- +--R 2 2 2 2 +-------+ +-------+ +--R (a e - 2a b d e + b d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R ((- 8A a b + 4B a )d e + 4B a b d )x - 4A a d e +--R + +--R 2 2 +--R (- 4A a b + 8B a )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 +--R (- A a b d - 4A a b)e +--R + +--R 2 2 2 2 +--R ((- A b + 2B a b)d + (- 4A a b + 8B a b)d)e +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 3 +--R (- A a d - 4A a )e + ((- 2A a b + 2B a )d + (- 8A a b + 8B a )d)e +--R + +--R 2 3 2 2 2 +--R (- A b + 2B a b)d + (- 4A a b + 8B a b)d +--R * +--R x +--R + +--R 2 2 3 2 3 2 3 2 +--R (- A a d - 4A a d)e + (- A a b + 2B a )d + (- 4A a b + 8B a )d +--R / +--R 3 3 2 2 2 2 3 3 2 +--R (2a b d e - 4a b d e + 2a b d e)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 2 2 4 +--R (2a d e - 2a b d e - 2a b d e + 2a b d )x + 2a d e - 4a b d e + 2a b d +--R Type: Union(Expression(Integer),...) +--E 1171 + +--S 1172 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (- A a d - 4A a )e + (- A b + 2B a)d + (- 4A a b + 8B a )d +--R (4) ----------------------------------------------------------- +--R 3 2 2 2 2 3 +--R 2a d e - 4a b d e + 2a b d +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1173 + +)clear all + +--S 1174 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b e x + (a e + 2b d e)x + (2a d e + b d )x + a d )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a+b*x))+_ + 2/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+_ + 4/3*(b*B*d-4*A*b*e+3*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((16A b - 12B a b)e - 4B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((8A a b - 6B a )e + (24A b - 20B a b)d e - 6B b d )x - 2A a e +--R + +--R 2 2 2 +--R (12A a b - 4B a )d e + (6A b - 12B a b)d +--R / +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (3a e - 9a b d e + 9a b d e - 3b d e)x + 3a d e - 9a b d e +--R + +--R 2 3 3 4 +--R 9a b d e - 3b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 3 2 +--R ((32A a b - 24B a b)d e - 8B a b d e)x +--R + +--R 2 3 2 2 2 2 3 2 4 +--R ((16A a b - 12B a )d e + (48A a b - 40B a b)d e - 12B a b d )x +--R + +--R 3 2 2 2 3 3 2 2 4 +--R - 4A a d e + (24A a b - 8B a )d e + (12A a b - 24B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 3 4 +--R (A a b d + 4A a b)e +--R + +--R 2 2 2 2 2 3 3 +--R ((- 6A a b + 2B a b)d + (- 24A a b + 8B a b)d)e +--R + +--R 3 2 3 3 2 2 2 2 +--R ((- 3A b + 6B a b )d + (- 12A a b + 24B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 4 4 2 3 2 3 4 3 +--R (A a d + 4A a )e + ((- 4A a b + 2B a )d + (- 16A a b + 8B a )d)e +--R + +--R 2 2 3 2 2 3 2 2 +--R ((- 15A a b + 10B a b)d + (- 60A a b + 40B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R ((- 6A b + 12B a b )d + (- 24A a b + 48B a b )d )e +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 +--R (2A a d + 8A a d)e +--R + +--R 2 3 3 3 4 2 2 +--R ((- 11A a b + 4B a )d + (- 44A a b + 16B a )d )e +--R + +--R 2 2 4 2 2 3 3 +--R ((- 12A a b + 14B a b)d + (- 48A a b + 56B a b)d )e +--R + +--R 3 2 5 3 2 2 4 +--R (- 3A b + 6B a b )d + (- 12A a b + 24B a b )d +--R * +--R x +--R + +--R 3 3 4 2 2 2 3 4 3 4 3 +--R (A a d + 4A a d )e + ((- 6A a b + 2B a )d + (- 24A a b + 8B a )d )e +--R + +--R 2 2 5 2 2 3 4 +--R (- 3A a b + 6B a b)d + (- 12A a b + 24B a b)d +--R / +--R 4 2 5 3 2 3 4 2 3 4 3 4 5 2 3 +--R (6a b d e - 18a b d e + 18a b d e - 6a b d e )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (6a d e - 6a b d e - 18a b d e + 30a b d e - 12a b d e)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (12a d e - 30a b d e + 18a b d e + 6a b d e - 6a b d )x + 6a d e +--R + +--R 4 5 2 3 2 6 2 3 7 +--R - 18a b d e + 18a b d e - 6a b d +--R Type: Union(Expression(Integer),...) +--E 1176 + +--S 1177 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 3 +--R (A a d + 4A a )e + ((- 6A a b + 2B a )d + (- 24A a b + 8B a )d)e +--R + +--R 2 3 2 2 2 +--R (- 3A b + 6B a b)d + (- 12A a b + 24B a b)d +--R / +--R 4 2 3 3 3 2 2 2 4 3 5 +--R 6a d e - 18a b d e + 18a b d e - 6a b d +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1178 + +)clear all + +--S 1179 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(7/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 3 4 3 2 3 2 2 2 2 3 +--R b e x + (a e + 3b d e )x + (3a d e + 3b d e)x + (3a d e + b d )x +--R + +--R 3 +--R a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a+b*x))+_ + 2/5*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+_ + 8/15*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(3/2))+_ + 16/15*b*(b*B*d-6*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((- 96A b + 80B a b )e + 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 48A a b + 40B a b)e + (- 240A b + 208B a b )d e + 40B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (12A a b - 10B a )e + (- 120A a b + 98B a b)d e +--R + +--R 3 2 2 3 3 +--R (- 180A b + 170B a b )d e + 30B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 6A a e + (30A a b - 4B a )d e + (- 90A a b + 40B a b)d e +--R + +--R 3 2 3 +--R (- 30A b + 60B a b )d +--R / +--R 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (15a e - 60a b d e + 90a b d e - 60a b d e + 15b d e )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a d e - 120a b d e + 180a b d e - 120a b d e + 30b d e)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a d e - 60a b d e + 90a b d e - 60a b d e + 15b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 3 3 4 2 3 +--R ((- 384A a b + 320B a b )d e + 64B a b d e )x +--R + +--R 2 2 3 3 3 3 2 2 4 2 +--R (- 192A a b + 160B a b)d e + (- 960A a b + 832B a b )d e +--R + +--R 3 5 +--R 160B a b d e +--R * +--R 2 +--R x +--R + +--R 3 4 3 3 2 2 3 4 2 +--R (48A a b - 40B a )d e + (- 480A a b + 392B a b)d e +--R + +--R 3 2 2 5 3 6 +--R (- 720A a b + 680B a b )d e + 120B a b d +--R * +--R x +--R + +--R 4 3 3 3 4 4 2 2 2 3 5 +--R - 24A a d e + (120A a b - 16B a )d e + (- 360A a b + 160B a b)d e +--R + +--R 3 2 2 6 +--R (- 120A a b + 240B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 4 6 +--R (3A a b d + 48A a b)e +--R + +--R 2 2 3 2 3 2 4 5 +--R ((- 15A a b + 2B a b)d + (- 240A a b + 32B a b)d)e +--R + +--R 3 2 2 3 2 3 3 2 2 4 +--R ((45A a b - 20B a b )d + (720A a b - 320B a b )d )e +--R + +--R 4 3 4 4 2 3 3 3 +--R ((15A b - 30B a b )d + (240A a b - 480B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 5 6 +--R (3A a d + 48A a )e +--R + +--R 3 4 2 4 5 5 +--R ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d)e +--R + +--R 3 3 4 2 4 +--R (- 14B a b d - 224B a b d )e +--R + +--R 3 2 2 4 2 3 3 2 3 3 +--R ((150A a b - 90B a b )d + (2400A a b - 1440B a b )d )e +--R + +--R 4 3 5 4 2 3 4 2 +--R ((45A b - 90B a b )d + (720A a b - 1440B a b )d )e +--R * +--R 3 +--R x +--R + +--R 4 2 5 5 +--R (9A a d + 144A a d)e +--R + +--R 3 4 3 4 5 2 4 +--R ((- 36A a b + 6B a )d + (- 576A a b + 96B a )d )e +--R + +--R 2 2 3 4 3 2 4 3 3 +--R ((90A a b - 54B a b)d + (1440A a b - 864B a b)d )e +--R + +--R 3 2 2 5 2 3 3 2 4 2 +--R ((180A a b - 150B a b )d + (2880A a b - 2400B a b )d )e +--R + +--R 4 3 6 4 2 3 5 +--R ((45A b - 90B a b )d + (720A a b - 1440B a b )d )e +--R * +--R 2 +--R x +--R + +--R 4 3 5 2 4 +--R (9A a d + 144A a d )e +--R + +--R 3 4 4 4 5 3 3 +--R ((- 42A a b + 6B a )d + (- 672A a b + 96B a )d )e +--R + +--R 2 2 3 5 3 2 4 4 2 +--R ((120A a b - 58B a b)d + (1920A a b - 928B a b)d )e +--R + +--R 3 2 2 6 2 3 3 2 5 +--R ((90A a b - 110B a b )d + (1440A a b - 1760B a b )d )e +--R + +--R 4 3 7 4 2 3 6 +--R (15A b - 30B a b )d + (240A a b - 480B a b )d +--R * +--R x +--R + +--R 4 4 5 3 3 +--R (3A a d + 48A a d )e +--R + +--R 3 4 5 4 5 4 2 +--R ((- 15A a b + 2B a )d + (- 240A a b + 32B a )d )e +--R + +--R 2 2 3 6 3 2 4 5 +--R ((45A a b - 20B a b)d + (720A a b - 320B a b)d )e +--R + +--R 3 2 2 7 2 3 3 2 6 +--R (15A a b - 30B a b )d + (240A a b - 480B a b )d +--R / +--R 5 3 7 4 2 4 6 3 3 5 5 2 4 6 4 5 7 3 4 +--R (60a b d e - 240a b d e + 360a b d e - 240a b d e + 60a b d e )x +--R + +--R 6 3 7 5 4 6 4 2 5 5 3 3 6 4 2 4 7 3 +--R 60a d e - 60a b d e - 360a b d e + 840a b d e - 660a b d e +--R + +--R 5 8 2 +--R 180a b d e +--R * +--R 3 +--R x +--R + +--R 6 4 6 5 5 5 4 2 6 4 3 3 7 3 2 4 8 2 +--R 180a d e - 540a b d e + 360a b d e + 360a b d e - 540a b d e +--R + +--R 5 9 +--R 180a b d e +--R * +--R 2 +--R x +--R + +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 2 4 9 +--R 180a d e - 660a b d e + 840a b d e - 360a b d e - 60a b d e +--R + +--R 5 10 +--R 60a b d +--R * +--R x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 2 4 10 +--R 60a d e - 240a b d e + 360a b d e - 240a b d e + 60a b d +--R Type: Union(Expression(Integer),...) +--E 1181 + +--S 1182 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 3 2 3 4 2 +--R (3A a d + 48A a )e + ((- 15A a b + 2B a )d + (- 240A a b + 32B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((45A a b - 20B a b)d + (720A a b - 320B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (15A b - 30B a b )d + (240A a b - 480B a b )d +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 +--R 60a d e - 240a b d e + 360a b d e - 240a b d e + 60a b d +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1183 + +)clear all + +--S 1184 of 1293 +t0:=(A+B*x)/((a+b*x)^(3/2)*(d+e*x)^(9/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 4 5 4 3 4 3 2 2 3 +--R b e x + (a e + 4b d e )x + (4a d e + 6b d e )x +--R + +--R 2 2 3 2 3 4 4 +--R (6a d e + 4b d e)x + (4a d e + b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1293 +r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a+b*x))+_ + 2/7*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/(b*(b*d-a*e)^2*(d+e*x)^(7/2))+_ + 12/35*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^3*(d+e*x)^(5/2))+_ + 16/35*b*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))+_ + 32/35*b^2*(b*B*d-8*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((256A b - 224B a b )e - 32B b d e )x +--R + +--R 3 2 2 4 4 3 3 4 2 2 3 +--R ((128A a b - 112B a b )e + (896A b - 800B a b )d e - 112B b d e )x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 32A a b + 28B a b)e + (448A a b - 388B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (1120A b - 1036B a b )d e - 140B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (16A a b - 14B a )e + (- 112A a b + 96B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (560A a b - 476B a b )d e + (560A b - 560B a b )d e - 70B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 10A a e + (56A a b - 4B a )d e + (- 140A a b + 28B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (280A a b - 140B a b )d e + (70A b - 140B a b )d +--R / +--R 5 8 4 7 3 2 2 6 2 3 3 5 4 4 4 +--R 35a e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 5 5 3 +--R - 35b d e +--R * +--R 3 +--R x +--R + +--R 5 7 4 2 6 3 2 3 5 2 3 4 4 4 5 3 +--R 105a d e - 525a b d e + 1050a b d e - 1050a b d e + 525a b d e +--R + +--R 5 6 2 +--R - 105b d e +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 5 3 2 4 4 2 3 5 3 4 6 2 +--R 105a d e - 525a b d e + 1050a b d e - 1050a b d e + 525a b d e +--R + +--R 5 7 +--R - 105b d e +--R * +--R x +--R + +--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2 4 7 5 8 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e - 35b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 4 4 5 3 4 +--R ((256A a b - 224B a b )d e - 32B a b d e )x +--R + +--R 2 3 3 2 4 4 4 2 3 5 3 +--R (128A a b - 112B a b )d e + (896A a b - 800B a b )d e +--R + +--R 4 6 2 +--R - 112B a b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 4 2 3 3 2 5 3 +--R (- 32A a b + 28B a b)d e + (448A a b - 388B a b )d e +--R + +--R 4 2 3 6 2 4 7 +--R (1120A a b - 1036B a b )d e - 140B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 4 4 3 2 4 5 3 +--R (16A a b - 14B a )d e + (- 112A a b + 96B a b)d e +--R + +--R 2 3 3 2 6 2 4 2 3 7 +--R (560A a b - 476B a b )d e + (560A a b - 560B a b )d e +--R + +--R 4 8 +--R - 70B a b d +--R * +--R x +--R + +--R 5 4 4 4 5 5 3 3 2 4 6 2 +--R - 10A a d e + (56A a b - 4B a )d e + (- 140A a b + 28B a b)d e +--R + +--R 2 3 3 2 7 4 2 3 8 +--R (280A a b - 140B a b )d e + (70A a b - 140B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 5 8 +--R (- 5A a b d - 5A a b)e +--R + +--R 3 2 4 2 4 2 5 7 +--R ((28A a b - 2B a b)d + (28A a b - 2B a b)d)e +--R + +--R 2 3 3 2 3 3 3 4 2 2 6 +--R ((- 70A a b + 14B a b )d + (- 70A a b + 14B a b )d )e +--R + +--R 4 2 3 4 2 4 3 3 3 5 +--R ((140A a b - 70B a b )d + (140A a b - 70B a b )d )e +--R + +--R 5 4 5 5 2 4 4 4 +--R ((35A b - 70B a b )d + (35A a b - 70B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 6 8 4 5 2 5 6 7 +--R (- 5A a d - 5A a )e + ((8A a b - 2B a )d + (8A a b - 2B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 6 +--R ((42A a b + 6B a b)d + (42A a b + 6B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 5 +--R ((- 140A a b - 14B a b )d + (- 140A a b - 14B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 4 +--R ((595A a b - 350B a b )d + (595A a b - 350B a b )d )e +--R + +--R 5 4 6 5 2 4 5 3 +--R ((140A b - 280B a b )d + (140A a b - 280B a b )d )e +--R * +--R 4 +--R x +--R + +--R 5 2 6 7 +--R (- 20A a d - 20A a d)e +--R + +--R 4 5 3 5 6 2 6 +--R ((82A a b - 8B a )d + (82A a b - 8B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 5 +--R ((- 112A a b + 44B a b)d + (- 112A a b + 44B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 4 +--R ((140A a b - 196B a b )d + (140A a b - 196B a b )d )e +--R + +--R 4 2 3 6 2 4 3 3 5 3 +--R ((980A a b - 700B a b )d + (980A a b - 700B a b )d )e +--R + +--R 5 4 7 5 2 4 6 2 +--R ((210A b - 420B a b )d + (210A a b - 420B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 3 6 2 6 +--R (- 30A a d - 30A a d )e +--R + +--R 4 5 4 5 6 3 5 +--R ((148A a b - 12B a )d + (148A a b - 12B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 4 +--R ((- 308A a b + 76B a b)d + (- 308A a b + 76B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 3 +--R ((560A a b - 364B a b )d + (560A a b - 364B a b )d )e +--R + +--R 4 2 3 7 2 4 3 3 6 2 +--R ((770A a b - 700B a b )d + (770A a b - 700B a b )d )e +--R + +--R 5 4 8 5 2 4 7 +--R ((140A b - 280B a b )d + (140A a b - 280B a b )d )e +--R * +--R 2 +--R x +--R + +--R 5 4 6 3 5 +--R (- 20A a d - 20A a d )e +--R + +--R 4 5 5 5 6 4 4 +--R ((107A a b - 8B a )d + (107A a b - 8B a )d )e +--R + +--R 3 2 4 6 4 2 5 5 3 +--R ((- 252A a b + 54B a b)d + (- 252A a b + 54B a b)d )e +--R + +--R 2 3 3 2 7 3 3 4 2 6 2 +--R ((490A a b - 266B a b )d + (490A a b - 266B a b )d )e +--R + +--R 4 2 3 8 2 4 3 3 7 +--R ((280A a b - 350B a b )d + (280A a b - 350B a b )d )e +--R + +--R 5 4 9 5 2 4 8 +--R (35A b - 70B a b )d + (35A a b - 70B a b )d +--R * +--R x +--R + +--R 5 5 6 4 4 4 5 6 5 6 5 3 +--R (- 5A a d - 5A a d )e + ((28A a b - 2B a )d + (28A a b - 2B a )d )e +--R + +--R 3 2 4 7 4 2 5 6 2 +--R ((- 70A a b + 14B a b)d + (- 70A a b + 14B a b)d )e +--R + +--R 2 3 3 2 8 3 3 4 2 7 +--R ((140A a b - 70B a b )d + (140A a b - 70B a b )d )e +--R + +--R 4 2 3 9 2 4 3 3 8 +--R (35A a b - 70B a b )d + (35A a b - 70B a b )d +--R / +--R 6 4 9 5 2 5 8 4 3 6 7 3 4 7 6 2 5 8 5 +--R 35a b d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 6 9 4 +--R - 35a b d e +--R * +--R 5 +--R x +--R + +--R 7 4 9 6 5 8 5 2 6 7 4 3 7 6 3 4 8 5 +--R 35a d e - 35a b d e - 350a b d e + 1050a b d e - 1225a b d e +--R + +--R 2 5 9 4 6 10 3 +--R 665a b d e - 140a b d e +--R * +--R 4 +--R x +--R + +--R 7 5 8 6 6 7 5 2 7 6 4 3 8 5 3 4 9 4 +--R 140a d e - 490a b d e + 350a b d e + 700a b d e - 1400a b d e +--R + +--R 2 5 10 3 6 11 2 +--R 910a b d e - 210a b d e +--R * +--R 3 +--R x +--R + +--R 7 6 7 6 7 6 5 2 8 5 4 3 9 4 3 4 10 3 +--R 210a d e - 910a b d e + 1400a b d e - 700a b d e - 350a b d e +--R + +--R 2 5 11 2 6 12 +--R 490a b d e - 140a b d e +--R * +--R 2 +--R x +--R + +--R 7 7 6 6 8 5 5 2 9 4 4 3 10 3 3 4 11 2 +--R 140a d e - 665a b d e + 1225a b d e - 1050a b d e + 350a b d e +--R + +--R 2 5 12 6 13 +--R 35a b d e - 35a b d +--R * +--R x +--R + +--R 7 8 5 6 9 4 5 2 10 3 4 3 11 2 3 4 12 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e +--R + +--R 2 5 13 +--R - 35a b d +--R Type: Union(Expression(Integer),...) +--E 1186 + +--S 1187 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 3 4 2 4 5 3 +--R (- 5A a d - 5A a )e + ((28A a b - 2B a )d + (28A a b - 2B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((- 70A a b + 14B a b)d + (- 70A a b + 14B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((140A a b - 70B a b )d + (140A a b - 70B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (35A b - 70B a b )d + (35A a b - 70B a b )d +--R / +--R 6 4 5 5 5 4 4 2 6 3 3 3 7 2 2 4 8 5 9 +--R 35a d e - 175a b d e + 350a b d e - 350a b d e + 175a b d e - 35a b d +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1188 + +)clear all + +--S 1189 of 1293 +t0:=(A+B*x)*(d+e*x)^(7/2)/(a+b*x)^(5/2) +--R +--R +--R (1) +--R 3 4 3 2 3 2 2 2 2 3 +--R B e x + (A e + 3B d e )x + (3A d e + 3B d e)x + (3A d e + B d )x +--R + +--R 3 +--R A d +--R * +--R +-------+ +--R \|e x + d +--R / +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 35/8*(b*d-a*e)^2*(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(11/2)-_ + 2*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+_ + 35/12*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/b^4+_ + 7/3*e*(b*B*d+2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)*sqrt(a+b*x)/_ + (b^3*(b*d-a*e))+35/8*e*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 3 2 2 2 +--R (210A a b - 315B a b)e + (- 420A a b + 735B a b )d e +--R + +--R 4 3 2 4 3 +--R (210A b - 525B a b )d e + 105B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (210A a b - 315B a )e + (- 420A a b + 735B a b)d e +--R + +--R 3 2 2 2 3 3 +--R (210A a b - 525B a b )d e + 105B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|e \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 4 3 4 4 3 3 4 2 3 +--R 8B b e x + ((12A b - 18B a b )e + 38B b d e )x +--R + +--R 3 2 2 3 4 3 2 4 2 2 +--R ((- 42A a b + 63B a b )e + (78A b - 138B a b )d e + 87B b d e)x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 280A a b + 420B a b)e + (476A a b - 854B a b )d e +--R + +--R 4 3 2 4 3 +--R (- 160A b + 478B a b )d e - 48B b d +--R * +--R x +--R + +--R 3 4 3 2 2 3 2 +--R (- 210A a b + 315B a )e + (350A a b - 630B a b)d e +--R + +--R 3 2 2 2 4 3 3 +--R (- 112A a b + 343B a b )d e + (- 16A b - 32B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 6 5 +-+ +-------+ +--R (24b x + 24a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1293 +--a0:=integrate(t0,x) +--E 1191 + +--S 1192 of 1293 +--m0:=a0-r0 +--E 1192 + +--S 1193 of 1293 +--d0:=D(m0,x) +--E 1193 + +)clear all + +--S 1194 of 1293 +t0:=(A+B*x)*(d+e*x)^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 3 2 2 2 2 +-------+ +--R (B e x + (A e + 2B d e)x + (2A d e + B d )x + A d )\|e x + d +--R (1) ---------------------------------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 5/4*(b*d-a*e)*(3*b*B*d+4*A*b*e-7*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(9/2)-2/3*(3*b*B*d+4*A*b*e-7*a*B*e)*_ + (d+e*x)^(5/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+5/6*e*_ + (3*b*B*d+4*A*b*e-7*a*B*e)*(d+e*x)^(3/2)*sqrt(a+b*x)/(b^3*(b*d-a*e))+_ + 5/4*e*(3*b*B*d+4*A*b*e-7*a*B*e)*sqrt(a+b*x)*sqrt(d+e*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 +--R ((- 60A a b + 105B a b)e + (60A b - 150B a b )d e + 45B b d )x +--R + +--R 2 3 2 2 2 2 2 +--R (- 60A a b + 105B a )e + (60A a b - 150B a b)d e + 45B a b d +--R * +--R +-+ +-------+ +--R +-+ +-------+ \|e \|b x + a +--R \|e \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 3 2 3 3 2 2 3 2 +--R 6B b e x + ((12A b - 21B a b )e + 27B b d e)x +--R + +--R 2 2 2 3 2 3 2 +--R ((80A a b - 140B a b)e + (- 56A b + 158B a b )d e - 24B b d )x +--R + +--R 2 3 2 2 2 +--R (60A a b - 105B a )e + (- 40A a b + 115B a b)d e +--R + +--R 3 2 2 +--R (- 8A b - 16B a b )d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 5 4 +-+ +-------+ +--R (12b x + 12a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1293 +--a0:=integrate(t0,x) +--E 1196 + +--S 1197 of 1293 +--m0:=a0-r0 +--E 1197 + +--S 1198 of 1293 +--d0:=D(m0,x) +--E 1198 + +)clear all + +--S 1199 of 1293 +t0:=(A+B*x)*(d+e*x)^(3/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-------+ +--R (B e x + (A e + B d)x + A d)\|e x + d +--R (1) --------------------------------------- +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + (3*b*B*d+2*A*b*e-5*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(d+e*x)))*sqrt(e)/b^(7/2)-2/3*(3*b*B*d+2*A*b*e-5*a*B*e)*_ + (d+e*x)^(3/2)/(b^2*(b*d-a*e)*sqrt(a+b*x))+e*(3*b*B*d+2*A*b*e-5*a*B*e)*_ + sqrt(a+b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)) +--R +--R +--R (2) +--R 2 2 2 +-+ +--R (((6A b - 15B a b)e + 9B b d)x + (6A a b - 15B a )e + 9B a b d)\|e +--R * +--R +-+ +-------+ +--R +-------+ \|e \|b x + a +--R \|b x + a atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 2 +--R 3B b e x + ((- 8A b + 20B a b)e - 6B b d)x + (- 6A a b + 15B a )e +--R + +--R 2 +--R (- 2A b - 4B a b)d +--R * +--R +-+ +-------+ +--R \|b \|e x + d +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1293 +--a0:=integrate(t0,x) +--E 1201 + +--S 1202 of 1293 +--m0:=a0-r0 +--E 1202 + +--S 1203 of 1293 +--d0:=D(m0,x) +--E 1203 + +)clear all + +--S 1204 of 1293 +t0:=(A+B*x)*sqrt(d+e*x)/(a+b*x)^(5/2) +--R +--R +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1293 +r0:=-2/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ + 2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))*sqrt(e)/b^(5/2)-_ + 2*B*sqrt(d+e*x)/(b^2*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 +-+ +-------+ +--R ((6B a b e - 6B b d)x + 6B a e - 6B a b d)\|e \|b x + a +--R * +--R +-+ +-------+ +--R \|e \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|e x + d +--R + +--R 2 2 2 2 +-+ +-------+ +--R (((2A b - 8B a b)e + 6B b d)x - 6B a e + (2A b + 4B a b)d)\|b \|e x + d +--R / +--R 3 4 2 2 3 +-+ +-------+ +--R ((3a b e - 3b d)x + 3a b e - 3a b d)\|b \|b x + a +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1293 +--a0:=integrate(t0,x) +--E 1206 + +--S 1207 of 1293 +--m0:=a0-r0 +--E 1207 + +--S 1208 of 1293 +--d0:=D(m0,x) +--E 1208 + +)clear all + +--S 1209 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*sqrt(d+e*x)) +--R +--R +--R B x + A +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (b x + 2a b x + a )\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1293 +r0:=-2/3*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^(3/2))-_ + 2/3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a+b*x)) +--R +--R +--R +-------+ +--R (((4A b + 2B a)e - 6B b d)x + 6A a e + (- 2A b - 4B a)d)\|e x + d +--R (2) ---------------------------------------------------------------------- +--R 2 2 2 3 2 3 2 2 2 2 +-------+ +--R ((3a b e - 6a b d e + 3b d )x + 3a e - 6a b d e + 3a b d )\|b x + a +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 3 2 3 +--R (((8A a b + 4B a )e - 12B a b d)x + 12A a e + (- 4A a b - 8B a )d) +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 2 3 2 2 3 2 2 2 +--R ((- 3A a b d - 12A a b )e + (A b + 2B a b )d + (4A a b + 8B a b )d)x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 6A a b d - 24A a b)e + (2A a b + 4B a b)d + (8A a b + 16B a b)d)x +--R + +--R 3 4 2 3 2 3 4 +--R (- 3A a d - 12A a )e + (A a b + 2B a )d + (4A a b + 8B a )d +--R / +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (6a b e - 12a b d e + 6a b d )x + (12a b e - 24a b d e + 12a b d )x +--R + +--R 6 2 5 4 2 2 +--R 6a e - 12a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 1211 + +--S 1212 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R (- 3A a d - 12A a )e + (A b + 2B a)d + (4A a b + 8B a )d +--R (4) --------------------------------------------------------- +--R 4 2 3 2 2 2 +--R 6a e - 12a b d e + 6a b d +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1213 + +)clear all + +--S 1214 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(3/2)) +--R +--R +--R (1) +--R B x + A +--R ----------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b e x + (2a b e + b d)x + (a e + 2a b d)x + a d)\|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1293 +r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*sqrt(d+e*x))+_ + 2/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/(e*(b*d-a*e)^2*(a+b*x)^(3/2))-_ + 4/3*(3*b*B*d-4*A*b*e+a*B*e)*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 2 +--R ((- 16A b + 4B a b)e + 12B b d e)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- 24A a b + 6B a )e + (- 8A b + 20B a b)d e + 6B b d )x - 6A a e +--R + +--R 2 2 2 +--R (- 12A a b + 12B a )d e + (2A b + 4B a b)d +--R / +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (3a b e - 9a b d e + 9a b d e - 3b d )x + 3a e - 9a b d e +--R + +--R 2 2 2 3 3 +--R 9a b d e - 3a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 2 2 2 2 +--R ((- 64A a b + 16B a b)d e + 48B a b d e)x +--R + +--R 3 4 2 2 2 3 2 2 2 3 +--R ((- 96A a b + 24B a )d e + (- 32A a b + 80B a b)d e + 24B a b d )x +--R + +--R 4 2 3 4 2 2 2 3 3 +--R - 24A a d e + (- 48A a b + 48B a )d e + (8A a b + 16B a b)d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 2 2 3 2 3 +--R (- 3A a b d - 48A a b )e +--R + +--R 3 2 2 2 2 3 3 2 2 +--R ((- 6A a b + 6B a b )d + (- 96A a b + 96B a b )d)e +--R + +--R 4 3 3 4 2 3 2 +--R ((A b + 2B a b )d + (16A a b + 32B a b )d )e +--R * +--R 3 +--R x +--R + +--R 3 4 3 +--R (- 6A a b d - 96A a b)e +--R + +--R 2 2 3 2 3 2 4 2 +--R ((- 15A a b + 12B a b)d + (- 240A a b + 192B a b)d)e +--R + +--R 3 2 2 3 2 3 3 2 2 +--R ((- 4A a b + 10B a b )d + (- 64A a b + 160B a b )d )e +--R + +--R 4 3 4 4 2 3 3 +--R (A b + 2B a b )d + (16A a b + 32B a b )d +--R * +--R 2 +--R x +--R + +--R 4 5 3 +--R (- 3A a d - 48A a )e +--R + +--R 3 4 2 4 5 2 +--R ((- 12A a b + 6B a )d + (- 192A a b + 96B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 +--R ((- 11A a b + 14B a b)d + (- 176A a b + 224B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R (2A a b + 4B a b )d + (32A a b + 64B a b )d +--R * +--R x +--R + +--R 4 2 5 2 +--R (- 3A a d - 48A a d)e +--R + +--R 3 4 3 4 5 2 2 2 3 4 +--R ((- 6A a b + 6B a )d + (- 96A a b + 96B a )d )e + (A a b + 2B a b)d +--R + +--R 3 2 4 3 +--R (16A a b + 32B a b)d +--R / +--R 5 2 4 4 3 2 3 3 4 3 2 2 5 4 3 +--R (12a b d e - 36a b d e + 36a b d e - 12a b d e)x +--R + +--R 6 4 5 2 2 3 4 3 3 2 3 4 4 2 5 5 2 +--R (24a b d e - 60a b d e + 36a b d e + 12a b d e - 12a b d )x +--R + +--R 7 4 6 2 3 5 2 3 2 4 3 4 3 4 5 7 2 3 +--R (12a d e - 12a b d e - 36a b d e + 60a b d e - 24a b d )x + 12a d e +--R + +--R 6 3 2 5 2 4 4 3 5 +--R - 36a b d e + 36a b d e - 12a b d +--R Type: Union(Expression(Integer),...) +--E 1216 + +--S 1217 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 2 2 3 +--R (- 3A a d - 27A a )e + ((- 6A a b + 6B a )d + (- 54A a b + 54B a )d)e +--R + +--R 2 3 2 2 2 +--R (A b + 2B a b)d + (9A a b + 18B a b)d +--R / +--R 5 3 4 2 2 3 2 3 2 3 4 +--R 9a d e - 27a b d e + 27a b d e - 9a b d +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1218 + +)clear all + +--S 1219 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(5/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b e x + (2a b e + 2b d e)x + (a e + 4a b d e + b d )x +--R + +--R 2 2 2 2 +--R (2a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1293 +r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2))+_ + 2/3*(b*B*d-2*A*b*e+a*B*e)/(e*(b*d-a*e)^2*(a+b*x)^(3/2)*sqrt(d+e*x))-_ + 8/3*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*sqrt(a+b*x)*sqrt(d+e*x))-_ + 16/3*e*(b*B*d-2*A*b*e+a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)) +--R +--R +--R (2) +--R 3 2 3 3 2 3 +--R ((32A b - 16B a b )e - 16B b d e )x +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((48A a b - 24B a b)e + (48A b - 48B a b )d e - 24B b d e)x +--R + +--R 2 3 3 2 2 2 +--R (12A a b - 6B a )e + (72A a b - 42B a b)d e +--R + +--R 3 2 2 3 3 +--R (12A b - 42B a b )d e - 6B b d +--R * +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - 2A a e + (18A a b - 4B a )d e + (18A a b - 24B a b)d e +--R + +--R 3 2 3 +--R (- 2A b - 4B a b )d +--R / +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (3a b e - 12a b d e + 18a b d e - 12a b d e + 3b d e)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (3a e - 9a b d e + 6a b d e + 6a b d e - 9a b d e + 3b d )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R 3a d e - 12a b d e + 18a b d e - 12a b d e + 3a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 3 2 3 3 2 3 +--R ((64A a b - 32B a b )d e - 32B a b d e )x +--R + +--R 3 2 4 2 3 2 3 3 2 3 2 +--R (96A a b - 48B a b)d e + (96A a b - 96B a b )d e +--R + +--R 2 3 4 +--R - 48B a b d e +--R * +--R 2 +--R x +--R + +--R 4 5 2 3 3 2 4 3 2 +--R (24A a b - 12B a )d e + (144A a b - 84B a b)d e +--R + +--R 2 3 3 2 4 2 3 5 +--R (24A a b - 84B a b )d e - 12B a b d +--R * +--R x +--R + +--R 5 2 3 4 5 3 2 3 2 4 4 +--R - 4A a d e + (36A a b - 8B a )d e + (36A a b - 48B a b)d e +--R + +--R 2 3 3 2 5 +--R (- 4A a b - 8B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 3 2 4 2 5 +--R (A a b d + 4A a b )e +--R + +--R 2 3 3 2 2 3 3 4 2 4 +--R ((- 9A a b + 2B a b )d + (- 36A a b + 8B a b )d)e +--R + +--R 4 2 3 3 2 4 3 3 2 3 +--R ((- 9A a b + 12B a b )d + (- 36A a b + 48B a b )d )e +--R + +--R 5 4 4 5 2 4 3 2 +--R ((A b + 2B a b )d + (4A a b + 8B a b )d )e +--R * +--R 4 +--R x +--R + +--R 4 5 5 +--R (2A a b d + 8A a b)e +--R + +--R 3 2 4 2 4 2 5 4 +--R ((- 16A a b + 4B a b)d + (- 64A a b + 16B a b)d)e +--R + +--R 2 3 3 2 3 3 3 4 2 2 3 +--R ((- 36A a b + 28B a b )d + (- 144A a b + 112B a b )d )e +--R + +--R 4 2 3 4 2 4 3 3 3 2 +--R ((- 16A a b + 28B a b )d + (- 64A a b + 112B a b )d )e +--R + +--R 5 4 5 5 2 4 4 +--R ((2A b + 4B a b )d + (8A a b + 16B a b )d )e +--R * +--R 3 +--R x +--R + +--R 5 6 5 4 5 2 5 6 4 +--R (A a d + 4A a )e + ((- 5A a b + 2B a )d + (- 20A a b + 8B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 3 +--R ((- 44A a b + 20B a b)d + (- 176A a b + 80B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 2 +--R ((- 44A a b + 52B a b )d + (- 176A a b + 208B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 +--R ((- 5A a b + 20B a b )d + (- 20A a b + 80B a b )d )e +--R + +--R 5 4 6 5 2 4 5 +--R (A b + 2B a b )d + (4A a b + 8B a b )d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 +--R (2A a d + 8A a d)e +--R + +--R 4 5 3 5 6 2 3 +--R ((- 16A a b + 4B a )d + (- 64A a b + 16B a )d )e +--R + +--R 3 2 4 4 4 2 5 3 2 +--R ((- 36A a b + 28B a b)d + (- 144A a b + 112B a b)d )e +--R + +--R 2 3 3 2 5 3 3 4 2 4 +--R ((- 16A a b + 28B a b )d + (- 64A a b + 112B a b )d )e +--R + +--R 4 2 3 6 2 4 3 3 5 +--R (2A a b + 4B a b )d + (8A a b + 16B a b )d +--R * +--R x +--R + +--R 5 3 6 2 3 4 5 4 5 6 3 2 +--R (A a d + 4A a d )e + ((- 9A a b + 2B a )d + (- 36A a b + 8B a )d )e +--R + +--R 3 2 4 5 4 2 5 4 +--R ((- 9A a b + 12B a b)d + (- 36A a b + 48B a b)d )e +--R + +--R 2 3 3 2 6 3 3 4 2 5 +--R (A a b + 2B a b )d + (4A a b + 8B a b )d +--R / +--R 6 2 2 6 5 3 3 5 4 4 4 4 3 5 5 3 2 6 6 2 4 +--R (6a b d e - 24a b d e + 36a b d e - 24a b d e + 6a b d e )x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 +--R 12a b d e - 36a b d e + 24a b d e + 24a b d e - 36a b d e +--R + +--R 2 6 7 +--R 12a b d e +--R * +--R 3 +--R x +--R + +--R 8 2 6 6 2 4 4 5 3 5 3 4 4 6 2 2 6 8 2 +--R (6a d e - 54a b d e + 96a b d e - 54a b d e + 6a b d )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R (12a d e - 36a b d e + 24a b d e + 24a b d e - 36a b d e + 12a b d )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Union(Expression(Integer),...) +--E 1221 + +--S 1222 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4 3 2 3 2 3 4 2 +--R (A a d + 4A a )e + ((- 9A a b + 2B a )d + (- 36A a b + 8B a )d)e +--R + +--R 2 2 3 2 2 3 2 +--R ((- 9A a b + 12B a b)d + (- 36A a b + 48B a b)d )e +--R + +--R 3 2 4 3 2 2 3 +--R (A b + 2B a b )d + (4A a b + 8B a b )d +--R / +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R 6a d e - 24a b d e + 36a b d e - 24a b d e + 6a b d +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1223 + +)clear all + +--S 1224 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(7/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b e x + (2a b e + 3b d e )x + (a e + 6a b d e + 3b d e)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a d e + 6a b d e + b d )x + (3a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1293 +r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2))-_ + 2/3*(3*b*B*d-8*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*_ + (d+e*x)^(5/2)*sqrt(a+b*x))-4/5*e*(3*b*B*d-8*A*b*e+5*a*B*e)*_ + sqrt(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(5/2))-16/15*e*_ + (3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2))-_ + 32/15*b*e*(3*b*B*d-8*A*b*e+5*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)) +--R +--R +--R (2) +--R 4 3 4 4 3 4 +--R ((- 256A b + 160B a b )e + 96B b d e )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 384A a b + 240B a b )e + (- 640A b + 544B a b )d e +--R + +--R 4 2 2 +--R 240B b d e +--R * +--R 3 +--R x +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 96A a b + 60B a b)e + (- 960A a b + 636B a b )d e +--R + +--R 4 3 2 2 4 3 +--R (- 480A b + 660B a b )d e + 180B b d e +--R * +--R 2 +--R x +--R + +--R 3 4 4 2 2 3 3 +--R (16A a b - 10B a )e + (- 240A a b + 144B a b)d e +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 720A a b + 540B a b )d e + (- 80A b + 320B a b )d e + 30B b d +--R * +--R x +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 6A a e + (40A a b - 4B a )d e + (- 180A a b + 60B a b)d e +--R + +--R 3 2 2 3 4 3 4 +--R (- 120A a b + 180B a b )d e + (10A b + 20B a b )d +--R / +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 +--R 15a b e - 75a b d e + 150a b d e - 150a b d e + 75a b d e +--R + +--R 6 5 2 +--R - 15b d e +--R * +--R 3 +--R x +--R + +--R 6 7 5 6 3 3 3 4 2 4 4 3 5 5 2 +--R 15a e - 45a b d e + 150a b d e - 225a b d e + 135a b d e +--R + +--R 6 6 +--R - 30b d e +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 5 6 +--R 30a d e - 135a b d e + 225a b d e - 150a b d e + 45a b d e +--R + +--R 6 7 +--R - 15b d +--R * +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R 15a d e - 75a b d e + 150a b d e - 150a b d e + 75a b d e - 15a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 3 3 4 2 4 4 3 4 +--R ((- 768A a b + 480B a b )d e + 288B a b d e )x +--R + +--R 3 3 4 2 3 4 2 4 3 3 4 3 +--R (- 1152A a b + 720B a b )d e + (- 1920A a b + 1632B a b )d e +--R + +--R 2 4 5 2 +--R 720B a b d e +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 3 3 4 2 4 3 +--R (- 288A a b + 180B a b)d e + (- 2880A a b + 1908B a b )d e +--R + +--R 2 4 3 3 5 2 2 4 6 +--R (- 1440A a b + 1980B a b )d e + 540B a b d e +--R * +--R 2 +--R x +--R + +--R 5 6 3 4 4 2 5 4 3 +--R (48A a b - 30B a )d e + (- 720A a b + 432B a b)d e +--R + +--R 3 3 4 2 5 2 2 4 3 3 6 +--R (- 2160A a b + 1620B a b )d e + (- 240A a b + 960B a b )d e +--R + +--R 2 4 7 +--R 90B a b d +--R * +--R x +--R + +--R 6 3 4 5 6 4 3 4 2 5 5 2 +--R - 18A a d e + (120A a b - 12B a )d e + (- 540A a b + 180B a b)d e +--R + +--R 3 3 4 2 6 2 4 3 3 7 +--R (- 360A a b + 540B a b )d e + (30A a b + 60B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 4 2 5 2 7 +--R (3A a b d + 27A a b )e +--R + +--R 3 3 4 2 2 4 3 5 2 6 +--R ((- 20A a b + 2B a b )d + (- 180A a b + 18B a b )d)e +--R + +--R 2 4 3 3 3 3 4 4 3 2 5 +--R ((90A a b - 30B a b )d + (810A a b - 270B a b )d )e +--R + +--R 5 2 4 4 2 5 3 4 3 4 +--R ((60A a b - 90B a b )d + (540A a b - 810B a b )d )e +--R + +--R 6 5 5 6 2 5 4 3 +--R ((- 5A b - 10B a b )d + (- 45A a b - 90B a b )d )e +--R * +--R 5 +--R x +--R + +--R 5 6 7 +--R (6A a b d + 54A a b)e +--R + +--R 4 2 5 2 5 2 6 6 +--R ((- 31A a b + 4B a b)d + (- 279A a b + 36B a b)d)e +--R + +--R 3 3 4 2 3 4 3 5 2 2 5 +--R ((120A a b - 54B a b )d + (1080A a b - 486B a b )d )e +--R + +--R 2 4 3 3 4 3 4 4 3 3 4 +--R ((390A a b - 270B a b )d + (3510A a b - 2430B a b )d )e +--R + +--R 5 2 4 5 2 5 3 4 4 3 +--R ((170A a b - 290B a b )d + (1530A a b - 2610B a b )d )e +--R + +--R 6 5 6 6 2 5 5 2 +--R ((- 15A b - 30B a b )d + (- 135A a b - 270B a b )d )e +--R * +--R 4 +--R x +--R + +--R 6 7 7 +--R (3A a d + 27A a )e +--R + +--R 5 6 2 6 7 6 +--R ((- 2A a b + 2B a )d + (- 18A a b + 18B a )d)e +--R + +--R 4 2 5 3 5 2 6 2 5 +--R ((- 21A a b - 18B a b)d + (- 189A a b - 162B a b)d )e +--R + +--R 3 3 4 2 4 4 3 5 2 3 4 +--R ((540A a b - 264B a b )d + (4860A a b - 2376B a b )d )e +--R + +--R 2 4 3 3 5 3 4 4 3 4 3 +--R ((625A a b - 640B a b )d + (5625A a b - 5760B a b )d )e +--R + +--R 5 2 4 6 2 5 3 4 5 2 +--R ((150A a b - 330B a b )d + (1350A a b - 2970B a b )d )e +--R + +--R 6 5 7 6 2 5 6 +--R ((- 15A b - 30B a b )d + (- 135A a b - 270B a b )d )e +--R * +--R 3 +--R x +--R + +--R 6 2 7 6 +--R (9A a d + 81A a d)e +--R + +--R 5 6 3 6 7 2 5 +--R ((- 42A a b + 6B a )d + (- 378A a b + 54B a )d )e +--R + +--R 4 2 5 4 5 2 6 3 4 +--R ((153A a b - 78B a b)d + (1377A a b - 702B a b)d )e +--R + +--R 3 3 4 2 5 4 3 5 2 4 3 +--R ((700A a b - 448B a b )d + (6300A a b - 4032B a b )d )e +--R + +--R 2 4 3 3 6 3 4 4 3 5 2 +--R ((435A a b - 600B a b )d + (3915A a b - 5400B a b )d )e +--R + +--R 5 2 4 7 2 5 3 4 6 +--R ((30A a b - 150B a b )d + (270A a b - 1350B a b )d )e +--R + +--R 6 5 8 6 2 5 7 +--R (- 5A b - 10B a b )d + (- 45A a b - 90B a b )d +--R * +--R 2 +--R x +--R + +--R 6 3 7 2 5 +--R (9A a d + 81A a d )e +--R + +--R 5 6 4 6 7 3 4 +--R ((- 54A a b + 6B a )d + (- 486A a b + 54B a )d )e +--R + +--R 4 2 5 5 5 2 6 4 3 +--R ((230A a b - 86B a b)d + (2070A a b - 774B a b)d )e +--R + +--R 3 3 4 2 6 4 3 5 2 5 2 +--R ((360A a b - 330B a b )d + (3240A a b - 2970B a b )d )e +--R + +--R 2 4 3 3 7 3 4 4 3 6 +--R ((105A a b - 210B a b )d + (945A a b - 1890B a b )d )e +--R + +--R 5 2 4 8 2 5 3 4 7 +--R (- 10A a b - 20B a b )d + (- 90A a b - 180B a b )d +--R * +--R x +--R + +--R 6 4 7 3 4 +--R (3A a d + 27A a d )e +--R + +--R 5 6 5 6 7 4 3 +--R ((- 20A a b + 2B a )d + (- 180A a b + 18B a )d )e +--R + +--R 4 2 5 6 5 2 6 5 2 +--R ((90A a b - 30B a b)d + (810A a b - 270B a b)d )e +--R + +--R 3 3 4 2 7 4 3 5 2 6 +--R ((60A a b - 90B a b )d + (540A a b - 810B a b )d )e +--R + +--R 2 4 3 3 8 3 4 4 3 7 +--R (- 5A a b - 10B a b )d + (- 45A a b - 90B a b )d +--R / +--R 7 2 3 8 6 3 4 7 5 4 5 6 4 5 6 5 3 6 7 4 +--R 45a b d e - 225a b d e + 450a b d e - 450a b d e + 225a b d e +--R + +--R 2 7 8 3 +--R - 45a b d e +--R * +--R 5 +--R x +--R + +--R 8 3 8 7 2 4 7 6 3 5 6 5 4 6 5 4 5 7 4 +--R 90a b d e - 315a b d e + 225a b d e + 450a b d e - 900a b d e +--R + +--R 3 6 8 3 2 7 9 2 +--R 585a b d e - 135a b d e +--R * +--R 4 +--R x +--R + +--R 9 3 8 8 4 7 7 2 5 6 6 3 6 5 5 4 7 4 +--R 45a d e + 45a b d e - 765a b d e + 1575a b d e - 1125a b d e +--R + +--R 4 5 8 3 3 6 9 2 2 7 10 +--R - 45a b d e + 405a b d e - 135a b d e +--R * +--R 3 +--R x +--R + +--R 9 4 7 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 +--R 135a d e - 405a b d e + 45a b d e + 1125a b d e - 1575a b d e +--R + +--R 4 5 9 2 3 6 10 2 7 11 +--R 765a b d e - 45a b d e - 45a b d +--R * +--R 2 +--R x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 +--R 135a d e - 585a b d e + 900a b d e - 450a b d e - 225a b d e +--R + +--R 4 5 10 3 6 11 +--R 315a b d e - 90a b d +--R * +--R x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 +--R 45a d e - 225a b d e + 450a b d e - 450a b d e + 225a b d e +--R + +--R 4 5 11 +--R - 45a b d +--R Type: Union(Expression(Integer),...) +--E 1226 + +--S 1227 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 4 3 4 2 4 5 3 +--R (3A a d + 27A a )e + ((- 20A a b + 2B a )d + (- 180A a b + 18B a )d)e +--R + +--R 2 2 3 3 3 2 4 2 2 +--R ((90A a b - 30B a b)d + (810A a b - 270B a b)d )e +--R + +--R 3 2 2 4 2 3 3 2 3 +--R ((60A a b - 90B a b )d + (540A a b - 810B a b )d )e +--R + +--R 4 3 5 4 2 3 4 +--R (- 5A b - 10B a b )d + (- 45A a b - 90B a b )d +--R / +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R 45a d e - 225a b d e + 450a b d e - 450a b d e + 225a b d e - 45a b d +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1228 + +)clear all + +--S 1229 of 1293 +t0:=(A+B*x)/((a+b*x)^(5/2)*(d+e*x)^(9/2)) +--R +--R +--R (1) +--R B x + A +--R / +--R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 +--R b e x + (2a b e + 4b d e )x + (a e + 8a b d e + 6b d e )x +--R + +--R 2 3 2 2 2 3 3 2 2 2 3 2 4 2 +--R (4a d e + 12a b d e + 4b d e)x + (6a d e + 8a b d e + b d )x +--R + +--R 2 3 4 2 4 +--R (4a d e + 2a b d )x + a d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1293 +r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(7/2))-_ + 2/3*(3*b*B*d-10*A*b*e+7*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(7/2)*_ + sqrt(a+b*x))-16/21*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/_ + (b*(b*d-a*e)^3*(d+e*x)^(7/2))-32/35*e*(3*b*B*d-10*A*b*e+7*a*B*e)*_ + sqrt(a+b*x)/((b*d-a*e)^4*(d+e*x)^(5/2))-128/105*b*e*_ + (3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/((b*d-a*e)^5*(d+e*x)^(3/2))-_ + 256/105*b^2*e*(3*b*B*d-10*A*b*e+7*a*B*e)*sqrt(a+b*x)/_ + ((b*d-a*e)^6*sqrt(d+e*x)) +--R +--R +--R (2) +--R 5 4 5 5 4 5 +--R ((2560A b - 1792B a b )e - 768B b d e )x +--R + +--R 4 2 3 5 5 4 4 +--R (3840A a b - 2688B a b )e + (8960A b - 7424B a b )d e +--R + +--R 5 2 3 +--R - 2688B b d e +--R * +--R 4 +--R x +--R + +--R 2 3 3 2 5 4 2 3 4 +--R (960A a b - 672B a b )e + (13440A a b - 9696B a b )d e +--R + +--R 5 4 2 3 5 3 2 +--R (11200A b - 11872B a b )d e - 3360B b d e +--R * +--R 3 +--R x +--R + +--R 3 2 4 5 2 3 3 2 4 +--R (- 160A a b + 112B a b)e + (3360A a b - 2304B a b )d e +--R + +--R 4 2 3 2 3 5 4 3 2 +--R (16800A a b - 12768B a b )d e + (5600A b - 8960B a b )d e +--R + +--R 5 4 +--R - 1680B b d e +--R * +--R 2 +--R x +--R + +--R 4 5 5 3 2 4 4 +--R (60A a b - 42B a )e + (- 560A a b + 374B a b)d e +--R + +--R 2 3 3 2 2 3 4 2 3 3 2 +--R (4200A a b - 2772B a b )d e + (8400A a b - 7140B a b )d e +--R + +--R 5 4 4 5 5 +--R (700A b - 3010B a b )d e - 210B b d +--R * +--R x +--R + +--R 5 5 4 5 4 3 2 4 2 3 +--R - 30A a e + (210A a b - 12B a )d e + (- 700A a b + 112B a b)d e +--R + +--R 2 3 3 2 3 2 4 2 3 4 +--R (2100A a b - 840B a b )d e + (1050A a b - 1680B a b )d e +--R + +--R 5 4 5 +--R (- 70A b - 140B a b )d +--R / +--R 6 9 5 2 8 4 3 2 7 3 4 3 6 +--R 105a b e - 630a b d e + 1575a b d e - 2100a b d e +--R + +--R 2 5 4 5 6 5 4 7 6 3 +--R 1575a b d e - 630a b d e + 105b d e +--R * +--R 4 +--R x +--R + +--R 7 9 6 8 5 2 2 7 4 3 3 6 3 4 4 5 +--R 105a e - 315a b d e - 315a b d e + 2625a b d e - 4725a b d e +--R + +--R 2 5 5 4 6 6 3 7 7 2 +--R 4095a b d e - 1785a b d e + 315b d e +--R * +--R 3 +--R x +--R + +--R 7 8 6 2 7 5 2 3 6 4 3 4 5 +--R 315a d e - 1575a b d e + 2835a b d e - 1575a b d e +--R + +--R 3 4 5 4 2 5 6 3 6 7 2 7 8 +--R - 1575a b d e + 2835a b d e - 1575a b d e + 315b d e +--R * +--R 2 +--R x +--R + +--R 7 2 7 6 3 6 5 2 4 5 4 3 5 4 +--R 315a d e - 1785a b d e + 4095a b d e - 4725a b d e +--R + +--R 3 4 6 3 2 5 7 2 6 8 7 9 +--R 2625a b d e - 315a b d e - 315a b d e + 105b d +--R * +--R x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 +--R 105a d e - 630a b d e + 1575a b d e - 2100a b d e + 1575a b d e +--R + +--R 2 5 8 6 9 +--R - 630a b d e + 105a b d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1293 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 4 4 5 2 5 5 4 5 +--R ((12800A a b - 8960B a b )d e - 3840B a b d e )x +--R + +--R 3 4 4 3 4 5 2 5 3 4 5 4 +--R (19200A a b - 13440B a b )d e + (44800A a b - 37120B a b )d e +--R + +--R 2 5 6 3 +--R - 13440B a b d e +--R * +--R 4 +--R x +--R + +--R 4 3 5 2 4 5 3 4 4 3 5 4 +--R (4800A a b - 3360B a b )d e + (67200A a b - 48480B a b )d e +--R + +--R 2 5 3 4 6 3 2 5 7 2 +--R (56000A a b - 59360B a b )d e - 16800B a b d e +--R * +--R 3 +--R x +--R + +--R 5 2 6 4 5 4 3 5 2 5 4 +--R (- 800A a b + 560B a b)d e + (16800A a b - 11520B a b )d e +--R + +--R 3 4 4 3 6 3 2 5 3 4 7 2 +--R (84000A a b - 63840B a b )d e + (28000A a b - 44800B a b )d e +--R + +--R 2 5 8 +--R - 8400B a b d e +--R * +--R 2 +--R x +--R + +--R 6 7 4 5 5 2 6 5 4 +--R (300A a b - 210B a )d e + (- 2800A a b + 1870B a b)d e +--R + +--R 4 3 5 2 6 3 3 4 4 3 7 2 +--R (21000A a b - 13860B a b )d e + (42000A a b - 35700B a b )d e +--R + +--R 2 5 3 4 8 2 5 9 +--R (3500A a b - 15050B a b )d e - 1050B a b d +--R * +--R x +--R + +--R 7 4 5 6 7 5 4 +--R - 150A a d e + (1050A a b - 60B a )d e +--R + +--R 5 2 6 6 3 4 3 5 2 7 2 +--R (- 3500A a b + 560B a b)d e + (10500A a b - 4200B a b )d e +--R + +--R 3 4 4 3 8 2 5 3 4 9 +--R (5250A a b - 8400B a b )d e + (- 350A a b - 700B a b )d +--R * +--R +-------+ +-------+ +--R \|b x + a \|e x + d +--R + +--R 5 2 6 2 9 +--R (- 15A a b d - 375A a b )e +--R + +--R 4 3 5 2 2 5 3 6 2 8 +--R ((105A a b - 6B a b )d + (2625A a b - 150B a b )d)e +--R + +--R 3 4 4 3 3 4 4 5 3 2 7 +--R ((- 350A a b + 56B a b )d + (- 8750A a b + 1400B a b )d )e +--R + +--R 2 5 3 4 4 3 5 4 4 3 6 +--R ((1050A a b - 420B a b )d + (26250A a b - 10500B a b )d )e +--R + +--R 6 2 5 5 2 6 3 5 4 5 +--R ((525A a b - 840B a b )d + (13125A a b - 21000B a b )d )e +--R + +--R 7 6 6 7 2 6 5 4 +--R ((- 35A b - 70B a b )d + (- 875A a b - 1750B a b )d )e +--R * +--R 6 +--R x +--R + +--R 6 7 9 +--R (- 30A a b d - 750A a b)e +--R + +--R 5 2 6 2 6 2 7 8 +--R ((150A a b - 12B a b)d + (3750A a b - 300B a b)d)e +--R + +--R 4 3 5 2 3 5 3 6 2 2 7 +--R ((- 280A a b + 88B a b )d + (- 7000A a b + 2200B a b )d )e +--R + +--R 3 4 4 3 4 4 4 5 3 3 6 +--R ((700A a b - 616B a b )d + (17500A a b - 15400B a b )d )e +--R + +--R 2 5 3 4 5 3 5 4 4 4 5 +--R ((5250A a b - 3360B a b )d + (131250A a b - 84000B a b )d )e +--R + +--R 6 2 5 6 2 6 3 5 5 4 +--R ((2030A a b - 3500B a b )d + (50750A a b - 87500B a b )d )e +--R + +--R 7 6 7 7 2 6 6 3 +--R ((- 140A b - 280B a b )d + (- 3500A a b - 7000B a b )d )e +--R * +--R 5 +--R x +--R + +--R 7 8 9 +--R (- 15A a d - 375A a )e +--R + +--R 6 7 2 7 8 8 +--R ((- 15A a b - 6B a )d + (- 375A a b - 150B a )d)e +--R + +--R 5 2 6 3 6 2 7 2 7 +--R ((400A a b + 8B a b)d + (10000A a b + 200B a b)d )e +--R + +--R 4 3 5 2 4 5 3 6 2 3 6 +--R ((- 1120A a b - 8B a b )d + (- 28000A a b - 200B a b )d )e +--R + +--R 3 4 4 3 5 4 4 5 3 4 5 +--R ((6825A a b - 3864B a b )d + (170625A a b - 96600B a b )d )e +--R + +--R 2 5 3 4 6 3 5 4 4 5 4 +--R ((10465A a b - 9310B a b )d + (261625A a b - 232750B a b )d )e +--R + +--R 6 2 5 7 2 6 3 5 6 3 +--R ((2870A a b - 5600B a b )d + (71750A a b - 140000B a b )d )e +--R + +--R 7 6 8 7 2 6 7 2 +--R ((- 210A b - 420B a b )d + (- 5250A a b - 10500B a b )d )e +--R * +--R 4 +--R x +--R + +--R 7 2 8 8 +--R (- 60A a d - 1500A a d)e +--R + +--R 6 7 3 7 8 2 7 +--R ((240A a b - 24B a )d + (6000A a b - 600B a )d )e +--R + +--R 5 2 6 4 6 2 7 3 6 +--R ((- 200A a b + 152B a b)d + (- 5000A a b + 3800B a b)d )e +--R + +--R 4 3 5 2 5 5 3 6 2 4 5 +--R ((420A a b - 1032B a b )d + (10500A a b - 25800B a b )d )e +--R + +--R 3 4 4 3 6 4 4 5 3 5 4 +--R ((13300A a b - 8176B a b )d + (332500A a b - 204400B a b )d )e +--R + +--R 2 5 3 4 7 3 5 4 4 6 3 +--R ((10360A a b - 12040B a b )d + (259000A a b - 301000B a b )d )e +--R + +--R 6 2 5 8 2 6 3 5 7 2 +--R ((1680A a b - 4200B a b )d + (42000A a b - 105000B a b )d )e +--R + +--R 7 6 9 7 2 6 8 +--R ((- 140A b - 280B a b )d + (- 3500A a b - 7000B a b )d )e +--R * +--R 3 +--R x +--R + +--R 7 3 8 2 7 +--R (- 90A a d - 2250A a d )e +--R + +--R 6 7 4 7 8 3 6 +--R ((510A a b - 36B a )d + (12750A a b - 900B a )d )e +--R + +--R 5 2 6 5 6 2 7 4 5 +--R ((- 1275A a b + 288B a b)d + (- 31875A a b + 7200B a b)d )e +--R + +--R 4 3 5 2 6 5 3 6 2 5 4 +--R ((3605A a b - 2078B a b )d + (90125A a b - 51950B a b )d )e +--R + +--R 3 4 4 3 7 4 4 5 3 6 3 +--R ((11200A a b - 8344B a b )d + (280000A a b - 208600B a b )d )e +--R + +--R 2 5 3 4 8 3 5 4 4 7 2 +--R ((5040A a b - 7560B a b )d + (126000A a b - 189000B a b )d )e +--R + +--R 6 2 5 9 2 6 3 5 8 +--R ((245A a b - 1400B a b )d + (6125A a b - 35000B a b )d )e +--R + +--R 7 6 10 7 2 6 9 +--R (- 35A b - 70B a b )d + (- 875A a b - 1750B a b )d +--R * +--R 2 +--R x +--R + +--R 7 4 8 3 6 +--R (- 60A a d - 1500A a d )e +--R + +--R 6 7 5 7 8 4 5 +--R ((390A a b - 24B a )d + (9750A a b - 600B a )d )e +--R + +--R 5 2 6 6 6 2 7 5 4 +--R ((- 1190A a b + 212B a b)d + (- 29750A a b + 5300B a b)d )e +--R + +--R 4 3 5 2 7 5 3 6 2 6 3 +--R ((3500A a b - 1568B a b )d + (87500A a b - 39200B a b )d )e +--R + +--R 3 4 4 3 8 4 4 5 3 7 2 +--R ((4200A a b - 4200B a b )d + (105000A a b - 105000B a b )d )e +--R + +--R 2 5 3 4 9 3 5 4 4 8 +--R ((910A a b - 1960B a b )d + (22750A a b - 49000B a b )d )e +--R + +--R 6 2 5 10 2 6 3 5 9 +--R (- 70A a b - 140B a b )d + (- 1750A a b - 3500B a b )d +--R * +--R x +--R + +--R 7 5 8 4 5 +--R (- 15A a d - 375A a d )e +--R + +--R 6 7 6 7 8 5 4 +--R ((105A a b - 6B a )d + (2625A a b - 150B a )d )e +--R + +--R 5 2 6 7 6 2 7 6 3 +--R ((- 350A a b + 56B a b)d + (- 8750A a b + 1400B a b)d )e +--R + +--R 4 3 5 2 8 5 3 6 2 7 2 +--R ((1050A a b - 420B a b )d + (26250A a b - 10500B a b )d )e +--R + +--R 3 4 4 3 9 4 4 5 3 8 +--R ((525A a b - 840B a b )d + (13125A a b - 21000B a b )d )e +--R + +--R 2 5 3 4 10 3 5 4 4 9 +--R (- 35A a b - 70B a b )d + (- 875A a b - 1750B a b )d +--R / +--R 8 2 4 10 7 3 5 9 6 4 6 8 5 5 7 7 +--R 525a b d e - 3150a b d e + 7875a b d e - 10500a b d e +--R + +--R 4 6 8 6 3 7 9 5 2 8 10 4 +--R 7875a b d e - 3150a b d e + 525a b d e +--R * +--R 6 +--R x +--R + +--R 9 4 10 8 2 5 9 7 3 6 8 6 4 7 7 +--R 1050a b d e - 4200a b d e + 3150a b d e + 10500a b d e +--R + +--R 5 5 8 6 4 6 9 5 3 7 10 4 2 8 11 3 +--R - 26250a b d e + 25200a b d e - 11550a b d e + 2100a b d e +--R * +--R 5 +--R x +--R + +--R 10 4 10 9 5 9 8 2 6 8 7 3 7 7 +--R 525a d e + 1050a b d e - 14175a b d e + 33600a b d e +--R + +--R 6 4 8 6 5 5 9 5 4 6 10 4 3 7 11 3 +--R - 28875a b d e - 3150a b d e + 22575a b d e - 14700a b d e +--R + +--R 2 8 12 2 +--R 3150a b d e +--R * +--R 4 +--R x +--R + +--R 10 5 9 9 6 8 8 2 7 7 7 3 8 6 +--R 2100a d e - 6300a b d e - 4200a b d e + 39900a b d e +--R + +--R 6 4 9 5 5 5 10 4 4 6 11 3 3 7 12 2 +--R - 63000a b d e + 39900a b d e - 4200a b d e - 6300a b d e +--R + +--R 2 8 13 +--R 2100a b d e +--R * +--R 3 +--R x +--R + +--R 10 6 8 9 7 7 8 2 8 6 7 3 9 5 +--R 3150a d e - 14700a b d e + 22575a b d e - 3150a b d e +--R + +--R 6 4 10 4 5 5 11 3 4 6 12 2 3 7 13 +--R - 28875a b d e + 33600a b d e - 14175a b d e + 1050a b d e +--R + +--R 2 8 14 +--R 525a b d +--R * +--R 2 +--R x +--R + +--R 10 7 7 9 8 6 8 2 9 5 7 3 10 4 +--R 2100a d e - 11550a b d e + 25200a b d e - 26250a b d e +--R + +--R 6 4 11 3 5 5 12 2 4 6 13 3 7 14 +--R 10500a b d e + 3150a b d e - 4200a b d e + 1050a b d +--R * +--R x +--R + +--R 10 8 6 9 9 5 8 2 10 4 7 3 11 3 +--R 525a d e - 3150a b d e + 7875a b d e - 10500a b d e +--R + +--R 6 4 12 2 5 5 13 4 6 14 +--R 7875a b d e - 3150a b d e + 525a b d +--R Type: Union(Expression(Integer),...) +--E 1231 + +--S 1232 of 1293 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 +--R (- 15A a d - 375A a )e +--R + +--R 4 5 2 5 6 4 +--R ((105A a b - 6B a )d + (2625A a b - 150B a )d)e +--R + +--R 3 2 4 3 4 2 5 2 3 +--R ((- 350A a b + 56B a b)d + (- 8750A a b + 1400B a b)d )e +--R + +--R 2 3 3 2 4 3 3 4 2 3 2 +--R ((1050A a b - 420B a b )d + (26250A a b - 10500B a b )d )e +--R + +--R 4 2 3 5 2 4 3 3 4 +--R ((525A a b - 840B a b )d + (13125A a b - 21000B a b )d )e +--R + +--R 5 4 6 5 2 4 5 +--R (- 35A b - 70B a b )d + (- 875A a b - 1750B a b )d +--R / +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 +--R 525a d e - 3150a b d e + 7875a b d e - 10500a b d e + 7875a b d e +--R + +--R 3 5 9 2 6 10 +--R - 3150a b d e + 525a b d +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1233 + +)clear all + +--S 1234 of 1293 +t0:=(a+b*x)*(c+d*x)^n/(e+f*x)^n +--R +--R +--R n +--R (b x + a)(d x + c) +--R (1) ------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1293 +--r0:=1/2*b*(c+d*x)^(1+n)*(e+f*x)^(1-n)/(d*f)+1/2*(2*a*d*f-b*(c*f*(1-n)+_ +--d*e*(1+n)))*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/_ +--(d*f^2*(1-n)*(-f*(c+d*x)/(d*e-c*f))^n) +--E 1235 + +--S 1236 of 1293 +--a0:=integrate(t0,x) +--E 1236 + +--S 1237 of 1293 +--m0:=a0-r0 +--E 1237 + +--S 1238 of 1293 +--d0:=D(m0,x) +--E 1238 + +)clear all + +--S 1239 of 1293 +t0:=(a+b*x)*(c+d*x)^(-1+n)/(e+f*x)^n +--R +--R +--R n - 1 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1293 +--r0:=-(b*c-a*d)*(c+d*x)^n*(e+f*x)^(1-n)/(d*(d*e-c*f)*n)-(a*d*f-b*(c*f*(1-n)+_ +--d*e*n))*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/(d*f*(d*e-c*f)*(1-n)*n*_ +--(-f*(c+d*x)/(d*e-c*f))^n) +--E 1240 + +--S 1241 of 1293 +--a0:=integrate(t0,x) +--E 1241 + +--S 1242 of 1293 +--m0:=a0-r0 +--E 1242 + +--S 1243 of 1293 +--d0:=D(m0,x) +--E 1243 + +)clear all + +--S 1244 of 1293 +t0:=(a+b*x)*(c+d*x)^(-2+n)/(e+f*x)^n +--R +--R +--R n - 2 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1293 +--r0:=(b*c-a*d)*(c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(1-n))+_ +--b*(c+d*x)^n*(e+f*x)^(1-n)/(d*(d*e-c*f)*n)-b*(c+d*x)^n*(e+f*x)^(1-n)*_ +--hypergeometric(1-n,-n,2-n,d*(e+f*x)/(d*e-c*f))/(d*(d*e-c*f)*(1-n)*n*_ +--(-f*(c+d*x)/(d*e-c*f))^n) +--E 1245 + +--S 1246 of 1293 +--a0:=integrate(t0,x) +--E 1246 + +--S 1247 of 1293 +--m0:=a0-r0 +--E 1247 + +--S 1248 of 1293 +--d0:=D(m0,x) +--E 1248 + +)clear all + +--S 1249 of 1293 +t0:=(a+b*x)*(c+d*x)^(-3+n)/(e+f*x)^n +--R +--R +--R n - 3 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(2-n))+_ + (a*d*f+b*(c*f*(1-n)-d*e*(2-n)))*(c+d*x)^(-1+n)*_ + (e+f*x)^(1-n)/(d*(d*e-c*f)^2*(1-n)*(2-n)) +--R +--R +--R (2) +--R n - 1 +--R ((- b c f + b d e)n + (a d + b c)f - 2b d e)(d x + c) +--R + +--R 2 2 2 +--R ((- a c d + b c )f + (a d - b c d)e)n + (a c d - b c )f +--R + +--R 2 +--R (- a d + b c d)e +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 2 2 2 3 2 2 2 2 2 3 2 2 2 +--R (c d f - 2c d e f + d e )n + (- 3c d f + 6c d e f - 3d e )n + 2c d f +--R + +--R 2 3 2 +--R - 4c d e f + 2d e +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 3 +--R ((- b c d f + b d e f)n + (a d + b c d)f - 2b d e f)x +--R + +--R 2 2 2 2 2 2 2 +--R ((- a c d - b c )f + a d e f + b d e )n + (3a c d + b c )f +--R + +--R 2 2 +--R - 2b c d e f - 2b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (- a c f - b c e f + (a d + b c d)e )n + 2a c f + 2a c d e f +--R + +--R 2 2 +--R (- a d - 3b c d)e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R (- a c e f + a c d e )n + 2a c e f + (- a c d - b c )e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (c f - 2c d e f + d e )n + (- 3c f + 6c d e f - 3d e )n + 2c f +--R + +--R 2 2 +--R - 4c d e f + 2d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1251 + +--S 1252 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R n - 1 +--R ((b c f - b d e)n + (- a d - b c)f + 2b d e)(d x + c) +--R + +--R 2 2 2 +--R ((a c d - b c )f + (- a d + b c d)e)n + (- a c d + b c )f +--R + +--R 2 +--R (a d - b c d)e +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 2 2 3 3 2 2 3 3 +--R ((- b c d f + b d e f)n + (a d + b c d )f - 2b d e f)x +--R + +--R 2 2 2 3 3 2 2 2 2 +--R ((- a c d - b c d)f + a d e f + b d e )n + (3a c d + b c d)f +--R + +--R 2 3 2 +--R - 2b c d e f - 2b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 3 2 2 2 2 +--R (- a c d f - b c d e f + (a d + b c d )e )n + 2a c d f +--R + +--R 2 3 2 2 +--R 2a c d e f + (- a d - 3b c d )e +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (- a c d e f + a c d e )n + 2a c d e f + (- a c d - b c d)e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 3 2 2 2 2 2 3 2 +--R (c d f - 2c d e f + d e )n + (- 3c d f + 6c d e f - 3d e )n +--R + +--R 2 2 2 3 2 +--R 2c d f - 4c d e f + 2d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 2 n - 2 +--R ((b c d f - b d e)n + (- a d - b c d)f + 2b d e)(d x + c) +--R + +--R 2 2 3 2 +--R ((a c d - b c d)f + (- a d + b c d )e)n +--R + +--R 2 2 3 2 +--R (- 2a c d + 2b c d)f + (2a d - 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 2 2 n - 1 +--R ((- b c f + b d e f)n + (a d + b c)f - 2b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R ((- a c d + b c )f + (a d - b c d)e f)n + (a c d - b c )f +--R + +--R 2 +--R (- a d + b c d)e f +--R * +--R n - 2 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 2 2 2 3 2 2 2 2 +--R (b c d f - 2b c d e f + b d e )n - 2b c d f + 4b c d e f +--R + +--R 3 2 +--R - 2b d e +--R * +--R x +--R + +--R 2 2 2 3 2 2 2 2 3 2 +--R (a c d f - 2a c d e f + a d e )n - 2a c d f + 4a c d e f - 2a d e +--R * +--R (n - 3)log(d x + c) +--R %e +--R / +--R 2 2 2 3 2 2 2 2 3 2 n log(f x + e) +--R ((c d f - 2c d e f + d e )n - 2c d f + 4c d e f - 2d e )%e +--R Type: Expression(Integer) +--E 1253 + +)clear all + +--S 1254 of 1293 +t0:=(a+b*x)*(c+d*x)^(-4+n)/(e+f*x)^n +--R +--R +--R n - 4 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(3-n))+_ + (2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/_ + (d*(d*e-c*f)^2*(2-n)*(3-n))-f*(2*a*d*f+b*(c*f*(1-n)-d*e*(3-n)))*_ + (c+d*x)^(-1+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(1-n)*(2-n)*(3-n)) +--R +--R +--R (2) +--R 2 2 n - 1 +--R ((b c f - b d e f)n + (- 2a d - b c)f + 3b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R (- b c f + 2b c d e f - b d e )n +--R + +--R 2 2 2 2 2 +--R ((2a c d + 2b c )f + (- 2a d - 6b c d)e f + 4b d e )n +--R + +--R 2 2 2 2 2 +--R (- 2a c d - b c )f + (2a d + 4b c d)e f - 3b d e +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 2 +--R (- a c d + b c )f + (2a c d - 2b c d)e f +--R + +--R 3 2 2 +--R (- a d + b c d )e +--R * +--R 2 +--R n +--R + +--R 2 3 2 2 2 +--R (3a c d - 3b c )f + (- 6a c d + 6b c d)e f +--R + +--R 3 2 2 +--R (3a d - 3b c d )e +--R * +--R n +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 2a c d + 2b c )f + (4a c d - 4b c d)e f + (- 2a d + 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 3 3 2 2 2 3 2 4 3 3 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 6c d f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (11c d f - 33c d e f + 33c d e f - 11d e )n - 6c d f + 18c d e f +--R + +--R 3 2 4 3 +--R - 18c d e f + 6d e +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 3 3 2 4 +--R ((b c d f - b d e f )n + (- 2a d - b c d )f + 3b d e f )x +--R + +--R 2 3 2 2 3 2 2 +--R (- b c d f + 2b c d e f - b d e f)n +--R + +--R 2 2 3 3 2 2 3 2 +--R ((2a c d + 5b c d)f + (- 2a d - 8b c d )e f + 3b d e f)n +--R + +--R 2 2 3 2 2 +--R (- 8a c d - 4b c d)f + 12b c d e f +--R * +--R 3 +--R x +--R + +--R 2 3 3 2 2 2 +--R (- a c d - b c )f + (2a c d + b c d)e f +--R + +--R 3 2 2 3 3 +--R (- a d + b c d )e f - b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (7a c d + 4b c )f + (- 8a c d - 4b c d)e f +--R + +--R 3 2 2 3 3 +--R (a d - 4b c d )e f + 4b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 2 3 3 +--R (- 12a c d - 3b c )f + 9b c d e f + 9b c d e f - 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 2 3 2 2 2 2 +--R - a c f + (a c d - b c )e f + (a c d + 2b c d)e f +--R + +--R 3 2 3 +--R (- a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 3 3 2 3 2 2 2 2 +--R 5a c f + (- a c d + 3b c )e f + (- 7a c d - 8b c d)e f +--R + +--R 3 2 3 +--R (3a d + 5b c d )e +--R * +--R n +--R + +--R 3 3 2 2 2 2 2 +--R - 6a c f - 6a c d e f + (6a c d + 12b c d)e f +--R + +--R 3 2 3 +--R (- 2a d - 4b c d )e +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 +--R (- a c e f + 2a c d e f - a c d e )n +--R + +--R 3 2 2 3 2 2 2 3 3 2 +--R (5a c e f + (- 8a c d - b c )e f + (3a c d + b c d)e )n - 6a c e f +--R + +--R 2 3 2 2 2 3 +--R (6a c d + 3b c )e f + (- 2a c d - b c d)e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (c f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6c f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11c f - 33c d e f + 33c d e f - 11d e )n - 6c f + 18c d e f +--R + +--R 2 2 3 3 +--R - 18c d e f + 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1256 + +--S 1257 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n - 1 +--R ((- b c f + b d e f)n + (2a d + b c)f - 3b d e f)(d x + c) +--R + +--R 2 2 2 2 2 +--R (b c f - 2b c d e f + b d e )n +--R + +--R 2 2 2 2 2 +--R ((- 2a c d - 2b c )f + (2a d + 6b c d)e f - 4b d e )n +--R + +--R 2 2 2 2 2 +--R (2a c d + b c )f + (- 2a d - 4b c d)e f + 3b d e +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 2 +--R (a c d - b c )f + (- 2a c d + 2b c d)e f +--R + +--R 3 2 2 +--R (a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 2 3 2 2 2 +--R (- 3a c d + 3b c )f + (6a c d - 6b c d)e f +--R + +--R 3 2 2 +--R (- 3a d + 3b c d )e +--R * +--R n +--R + +--R 2 3 2 2 2 3 2 2 +--R (2a c d - 2b c )f + (- 4a c d + 4b c d)e f + (2a d - 2b c d )e +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 3 3 4 2 4 3 3 4 2 4 +--R ((b c d f - b d e f )n + (- 2a d - b c d )f + 3b d e f )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (- b c d f + 2b c d e f - b d e f)n +--R + +--R 3 2 2 3 4 3 2 4 2 +--R ((2a c d + 5b c d )f + (- 2a d - 8b c d )e f + 3b d e f)n +--R + +--R 3 2 2 3 3 2 +--R (- 8a c d - 4b c d )f + 12b c d e f +--R * +--R 3 +--R x +--R + +--R 2 2 3 3 3 2 2 2 +--R (- a c d - b c d)f + (2a c d + b c d )e f +--R + +--R 4 3 2 4 3 +--R (- a d + b c d )e f - b d e +--R * +--R 2 +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (7a c d + 4b c d)f + (- 8a c d - 4b c d )e f +--R + +--R 4 3 2 4 3 +--R (a d - 4b c d )e f + 4b d e +--R * +--R n +--R + +--R 2 2 3 3 2 2 2 3 2 4 3 +--R (- 12a c d - 3b c d)f + 9b c d e f + 9b c d e f - 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 2 2 3 2 3 2 2 2 +--R - a c d f + (a c d - b c d)e f + (a c d + 2b c d )e f +--R + +--R 4 3 3 +--R (- a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 3 3 2 2 3 2 +--R 5a c d f + (- a c d + 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 7a c d - 8b c d )e f + (3a d + 5b c d )e +--R * +--R n +--R + +--R 3 3 2 2 2 3 2 2 2 +--R - 6a c d f - 6a c d e f + (6a c d + 12b c d )e f +--R + +--R 4 3 3 +--R (- 2a d - 4b c d )e +--R * +--R x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- a c d e f + 2a c d e f - a c d e )n +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R (5a c d e f + (- 8a c d - b c d)e f + (3a c d + b c d )e )n +--R + +--R 3 2 2 2 3 2 3 2 2 3 +--R - 6a c d e f + (6a c d + 3b c d)e f + (- 2a c d - b c d )e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 3 2 4 3 3 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (- 6c d f + 18c d e f - 18c d e f + 6d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (11c d f - 33c d e f + 33c d e f - 11d e )n - 6c d f + 18c d e f +--R + +--R 3 2 4 3 +--R - 18c d e f + 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 2 2 2 2 +--R ((- b c d f + b d e f)n + (2a d + b c d)f - 3b d e f) +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 2 2 3 2 2 +--R (b c d f - 2b c d e f + b d e )n +--R + +--R 2 2 2 3 2 3 2 +--R ((- 2a c d - 3b c d)f + (2a d + 8b c d )e f - 5b d e )n +--R + +--R 2 2 2 3 2 3 2 +--R (4a c d + 2b c d)f + (- 4a d - 8b c d )e f + 6b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 2 2 3 2 3 2 2 +--R (a c d - b c d)f + (- 2a c d + 2b c d )e f +--R + +--R 4 3 2 +--R (a d - b c d )e +--R * +--R 2 +--R n +--R + +--R 2 2 3 2 3 2 2 +--R (- 5a c d + 5b c d)f + (10a c d - 10b c d )e f +--R + +--R 4 3 2 +--R (- 5a d + 5b c d )e +--R * +--R n +--R + +--R 2 2 3 2 3 2 2 +--R (6a c d - 6b c d)f + (- 12a c d + 12b c d )e f +--R + +--R 4 3 2 +--R (6a d - 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 3 2 3 2 +--R ((b c f - b d e f )n + (- 2a d - b c)f + 3b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 3 2 2 2 2 +--R (- b c f + 2b c d e f - b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((2a c d + 2b c )f + (- 2a d - 6b c d)e f + 4b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (- 2a c d - b c )f + (2a d + 4b c d)e f - 3b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 3 2 2 2 +--R (- a c d + b c )f + (2a c d - 2b c d)e f +--R + +--R 3 2 2 +--R (- a d + b c d )e f +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (3a c d - 3b c )f + (- 6a c d + 6b c d)e f +--R + +--R 3 2 2 +--R (3a d - 3b c d )e f +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 2a c d + 2b c )f + (4a c d - 4b c d)e f +--R + +--R 3 2 2 +--R (- 2a d + 2b c d )e f +--R * +--R n - 3 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (b c d f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (- 5b c d f + 15b c d e f - 15b c d e f + 5b d e )n + 6b c d f +--R + +--R 2 2 2 3 2 4 3 +--R - 18b c d e f + 18b c d e f - 6b d e +--R * +--R x +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (a c d f - 3a c d e f + 3a c d e f - a d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 +--R (- 5a c d f + 15a c d e f - 15a c d e f + 5a d e )n + 6a c d f +--R + +--R 2 2 2 3 2 4 3 +--R - 18a c d e f + 18a c d e f - 6a d e +--R * +--R (n - 4)log(d x + c) +--R %e +--R / +--R 3 3 2 2 2 3 2 4 3 2 +--R (c d f - 3c d e f + 3c d e f - d e )n +--R + +--R 3 3 2 2 2 3 2 4 3 3 3 2 2 2 +--R (- 5c d f + 15c d e f - 15c d e f + 5d e )n + 6c d f - 18c d e f +--R + +--R 3 2 4 3 +--R 18c d e f - 6d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1258 + +)clear all + +--S 1259 of 1293 +t0:=(a+b*x)*(c+d*x)^(-5+n)/(e+f*x)^n +--R +--R +--R n - 5 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1293 +r0:=(b*c-a*d)*(c+d*x)^(-4+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(4-n))+_ + (3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/_ + (d*(d*e-c*f)^2*(3-n)*(4-n))-2*f*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*_ + (c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)^3*(2-n)*(3-n)*(4-n))+_ + 2*f^2*(3*a*d*f+b*(c*f*(1-n)-d*e*(4-n)))*(c+d*x)^(-1+n)*_ + (e+f*x)^(1-n)/(d*(d*e-c*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) +--R +--R +--R (2) +--R 3 2 3 2 n - 1 +--R ((- 2b c f + 2b d e f )n + (6a d + 2b c)f - 8b d e f )(d x + c) +--R + +--R 2 3 2 2 2 2 +--R (2b c f - 4b c d e f + 2b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((- 6a c d - 4b c )f + (6a d + 14b c d)e f - 10b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (6a c d + 2b c )f + (- 6a d - 10b c d)e f + 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- b c f + 3b c d e f - 3b c d e f + b d e )n +--R + +--R 2 3 3 2 2 2 +--R (3a c d + 4b c )f + (- 6a c d - 15b c d)e f +--R + +--R 3 2 2 3 3 +--R (3a d + 18b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 9a c d - 5b c )f + (18a c d + 24b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 9a d - 33b c d )e f + 14b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (6a c d + 2b c )f + (- 12a c d - 12b c d)e f +--R + +--R 3 2 2 3 3 +--R (6a d + 18b c d )e f - 8b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 3 2 2 3 2 +--R (- a c d + b c )f + (3a c d - 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 3a c d + 3b c d )e f + (a d - b c d )e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 11a c d + 11b c )f + (33a c d - 33b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 33a c d + 33b c d )e f + (11a d - 11b c d )e +--R * +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 10c d f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (35c d f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 50c d f + 200c d e f - 300c d e f + 200c d e f - 50d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 24c d f - 96c d e f + 144c d e f - 96c d e f + 24d e +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 4 3 4 4 3 5 +--R ((- 2b c d f + 2b d e f )n + (6a d + 2b c d )f - 8b d e f )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2b c d f - 4b c d e f + 2b d e f )n +--R + +--R 3 2 2 4 4 3 3 4 2 2 +--R ((- 6a c d - 12b c d )f + (6a d + 20b c d )e f - 8b d e f )n +--R + +--R 3 2 2 4 3 3 +--R (30a c d + 10b c d )f - 40b c d e f +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- b c d f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 2 3 4 3 2 2 3 +--R (3a c d + 10b c d)f + (- 6a c d - 25b c d )e f +--R + +--R 4 3 2 2 4 3 +--R (3a d + 20b c d )e f - 5b d e f +--R * +--R 2 +--R n +--R + +--R 2 2 3 4 3 2 2 3 +--R (- 27a c d - 29b c d)f + (30a c d + 66b c d )e f +--R + +--R 4 3 2 2 4 3 +--R (- 3a d - 41b c d )e f + 4b d e f +--R * +--R n +--R + +--R 2 2 3 4 2 2 3 +--R (60a c d + 20b c d)f - 80b c d e f +--R * +--R 3 +--R x +--R + +--R 3 4 4 2 2 3 3 3 2 2 +--R (- a c d - b c )f + (3a c d + 2b c d)e f - 3a c d e f +--R + +--R 4 3 3 4 4 +--R (a d - 2b c d )e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (12a c d + 8b c )f + (- 27a c d - 14b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (18a c d - 3b c d )e f + (- 3a d + 16b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (- 47a c d - 19b c )f + (60a c d + 36b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 4 4 +--R (- 15a c d + 15b c d )e f + (2a d - 46b c d )e f + 14b d e +--R * +--R n +--R + +--R 3 4 4 3 3 2 2 2 2 3 3 +--R (60a c d + 12b c )f - 48b c d e f - 48b c d e f + 32b c d e f +--R + +--R 4 4 +--R - 8b d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 4 3 3 2 2 +--R - a c f + (2a c d - b c )e f + 3b c d e f +--R + +--R 3 2 2 3 4 3 4 +--R (- 2a c d - 3b c d )e f + (a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R 9a c f + (- 12a c d + 7b c )e f + (- 9a c d - 22b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (18a c d + 23b c d )e f + (- 6a d - 8b c d )e +--R * +--R 2 +--R n +--R + +--R 4 4 3 4 3 2 2 3 2 2 +--R - 26a c f + (10a c d - 12b c )e f + (45a c d + 55b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (- 40a c d - 60b c d )e f + (11a d + 17b c d )e +--R * +--R n +--R + +--R 4 4 3 3 2 2 3 2 2 +--R 24a c f + 24a c d e f + (- 36a c d - 60b c d)e f +--R + +--R 3 2 2 3 4 3 4 +--R (24a c d + 40b c d )e f + (- 6a d - 10b c d )e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- a c e f + 3a c d e f - 3a c d e f + a c d e )n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 9a c e f + (- 24a c d - b c )e f + (21a c d + 2b c d)e f +--R + +--R 3 2 2 4 +--R (- 6a c d - b c d )e +--R * +--R 2 +--R n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R - 26a c e f + (57a c d + 7b c )e f + (- 42a c d - 10b c d)e f +--R + +--R 3 2 2 4 +--R (11a c d + 3b c d )e +--R * +--R n +--R + +--R 4 3 3 4 2 2 2 2 3 3 +--R 24a c e f + (- 36a c d - 12b c )e f + (24a c d + 8b c d)e f +--R + +--R 3 2 2 4 +--R (- 6a c d - 2b c d )e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (c f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 10c f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35c f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (- 50c f + 200c d e f - 300c d e f + 200c d e f - 50d e )n + 24c f +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96c d e f + 144c d e f - 96c d e f + 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1261 + +--S 1262 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 2 +--R ((2b c f - 2b d e f )n + (- 6a d - 2b c)f + 8b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 3 2 2 2 2 +--R (- 2b c f + 4b c d e f - 2b d e f)n +--R + +--R 2 3 2 2 2 2 +--R ((6a c d + 4b c )f + (- 6a d - 14b c d)e f + 10b d e f)n +--R + +--R 2 3 2 2 2 2 +--R (- 6a c d - 2b c )f + (6a d + 10b c d)e f - 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (b c f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 2 3 3 2 2 2 +--R (- 3a c d - 4b c )f + (6a c d + 15b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 3a d - 18b c d )e f + 7b d e +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 2 2 +--R (9a c d + 5b c )f + (- 18a c d - 24b c d)e f +--R + +--R 3 2 2 3 3 +--R (9a d + 33b c d )e f - 14b d e +--R * +--R n +--R + +--R 2 3 3 2 2 2 +--R (- 6a c d - 2b c )f + (12a c d + 12b c d)e f +--R + +--R 3 2 2 3 3 +--R (- 6a d - 18b c d )e f + 8b d e +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 3 2 2 3 2 +--R (a c d - b c )f + (- 3a c d + 3b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (3a c d - 3b c d )e f + (- a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 6a c d + 6b c )f + (18a c d - 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 18a c d + 18b c d )e f + (6a d - 6b c d )e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (11a c d - 11b c )f + (- 33a c d + 33b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (33a c d - 33b c d )e f + (- 11a d + 11b c d )e +--R * +--R n +--R + +--R 3 4 3 2 2 3 2 +--R (- 6a c d + 6b c )f + (18a c d - 18b c d)e f +--R + +--R 3 2 2 2 4 3 3 +--R (- 18a c d + 18b c d )e f + (6a d - 6b c d )e +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n + 1 n log(f x + e) +--R (f x + e) %e +--R + +--R 4 4 5 3 5 4 4 5 3 5 +--R ((- 2b c d f + 2b d e f )n + (6a d + 2b c d )f - 8b d e f )x +--R + +--R 2 3 4 4 3 5 2 2 2 +--R (2b c d f - 4b c d e f + 2b d e f )n +--R + +--R 4 2 3 4 5 4 3 5 2 2 +--R ((- 6a c d - 12b c d )f + (6a d + 20b c d )e f - 8b d e f )n +--R + +--R 4 2 3 4 4 3 +--R (30a c d + 10b c d )f - 40b c d e f +--R * +--R 4 +--R x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 3 +--R (- b c d f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (3a c d + 10b c d )f + (- 6a c d - 25b c d )e f +--R + +--R 5 4 2 2 5 3 +--R (3a d + 20b c d )e f - 5b d e f +--R * +--R 2 +--R n +--R + +--R 2 3 3 2 4 4 2 3 3 +--R (- 27a c d - 29b c d )f + (30a c d + 66b c d )e f +--R + +--R 5 4 2 2 5 3 +--R (- 3a d - 41b c d )e f + 4b d e f +--R * +--R n +--R + +--R 2 3 3 2 4 2 3 3 +--R (60a c d + 20b c d )f - 80b c d e f +--R * +--R 3 +--R x +--R + +--R 3 2 4 4 2 3 3 2 3 4 2 2 +--R (- a c d - b c d)f + (3a c d + 2b c d )e f - 3a c d e f +--R + +--R 5 4 3 5 4 +--R (a d - 2b c d )e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (12a c d + 8b c d)f + (- 27a c d - 14b c d )e f +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (18a c d - 3b c d )e f + (- 3a d + 16b c d )e f - 7b d e +--R * +--R 2 +--R n +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- 47a c d - 19b c d)f + (60a c d + 36b c d )e f +--R + +--R 4 2 3 2 2 5 4 3 5 4 +--R (- 15a c d + 15b c d )e f + (2a d - 46b c d )e f + 14b d e +--R * +--R n +--R + +--R 3 2 4 4 3 2 3 2 3 2 2 +--R (60a c d + 12b c d)f - 48b c d e f - 48b c d e f +--R + +--R 4 3 5 4 +--R 32b c d e f - 8b d e +--R * +--R 2 +--R x +--R + +--R 4 4 3 2 4 3 3 2 2 2 +--R - a c d f + (2a c d - b c d)e f + 3b c d e f +--R + +--R 4 2 3 3 5 4 4 +--R (- 2a c d - 3b c d )e f + (a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 4 4 3 2 4 3 +--R 9a c d f + (- 12a c d + 7b c d)e f +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (- 9a c d - 22b c d )e f + (18a c d + 23b c d )e f +--R + +--R 5 4 4 +--R (- 6a d - 8b c d )e +--R * +--R 2 +--R n +--R + +--R 4 4 3 2 4 3 +--R - 26a c d f + (10a c d - 12b c d)e f +--R + +--R 2 3 3 2 2 2 4 2 3 3 +--R (45a c d + 55b c d )e f + (- 40a c d - 60b c d )e f +--R + +--R 5 4 4 +--R (11a d + 17b c d )e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 3 2 2 2 +--R 24a c d f + 24a c d e f + (- 36a c d - 60b c d )e f +--R + +--R 4 2 3 3 5 4 4 +--R (24a c d + 40b c d )e f + (- 6a d - 10b c d )e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- a c d e f + 3a c d e f - 3a c d e f + a c d e )n +--R + +--R 4 3 3 2 4 2 2 2 3 3 2 3 +--R 9a c d e f + (- 24a c d - b c d)e f + (21a c d + 2b c d )e f +--R + +--R 4 2 3 4 +--R (- 6a c d - b c d )e +--R * +--R 2 +--R n +--R + +--R 4 3 3 2 4 2 2 +--R - 26a c d e f + (57a c d + 7b c d)e f +--R + +--R 2 3 3 2 3 4 2 3 4 +--R (- 42a c d - 10b c d )e f + (11a c d + 3b c d )e +--R * +--R n +--R + +--R 4 3 3 2 4 2 2 2 3 3 2 3 +--R 24a c d e f + (- 36a c d - 12b c d)e f + (24a c d + 8b c d )e f +--R + +--R 4 2 3 4 +--R (- 6a c d - 2b c d )e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 4 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (- 10c d f + 40c d e f - 60c d e f + 40c d e f - 10d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (35c d f - 140c d e f + 210c d e f - 140c d e f + 35d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (- 50c d f + 200c d e f - 300c d e f + 200c d e f - 50d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R 24c d f - 96c d e f + 144c d e f - 96c d e f + 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1293 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 2 2 3 2 2 +--R ((2b c d f - 2b d e f )n + (- 6a d - 2b c d)f + 8b d e f ) +--R * +--R n - 2 +--R (d x + c) +--R + +--R 2 3 2 2 3 2 2 +--R (- 2b c d f + 4b c d e f - 2b d e f)n +--R + +--R 2 2 3 3 2 2 +--R (6a c d + 6b c d)f + (- 6a d - 18b c d )e f +--R + +--R 3 2 +--R 12b d e f +--R * +--R n +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 12a c d - 4b c d)f + (12a d + 20b c d )e f - 16b d e f +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 3 2 2 2 3 2 4 3 3 +--R (b c d f - 3b c d e f + 3b c d e f - b d e )n +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 3a c d - 6b c d)f + (6a c d + 21b c d )e f +--R + +--R 4 3 2 4 3 +--R (- 3a d - 24b c d )e f + 9b d e +--R * +--R 2 +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (15a c d + 11b c d)f + (- 30a c d - 48b c d )e f +--R + +--R 4 3 2 4 3 +--R (15a d + 63b c d )e f - 26b d e +--R * +--R n +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 18a c d - 6b c d)f + (36a c d + 36b c d )e f +--R + +--R 4 3 2 4 3 +--R (- 18a d - 54b c d )e f + 24b d e +--R * +--R n - 4 +--R (d x + c) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (a c d - b c d)f + (- 3a c d + 3b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (3a c d - 3b c d )e f + (- a d + b c d )e +--R * +--R 3 +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 9a c d + 9b c d)f + (27a c d - 27b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (- 27a c d + 27b c d )e f + (9a d - 9b c d )e +--R * +--R 2 +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (26a c d - 26b c d)f + (- 78a c d + 78b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (78a c d - 78b c d )e f + (- 26a d + 26b c d )e +--R * +--R n +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 24a c d + 24b c d)f + (72a c d - 72b c d )e f +--R + +--R 4 2 3 2 5 4 3 +--R (- 72a c d + 72b c d )e f + (24a d - 24b c d )e +--R * +--R n - 5 +--R (d x + c) +--R * +--R - n + 1 +--R (f x + e) +--R + +--R 4 3 4 3 +--R ((- 2b c f + 2b d e f )n + (6a d + 2b c)f - 8b d e f ) +--R * +--R n - 1 +--R (d x + c) +--R + +--R 2 4 3 2 2 2 2 +--R (2b c f - 4b c d e f + 2b d e f )n +--R + +--R 2 4 2 3 2 2 2 +--R ((- 6a c d - 4b c )f + (6a d + 14b c d)e f - 10b d e f )n +--R + +--R 2 4 2 3 2 2 2 +--R (6a c d + 2b c )f + (- 6a d - 10b c d)e f + 8b d e f +--R * +--R n - 2 +--R (d x + c) +--R + +--R 3 4 2 3 2 2 2 3 3 3 +--R (- b c f + 3b c d e f - 3b c d e f + b d e f)n +--R + +--R 2 3 4 2 2 3 +--R (3a c d + 4b c )f + (- 6a c d - 15b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (3a d + 18b c d )e f - 7b d e f +--R * +--R 2 +--R n +--R + +--R 2 3 4 2 2 3 +--R (- 9a c d - 5b c )f + (18a c d + 24b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (- 9a d - 33b c d )e f + 14b d e f +--R * +--R n +--R + +--R 2 3 4 2 2 3 +--R (6a c d + 2b c )f + (- 12a c d - 12b c d)e f +--R + +--R 3 2 2 2 3 3 +--R (6a d + 18b c d )e f - 8b d e f +--R * +--R n - 3 +--R (d x + c) +--R + +--R 3 4 4 2 2 3 3 +--R (- a c d + b c )f + (3a c d - 3b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 3a c d + 3b c d )e f + (a d - b c d )e f +--R * +--R 3 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e f +--R * +--R 2 +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (- 11a c d + 11b c )f + (33a c d - 33b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (- 33a c d + 33b c d )e f + (11a d - 11b c d )e f +--R * +--R n +--R + +--R 3 4 4 2 2 3 3 +--R (6a c d - 6b c )f + (- 18a c d + 18b c d)e f +--R + +--R 3 2 2 2 2 4 3 3 +--R (18a c d - 18b c d )e f + (- 6a d + 6b c d )e f +--R * +--R n - 4 +--R (d x + c) +--R * +--R - n +--R (f x + e) +--R * +--R n log(f x + e) +--R %e +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (b c d f - 4b c d e f + 6b c d e f - 4b c d e f + b d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 9b c d f + 36b c d e f - 54b c d e f + 36b c d e f +--R + +--R 5 4 +--R - 9b d e +--R * +--R 2 +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 26b c d f - 104b c d e f + 156b c d e f - 104b c d e f +--R + +--R 5 4 +--R 26b d e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R - 24b c d f + 96b c d e f - 144b c d e f + 96b c d e f +--R + +--R 5 4 +--R - 24b d e +--R * +--R x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (a c d f - 4a c d e f + 6a c d e f - 4a c d e f + a d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (- 9a c d f + 36a c d e f - 54a c d e f + 36a c d e f - 9a d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 +--R 26a c d f - 104a c d e f + 156a c d e f - 104a c d e f +--R + +--R 5 4 +--R 26a d e +--R * +--R n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 24a c d f + 96a c d e f - 144a c d e f + 96a c d e f - 24a d e +--R * +--R (n - 5)log(d x + c) +--R %e +--R / +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3 +--R (c d f - 4c d e f + 6c d e f - 4c d e f + d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2 +--R (- 9c d f + 36c d e f - 54c d e f + 36c d e f - 9d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (26c d f - 104c d e f + 156c d e f - 104c d e f + 26d e )n +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R - 24c d f + 96c d e f - 144c d e f + 96c d e f - 24d e +--R * +--R n log(f x + e) +--R %e +--R Type: Expression(Integer) +--E 1263 + +)clear all + +--S 1264 of 1293 +t0:=(c+d*x)*(e+f*x)^n/(a+b*x)^n +--R +--R +--R n +--R (d x + c)(f x + e) +--R (1) ------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1293 +--r0:=1/2*d*(a+b*x)^(1-n)*(e+f*x)^(1+n)/(b*f)+1/2*(b*(2*c*f-d*e*(1-n))-_ +--a*d*f*(1+n))*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*_ +--hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/(b*f^2*(1+n)*(a+b*x)^n) +--E 1265 + +--S 1266 of 1293 +--a0:=integrate(t0,x) +--E 1266 + +--S 1267 of 1293 +--m0:=a0-r0 +--E 1267 + +--S 1268 of 1293 +--d0:=D(m0,x) +--E 1268 + +)clear all + +--S 1269 of 1293 +t0:=(c+d*x)*(e+f*x)^(-1+n)/(a+b*x)^n +--R +--R +--R n - 1 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1293 +--r0:=(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^n/(f*(b*e-a*f)*n)+(b*(c*f-d*e*(1-n))-_ +--a*d*f*n)*(-f*(a+b*x)/(b*e-a*f))^n*(e+f*x)^(1+n)*_ +--hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/(f^2*(b*e-a*f)*n*_ +--(1+n)*(a+b*x)^n) +--E 1270 + +--S 1271 of 1293 +--a0:=integrate(t0,x) +--E 1271 + +--S 1272 of 1293 +--m0:=a0-r0 +--E 1272 + +--S 1273 of 1293 +--d0:=D(m0,x) +--E 1273 + +)clear all + +--S 1274 of 1293 +t0:=(c+d*x)*(e+f*x)^(-2+n)/(a+b*x)^n +--R +--R +--R n - 2 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1293 +--r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)*(1-n))-_ +--d*(a+b*x)^(1-n)*(e+f*x)^n/(f*(b*e-a*f)*n)+b*d*(-f*(a+b*x)/(b*e-a*f))^n*_ +--(e+f*x)^(1+n)*hypergeometric(n,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +--(f^2*(b*e-a*f)*n*(1+n)*(a+b*x)^n) +--E 1275 + +--S 1276 of 1293 +--a0:=integrate(t0,x) +--E 1276 + +--S 1277 of 1293 +--m0:=a0-r0 +--E 1277 + +--S 1278 of 1293 +--d0:=D(m0,x) +--E 1278 + +)clear all + +--S 1279 of 1293 +t0:=(c+d*x)*(e+f*x)^(-3+n)/(a+b*x)^n +--R +--R +--R n - 3 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)*(2-n))-_ + (a*d*f*(2-n)-b*(c*f+d*(e-e*n)))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/_ + (f*(b*e-a*f)^2*(1-n)*(2-n)) +--R +--R +--R (2) +--R - n + 1 +--R ((a d f - b d e)n + (- 2a d + b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 +--R (a c f + (- a d - b c)e f + b d e )n - a c f + (a d + b c)e f +--R + +--R 2 +--R - b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R / +--R 2 3 2 2 2 2 2 3 2 2 2 2 3 +--R (a f - 2a b e f + b e f)n + (- 3a f + 6a b e f - 3b e f)n + 2a f +--R + +--R 2 2 2 +--R - 4a b e f + 2b e f +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 3 +--R ((a b d f - b d e f)n + (- 2a b d + b c)f + b d e f)x +--R + +--R 2 2 2 2 2 2 2 +--R ((a d + a b c)f - b c e f - b d e )n - 2a d f +--R + +--R 2 2 2 +--R (- 2a b d + 3b c)e f + b d e +--R * +--R 2 +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (a c f + a d e f + (- a b d - b c)e )n - a c f +--R + +--R 2 2 2 +--R (- 3a d + 2a b c)e f + 2b c e +--R * +--R x +--R + +--R 2 2 2 2 2 +--R (a c e f - a b c e )n - a c e f + (- a d + 2a b c)e +--R * +--R (n - 3)log(f x + e) +--R %e +--R / +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a f - 2a b e f + b e )n + (- 3a f + 6a b e f - 3b e )n + 2a f +--R + +--R 2 2 +--R - 4a b e f + 2b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1281 + +--S 1282 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 2 3 2 2 3 +--R ((a b d f - b d e f )n + (- 2a b d + b c)f + b d e f )x +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a d + a b c)f - b c e f - b d e f)n - 2a d f +--R + +--R 2 2 2 2 +--R (- 2a b d + 3b c)e f + b d e f +--R * +--R 2 +--R x +--R + +--R 2 3 2 2 2 2 2 3 +--R (a c f + a d e f + (- a b d - b c)e f)n - a c f +--R + +--R 2 2 2 2 +--R (- 3a d + 2a b c)e f + 2b c e f +--R * +--R x +--R + +--R 2 2 2 2 2 2 2 +--R (a c e f - a b c e f)n - a c e f + (- a d + 2a b c)e f +--R * +--R (n - 3)log(f x + e) +--R %e +--R + +--R - n + 1 +--R ((- a d f + b d e)n + (2a d - b c)f - b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )n + a c f + (- a d - b c)e f +--R + +--R 2 +--R b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 2 3 2 2 2 2 2 3 2 2 2 2 3 +--R (a f - 2a b e f + b e f)n + (- 3a f + 6a b e f - 3b e f)n + 2a f +--R + +--R 2 2 2 +--R - 4a b e f + 2b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1283 + +)clear all + +--S 1284 of 1293 +t0:=(c+d*x)*(e+f*x)^(-4+n)/(a+b*x)^n +--R +--R +--R n - 4 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)*(3-n))+_ + (b*(2*c*f+d*e*(1-n))-a*d*f*(3-n))*(a+b*x)^(1-n)*_ + (e+f*x)^(-2+n)/(f*(b*e-a*f)^2*(2-n)*(3-n))+b*(b*(2*c*f+d*e*(1-n))-_ + a*d*f*(3-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/(f*(b*e-a*f)^3*(1-n)*_ + (2-n)*(3-n)) +--R +--R +--R (2) +--R 2 2 2 - n + 1 +--R ((a b d f - b d e)n + (- 3a b d + 2b c)f + b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 2 2 +--R (a d f - 2a b d e f + b d e )n +--R + +--R 2 2 2 2 2 +--R ((- 4a d + 2a b c)f + (6a b d - 2b c)e f - 2b d e )n +--R + +--R 2 2 2 2 2 +--R (3a d - 2a b c)f + (- 4a b d + 2b c)e f + b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (a c f + (- a d - 2a b c)e f + (2a b d + b c)e f - b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R (- 3a c f + (3a d + 6a b c)e f + (- 6a b d - 3b c)e f + 3b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R 2a c f + (- 2a d - 4a b c)e f + (4a b d + 2b c)e f - 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R / +--R 3 4 2 3 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (11a f - 33a b e f + 33a b e f - 11b e f)n - 6a f + 18a b e f +--R + +--R 2 2 2 3 3 +--R - 18a b e f + 6b e f +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 3 3 3 2 4 +--R ((a b d f - b d e f )n + (- 3a b d + 2b c)f + b d e f )x +--R + +--R 2 3 2 2 3 2 2 +--R (a b d f - 2a b d e f + b d e f)n +--R + +--R 2 2 3 2 3 2 3 2 +--R ((- 3a b d + 2a b c)f + (8a b d - 2b c)e f - 5b d e f)n +--R + +--R 2 3 2 3 2 +--R (- 12a b d + 8b c)e f + 4b d e f +--R * +--R 3 +--R x +--R + +--R 3 2 3 2 2 2 2 3 2 +--R (a d + a b c)f + (- a b d - 2a b c)e f + (- a b d + b c)e f +--R + +--R 3 3 +--R b d e +--R * +--R 2 +--R n +--R + +--R 3 2 3 2 2 2 2 3 2 +--R (- 4a d - a b c)f + (4a b d + 8a b c)e f + (4a b d - 7b c)e f +--R + +--R 3 3 +--R - 4b d e +--R * +--R n +--R + +--R 3 3 2 2 2 3 2 3 3 +--R 3a d f - 9a b d e f + (- 9a b d + 12b c)e f + 3b d e +--R * +--R 2 +--R x +--R + +--R 3 3 3 2 2 2 2 2 +--R a c f + (a d - a b c)e f + (- 2a b d - a b c)e f +--R + +--R 2 3 3 +--R (a b d + b c)e +--R * +--R 2 +--R n +--R + +--R 3 3 3 2 2 2 2 2 +--R - 3a c f + (- 5a d + 7a b c)e f + (8a b d + a b c)e f +--R + +--R 2 3 3 +--R (- 3a b d - 5b c)e +--R * +--R n +--R + +--R 3 3 3 2 2 2 2 2 3 3 +--R 2a c f + (4a d - 6a b c)e f + (- 12a b d + 6a b c)e f + 6b c e +--R * +--R x +--R + +--R 3 2 2 2 2 3 2 +--R (a c e f - 2a b c e f + a b c e )n +--R + +--R 3 2 3 2 2 2 2 3 3 2 +--R (- 3a c e f + (- a d + 8a b c)e f + (a b d - 5a b c)e )n + 2a c e f +--R + +--R 3 2 2 2 2 3 +--R (a d - 6a b c)e f + (- 3a b d + 6a b c)e +--R * +--R (n - 4)log(f x + e) +--R %e +--R / +--R 3 3 2 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (11a f - 33a b e f + 33a b e f - 11b e )n - 6a f + 18a b e f +--R + +--R 2 2 3 3 +--R - 18a b e f + 6b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1286 + +--S 1287 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 3 3 2 3 4 3 3 4 +--R ((a b d f - b d e f )n + (- 3a b d + 2b c)f + b d e f )x +--R + +--R 2 4 2 3 3 2 2 2 +--R (a b d f - 2a b d e f + b d e f )n +--R + +--R 2 2 4 2 3 3 3 2 2 +--R ((- 3a b d + 2a b c)f + (8a b d - 2b c)e f - 5b d e f )n +--R + +--R 2 3 3 3 2 2 +--R (- 12a b d + 8b c)e f + 4b d e f +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 2 3 +--R (a d + a b c)f + (- a b d - 2a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (- a b d + b c)e f + b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 4 2 2 3 +--R (- 4a d - a b c)f + (4a b d + 8a b c)e f +--R + +--R 2 3 2 2 3 3 +--R (4a b d - 7b c)e f - 4b d e f +--R * +--R n +--R + +--R 3 4 2 3 2 3 2 2 3 3 +--R 3a d f - 9a b d e f + (- 9a b d + 12b c)e f + 3b d e f +--R * +--R 2 +--R x +--R + +--R 3 4 3 2 3 2 2 2 2 +--R a c f + (a d - a b c)e f + (- 2a b d - a b c)e f +--R + +--R 2 3 3 +--R (a b d + b c)e f +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - 3a c f + (- 5a d + 7a b c)e f + (8a b d + a b c)e f +--R + +--R 2 3 3 +--R (- 3a b d - 5b c)e f +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 3 3 +--R 2a c f + (4a d - 6a b c)e f + (- 12a b d + 6a b c)e f + 6b c e f +--R * +--R x +--R + +--R 3 3 2 2 2 2 3 2 +--R (a c e f - 2a b c e f + a b c e f)n +--R + +--R 3 3 3 2 2 2 2 2 3 +--R (- 3a c e f + (- a d + 8a b c)e f + (a b d - 5a b c)e f)n +--R + +--R 3 3 3 2 2 2 2 2 3 +--R 2a c e f + (a d - 6a b c)e f + (- 3a b d + 6a b c)e f +--R * +--R (n - 4)log(f x + e) +--R %e +--R + +--R 2 2 2 - n + 1 +--R ((- a b d f + b d e)n + (3a b d - 2b c)f - b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 2 2 +--R (- a d f + 2a b d e f - b d e )n +--R + +--R 2 2 2 2 2 +--R ((4a d - 2a b c)f + (- 6a b d + 2b c)e f + 2b d e )n +--R + +--R 2 2 2 2 2 +--R (- 3a d + 2a b c)f + (4a b d - 2b c)e f - b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 2 3 2 2 2 2 2 3 2 +--R (- a c f + (a d + 2a b c)e f + (- 2a b d - b c)e f + b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R (3a c f + (- 3a d - 6a b c)e f + (6a b d + 3b c)e f - 3b d e )n +--R + +--R 2 3 2 2 2 2 2 3 +--R - 2a c f + (2a d + 4a b c)e f + (- 4a b d - 2b c)e f + 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 4 2 3 2 2 2 3 3 3 +--R (a f - 3a b e f + 3a b e f - b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (- 6a f + 18a b e f - 18a b e f + 6b e f)n +--R + +--R 3 4 2 3 2 2 2 3 3 3 4 2 3 +--R (11a f - 33a b e f + 33a b e f - 11b e f)n - 6a f + 18a b e f +--R + +--R 2 2 2 3 3 +--R - 18a b e f + 6b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1288 + +)clear all + +--S 1289 of 1293 +t0:=(c+d*x)*(e+f*x)^(-5+n)/(a+b*x)^n +--R +--R +--R n - 5 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1293 +r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-4+n)/(f*(b*e-a*f)*(4-n))+_ + (b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/_ + (f*(b*e-a*f)^2*(3-n)*(4-n))+2*b*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*_ + (a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)^3*(2-n)*(3-n)*(4-n))+_ + 2*b^2*(b*(3*c*f+d*e*(1-n))-a*d*f*(4-n))*(a+b*x)^(1-n)*(e+f*x)^(-1+n)/_ + (f*(b*e-a*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) +--R +--R +--R (2) +--R 2 3 2 3 3 - n + 1 +--R ((2a b d f - 2b d e)n + (- 8a b d + 6b c)f + 2b d e)(b x + a) +--R * +--R n - 1 +--R (f x + e) +--R + +--R 2 2 2 3 2 2 +--R (2a b d f - 4a b d e f + 2b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R ((- 10a b d + 6a b c)f + (14a b d - 6b c)e f - 4b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R (8a b d - 6a b c)f + (- 10a b d + 6b c)e f + 2b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d f - 3a b d e f + 3a b d e f - b d e )n +--R + +--R 3 2 3 2 2 2 +--R (- 7a d + 3a b c)f + (18a b d - 6a b c)e f +--R + +--R 2 3 2 3 3 +--R (- 15a b d + 3b c)e f + 4b d e +--R * +--R 2 +--R n +--R + +--R 3 2 3 2 2 2 +--R (14a d - 9a b c)f + (- 33a b d + 18a b c)e f +--R + +--R 2 3 2 3 3 +--R (24a b d - 9b c)e f - 5b d e +--R * +--R n +--R + +--R 3 2 3 2 2 2 2 3 2 +--R (- 8a d + 6a b c)f + (18a b d - 12a b c)e f + (- 12a b d + 6b c)e f +--R + +--R 3 3 +--R 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R + +--R 3 4 3 2 3 2 2 2 2 +--R a c f + (- a d - 3a b c)e f + (3a b d + 3a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 3a b d - b c)e f + b d e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - 6a c f + (6a d + 18a b c)e f + (- 18a b d - 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (18a b d + 6b c)e f - 6b d e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 11a c f + (- 11a d - 33a b c)e f + (33a b d + 33a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 33a b d - 11b c)e f + 11b d e +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - 6a c f + (6a d + 18a b c)e f + (- 18a b d - 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (18a b d + 6b c)e f - 6b d e +--R * +--R - n + 1 n - 4 +--R (b x + a) (f x + e) +--R / +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 5 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e f)n + 24a f +--R + +--R 3 4 2 2 2 3 3 3 2 4 4 +--R - 96a b e f + 144a b e f - 96a b e f + 24b e f +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1293 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 3 4 4 4 3 5 +--R ((2a b d f - 2b d e f )n + (- 8a b d + 6b c)f + 2b d e f )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (2a b d f - 4a b d e f + 2b d e f )n +--R + +--R 2 2 3 4 3 4 3 4 2 2 +--R ((- 8a b d + 6a b c)f + (20a b d - 6b c)e f - 12b d e f )n +--R + +--R 3 4 3 4 2 2 +--R (- 40a b d + 30b c)e f + 10b d e f +--R * +--R 4 +--R x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (a b d f - 3a b d e f + 3a b d e f - b d e f)n +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 5a b d + 3a b c)f + (20a b d - 6a b c)e f +--R + +--R 3 4 2 2 4 3 +--R (- 25a b d + 3b c)e f + 10b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 2 4 2 2 3 3 +--R (4a b d - 3a b c)f + (- 41a b d + 30a b c)e f +--R + +--R 3 4 2 2 4 3 +--R (66a b d - 27b c)e f - 29b d e f +--R * +--R n +--R + +--R 3 4 2 2 4 3 +--R (- 80a b d + 60b c)e f + 20b d e f +--R * +--R 3 +--R x +--R + +--R 4 3 4 3 2 2 3 3 2 2 +--R (a d + a b c)f + (- 2a b d - 3a b c)e f + 3a b c e f +--R + +--R 3 4 3 4 4 +--R (2a b d - b c)e f - b d e +--R * +--R 3 +--R n +--R + +--R 4 3 4 3 2 2 3 +--R (- 7a d - 3a b c)f + (16a b d + 18a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (- 3a b d - 27a b c)e f + (- 14a b d + 12b c)e f + 8b d e +--R * +--R 2 +--R n +--R + +--R 4 3 4 3 2 2 3 +--R (14a d + 2a b c)f + (- 46a b d - 15a b c)e f +--R + +--R 2 2 3 2 2 3 4 3 4 4 +--R (15a b d + 60a b c)e f + (36a b d - 47b c)e f - 19b d e +--R * +--R n +--R + +--R 4 4 3 3 2 2 2 2 3 4 3 +--R - 8a d f + 32a b d e f - 48a b d e f + (- 48a b d + 60b c)e f +--R + +--R 4 4 +--R 12b d e +--R * +--R 2 +--R x +--R + +--R 4 4 4 3 3 3 2 2 +--R a c f + (a d - 2a b c)e f - 3a b d e f +--R + +--R 2 2 3 3 3 4 4 +--R (3a b d + 2a b c)e f + (- a b d - b c)e +--R * +--R 3 +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R - 6a c f + (- 8a d + 18a b c)e f + (23a b d - 9a b c)e f +--R + +--R 2 2 3 3 3 4 4 +--R (- 22a b d - 12a b c)e f + (7a b d + 9b c)e +--R * +--R 2 +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R 11a c f + (17a d - 40a b c)e f + (- 60a b d + 45a b c)e f +--R + +--R 2 2 3 3 3 4 4 +--R (55a b d + 10a b c)e f + (- 12a b d - 26b c)e +--R * +--R n +--R + +--R 4 4 4 3 3 3 2 2 2 2 +--R - 6a c f + (- 10a d + 24a b c)e f + (40a b d - 36a b c)e f +--R + +--R 2 2 3 3 4 4 +--R (- 60a b d + 24a b c)e f + 24b c e +--R * +--R x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (a c e f - 3a b c e f + 3a b c e f - a b c e )n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R - 6a c e f + (- a d + 21a b c)e f + (2a b d - 24a b c)e f +--R + +--R 2 2 3 4 +--R (- a b d + 9a b c)e +--R * +--R 2 +--R n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R 11a c e f + (3a d - 42a b c)e f + (- 10a b d + 57a b c)e f +--R + +--R 2 2 3 4 +--R (7a b d - 26a b c)e +--R * +--R n +--R + +--R 4 3 4 3 2 2 3 2 2 3 +--R - 6a c e f + (- 2a d + 24a b c)e f + (8a b d - 36a b c)e f +--R + +--R 2 2 3 4 +--R (- 12a b d + 24a b c)e +--R * +--R (n - 5)log(f x + e) +--R %e +--R / +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e )n +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 4 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e )n + 24a f +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 96a b e f + 144a b e f - 96a b e f + 24b e +--R * +--R n log(b x + a) +--R %e +--R Type: Union(Expression(Integer),...) +--E 1291 + +--S 1292 of 1293 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5 4 4 3 4 5 4 4 5 +--R ((2a b d f - 2b d e f )n + (- 8a b d + 6b c)f + 2b d e f )x +--R + +--R 2 2 5 3 4 4 2 3 2 +--R (2a b d f - 4a b d e f + 2b d e f )n +--R + +--R 2 2 3 5 3 4 4 4 2 3 +--R ((- 8a b d + 6a b c)f + (20a b d - 6b c)e f - 12b d e f )n +--R + +--R 3 4 4 4 2 3 +--R (- 40a b d + 30b c)e f + 10b d e f +--R * +--R 4 +--R x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (a b d f - 3a b d e f + 3a b d e f - b d e f )n +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 5a b d + 3a b c)f + (20a b d - 6a b c)e f +--R + +--R 3 4 2 3 4 3 2 +--R (- 25a b d + 3b c)e f + 10b d e f +--R * +--R 2 +--R n +--R + +--R 3 2 2 5 2 2 3 4 +--R (4a b d - 3a b c)f + (- 41a b d + 30a b c)e f +--R + +--R 3 4 2 3 4 3 2 +--R (66a b d - 27b c)e f - 29b d e f +--R * +--R n +--R + +--R 3 4 2 3 4 3 2 +--R (- 80a b d + 60b c)e f + 20b d e f +--R * +--R 3 +--R x +--R + +--R 4 3 5 3 2 2 4 3 2 3 +--R (a d + a b c)f + (- 2a b d - 3a b c)e f + 3a b c e f +--R + +--R 3 4 3 2 4 4 +--R (2a b d - b c)e f - b d e f +--R * +--R 3 +--R n +--R + +--R 4 3 5 3 2 2 4 +--R (- 7a d - 3a b c)f + (16a b d + 18a b c)e f +--R + +--R 2 2 3 2 3 3 4 3 2 4 4 +--R (- 3a b d - 27a b c)e f + (- 14a b d + 12b c)e f + 8b d e f +--R * +--R 2 +--R n +--R + +--R 4 3 5 3 2 2 4 +--R (14a d + 2a b c)f + (- 46a b d - 15a b c)e f +--R + +--R 2 2 3 2 3 3 4 3 2 4 4 +--R (15a b d + 60a b c)e f + (36a b d - 47b c)e f - 19b d e f +--R * +--R n +--R + +--R 4 5 3 4 2 2 2 3 3 4 3 2 +--R - 8a d f + 32a b d e f - 48a b d e f + (- 48a b d + 60b c)e f +--R + +--R 4 4 +--R 12b d e f +--R * +--R 2 +--R x +--R + +--R 4 5 4 3 4 3 2 3 +--R a c f + (a d - 2a b c)e f - 3a b d e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (3a b d + 2a b c)e f + (- a b d - b c)e f +--R * +--R 3 +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R - 6a c f + (- 8a d + 18a b c)e f + (23a b d - 9a b c)e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (- 22a b d - 12a b c)e f + (7a b d + 9b c)e f +--R * +--R 2 +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R 11a c f + (17a d - 40a b c)e f + (- 60a b d + 45a b c)e f +--R + +--R 2 2 3 3 2 3 4 4 +--R (55a b d + 10a b c)e f + (- 12a b d - 26b c)e f +--R * +--R n +--R + +--R 4 5 4 3 4 3 2 2 2 3 +--R - 6a c f + (- 10a d + 24a b c)e f + (40a b d - 36a b c)e f +--R + +--R 2 2 3 3 2 4 4 +--R (- 60a b d + 24a b c)e f + 24b c e f +--R * +--R x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 3 +--R (a c e f - 3a b c e f + 3a b c e f - a b c e f)n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R - 6a c e f + (- a d + 21a b c)e f + (2a b d - 24a b c)e f +--R + +--R 2 2 3 4 +--R (- a b d + 9a b c)e f +--R * +--R 2 +--R n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R 11a c e f + (3a d - 42a b c)e f + (- 10a b d + 57a b c)e f +--R + +--R 2 2 3 4 +--R (7a b d - 26a b c)e f +--R * +--R n +--R + +--R 4 4 4 3 2 3 3 2 2 3 2 +--R - 6a c e f + (- 2a d + 24a b c)e f + (8a b d - 36a b c)e f +--R + +--R 2 2 3 4 +--R (- 12a b d + 24a b c)e f +--R * +--R (n - 5)log(f x + e) +--R %e +--R + +--R 2 3 2 3 3 +--R ((- 2a b d f + 2b d e)n + (8a b d - 6b c)f - 2b d e) +--R * +--R - n + 1 n - 1 +--R (b x + a) (f x + e) +--R + +--R 2 2 2 3 2 2 +--R (- 2a b d f + 4a b d e f - 2b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R ((10a b d - 6a b c)f + (- 14a b d + 6b c)e f + 4b d e )n +--R + +--R 2 2 2 2 3 3 2 +--R (- 8a b d + 6a b c)f + (10a b d - 6b c)e f - 2b d e +--R * +--R - n + 1 n - 2 +--R (b x + a) (f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d f + 3a b d e f - 3a b d e f + b d e )n +--R + +--R 3 2 3 2 2 2 +--R (7a d - 3a b c)f + (- 18a b d + 6a b c)e f +--R + +--R 2 3 2 3 3 +--R (15a b d - 3b c)e f - 4b d e +--R * +--R 2 +--R n +--R + +--R 3 2 3 2 2 2 +--R (- 14a d + 9a b c)f + (33a b d - 18a b c)e f +--R + +--R 2 3 2 3 3 +--R (- 24a b d + 9b c)e f + 5b d e +--R * +--R n +--R + +--R 3 2 3 2 2 2 +--R (8a d - 6a b c)f + (- 18a b d + 12a b c)e f +--R + +--R 2 3 2 3 3 +--R (12a b d - 6b c)e f - 2b d e +--R * +--R - n + 1 n - 3 +--R (b x + a) (f x + e) +--R + +--R 3 4 3 2 3 2 2 2 2 +--R - a c f + (a d + 3a b c)e f + (- 3a b d - 3a b c)e f +--R + +--R 2 3 3 3 4 +--R (3a b d + b c)e f - b d e +--R * +--R 3 +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 6a c f + (- 6a d - 18a b c)e f + (18a b d + 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 18a b d - 6b c)e f + 6b d e +--R * +--R 2 +--R n +--R + +--R 3 4 3 2 3 +--R - 11a c f + (11a d + 33a b c)e f +--R + +--R 2 2 2 2 2 3 3 3 4 +--R (- 33a b d - 33a b c)e f + (33a b d + 11b c)e f - 11b d e +--R * +--R n +--R + +--R 3 4 3 2 3 2 2 2 2 +--R 6a c f + (- 6a d - 18a b c)e f + (18a b d + 18a b c)e f +--R + +--R 2 3 3 3 4 +--R (- 18a b d - 6b c)e f + 6b d e +--R * +--R - n + 1 n - 4 +--R (b x + a) (f x + e) +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 +--R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 10a f + 40a b e f - 60a b e f + 40a b e f - 10b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (35a f - 140a b e f + 210a b e f - 140a b e f + 35b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R (- 50a f + 200a b e f - 300a b e f + 200a b e f - 50b e f)n +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R 24a f - 96a b e f + 144a b e f - 96a b e f + 24b e f +--R * +--R n log(b x + a) +--R %e +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1293 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1293 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich2.input.pdf b/src/axiom-website/CATS/rich2.input.pdf new file mode 100644 index 0000000..9c3f4dd Binary files /dev/null and b/src/axiom-website/CATS/rich2.input.pdf differ diff --git a/src/axiom-website/CATS/rich3a.input.pamphlet b/src/axiom-website/CATS/rich3a.input.pamphlet new file mode 100644 index 0000000..fc946de --- /dev/null +++ b/src/axiom-website/CATS/rich3a.input.pamphlet @@ -0,0 +1,24157 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 208 integrals in this file. +\item 210 supplied "optimal results". +\item 170 matching answers. +\item 23 cases where Axiom supplied 2 results. +\item 25 cases that Axiom failed to integrate. +\item 12 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3a.output +)spool rich3a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x) +--R +--R +--R 3 2 n +--R (1) (d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1092 +r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ + a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+_ + (b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 3 2 n + 4 +--R (d n + 6d n + 11d n + 6d)(b x + a) +--R + +--R 3 2 +--R (- 3a d + b c)n + (- 21a d + 7b c)n + (- 42a d + 14b c)n - 24a d +--R + +--R 8b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 2 +--R (3a d - 2a b c)n + (24a d - 16a b c)n + (57a d - 38a b c)n + 36a d +--R + +--R - 24a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- a d + a b c)n + (- 9a d + 9a b c)n + (- 26a d + 26a b c)n +--R + +--R 3 2 +--R - 24a d + 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (b d n + 6b d n + 11b d n + 6b d)x +--R + +--R 3 4 3 3 4 2 3 4 4 3 +--R ((a b d + b c)n + (3a b d + 7b c)n + (2a b d + 14b c)n + 8b c)x +--R + +--R 3 3 2 2 3 2 2 2 3 2 +--R (a b c n + (- 3a b d + 5a b c)n + (- 3a b d + 4a b c)n)x +--R + +--R 2 2 2 3 2 2 3 4 3 +--R (- 2a b c n + (6a b d - 8a b c)n)x + 2a b c n - 6a d + 8a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (b d n + 6b d n + 11b d n + 6b d)x +--R + +--R 3 4 3 3 4 2 3 4 4 3 +--R ((a b d + b c)n + (3a b d + 7b c)n + (2a b d + 14b c)n + 8b c)x +--R + +--R 3 3 2 2 3 2 2 2 3 2 +--R (a b c n + (- 3a b d + 5a b c)n + (- 3a b d + 4a b c)n)x +--R + +--R 2 2 2 3 2 2 3 4 3 +--R (- 2a b c n + (6a b d - 8a b c)n)x + 2a b c n - 6a d + 8a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 2 n + 4 +--R (- d n - 6d n - 11d n - 6d)(b x + a) +--R + +--R 3 2 +--R ((3a d - b c)n + (21a d - 7b c)n + (42a d - 14b c)n + 24a d - 8b c) +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 +--R (- 3a d + 2a b c)n + (- 24a d + 16a b c)n + (- 57a d + 38a b c)n +--R + +--R 2 +--R - 36a d + 24a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 3 3 2 2 3 2 3 +--R (a d - a b c)n + (9a d - 9a b c)n + (26a d - 26a b c)n + 24a d +--R + +--R 2 +--R - 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1092 +t0:=x*(a+b*x)^n*(c+d*x) +--R +--R +--R 2 n +--R (1) (d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1092 +r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ + (b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 n + 3 +--R (d n + 3d n + 2d)(b x + a) +--R + +--R 2 n + 2 +--R ((- 2a d + b c)n + (- 8a d + 4b c)n - 6a d + 3b c)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R ((a d - a b c)n + (5a d - 5a b c)n + 6a d - 6a b c)(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 +--R (b d n + 3b d n + 2b d)x +--R + +--R 2 3 2 2 3 3 2 +--R ((a b d + b c)n + (a b d + 4b c)n + 3b c)x +--R + +--R 2 2 2 2 2 3 2 +--R (a b c n + (- 2a b d + 3a b c)n)x - a b c n + 2a d - 3a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 +--R (b d n + 3b d n + 2b d)x +--R + +--R 2 3 2 2 3 3 2 +--R ((a b d + b c)n + (a b d + 4b c)n + 3b c)x +--R + +--R 2 2 2 2 2 3 2 +--R (a b c n + (- 2a b d + 3a b c)n)x - a b c n + 2a d - 3a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 n + 3 +--R (- d n - 3d n - 2d)(b x + a) +--R + +--R 2 n + 2 +--R ((2a d - b c)n + (8a d - 4b c)n + 6a d - 3b c)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R ((- a d + a b c)n + (- 5a d + 5a b c)n - 6a d + 6a b c)(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1092 +t0:=(a+b*x)^n*(c+d*x) +--R +--R +--R n +--R (1) (d x + c)(b x + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1092 +r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) +--R +--R +--R n + 2 n + 1 +--R (d n + d)(b x + a) + ((- a d + b c)n - 2a d + 2b c)(b x + a) +--R (2) ---------------------------------------------------------------------- +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R ((b d n + b d)x + ((a b d + b c)n + 2b c)x + a b c n - a d + 2a b c) +--R * +--R n log(b x + a) +--R %e +--R / +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +--R ((b d n + b d)x + ((a b d + b c)n + 2b c)x + a b c n - a d + 2a b c) +--R * +--R n log(b x + a) +--R %e +--R + +--R n + 2 n + 1 +--R (- d n - d)(b x + a) + ((a d - b c)n + 2a d - 2b c)(b x + a) +--R / +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1092 +t0:=(a+b*x)^n*(c+d*x)/x +--R +--R +--R n +--R (d x + c)(b x + a) +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1092 +--r0:=d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 17 + +--S 18 of 1092 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1092 +--m0:=a0-r0 +--E 19 + +--S 20 of 1092 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1092 +t0:=x^m*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1092 +r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ + 5*c^3*d*(b*c+2*a*d)*x^(3+m)/(3+m)+10*c^2*d^2*(b*c+a*d)*_ + x^(4+m)/(4+m)+5*c*d^3*(2*b*c+a*d)*x^(5+m)/(5+m)+_ + d^4*(5*b*c+a*d)*x^(6+m)/(6+m)+b*d^5*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m + 1764b d m +--R + +--R 5 +--R 720b d +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 5 4 4 +--R (a d + 5b c d )m + (22a d + 110b c d )m + (190a d + 950b c d )m +--R + +--R 5 4 3 5 4 2 +--R (820a d + 4100b c d )m + (1849a d + 9245b c d )m +--R + +--R 5 4 5 4 +--R (2038a d + 10190b c d )m + 840a d + 4200b c d +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5a c d + b c )m + (130a c d + 26b c )m + (1350a c d + 270b c )m +--R + +--R 4 5 3 4 5 2 +--R (7100a c d + 1420b c )m + (19645a c d + 3929b c )m +--R + +--R 4 5 4 5 +--R (26370a c d + 5274b c )m + 12600a c d + 2520b c +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m + 8028a c m +--R + +--R 5 +--R 5040a c +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m + 1764b d m +--R + +--R 5 +--R 720b d +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (a d + 5b c d )m + (22a d + 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (190a d + 950b c d )m + (820a d + 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (1849a d + 9245b c d )m + (2038a d + 10190b c d )m + 840a d +--R + +--R 4 +--R 4200b c d +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5a c d + b c )m + (130a c d + 26b c )m + (1350a c d + 270b c )m +--R + +--R 4 5 3 4 5 2 +--R (7100a c d + 1420b c )m + (19645a c d + 3929b c )m +--R + +--R 4 5 4 5 +--R (26370a c d + 5274b c )m + 12600a c d + 2520b c +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m + 8028a c m +--R + +--R 5 +--R 5040a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 5 5 4 5 3 5 2 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m +--R + +--R 5 5 +--R 1764b d m + 720b d +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (a d + 5b c d )m + (22a d + 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (190a d + 950b c d )m + (820a d + 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (1849a d + 9245b c d )m + (2038a d + 10190b c d )m + 840a d +--R + +--R 4 +--R 4200b c d +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (5a c d + b c )m + (130a c d + 26b c )m +--R + +--R 4 5 4 4 5 3 +--R (1350a c d + 270b c )m + (7100a c d + 1420b c )m +--R + +--R 4 5 2 4 5 4 +--R (19645a c d + 3929b c )m + (26370a c d + 5274b c )m + 12600a c d +--R + +--R 5 +--R 2520b c +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m +--R + +--R 5 5 +--R 8028a c m + 5040a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - b d m - 21b d m - 175b d m - 735b d m - 1624b d m - 1764b d m +--R + +--R 5 +--R - 720b d +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (- a d - 5b c d )m + (- 22a d - 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (- 190a d - 950b c d )m + (- 820a d - 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (- 1849a d - 9245b c d )m + (- 2038a d - 10190b c d )m - 840a d +--R + +--R 4 +--R - 4200b c d +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 5a c d - 10b c d )m + (- 115a c d - 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (- 1035a c d - 2070b c d )m + (- 4625a c d - 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (- 10720a c d - 21440b c d )m + (- 12060a c d - 24120b c d )m +--R + +--R 4 2 3 +--R - 5040a c d - 10080b c d +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 10a c d - 10b c d )m + (- 240a c d - 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (- 2260a c d - 2260b c d )m + (- 10560a c d - 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 25450a c d - 25450b c d )m + (- 29520a c d - 29520b c d )m +--R + +--R 2 3 3 2 +--R - 12600a c d - 12600b c d +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 10a c d - 5b c d)m + (- 250a c d - 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 2470a c d - 1235b c d)m + (- 12190a c d - 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (- 31120a c d - 15560b c d)m + (- 37960a c d - 18980b c d)m +--R + +--R 3 2 4 +--R - 16800a c d - 8400b c d +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (- 5a c d - b c )m + (- 130a c d - 26b c )m +--R + +--R 4 5 4 4 5 3 +--R (- 1350a c d - 270b c )m + (- 7100a c d - 1420b c )m +--R + +--R 4 5 2 4 5 4 +--R (- 19645a c d - 3929b c )m + (- 26370a c d - 5274b c )m - 12600a c d +--R + +--R 5 +--R - 2520b c +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - a c m - 27a c m - 295a c m - 1665a c m - 5104a c m - 8028a c m +--R + +--R 5 +--R - 5040a c +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1092 +t0:=x^3*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 9 5 4 8 4 2 3 7 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1092 +r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ + 10/7*c^2*d^2*(b*c+a*d)*x^7+5/8*c*d^3*(2*b*c+a*d)*x^8+_ + 1/9*d^4*(5*b*c+a*d)*x^9+1/10*b*d^5*x^10 +--R +--R +--R (2) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- a c d + -- b c d )x + (- a c d + - b c d)x + (a c d + - b c )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - a c x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- a c d + -- b c d )x + (- a c d + - b c d)x + (a c d + - b c )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - a c x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1092 +t0:=x^2*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 8 5 4 7 4 2 3 6 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1092 +r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ + 1/8*(3*b*c-a*d)*(c+d*x)^8/d^4+1/9*b*(c+d*x)^9/d^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 5 8 10 2 7 7 +--R - b d x + (- a d + - b c d )x + (- a c d + -- b c d )x +--R 9 8 8 7 7 +--R + +--R 5 2 7 5 3 6 6 3 6 4 5 5 5 4 5 1 5 4 4 +--R (- a c d + - b c d )x + (2a c d + b c d )x + (- a c d + - b c d )x +--R 3 3 4 4 +--R + +--R 1 5 4 3 1 8 1 9 +--R - a c d x + --- a c d - --- b c +--R 3 168 504 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 32 + +--S 33 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 5 4 10 2 3 7 +--R - b d x + (- a d + - b c d )x + (- a c d + -- b c d )x +--R 9 8 8 7 7 +--R + +--R 5 2 3 5 3 2 6 3 2 4 5 5 4 1 5 4 +--R (- a c d + - b c d )x + (2a c d + b c d)x + (- a c d + - b c )x +--R 3 3 4 4 +--R + +--R 1 5 3 +--R - a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1092 +m0:=a0-r0 +--R +--R +--R 1 8 1 9 +--R - --- a c d + --- b c +--R 168 504 +--R (4) ---------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 34 + +--S 35 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 35 + +)clear all + +--S 36 of 1092 +t0:=x*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 7 5 4 6 4 2 3 5 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 4 3 2 4 3 4 5 2 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 1092 +r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ + 1/8*b*(c+d*x)^8/d^3 +--R +--R +--R (2) +--R 1 8 8 1 8 5 7 7 5 7 5 2 6 6 +--R - b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 8 7 7 6 3 +--R + +--R 2 6 3 5 5 5 3 5 5 4 4 4 5 4 4 1 5 3 3 +--R (2a c d + 2b c d )x + (- a c d + - b c d )x + (- a c d + - b c d )x +--R 2 4 3 3 +--R + +--R 1 5 3 2 1 7 1 8 +--R - a c d x - -- a c d + --- b c +--R 2 42 168 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 37 + +--S 38 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 8 1 5 5 4 7 5 4 5 2 3 6 +--R - b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 8 7 7 6 3 +--R + +--R 2 3 3 2 5 5 3 2 5 4 4 5 4 1 5 3 +--R (2a c d + 2b c d )x + (- a c d + - b c d)x + (- a c d + - b c )x +--R 2 4 3 3 +--R + +--R 1 5 2 +--R - a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 1092 +m0:=a0-r0 +--R +--R +--R 1 7 1 8 +--R -- a c d - --- b c +--R 42 168 +--R (4) ------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 39 + +--S 40 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 40 + +)clear all + +--S 41 of 1092 +t0:=(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 1092 +r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 +--R +--R +--R (2) +--R 1 7 7 1 7 5 6 6 6 2 5 5 +--R - b d x + (- a d + - b c d )x + (a c d + 2b c d )x +--R 7 6 6 +--R + +--R 5 2 5 5 3 4 4 10 3 4 5 4 3 3 +--R (- a c d + - b c d )x + (-- a c d + - b c d )x +--R 2 2 3 3 +--R + +--R 5 4 3 1 5 2 2 5 2 1 6 1 7 +--R (- a c d + - b c d )x + a c d x + - a c d - -- b c +--R 2 2 6 42 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 42 + +--S 43 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 7 1 5 5 4 6 4 2 3 5 +--R - b d x + (- a d + - b c d )x + (a c d + 2b c d )x +--R 7 6 6 +--R + +--R 5 2 3 5 3 2 4 10 3 2 5 4 3 5 4 1 5 2 +--R (- a c d + - b c d )x + (-- a c d + - b c d)x + (- a c d + - b c )x +--R 2 2 3 3 2 2 +--R + +--R 5 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 1092 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 +--R - - a c d + -- b c +--R 6 42 +--R (4) ------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 44 + +--S 45 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 45 + +)clear all + +--S 46 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1092 +r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ + 5/4*a*c*d^4*x^4+1/5*a*d^5*x^5+1/6*b*(c+d*x)^6/d+a*c^5*log(x) +--R +--R +--R (2) +--R 5 6 6 6 5 5 +--R 60a c d log(x) + 10b d x + (12a d + 60b c d )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (75a c d + 150b c d )x + (200a c d + 200b c d )x +--R + +--R 3 3 4 2 2 4 2 5 6 +--R (300a c d + 150b c d )x + (300a c d + 60b c d)x + 10b c +--R / +--R 60d +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 6 5 4 5 +--R 60a c log(x) + 10b d x + (12a d + 60b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (75a c d + 150b c d )x + (200a c d + 200b c d )x +--R + +--R 3 2 4 2 4 5 +--R (300a c d + 150b c d)x + (300a c d + 60b c )x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1092 +m0:=a0-r0 +--R +--R +--R 6 +--R b c +--R (4) - ---- +--R 6d +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1092 +r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ + 5/3*c*d^3*(2*b*c+a*d)*x^3+1/4*d^4*(5*b*c+a*d)*x^4+_ + 1/5*b*d^5*x^5+c^4*(b*c+5*a*d)*log(x) +--R +--R +--R (2) +--R 4 5 5 6 5 4 5 +--R (300a c d + 60b c )x log(x) + 12b d x + (15a d + 75b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100a c d + 200b c d )x + (300a c d + 300b c d )x +--R + +--R 3 2 4 2 5 +--R (600a c d + 300b c d)x - 60a c +--R / +--R 60x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 6 5 4 5 +--R (300a c d + 60b c )x log(x) + 12b d x + (15a d + 75b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100a c d + 200b c d )x + (300a c d + 300b c d )x +--R + +--R 3 2 4 2 5 +--R (600a c d + 300b c d)x - 60a c +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1092 +r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ + 5/2*c*d^3*(2*b*c+a*d)*x^2+1/3*d^4*(5*b*c+a*d)*x^3+_ + 1/4*b*d^5*x^4+5*c^3*d*(b*c+2*a*d)*log(x) +--R +--R +--R (2) +--R 3 2 4 2 5 6 5 4 5 +--R (120a c d + 60b c d)x log(x) + 3b d x + (4a d + 20b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30a c d + 60b c d )x + (120a c d + 120b c d )x +--R + +--R 4 5 5 +--R (- 60a c d - 12b c )x - 6a c +--R / +--R 2 +--R 12x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 5 6 5 4 5 +--R (120a c d + 60b c d)x log(x) + 3b d x + (4a d + 20b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30a c d + 60b c d )x + (120a c d + 120b c d )x +--R + +--R 4 5 5 +--R (- 60a c d - 12b c )x - 6a c +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1092 +t0:=x*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--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 61 + +--S 62 of 1092 +r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ + 1/19*b*(c+d*x)^19/d^3 +--R +--R +--R (2) +--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 62 + +--S 63 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 63 + +--S 64 of 1092 +m0:=a0-r0 +--R +--R +--R 1 18 1 19 +--R --- a c d - ---- b c +--R 306 2907 +--R (4) ----------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 64 + +--S 65 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 65 + +)clear all + +--S 66 of 1092 +t0:=x^2*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--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 66 + +--S 67 of 1092 +r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ + 1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4 +--R +--R +--R (2) +--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 67 + +--S 68 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 68 + +--S 69 of 1092 +m0:=a0-r0 +--R +--R +--R 1 19 1 20 +--R - ---- a c d + ----- b c +--R 2907 19380 +--R (4) --------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 69 + +--S 70 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 70 + +)clear all + +--S 71 of 1092 +t0:=x^3*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--R 16 20 16 15 19 15 2 14 18 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 17 3 13 4 12 16 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 15 5 11 6 10 14 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 13 7 9 8 8 12 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 11 9 7 10 6 10 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 9 11 5 12 4 8 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 7 13 3 14 2 6 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 5 15 16 4 16 3 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1092 +r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ + 3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+_ + 1/21*b*(c+d*x)^21/d^5 +--R +--R +--R (2) +--R 1 21 21 1 21 4 20 20 16 20 120 2 19 19 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 21 20 5 19 19 +--R + +--R 20 2 19 280 3 18 18 560 3 18 1820 4 17 17 +--R (-- a c d + --- b c d )x + (--- a c d + ---- b c d )x +--R 3 9 17 17 +--R + +--R 455 4 17 5 16 16 1456 5 16 8008 6 15 15 +--R (--- a c d + 273b c d )x + (---- a c d + ---- b c d )x +--R 4 5 15 +--R + +--R 6 15 5720 7 14 14 7 14 8 13 13 +--R (572a c d + ---- b c d )x + (880a c d + 990b c d )x +--R 7 +--R + +--R 2145 8 13 2860 9 12 12 9 12 10 11 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 728b c d )x +--R 2 3 +--R + +--R 4004 10 11 2184 11 10 10 1456 11 10 1820 12 9 9 +--R (---- a c d + ---- b c d )x + (---- a c d + ---- b c d )x +--R 5 5 3 9 +--R + +--R 455 12 9 13 8 8 13 8 120 14 7 7 +--R (--- a c d + 70b c d )x + (80a c d + --- b c d )x +--R 2 7 +--R + +--R 14 7 8 15 6 6 16 15 6 1 16 5 5 1 16 5 4 +--R (20a c d + - b c d )x + (-- a c d + - b c d )x + - a c d x +--R 3 5 5 4 +--R + +--R 1 20 1 21 +--R - ----- a c d + ------ b c +--R 19380 101745 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 16 21 1 16 4 15 20 16 15 120 2 14 19 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 21 20 5 19 19 +--R + +--R 20 2 14 280 3 13 18 560 3 13 1820 4 12 17 +--R (-- a c d + --- b c d )x + (--- a c d + ---- b c d )x +--R 3 9 17 17 +--R + +--R 455 4 12 5 11 16 1456 5 11 8008 6 10 15 +--R (--- a c d + 273b c d )x + (---- a c d + ---- b c d )x +--R 4 5 15 +--R + +--R 6 10 5720 7 9 14 7 9 8 8 13 +--R (572a c d + ---- b c d )x + (880a c d + 990b c d )x +--R 7 +--R + +--R 2145 8 8 2860 9 7 12 9 7 10 6 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 728b c d )x +--R 2 3 +--R + +--R 4004 10 6 2184 11 5 10 1456 11 5 1820 12 4 9 +--R (---- a c d + ---- b c d )x + (---- a c d + ---- b c d )x +--R 5 5 3 9 +--R + +--R 455 12 4 13 3 8 13 3 120 14 2 7 +--R (--- a c d + 70b c d )x + (80a c d + --- b c d )x +--R 2 7 +--R + +--R 14 2 8 15 6 16 15 1 16 5 1 16 4 +--R (20a c d + - b c d)x + (-- a c d + - b c )x + - a c x +--R 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1092 +m0:=a0-r0 +--R +--R +--R 1 20 1 21 +--R ----- a c d - ------ b c +--R 19380 101745 +--R (4) --------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 74 + +--S 75 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 75 + +)clear all + +--S 76 of 1092 +t0:=x^2*(2+x)^5*(2+3*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R (1) 3x + 32x + 140x + 320x + 400x + 256x + 64x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1092 +r0:=1/3*x^3*(2+x)^6 +--R +--R +--R 1 9 8 7 160 6 5 4 64 3 +--R (2) - x + 4x + 20x + --- x + 80x + 64x + -- x +--R 3 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 1 9 8 7 160 6 5 4 64 3 +--R (3) - x + 4x + 20x + --- x + 80x + 64x + -- x +--R 3 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 4 3 2 2 n +--R (1) (d x + 2c d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1092 +r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ + (a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*_ + (a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ + d^2*(a+b*x)^(5+n)/(b^5*(5+n)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 n + 5 +--R (d n + 10d n + 35d n + 50d n + 24d )(b x + a) +--R + +--R 2 4 2 3 +--R (- 4a d + 2b c d)n + (- 44a d + 22b c d)n +--R + +--R 2 2 2 2 +--R (- 164a d + 82b c d)n + (- 244a d + 122b c d)n - 120a d + 60b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (6a d - 6a b c d + b c )n + (72a d - 72a b c d + 12b c )n +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (294a d - 294a b c d + 49b c )n + (468a d - 468a b c d + 78b c )n +--R + +--R 2 2 2 2 +--R 240a d - 240a b c d + 40b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 2 2 2 2 4 +--R (- 4a d + 6a b c d - 2a b c )n +--R + +--R 3 2 2 2 2 3 +--R (- 52a d + 78a b c d - 26a b c )n +--R + +--R 3 2 2 2 2 2 +--R (- 236a d + 354a b c d - 118a b c )n +--R + +--R 3 2 2 2 2 3 2 2 +--R (- 428a d + 642a b c d - 214a b c )n - 240a d + 360a b c d +--R + +--R 2 2 +--R - 120a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 2 3 2 2 2 4 4 2 3 2 2 2 3 +--R (a d - 2a b c d + a b c )n + (14a d - 28a b c d + 14a b c )n +--R + +--R 4 2 3 2 2 2 2 +--R (71a d - 142a b c d + 71a b c )n +--R + +--R 4 2 3 2 2 2 4 2 3 2 2 2 +--R (154a d - 308a b c d + 154a b c )n + 120a d - 240a b c d + 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 5 2 3 5 2 2 5 2 5 2 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 2 5 4 4 2 5 3 +--R (a b d + 2b c d)n + (6a b d + 22b c d)n +--R + +--R 4 2 5 2 4 2 5 5 +--R (11a b d + 82b c d)n + (6a b d + 122b c d)n + 60b c d +--R * +--R 4 +--R x +--R + +--R 4 5 2 4 2 3 2 4 5 2 3 +--R (2a b c d + b c )n + (- 4a b d + 16a b c d + 12b c )n +--R + +--R 2 3 2 4 5 2 2 +--R (- 12a b d + 34a b c d + 49b c )n +--R + +--R 2 3 2 4 5 2 5 2 +--R (- 8a b d + 20a b c d + 78b c )n + 40b c +--R * +--R 3 +--R x +--R + +--R 4 2 4 2 3 4 2 3 +--R a b c n + (- 6a b c d + 10a b c )n +--R + +--R 3 2 2 2 3 4 2 2 +--R (12a b d - 36a b c d + 29a b c )n +--R + +--R 3 2 2 2 3 4 2 +--R (12a b d - 30a b c d + 20a b c )n +--R * +--R 2 +--R x +--R + +--R 2 3 2 3 3 2 2 3 2 2 +--R - 2a b c n + (12a b c d - 18a b c )n +--R + +--R 4 2 3 2 2 3 2 +--R (- 24a b d + 60a b c d - 40a b c )n +--R * +--R x +--R + +--R 3 2 2 2 4 3 2 2 5 2 4 3 2 2 +--R 2a b c n + (- 12a b c d + 18a b c )n + 24a d - 60a b c d + 40a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 5 2 3 5 2 2 5 2 5 2 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 2 5 4 4 2 5 3 +--R (a b d + 2b c d)n + (6a b d + 22b c d)n +--R + +--R 4 2 5 2 4 2 5 5 +--R (11a b d + 82b c d)n + (6a b d + 122b c d)n + 60b c d +--R * +--R 4 +--R x +--R + +--R 4 5 2 4 2 3 2 4 5 2 3 +--R (2a b c d + b c )n + (- 4a b d + 16a b c d + 12b c )n +--R + +--R 2 3 2 4 5 2 2 +--R (- 12a b d + 34a b c d + 49b c )n +--R + +--R 2 3 2 4 5 2 5 2 +--R (- 8a b d + 20a b c d + 78b c )n + 40b c +--R * +--R 3 +--R x +--R + +--R 4 2 4 2 3 4 2 3 +--R a b c n + (- 6a b c d + 10a b c )n +--R + +--R 3 2 2 2 3 4 2 2 +--R (12a b d - 36a b c d + 29a b c )n +--R + +--R 3 2 2 2 3 4 2 +--R (12a b d - 30a b c d + 20a b c )n +--R * +--R 2 +--R x +--R + +--R 2 3 2 3 3 2 2 3 2 2 +--R - 2a b c n + (12a b c d - 18a b c )n +--R + +--R 4 2 3 2 2 3 2 +--R (- 24a b d + 60a b c d - 40a b c )n +--R * +--R x +--R + +--R 3 2 2 2 4 3 2 2 5 2 4 3 2 2 +--R 2a b c n + (- 12a b c d + 18a b c )n + 24a d - 60a b c d + 40a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 4 2 3 2 2 2 2 n + 5 +--R (- d n - 10d n - 35d n - 50d n - 24d )(b x + a) +--R + +--R 2 4 2 3 2 2 +--R (4a d - 2b c d)n + (44a d - 22b c d)n + (164a d - 82b c d)n +--R + +--R 2 2 +--R (244a d - 122b c d)n + 120a d - 60b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (- 6a d + 6a b c d - b c )n + (- 72a d + 72a b c d - 12b c )n +--R + +--R 2 2 2 2 2 +--R (- 294a d + 294a b c d - 49b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 468a d + 468a b c d - 78b c )n - 240a d + 240a b c d - 40b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 2 2 2 2 4 3 2 2 2 2 3 +--R (4a d - 6a b c d + 2a b c )n + (52a d - 78a b c d + 26a b c )n +--R + +--R 3 2 2 2 2 2 +--R (236a d - 354a b c d + 118a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (428a d - 642a b c d + 214a b c )n + 240a d - 360a b c d + 120a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 2 3 2 2 2 4 4 2 3 2 2 2 3 +--R (- a d + 2a b c d - a b c )n + (- 14a d + 28a b c d - 14a b c )n +--R + +--R 4 2 3 2 2 2 2 +--R (- 71a d + 142a b c d - 71a b c )n +--R + +--R 4 2 3 2 2 2 4 2 3 +--R (- 154a d + 308a b c d - 154a b c )n - 120a d + 240a b c d +--R + +--R 2 2 2 +--R - 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1092 +t0:=x*(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 3 2 2 n +--R (1) (d x + 2c d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1092 +r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ + (a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/_ + (b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 n + 4 +--R (d n + 6d n + 11d n + 6d )(b x + a) +--R + +--R 2 3 2 2 2 +--R (- 3a d + 2b c d)n + (- 21a d + 14b c d)n + (- 42a d + 28b c d)n +--R + +--R 2 +--R - 24a d + 16b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 2 2 2 3 2 2 2 2 2 +--R (3a d - 4a b c d + b c )n + (24a d - 32a b c d + 8b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (57a d - 76a b c d + 19b c )n + 36a d - 48a b c d + 12b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 2 2 2 3 3 2 2 2 2 2 +--R (- a d + 2a b c d - a b c )n + (- 9a d + 18a b c d - 9a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (- 26a d + 52a b c d - 26a b c )n - 24a d + 48a b c d - 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 2 2 4 2 4 2 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 2 4 3 3 2 4 2 3 2 4 +--R (a b d + 2b c d)n + (3a b d + 14b c d)n + (2a b d + 28b c d)n +--R + +--R 4 +--R 16b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 2 2 3 4 2 2 +--R (2a b c d + b c )n + (- 3a b d + 10a b c d + 8b c )n +--R + +--R 2 2 2 3 4 2 4 2 +--R (- 3a b d + 8a b c d + 19b c )n + 12b c +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R a b c n + (- 4a b c d + 7a b c )n +--R + +--R 3 2 2 2 3 2 +--R (6a b d - 16a b c d + 12a b c )n +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R - a b c n + (4a b c d - 7a b c )n - 6a d + 16a b c d - 12a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 4 2 2 4 2 4 2 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 2 4 3 3 2 4 2 +--R (a b d + 2b c d)n + (3a b d + 14b c d)n +--R + +--R 3 2 4 4 +--R (2a b d + 28b c d)n + 16b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 2 2 3 4 2 2 +--R (2a b c d + b c )n + (- 3a b d + 10a b c d + 8b c )n +--R + +--R 2 2 2 3 4 2 4 2 +--R (- 3a b d + 8a b c d + 19b c )n + 12b c +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R a b c n + (- 4a b c d + 7a b c )n +--R + +--R 3 2 2 2 3 2 +--R (6a b d - 16a b c d + 12a b c )n +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R - a b c n + (4a b c d - 7a b c )n - 6a d + 16a b c d - 12a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 3 2 2 2 2 n + 4 +--R (- d n - 6d n - 11d n - 6d )(b x + a) +--R + +--R 2 3 2 2 2 +--R (3a d - 2b c d)n + (21a d - 14b c d)n + (42a d - 28b c d)n +--R + +--R 2 +--R 24a d - 16b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 2 2 2 3 2 2 2 2 2 +--R (- 3a d + 4a b c d - b c )n + (- 24a d + 32a b c d - 8b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 57a d + 76a b c d - 19b c )n - 36a d + 48a b c d - 12b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 2 2 2 3 3 2 2 2 2 2 +--R (a d - 2a b c d + a b c )n + (9a d - 18a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (26a d - 52a b c d + 26a b c )n + 24a d - 48a b c d + 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1092 +t0:=(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 2 2 n +--R (1) (d x + 2c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1092 +r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ + (b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 2 2 2 n + 3 +--R (d n + 3d n + 2d )(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2a d + 2b c d)n + (- 8a d + 8b c d)n - 6a d + 6b c d) +--R * +--R n + 2 +--R (b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (5a d - 10a b c d + 5b c )n + 6a d +--R + +--R 2 2 +--R - 12a b c d + 6b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 2 3 2 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)n + (a b d + 8b c d)n + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )n + (- 2a b d + 6a b c d + 5b c )n + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c n + (- 2a b c d + 5a b c )n + 2a d - 6a b c d + 6a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 3 2 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)n + (a b d + 8b c d)n + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )n + (- 2a b d + 6a b c d + 5b c )n + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c n + (- 2a b c d + 5a b c )n + 2a d - 6a b c d + 6a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 2 2 n + 3 +--R (- d n - 3d n - 2d )(b x + a) +--R + +--R 2 2 2 2 n + 2 +--R ((2a d - 2b c d)n + (8a d - 8b c d)n + 6a d - 6b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (- 5a d + 10a b c d - 5b c )n - 6a d +--R + +--R 2 2 +--R 12a b c d - 6b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1092 +t0:=(a+b*x)^n*(c+d*x)^2/x +--R +--R +--R 2 2 2 n +--R (d x + 2c d x + c )(b x + a) +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1092 +--r0:=-d*(a*d-b*c*(3+n))*(a+b*x)^(1+n)/(b^2*(1+n)*(2+n))+_ +-- d*(a+b*x)^(1+n)*(c+d*x)/(b*(2+n))-c^2*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 97 + +--S 98 of 1092 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 1092 +--m0:=a0-r0 +--E 99 + +--S 100 of 1092 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 1092 +t0:=x^m*(a+b*x)^2*(c+d*x)^5 +--R +--R +--R (1) +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b d x + (2a b d + 5b c d )x + (a d + 10a b c d + 10b c d )x +--R + +--R 2 4 2 3 2 3 2 4 2 2 3 3 2 2 4 3 +--R (5a c d + 20a b c d + 10b c d )x + (10a c d + 20a b c d + 5b c d)x +--R + +--R 2 3 2 4 2 5 2 2 4 5 2 5 +--R (10a c d + 10a b c d + b c )x + (5a c d + 2a b c )x + a c +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1092 +r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ + c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+_ + 5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+_ + 5*c*d^2*(2*b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(5+m)/(5+m)+_ + d^3*(10*b^2*c^2+10*a*b*c*d+a^2*d^2)*x^(6+m)/(6+m)+_ + b*d^4*(5*b*c+2*a*d)*x^(7+m)/(7+m)+b^2*d^5*x^(8+m)/(8+m) +--R +--R +--R (2) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 2 5 2 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m + 13132b d m +--R + +--R 2 5 2 5 +--R 13068b d m + 5040b d +--R * +--R m + 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R m + 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R m + 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R m + 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R m + 4 +--R x +--R + +--R 2 3 2 4 2 5 7 2 3 2 4 2 5 6 +--R (10a c d + 10a b c d + b c )m + (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R m + 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R m + 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R 13132b d m + 13068b d m + 5040b d +--R * +--R 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (10a c d + 10a b c d + b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R 13132b d m + 13068b d m + 5040b d +--R * +--R 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (10a c d + 10a b c d + b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - b d m - 28b d m - 322b d m - 1960b d m - 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R - 13132b d m - 13068b d m - 5040b d +--R * +--R m + 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (- 2a b d - 5b c d )m + (- 58a b d - 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (- 686a b d - 1715b c d )m + (- 4270a b d - 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (- 15008a b d - 37520b c d )m + (- 29512a b d - 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (- 29664a b d - 74160b c d )m - 11520a b d - 28800b c d +--R * +--R m + 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (- a d - 10a b c d - 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (- 30a d - 300a b c d - 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (- 366a d - 3660a b c d - 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (- 2340a d - 23400a b c d - 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (- 8409a d - 84090a b c d - 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (- 16830a d - 168300a b c d - 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (- 17144a d - 171440a b c d - 171440b c d )m - 6720a d +--R + +--R 4 2 2 3 +--R - 67200a b c d - 67200b c d +--R * +--R m + 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (- 5a c d - 20a b c d - 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (- 155a c d - 620a b c d - 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (- 1955a c d - 7820a b c d - 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (- 12905a c d - 51620a b c d - 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (- 47720a c d - 190880a b c d - 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (- 97820a c d - 391280a b c d - 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (- 101520a c d - 406080a b c d - 203040b c d )m - 40320a c d +--R + +--R 2 3 2 3 2 +--R - 161280a b c d - 80640b c d +--R * +--R m + 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (- 10a c d - 20a b c d - 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (- 320a c d - 640a b c d - 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (- 4180a c d - 8360a b c d - 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (- 28640a c d - 57280a b c d - 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (- 109930a c d - 219860a b c d - 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (- 233120a c d - 466240a b c d - 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (- 248760a c d - 497520a b c d - 124380b c d)m - 100800a c d +--R + +--R 3 2 2 4 +--R - 201600a b c d - 50400b c d +--R * +--R m + 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (- 10a c d - 10a b c d - b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (- 330a c d - 330a b c d - 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (- 4470a c d - 4470a b c d - 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (- 31950a c d - 31950a b c d - 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (- 128640a c d - 128640a b c d - 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (- 286920a c d - 286920a b c d - 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (- 320480a c d - 320480a b c d - 32048b c )m - 134400a c d +--R + +--R 4 2 5 +--R - 134400a b c d - 13440b c +--R * +--R m + 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (- 5a c d - 2a b c )m + (- 170a c d - 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (- 2390a c d - 956a b c )m + (- 17900a c d - 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (- 76445a c d - 30578a b c )m + (- 183530a c d - 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (- 223560a c d - 89424a b c )m - 100800a c d - 40320a b c +--R * +--R m + 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - a c m - 35a c m - 511a c m - 4025a c m - 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R - 48860a c m - 69264a c m - 40320a c +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1092 +t0:=x^3*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--R 2 16 21 16 2 15 20 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 19 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 18 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 17 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 16 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 15 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 14 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 13 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 12 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 11 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 10 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 9 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 8 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 7 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 6 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 5 2 15 16 4 2 16 3 +--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 106 + +--S 107 of 1092 +r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ + (b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+_ + 3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ + (c+d*x)^20/d^6-1/21*b*(5*b*c-2*a*d)*(c+d*x)^21/d^6+_ + 1/22*b^2*(c+d*x)^22/d^6 +--R +--R +--R (2) +--R 1 2 22 22 2 22 16 2 21 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 1 2 22 8 21 2 2 20 20 +--R (-- a d + - a b c d + 6b c d )x +--R 20 5 +--R + +--R 16 2 21 240 2 20 560 2 3 19 19 +--R (-- a c d + --- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 20 2 2 20 560 3 19 910 2 4 18 18 +--R (-- a c d + --- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 560 2 3 19 3640 4 18 4368 2 5 17 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 455 2 4 18 5 17 1001 2 6 16 16 +--R (--- a c d + 546a b c d + ---- b c d )x +--R 4 2 +--R + +--R 1456 2 5 17 16016 6 16 2288 2 7 15 15 +--R (---- a c d + ----- a b c d + ---- b c d )x +--R 5 15 3 +--R + +--R 2 6 16 11440 7 15 6435 2 8 14 14 +--R (572a c d + ----- a b c d + ---- b c d )x +--R 7 7 +--R + +--R 2 7 15 8 14 2 9 13 13 +--R (880a c d + 1980a b c d + 880b c d )x +--R + +--R 2145 2 8 14 5720 9 13 2002 2 10 12 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 2 3 3 +--R + +--R 2 9 13 10 12 4368 2 11 11 11 +--R (1040a c d + 1456a b c d + ---- b c d )x +--R 11 +--R + +--R 4004 2 10 12 4368 11 11 2 12 10 10 +--R (---- a c d + ---- a b c d + 182b c d )x +--R 5 5 +--R + +--R 1456 2 11 11 3640 12 10 560 2 13 9 9 +--R (---- a c d + ---- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 455 2 12 10 13 9 2 14 8 8 +--R (--- a c d + 140a b c d + 15b c d )x +--R 2 +--R + +--R 2 13 9 240 14 8 16 2 15 7 7 +--R (80a c d + --- a b c d + -- b c d )x +--R 7 7 +--R + +--R 2 14 8 16 15 7 1 2 16 6 6 16 2 15 7 2 16 6 5 +--R (20a c d + -- a b c d + - b c d )x + (-- a c d + - a b c d )x +--R 3 6 5 5 +--R + +--R 1 2 16 6 4 1 2 20 2 2 21 1 2 22 +--R - a c d x - ----- a c d + ------ a b c d - ------ b c +--R 4 19380 101745 447678 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 16 22 2 16 16 2 15 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 1 2 16 8 15 2 2 14 20 +--R (-- a d + - a b c d + 6b c d )x +--R 20 5 +--R + +--R 16 2 15 240 2 14 560 2 3 13 19 +--R (-- a c d + --- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 20 2 2 14 560 3 13 910 2 4 12 18 +--R (-- a c d + --- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 560 2 3 13 3640 4 12 4368 2 5 11 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 455 2 4 12 5 11 1001 2 6 10 16 +--R (--- a c d + 546a b c d + ---- b c d )x +--R 4 2 +--R + +--R 1456 2 5 11 16016 6 10 2288 2 7 9 15 +--R (---- a c d + ----- a b c d + ---- b c d )x +--R 5 15 3 +--R + +--R 2 6 10 11440 7 9 6435 2 8 8 14 +--R (572a c d + ----- a b c d + ---- b c d )x +--R 7 7 +--R + +--R 2 7 9 8 8 2 9 7 13 +--R (880a c d + 1980a b c d + 880b c d )x +--R + +--R 2145 2 8 8 5720 9 7 2002 2 10 6 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 2 3 3 +--R + +--R 2 9 7 10 6 4368 2 11 5 11 +--R (1040a c d + 1456a b c d + ---- b c d )x +--R 11 +--R + +--R 4004 2 10 6 4368 11 5 2 12 4 10 +--R (---- a c d + ---- a b c d + 182b c d )x +--R 5 5 +--R + +--R 1456 2 11 5 3640 12 4 560 2 13 3 9 +--R (---- a c d + ---- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 455 2 12 4 13 3 2 14 2 8 +--R (--- a c d + 140a b c d + 15b c d )x +--R 2 +--R + +--R 2 13 3 240 14 2 16 2 15 7 +--R (80a c d + --- a b c d + -- b c d)x +--R 7 7 +--R + +--R 2 14 2 16 15 1 2 16 6 16 2 15 2 16 5 1 2 16 4 +--R (20a c d + -- a b c d + - b c )x + (-- a c d + - a b c )x + - a c x +--R 3 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 1092 +m0:=a0-r0 +--R +--R +--R 1 2 20 2 2 21 1 2 22 +--R ----- a c d - ------ a b c d + ------ b c +--R 19380 101745 447678 +--R (4) ---------------------------------------------- +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 109 + +--S 110 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +)clear all + +--S 111 of 1092 +t0:=x^2*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--R 2 16 20 16 2 15 19 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 18 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 17 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 16 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 15 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 14 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 13 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 12 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 11 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 10 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 9 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 8 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 7 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 6 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 5 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 4 2 15 16 3 2 16 2 +--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 111 + +--S 112 of 1092 +r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ + (c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-_ + 1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5 +--R +--R +--R (2) +--R 1 2 21 21 1 21 4 2 20 20 +--R -- b d x + (-- a b d + - b c d )x +--R 21 10 5 +--R + +--R 1 2 21 32 20 120 2 2 19 19 +--R (-- a d + -- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 8 2 20 40 2 19 280 2 3 18 18 +--R (- a c d + -- a b c d + --- b c d )x +--R 9 3 9 +--R + +--R 120 2 2 19 1120 3 18 1820 2 4 17 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 2 3 18 455 4 17 2 5 16 16 +--R (35a c d + --- a b c d + 273b c d )x +--R 2 +--R + +--R 364 2 4 17 2912 5 16 8008 2 6 15 15 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 3 5 15 +--R + +--R 2 5 16 6 15 5720 2 7 14 14 +--R (312a c d + 1144a b c d + ---- b c d )x +--R 7 +--R + +--R 2 6 15 7 14 2 8 13 13 +--R (616a c d + 1760a b c d + 990b c d )x +--R + +--R 2860 2 7 14 8 13 2860 2 9 12 12 +--R (---- a c d + 2145a b c d + ---- b c d )x +--R 3 3 +--R + +--R 2 8 13 9 12 2 10 11 11 +--R (1170a c d + 2080a b c d + 728b c d )x +--R + +--R 2 9 12 8008 10 11 2184 2 11 10 10 +--R (1144a c d + ---- a b c d + ---- b c d )x +--R 5 5 +--R + +--R 8008 2 10 11 2912 11 10 1820 2 12 9 9 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 9 3 9 +--R + +--R 2 11 10 12 9 2 13 8 8 +--R (546a c d + 455a b c d + 70b c d )x +--R + +--R 2 12 9 13 8 120 2 14 7 7 +--R (260a c d + 160a b c d + --- b c d )x +--R 7 +--R + +--R 280 2 13 8 14 7 8 2 15 6 6 +--R (--- a c d + 40a b c d + - b c d )x +--R 3 3 +--R + +--R 2 14 7 32 15 6 1 2 16 5 5 2 15 6 1 16 5 4 +--R (24a c d + -- a b c d + - b c d )x + (4a c d + - a b c d )x +--R 5 5 2 +--R + +--R 1 2 16 5 3 1 2 19 2 1 20 1 2 21 +--R - a c d x + ---- a c d - ---- a b c d + ------ b c +--R 3 2907 9690 101745 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 16 21 1 16 4 2 15 20 +--R -- b d x + (-- a b d + - b c d )x +--R 21 10 5 +--R + +--R 1 2 16 32 15 120 2 2 14 19 +--R (-- a d + -- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 8 2 15 40 2 14 280 2 3 13 18 +--R (- a c d + -- a b c d + --- b c d )x +--R 9 3 9 +--R + +--R 120 2 2 14 1120 3 13 1820 2 4 12 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 2 3 13 455 4 12 2 5 11 16 +--R (35a c d + --- a b c d + 273b c d )x +--R 2 +--R + +--R 364 2 4 12 2912 5 11 8008 2 6 10 15 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 3 5 15 +--R + +--R 2 5 11 6 10 5720 2 7 9 14 +--R (312a c d + 1144a b c d + ---- b c d )x +--R 7 +--R + +--R 2 6 10 7 9 2 8 8 13 +--R (616a c d + 1760a b c d + 990b c d )x +--R + +--R 2860 2 7 9 8 8 2860 2 9 7 12 +--R (---- a c d + 2145a b c d + ---- b c d )x +--R 3 3 +--R + +--R 2 8 8 9 7 2 10 6 11 +--R (1170a c d + 2080a b c d + 728b c d )x +--R + +--R 2 9 7 8008 10 6 2184 2 11 5 10 +--R (1144a c d + ---- a b c d + ---- b c d )x +--R 5 5 +--R + +--R 8008 2 10 6 2912 11 5 1820 2 12 4 9 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 9 3 9 +--R + +--R 2 11 5 12 4 2 13 3 8 +--R (546a c d + 455a b c d + 70b c d )x +--R + +--R 2 12 4 13 3 120 2 14 2 7 +--R (260a c d + 160a b c d + --- b c d )x +--R 7 +--R + +--R 280 2 13 3 14 2 8 2 15 6 +--R (--- a c d + 40a b c d + - b c d)x +--R 3 3 +--R + +--R 2 14 2 32 15 1 2 16 5 2 15 1 16 4 1 2 16 3 +--R (24a c d + -- a b c d + - b c )x + (4a c d + - a b c )x + - a c x +--R 5 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 1092 +m0:=a0-r0 +--R +--R +--R 1 2 19 2 1 20 1 2 21 +--R - ---- a c d + ---- a b c d - ------ b c +--R 2907 9690 101745 +--R (4) --------------------------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 114 + +--S 115 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 115 + +)clear all + +--S 116 of 1092 +t0:=x*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--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 116 + +--S 117 of 1092 +r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ + (c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+_ + 1/20*b^2*(c+d*x)^20/d^4 +--R +--R +--R (2) +--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 117 + +--S 118 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 118 + +--S 119 of 1092 +m0:=a0-r0 +--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 (4) ----------------------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 119 + +--S 120 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 120 + +)clear all + +--S 121 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 n +--R (1) (d x + 3c d x + 3c d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1092 +r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ + (b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*_ + (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+_ + d*(3*b^2*c^2-12*a*b*c*d+10*a^2*d^2)*(a+b*x)^(4+n)/(b^6*(4+n))+_ + d^2*(3*b*c-5*a*d)*(a+b*x)^(5+n)/(b^6*(5+n))+d^3*(a+b*x)^(6+n)/(b^6*(6+n)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 n + 6 +--R (d n + 15d n + 85d n + 225d n + 274d n + 120d )(b x + a) +--R + +--R 3 2 5 3 2 4 +--R (- 5a d + 3b c d )n + (- 80a d + 48b c d )n +--R + +--R 3 2 3 3 2 2 +--R (- 475a d + 285b c d )n + (- 1300a d + 780b c d )n +--R + +--R 3 2 3 2 +--R (- 1620a d + 972b c d )n - 720a d + 432b c d +--R * +--R n + 5 +--R (b x + a) +--R + +--R 2 3 2 2 2 5 +--R (10a d - 12a b c d + 3b c d)n +--R + +--R 2 3 2 2 2 4 +--R (170a d - 204a b c d + 51b c d)n +--R + +--R 2 3 2 2 2 3 +--R (1070a d - 1284a b c d + 321b c d)n +--R + +--R 2 3 2 2 2 2 +--R (3070a d - 3684a b c d + 921b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (3960a d - 4752a b c d + 1188b c d)n + 1800a d - 2160a b c d +--R + +--R 2 2 +--R 540b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 10a d + 18a b c d - 9a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 180a d + 324a b c d - 162a b c d + 18b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 1210a d + 2178a b c d - 1089a b c d + 121b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 3720a d + 6696a b c d - 3348a b c d + 372b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 5080a d + 9144a b c d - 4572a b c d + 508b c )n - 2400a d +--R + +--R 2 2 2 2 3 3 +--R 4320a b c d - 2160a b c d + 240b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 5 +--R (5a d - 12a b c d + 9a b c d - 2a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (95a d - 228a b c d + 171a b c d - 38a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (685a d - 1644a b c d + 1233a b c d - 274a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (2305a d - 5532a b c d + 4149a b c d - 922a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (3510a d - 8424a b c d + 6318a b c d - 1404a b c )n + 1800a d +--R + +--R 3 2 2 2 2 3 3 +--R - 4320a b c d + 3240a b c d - 720a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 +--R (- a d + 3a b c d - 3a b c d + a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 4 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 155a d + 465a b c d - 465a b c d + 155a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- 580a d + 1740a b c d - 1740a b c d + 580a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 3 +--R (- 1044a d + 3132a b c d - 3132a b c d + 1044a b c )n - 720a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 2160a b c d - 2160a b c d + 720a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 6 3 4 6 3 3 6 3 2 6 3 6 3 6 +--R (b d n + 15b d n + 85b d n + 225b d n + 274b d n + 120b d )x +--R + +--R 5 3 6 2 5 5 3 6 2 4 +--R (a b d + 3b c d )n + (10a b d + 48b c d )n +--R + +--R 5 3 6 2 3 5 3 6 2 2 +--R (35a b d + 285b c d )n + (50a b d + 780b c d )n +--R + +--R 5 3 6 2 6 2 +--R (24a b d + 972b c d )n + 432b c d +--R * +--R 5 +--R x +--R + +--R 5 2 6 2 5 2 4 3 5 2 6 2 4 +--R (3a b c d + 3b c d)n + (- 5a b d + 36a b c d + 51b c d)n +--R + +--R 2 4 3 5 2 6 2 3 +--R (- 30a b d + 141a b c d + 321b c d)n +--R + +--R 2 4 3 5 2 6 2 2 +--R (- 55a b d + 216a b c d + 921b c d)n +--R + +--R 2 4 3 5 2 6 2 6 2 +--R (- 30a b d + 108a b c d + 1188b c d)n + 540b c d +--R * +--R 4 +--R x +--R + +--R 5 2 6 3 5 2 4 2 5 2 6 3 4 +--R (3a b c d + b c )n + (- 12a b c d + 42a b c d + 18b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (20a b d - 108a b c d + 195a b c d + 121b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (60a b d - 240a b c d + 336a b c d + 372b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 3 +--R (40a b d - 144a b c d + 180a b c d + 508b c )n + 240b c +--R * +--R 3 +--R x +--R + +--R 5 3 5 2 4 2 5 3 4 +--R a b c n + (- 9a b c d + 16a b c )n +--R + +--R 3 3 2 2 4 2 5 3 3 +--R (36a b c d - 108a b c d + 89a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 60a b d + 252a b c d - 369a b c d + 194a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 +--R (- 60a b d + 216a b c d - 270a b c d + 120a b c )n +--R * +--R 2 +--R x +--R + +--R 2 4 3 4 3 3 2 2 4 3 3 +--R - 2a b c n + (18a b c d - 30a b c )n +--R + +--R 4 2 2 3 3 2 2 4 3 2 +--R (- 72a b c d + 198a b c d - 148a b c )n +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (120a b d - 432a b c d + 540a b c d - 240a b c )n +--R * +--R x +--R + +--R 3 3 3 3 4 2 2 3 3 3 2 +--R 2a b c n + (- 18a b c d + 30a b c )n +--R + +--R 5 2 4 2 2 3 3 3 6 3 5 2 +--R (72a b c d - 198a b c d + 148a b c )n - 120a d + 432a b c d +--R + +--R 4 2 2 3 3 3 +--R - 540a b c d + 240a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 3 5 6 3 4 6 3 3 6 3 2 6 3 6 3 6 +--R (b d n + 15b d n + 85b d n + 225b d n + 274b d n + 120b d )x +--R + +--R 5 3 6 2 5 5 3 6 2 4 +--R (a b d + 3b c d )n + (10a b d + 48b c d )n +--R + +--R 5 3 6 2 3 5 3 6 2 2 +--R (35a b d + 285b c d )n + (50a b d + 780b c d )n +--R + +--R 5 3 6 2 6 2 +--R (24a b d + 972b c d )n + 432b c d +--R * +--R 5 +--R x +--R + +--R 5 2 6 2 5 2 4 3 5 2 6 2 4 +--R (3a b c d + 3b c d)n + (- 5a b d + 36a b c d + 51b c d)n +--R + +--R 2 4 3 5 2 6 2 3 +--R (- 30a b d + 141a b c d + 321b c d)n +--R + +--R 2 4 3 5 2 6 2 2 +--R (- 55a b d + 216a b c d + 921b c d)n +--R + +--R 2 4 3 5 2 6 2 6 2 +--R (- 30a b d + 108a b c d + 1188b c d)n + 540b c d +--R * +--R 4 +--R x +--R + +--R 5 2 6 3 5 2 4 2 5 2 6 3 4 +--R (3a b c d + b c )n + (- 12a b c d + 42a b c d + 18b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (20a b d - 108a b c d + 195a b c d + 121b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (60a b d - 240a b c d + 336a b c d + 372b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 3 +--R (40a b d - 144a b c d + 180a b c d + 508b c )n + 240b c +--R * +--R 3 +--R x +--R + +--R 5 3 5 2 4 2 5 3 4 +--R a b c n + (- 9a b c d + 16a b c )n +--R + +--R 3 3 2 2 4 2 5 3 3 +--R (36a b c d - 108a b c d + 89a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 60a b d + 252a b c d - 369a b c d + 194a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 +--R (- 60a b d + 216a b c d - 270a b c d + 120a b c )n +--R * +--R 2 +--R x +--R + +--R 2 4 3 4 3 3 2 2 4 3 3 +--R - 2a b c n + (18a b c d - 30a b c )n +--R + +--R 4 2 2 3 3 2 2 4 3 2 +--R (- 72a b c d + 198a b c d - 148a b c )n +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (120a b d - 432a b c d + 540a b c d - 240a b c )n +--R * +--R x +--R + +--R 3 3 3 3 4 2 2 3 3 3 2 +--R 2a b c n + (- 18a b c d + 30a b c )n +--R + +--R 5 2 4 2 2 3 3 3 6 3 5 2 +--R (72a b c d - 198a b c d + 148a b c )n - 120a d + 432a b c d +--R + +--R 4 2 2 3 3 3 +--R - 540a b c d + 240a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 5 3 4 3 3 3 2 3 3 n + 6 +--R (- d n - 15d n - 85d n - 225d n - 274d n - 120d )(b x + a) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R (5a d - 3b c d )n + (80a d - 48b c d )n + (475a d - 285b c d )n +--R + +--R 3 2 2 3 2 3 +--R (1300a d - 780b c d )n + (1620a d - 972b c d )n + 720a d +--R + +--R 2 +--R - 432b c d +--R * +--R n + 5 +--R (b x + a) +--R + +--R 2 3 2 2 2 5 +--R (- 10a d + 12a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 4 +--R (- 170a d + 204a b c d - 51b c d)n +--R + +--R 2 3 2 2 2 3 +--R (- 1070a d + 1284a b c d - 321b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 3070a d + 3684a b c d - 921b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 3960a d + 4752a b c d - 1188b c d)n - 1800a d + 2160a b c d +--R + +--R 2 2 +--R - 540b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (10a d - 18a b c d + 9a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (180a d - 324a b c d + 162a b c d - 18b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (1210a d - 2178a b c d + 1089a b c d - 121b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (3720a d - 6696a b c d + 3348a b c d - 372b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (5080a d - 9144a b c d + 4572a b c d - 508b c )n + 2400a d +--R + +--R 2 2 2 2 3 3 +--R - 4320a b c d + 2160a b c d - 240b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 5 +--R (- 5a d + 12a b c d - 9a b c d + 2a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (- 95a d + 228a b c d - 171a b c d + 38a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 685a d + 1644a b c d - 1233a b c d + 274a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (- 2305a d + 5532a b c d - 4149a b c d + 922a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 3510a d + 8424a b c d - 6318a b c d + 1404a b c )n - 1800a d +--R + +--R 3 2 2 2 2 3 3 +--R 4320a b c d - 3240a b c d + 720a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 +--R (a d - 3a b c d + 3a b c d - a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 4 +--R (20a d - 60a b c d + 60a b c d - 20a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (155a d - 465a b c d + 465a b c d - 155a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (580a d - 1740a b c d + 1740a b c d - 580a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 3 +--R (1044a d - 3132a b c d + 3132a b c d - 1044a b c )n + 720a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 2160a b c d + 2160a b c d - 720a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1092 +t0:=x*(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 n +--R (1) (d x + 3c d x + 3c d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1092 +r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ + (a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/_ + (b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ + d^3*(a+b*x)^(5+n)/(b^5*(5+n)) +--R +--R +--R (2) +--R 3 4 3 3 3 2 3 3 n + 5 +--R (d n + 10d n + 35d n + 50d n + 24d )(b x + a) +--R + +--R 3 2 4 3 2 3 +--R (- 4a d + 3b c d )n + (- 44a d + 33b c d )n +--R + +--R 3 2 2 3 2 3 +--R (- 164a d + 123b c d )n + (- 244a d + 183b c d )n - 120a d +--R + +--R 2 +--R 90b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 3 2 2 2 4 2 3 2 2 2 3 +--R (6a d - 9a b c d + 3b c d)n + (72a d - 108a b c d + 36b c d)n +--R + +--R 2 3 2 2 2 2 +--R (294a d - 441a b c d + 147b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (468a d - 702a b c d + 234b c d)n + 240a d - 360a b c d + 120b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 4a d + 9a b c d - 6a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 52a d + 117a b c d - 78a b c d + 13b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 236a d + 531a b c d - 354a b c d + 59b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 428a d + 963a b c d - 642a b c d + 107b c )n - 240a d +--R + +--R 2 2 2 2 3 3 +--R 540a b c d - 360a b c d + 60b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (a d - 3a b c d + 3a b c d - a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (14a d - 42a b c d + 42a b c d - 14a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (71a d - 213a b c d + 213a b c d - 71a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (154a d - 462a b c d + 462a b c d - 154a b c )n + 120a d +--R + +--R 3 2 2 2 2 3 3 +--R - 360a b c d + 360a b c d - 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 5 3 3 5 3 2 5 3 5 3 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 3 5 2 4 4 3 5 2 3 +--R (a b d + 3b c d )n + (6a b d + 33b c d )n +--R + +--R 4 3 5 2 2 4 3 5 2 5 2 +--R (11a b d + 123b c d )n + (6a b d + 183b c d )n + 90b c d +--R * +--R 4 +--R x +--R + +--R 4 2 5 2 4 2 3 3 4 2 5 2 3 +--R (3a b c d + 3b c d)n + (- 4a b d + 24a b c d + 36b c d)n +--R + +--R 2 3 3 4 2 5 2 2 +--R (- 12a b d + 51a b c d + 147b c d)n +--R + +--R 2 3 3 4 2 5 2 5 2 +--R (- 8a b d + 30a b c d + 234b c d)n + 120b c d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 2 3 2 4 2 5 3 3 +--R (3a b c d + b c )n + (- 9a b c d + 30a b c d + 13b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (12a b d - 54a b c d + 87a b c d + 59b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 3 +--R (12a b d - 45a b c d + 60a b c d + 107b c )n + 60b c +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 3 2 4 3 3 +--R a b c n + (- 6a b c d + 12a b c )n +--R + +--R 3 2 2 2 3 2 4 3 2 +--R (18a b c d - 54a b c d + 47a b c )n +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (- 24a b d + 90a b c d - 120a b c d + 60a b c )n +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R - a b c n + (6a b c d - 12a b c )n +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 +--R (- 18a b c d + 54a b c d - 47a b c )n + 24a d - 90a b c d +--R + +--R 3 2 2 2 3 3 +--R 120a b c d - 60a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 3 4 5 3 3 5 3 2 5 3 5 3 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 3 5 2 4 4 3 5 2 3 +--R (a b d + 3b c d )n + (6a b d + 33b c d )n +--R + +--R 4 3 5 2 2 4 3 5 2 5 2 +--R (11a b d + 123b c d )n + (6a b d + 183b c d )n + 90b c d +--R * +--R 4 +--R x +--R + +--R 4 2 5 2 4 2 3 3 4 2 5 2 3 +--R (3a b c d + 3b c d)n + (- 4a b d + 24a b c d + 36b c d)n +--R + +--R 2 3 3 4 2 5 2 2 +--R (- 12a b d + 51a b c d + 147b c d)n +--R + +--R 2 3 3 4 2 5 2 5 2 +--R (- 8a b d + 30a b c d + 234b c d)n + 120b c d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 2 3 2 4 2 5 3 3 +--R (3a b c d + b c )n + (- 9a b c d + 30a b c d + 13b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (12a b d - 54a b c d + 87a b c d + 59b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 3 +--R (12a b d - 45a b c d + 60a b c d + 107b c )n + 60b c +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 3 2 4 3 3 +--R a b c n + (- 6a b c d + 12a b c )n +--R + +--R 3 2 2 2 3 2 4 3 2 +--R (18a b c d - 54a b c d + 47a b c )n +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (- 24a b d + 90a b c d - 120a b c d + 60a b c )n +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R - a b c n + (6a b c d - 12a b c )n +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 +--R (- 18a b c d + 54a b c d - 47a b c )n + 24a d - 90a b c d +--R + +--R 3 2 2 2 3 3 +--R 120a b c d - 60a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 4 3 3 3 2 3 3 n + 5 +--R (- d n - 10d n - 35d n - 50d n - 24d )(b x + a) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (4a d - 3b c d )n + (44a d - 33b c d )n + (164a d - 123b c d )n +--R + +--R 3 2 3 2 +--R (244a d - 183b c d )n + 120a d - 90b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 3 2 2 2 4 +--R (- 6a d + 9a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 3 +--R (- 72a d + 108a b c d - 36b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 294a d + 441a b c d - 147b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 468a d + 702a b c d - 234b c d)n - 240a d + 360a b c d +--R + +--R 2 2 +--R - 120b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (4a d - 9a b c d + 6a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (52a d - 117a b c d + 78a b c d - 13b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (236a d - 531a b c d + 354a b c d - 59b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (428a d - 963a b c d + 642a b c d - 107b c )n + 240a d +--R + +--R 2 2 2 2 3 3 +--R - 540a b c d + 360a b c d - 60b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (- a d + 3a b c d - 3a b c d + a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 14a d + 42a b c d - 42a b c d + 14a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (- 71a d + 213a b c d - 213a b c d + 71a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 154a d + 462a b c d - 462a b c d + 154a b c )n - 120a d +--R + +--R 3 2 2 2 2 3 3 +--R 360a b c d - 360a b c d + 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1092 +t0:=(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 3 2 2 2 3 n +--R (1) (d x + 3c d x + 3c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1092 +r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ + (a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/_ + (b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 n + 4 +--R (d n + 6d n + 11d n + 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 +--R (- 3a d + 3b c d )n + (- 21a d + 21b c d )n +--R + +--R 3 2 3 2 +--R (- 42a d + 42b c d )n - 24a d + 24b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 2 3 2 2 2 2 +--R (3a d - 6a b c d + 3b c d)n + (24a d - 48a b c d + 24b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (57a d - 114a b c d + 57b c d)n + 36a d - 72a b c d + 36b c d +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a d + 78a b c d - 78a b c d + 26b c )n - 24a d + 72a b c d +--R + +--R 2 2 3 3 +--R - 72a b c d + 24b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )n + (3a b d + 21b c d )n +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )n + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)n + (- 3a b d + 15a b c d + 24b c d)n +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)n + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )n + (- 6a b c d + 21a b c d + 9b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )n + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c n + (- 3a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )n - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )n + (3a b d + 21b c d )n +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )n + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)n + (- 3a b d + 15a b c d + 24b c d)n +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)n + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )n + (- 6a b c d + 21a b c d + 9b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )n + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c n + (- 3a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )n - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 3 3 2 3 3 n + 4 +--R (- d n - 6d n - 11d n - 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a d - 3b c d )n + (21a d - 21b c d )n + (42a d - 42b c d )n +--R + +--R 3 2 +--R 24a d - 24b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 +--R (- 3a d + 6a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 24a d + 48a b c d - 24b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (- 57a d + 114a b c d - 57b c d)n - 36a d + 72a b c d - 36b c d +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a d - 78a b c d + 78a b c d - 26b c )n + 24a d - 72a b c d +--R + +--R 2 2 3 3 +--R 72a b c d - 24b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1092 +t0:=(a+b*x)^n*(c+d*x)^3/x +--R +--R +--R 3 3 2 2 2 3 n +--R (d x + 3c d x + 3c d x + c )(b x + a) +--R (1) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1092 +--r0:=3*c^2*d*(a+b*x)^(1+n)/(b*(1+n))-3*a*c*d^2*(a+b*x)^(1+n)/(b^2*(1+n))+_ +-- a^2*d^3*(a+b*x)^(1+n)/(b^3*(1+n))+3*c*d^2*(a+b*x)^(2+n)/(b^2*(2+n))-_ +-- 2*a*d^3*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-_ +-- c^3*(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 137 + +--S 138 of 1092 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 1092 +--m0:=a0-r0 +--E 139 + +--S 140 of 1092 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 1092 +t0:=x^m*(c+d*x)/(a+b*x) +--R +--R +--R m +--R (d x + c)x +--R (1) ----------- +--R b x + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1092 +--r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b*(1+m)) +--E 142 + +--S 143 of 1092 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 1092 +--m0:=a0-r0 +--E 144 + +--S 145 of 1092 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 1092 +t0:=x^4*(c+d*x)/(a+b*x) +--R +--R +--R 5 4 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1092 +r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ + 1/4*(b*c-a*d)*x^4/b^2+1/5*d*x^5/b+a^4*(b*c-a*d)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 4 5 5 4 5 4 +--R (- 60a d + 60a b c)log(b x + a) + 12b d x + (- 15a b d + 15b c)x +--R + +--R 2 3 4 3 3 2 2 3 2 4 3 2 +--R (20a b d - 20a b c)x + (- 30a b d + 30a b c)x + (60a b d - 60a b c)x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 4 +--R (- 60a d + 60a b c)log(b x + a) + 12b d x + (- 15a b d + 15b c)x +--R + +--R 2 3 4 3 3 2 2 3 2 4 3 2 +--R (20a b d - 20a b c)x + (- 30a b d + 30a b c)x + (60a b d - 60a b c)x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1092 +t0:=x^3*(c+d*x)/(a+b*x) +--R +--R +--R 4 3 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1092 +r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ + 1/4*d*x^4/b-a^3*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 3 +--R (12a d - 12a b c)log(b x + a) + 3b d x + (- 4a b d + 4b c)x +--R + +--R 2 2 3 2 3 2 2 +--R (6a b d - 6a b c)x + (- 12a b d + 12a b c)x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 3 +--R (12a d - 12a b c)log(b x + a) + 3b d x + (- 4a b d + 4b c)x +--R + +--R 2 2 3 2 3 2 2 +--R (6a b d - 6a b c)x + (- 12a b d + 12a b c)x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1092 +t0:=x^2*(c+d*x)/(a+b*x) +--R +--R +--R 3 2 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1092 +r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ + a^2*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 2 +--R (- 6a d + 6a b c)log(b x + a) + 2b d x + (- 3a b d + 3b c)x +--R + +--R 2 2 +--R (6a b d - 6a b c)x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 2 +--R (- 6a d + 6a b c)log(b x + a) + 2b d x + (- 3a b d + 3b c)x +--R + +--R 2 2 +--R (6a b d - 6a b c)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1092 +t0:=x*(c+d*x)/(a+b*x) +--R +--R +--R 2 +--R d x + c x +--R (1) ---------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1092 +r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x +--R (2) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x +--R (3) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1092 +t0:=(c+d*x)/(a+b*x) +--R +--R +--R d x + c +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1092 +r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (3) --------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1092 +t0:=(c+d*x)/(x*(a+b*x)) +--R +--R +--R d x + c +--R (1) ---------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1092 +r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) +--R +--R +--R (a d - b c)log(b x + a) + b c log(x) +--R (2) ------------------------------------ +--R a b +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (a d - b c)log(b x + a) + b c log(x) +--R (3) ------------------------------------ +--R a b +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1092 +t0:=(c+d*x)/(x^2*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1092 +r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 +--R +--R +--R (- a d + b c)x log(b x + a) + (a d - b c)x log(x) - a c +--R (2) ------------------------------------------------------- +--R 2 +--R a x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- a d + b c)x log(b x + a) + (a d - b c)x log(x) - a c +--R (3) ------------------------------------------------------- +--R 2 +--R a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1092 +t0:=(c+d*x)/(x^3*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1092 +r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ + b*(b*c-a*d)*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R (2a b d - 2b c)x log(b x + a) + (- 2a b d + 2b c)x log(x) +--R + +--R 2 2 +--R (- 2a d + 2a b c)x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2a b d - 2b c)x log(b x + a) + (- 2a b d + 2b c)x log(x) +--R + +--R 2 2 +--R (- 2a d + 2a b c)x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1092 +t0:=(c+d*x)/(x^4*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1092 +r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ + b^2*(b*c-a*d)*log(x)/a^4+b^2*(b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 3 3 2 3 3 +--R (- 6a b d + 6b c)x log(b x + a) + (6a b d - 6b c)x log(x) +--R + +--R 2 2 2 3 2 3 +--R (6a b d - 6a b c)x + (- 3a d + 3a b c)x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 3 +--R (- 6a b d + 6b c)x log(b x + a) + (6a b d - 6b c)x log(x) +--R + +--R 2 2 2 3 2 3 +--R (6a b d - 6a b c)x + (- 3a d + 3a b c)x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1092 +t0:=(c+d*x)/(x^5*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1092 +r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ + b^2*(b*c-a*d)/(a^4*x)+b^3*(b*c-a*d)*log(x)/a^5-_ + b^3*(b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 4 4 3 4 4 +--R (12a b d - 12b c)x log(b x + a) + (- 12a b d + 12b c)x log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 12a b d + 12a b c)x + (6a b d - 6a b c)x + (- 4a d + 4a b c)x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 4 4 +--R (12a b d - 12b c)x log(b x + a) + (- 12a b d + 12b c)x log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 12a b d + 12a b c)x + (6a b d - 6a b c)x + (- 4a d + 4a b c)x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1092 +t0:=x^m*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 2 2 m +--R (d x + 2c d x + c )x +--R (1) ---------------------- +--R b x + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1092 +--r0:=-d*(a*d*(2+m)-b*c*(3+m))*x^(1+m)/(b^2*(1+m)*(2+m))+_ +-- d*x^(1+m)*(c+d*x)/(b*(2+m))+(b*c-a*d)^2*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^2*(1+m)) +--E 197 + +--S 198 of 1092 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 1092 +--m0:=a0-r0 +--E 199 + +--S 200 of 1092 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 1092 +t0:=x^4*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 6 5 2 4 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1092 +r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ + 1/3*a*(b*c-a*d)^2*x^3/b^4+1/4*(b*c-a*d)^2*x^4/b^3+_ + 1/5*d*(2*b*c-a*d)*x^5/b^2+1/6*d^2*x^6/b+a^4*(b*c-a*d)^2*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 2 5 4 2 2 6 2 6 +--R (60a d - 120a b c d + 60a b c )log(b x + a) + 10b d x +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (- 12a b d + 24b c d)x + (15a b d - 30a b c d + 15b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 20a b d + 40a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 60a b d + 120a b c d - 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 5 4 2 2 6 2 6 +--R (60a d - 120a b c d + 60a b c )log(b x + a) + 10b d x +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (- 12a b d + 24b c d)x + (15a b d - 30a b c d + 15b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 20a b d + 40a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 60a b d + 120a b c d - 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1092 +t0:=x^3*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 5 4 2 3 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1092 +r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ + 1/3*(b*c-a*d)^2*x^3/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/5*d^2*x^5/b-_ + a^3*(b*c-a*d)^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 60a d + 120a b c d - 60a b c )log(b x + a) + 12b d x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 15a b d + 30b c d)x + (20a b d - 40a b c d + 20b c )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 30a b d + 60a b c d - 30a b c )x + (60a b d - 120a b c d + 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 3 2 2 5 2 5 +--R (- 60a d + 120a b c d - 60a b c )log(b x + a) + 12b d x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 15a b d + 30b c d)x + (20a b d - 40a b c d + 20b c )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 30a b d + 60a b c d - 30a b c )x + (60a b d - 120a b c d + 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1092 +t0:=x^2*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 4 3 2 2 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1092 +r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ + 1/4*d^2*x^4/b+a^2*(b*c-a*d)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (12a d - 24a b c d + 12a b c )log(b x + a) + 3b d x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 4a b d + 8b c d)x + (6a b d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 3 2 +--R (- 12a b d + 24a b c d - 12a b c )x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 2 4 2 4 +--R (12a d - 24a b c d + 12a b c )log(b x + a) + 3b d x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 4a b d + 8b c d)x + (6a b d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 3 2 +--R (- 12a b d + 24a b c d - 12a b c )x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1092 +t0:=x*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 3 2 2 +--R d x + 2c d x + c x +--R (1) -------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1092 +r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ + a*(b*c-a*d)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 2 3 +--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1092 +t0:=(c+d*x)^2/(a+b*x) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1092 +r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x +--R + +--R 2 2 +--R b c +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x +--R ----------------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1092 +m0:=a0-r0 +--R +--R +--R 2 +--R c +--R (4) - -- +--R 2b +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1092 +t0:=(c+d*x)^2/(x*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1092 +r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )log(b x + a) + b c log(x) + a b d x +--R (2) ------------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )log(b x + a) + b c log(x) + a b d x +--R (3) ------------------------------------------------------------- +--R 2 +--R a b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1092 +t0:=(c+d*x)^2/(x^2*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1092 +r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )x log(b x + a) + (2a b c d - b c )x log(x) - a b c +--R --------------------------------------------------------------------------- +--R 2 +--R a b x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )x log(b x + a) + (2a b c d - b c )x log(x) - a b c +--R --------------------------------------------------------------------------- +--R 2 +--R a b x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1092 +t0:=(c+d*x)^2/(x^3*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1092 +r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ + (b*c-a*d)^2*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )x log(x) + (- 4a c d + 2a b c )x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )x log(x) + (- 4a c d + 2a b c )x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1092 +t0:=(c+d*x)^2/(x^4*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1092 +r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ + b*(b*c-a*d)^2*log(x)/a^4+b*(b*c-a*d)^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 +--R (6a b d - 12a b c d + 6b c )x log(b x + a) +--R + +--R 2 2 2 3 2 3 +--R (- 6a b d + 12a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- 6a d + 12a b c d - 6a b c )x + (- 6a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 +--R (6a b d - 12a b c d + 6b c )x log(b x + a) +--R + +--R 2 2 2 3 2 3 +--R (- 6a b d + 12a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- 6a d + 12a b c d - 6a b c )x + (- 6a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1092 +t0:=(c+d*x)^2/(x^5*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1092 +r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ + 1/2*(b*c-a*d)^2/(a^3*x^2)+b*(b*c-a*d)^2/(a^4*x)+_ + b^2*(b*c-a*d)^2*log(x)/a^5-b^2*(b*c-a*d)^2*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 +--R (- 12a b d + 24a b c d - 12b c )x log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (12a b d - 24a b c d + 12b c )x log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (12a b d - 24a b c d + 12a b c )x + (- 6a d + 12a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 8a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 4 +--R (- 12a b d + 24a b c d - 12b c )x log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (12a b d - 24a b c d + 12b c )x log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (12a b d - 24a b c d + 12a b c )x + (- 6a d + 12a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 8a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1092 +t0:=(c+d*x)^2/(x^6*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 7 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1092 +r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ + 1/3*(b*c-a*d)^2/(a^3*x^3)+1/2*b*(b*c-a*d)^2/(a^4*x^2)-_ + b^2*(b*c-a*d)^2/(a^5*x)-b^3*(b*c-a*d)^2*log(x)/a^6+_ + b^3*(b*c-a*d)^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 2 5 +--R (60a b d - 120a b c d + 60b c )x log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (- 60a b d + 120a b c d - 60b c )x log(x) +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 60a b d + 120a b c d - 60a b c )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 20a d + 40a b c d - 20a b c )x +--R + +--R 5 4 2 5 2 +--R (- 30a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 5 +--R (60a b d - 120a b c d + 60b c )x log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (- 60a b d + 120a b c d - 60b c )x log(x) +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 60a b d + 120a b c d - 60a b c )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 20a d + 40a b c d - 20a b c )x +--R + +--R 5 4 2 5 2 +--R (- 30a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1092 +t0:=x^m*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 m +--R (d x + 3c d x + 3c d x + c )x +--R (1) -------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1092 +--r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^(1+m)/(b^3*(1+m))+_ +-- d^2*(3*b*c-a*d)*x^(2+m)/(b^2*(2+m))+d^3*x^(3+m)/(b*(3+m))+_ +-- (b*c-a*d)^3*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^3*(1+m)) +--E 257 + +--S 258 of 1092 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 1092 +--m0:=a0-r0 +--E 259 + +--S 260 of 1092 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 1092 +t0:=x^4*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 7 2 6 2 5 3 4 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1092 +r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ + x^3/b^5+1/4*(b*c-a*d)^3*x^4/b^4+1/5*d*(3*b^2*c^2-_ + 3*a*b*c*d+a^2*d^2)*x^5/b^3+1/6*d^2*(3*b*c-a*d)*x^6/b^2+_ + 1/7*d^3*x^7/b+a^4*(b*c-a*d)^3*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 7 3 6 2 5 2 2 4 3 3 +--R (- 420a d + 1260a b c d - 1260a b c d + 420a b c )log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 60b d x + (- 70a b d + 210b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (84a b d - 252a b c d + 252b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (140a b d - 420a b c d + 420a b c d - 140a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 630a b c d - 630a b c d + 210a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 +--R (420a b d - 1260a b c d + 1260a b c d - 420a b c )x +--R / +--R 8 +--R 420b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 6 2 5 2 2 4 3 3 +--R (- 420a d + 1260a b c d - 1260a b c d + 420a b c )log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 60b d x + (- 70a b d + 210b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (84a b d - 252a b c d + 252b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (140a b d - 420a b c d + 420a b c d - 140a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 630a b c d - 630a b c d + 210a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 +--R (420a b d - 1260a b c d + 1260a b c d - 420a b c )x +--R / +--R 8 +--R 420b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1092 +r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ + 1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_ + 1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/6*d^3*x^6/b-a^3*(b*c-a*d)^3*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 3 5 2 4 2 2 3 3 3 6 3 6 +--R (60a d - 180a b c d + 180a b c d - 60a b c )log(b x + a) + 10b d x +--R + +--R 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R (- 12a b d + 36b c d )x + (15a b d - 45a b c d + 45b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 60a b c d - 60a b c d + 20b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 2 4 2 2 3 3 3 6 3 6 +--R (60a d - 180a b c d + 180a b c d - 60a b c )log(b x + a) + 10b d x +--R + +--R 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R (- 12a b d + 36b c d )x + (15a b d - 45a b c d + 45b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 60a b c d - 60a b c d + 20b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1092 +r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ + 1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_ + 1/4*d^2*(3*b*c-a*d)*x^4/b^2+1/5*d^3*x^5/b+a^2*(b*c-a*d)^3*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 3 4 2 3 2 2 2 3 3 5 3 5 +--R (- 60a d + 180a b c d - 180a b c d + 60a b c )log(b x + a) + 12b d x +--R + +--R 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R (- 15a b d + 45b c d )x + (20a b d - 60a b c d + 60b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 90a b c d - 90a b c d + 30b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 2 3 2 2 2 3 3 5 3 5 +--R (- 60a d + 180a b c d - 180a b c d + 60a b c )log(b x + a) + 12b d x +--R + +--R 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R (- 15a b d + 45b c d )x + (20a b d - 60a b c d + 60b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 90a b c d - 90a b c d + 30b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1092 +t0:=x*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1092 +r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ + 1/3*d^2*(3*b*c-a*d)*x^3/b^2+1/4*d^3*x^4/b-a*(b*c-a*d)^3*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 2 2 2 2 3 3 4 3 4 +--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 2 2 2 2 3 3 4 3 4 +--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1092 +t0:=(c+d*x)^3/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1092 +r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ + 1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--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(b x + a) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x - 3a b c d +--R + +--R 3 3 +--R 5b c +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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(b x + a) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1092 +m0:=a0-r0 +--R +--R +--R 2 3 +--R 3a c d - 5b c +--R (4) -------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1092 +r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ + c^3*log(x)/a-(b*c-a*d)^3*log(a+b*x)/(a*b^3) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 2b c log(x) +--R + +--R 2 3 2 2 3 2 2 +--R a b d x + (- 2a b d + 6a b c d )x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 2b c log(x) +--R + +--R 2 3 2 2 3 2 2 +--R a b d x + (- 2a b d + 6a b c d )x +--R / +--R 3 +--R 2a b +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1092 +r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ + (b*c-a*d)^3*log(a+b*x)/(a^2*b^2) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a) +--R + +--R 2 2 3 3 2 3 2 2 3 +--R (3a b c d - b c )x log(x) + a b d x - a b c +--R / +--R 2 2 +--R a b x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a) +--R + +--R 2 2 3 3 2 3 2 2 3 +--R (3a b c d - b c )x log(x) + a b d x - a b c +--R / +--R 2 2 +--R a b x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1092 +r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(x)/a^3-(b*c-a*d)^3*log(a+b*x)/(a^3*b) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 3 3 2 2 2 2 3 2 3 +--R (6a b c d - 6a b c d + 2b c )x log(x) + (- 6a b c d + 2a b c )x - a b c +--R / +--R 3 2 +--R 2a b x +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 3 3 2 2 2 2 3 2 3 +--R (6a b c d - 6a b c d + 2b c )x log(x) + (- 6a b c d + 2a b c )x - a b c +--R / +--R 3 2 +--R 2a b x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1092 +r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x)-_ + (b*c-a*d)^3*log(x)/a^4+(b*c-a*d)^3*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )x log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 9a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )x log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 9a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1092 +t0:=(c+d*x)^3/(x^5*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1092 +r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ + 1/2*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^2)+_ + (b*c-a*d)^3/(a^4*x)+b*(b*c-a*d)^3*log(x)/a^5-b*(b*c-a*d)^3*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 36a b c d + 36a b c d - 12b c )x log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 12a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 36a b c d + 36a b c d - 12b c )x log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 12a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1092 +t0:=(c+d*x)^3/(x^6*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 7 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1092 +r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ + 1/3*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^3)+_ + 1/2*(b*c-a*d)^3/(a^4*x^2)-b*(b*c-a*d)^3/(a^5*x)-_ + b^2*(b*c-a*d)^3*log(x)/a^6+b^2*(b*c-a*d)^3*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 30a d + 90a b c d - 90a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 60a c d + 60a b c d - 20a b c )x + (- 45a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 30a d + 90a b c d - 90a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 60a c d + 60a b c d - 20a b c )x + (- 45a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1092 +t0:=(c+d*x)^3/(x^7*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 8 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1092 +r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ + 1/4*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^4)+_ + 1/3*(b*c-a*d)^3/(a^4*x^3)-1/2*b*(b*c-a*d)^3/(a^5*x^2)+_ + b^2*(b*c-a*d)^3/(a^6*x)+b^3*(b*c-a*d)^3*log(x)/a^7-_ + b^3*(b*c-a*d)^3*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 45a c d + 45a b c d - 15a b c )x + (- 36a c d + 12a b c )x - 10a c +--R / +--R 7 6 +--R 60a x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 45a c d + 45a b c d - 15a b c )x + (- 36a c d + 12a b c )x - 10a c +--R / +--R 7 6 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)) +--R +--R +--R m +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1092 +--r0:=b*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)*(1+m))-_ +-- d*x^(1+m)*hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)*(1+m)) +--E 322 + +--S 323 of 1092 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 1092 +--m0:=a0-r0 +--E 324 + +--S 325 of 1092 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)) +--R +--R +--R 5 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1092 +r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ + 1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*x^2/(b^3*d^3)-_ + 1/3*(b*c+a*d)*x^3/(b^2*d^2)+1/4*x^4/(b*d)-_ + a^5*log(a+b*x)/(b^5*(b*c-a*d))+c^5*log(c+d*x)/(d^5*(b*c-a*d)) +--R +--R +--R (2) +--R 5 5 5 5 4 5 5 4 4 +--R - 12b c log(d x + c) + 12a d log(b x + a) + (3a b d - 3b c d )x +--R + +--R 2 3 5 5 2 3 3 3 2 5 5 3 2 2 4 5 5 4 +--R (- 4a b d + 4b c d )x + (6a b d - 6b c d )x + (- 12a b d + 12b c d)x +--R / +--R 5 6 6 5 +--R 12a b d - 12b c d +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 5 5 4 4 +--R - 12b c log(d x + c) + 12a d log(b x + a) + (3a b d - 3b c d )x +--R + +--R 2 3 5 5 2 3 3 3 2 5 5 3 2 2 4 5 5 4 +--R (- 4a b d + 4b c d )x + (6a b d - 6b c d )x + (- 12a b d + 12b c d)x +--R / +--R 5 6 6 5 +--R 12a b d - 12b c d +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)) +--R +--R +--R 4 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1092 +r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ + 1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/3*x^3/(b*d)+_ + a^4*log(a+b*x)/(b^4*(b*c-a*d))-c^4*log(c+d*x)/(d^4*(b*c-a*d)) +--R +--R +--R (2) +--R 4 4 4 4 3 4 4 3 3 +--R 6b c log(d x + c) - 6a d log(b x + a) + (2a b d - 2b c d )x +--R + +--R 2 2 4 4 2 2 2 3 4 4 3 +--R (- 3a b d + 3b c d )x + (6a b d - 6b c d)x +--R / +--R 4 5 5 4 +--R 6a b d - 6b c d +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 4 4 3 3 +--R 6b c log(d x + c) - 6a d log(b x + a) + (2a b d - 2b c d )x +--R + +--R 2 2 4 4 2 2 2 3 4 4 3 +--R (- 3a b d + 3b c d )x + (6a b d - 6b c d)x +--R / +--R 4 5 5 4 +--R 6a b d - 6b c d +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)) +--R +--R +--R 3 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1092 +r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ + c^3*log(c+d*x)/(d^3*(b*c-a*d)) +--R +--R +--R (2) +--R 3 3 3 3 2 3 3 2 2 +--R - 2b c log(d x + c) + 2a d log(b x + a) + (a b d - b c d )x +--R + +--R 2 3 3 2 +--R (- 2a b d + 2b c d)x +--R / +--R 3 4 4 3 +--R 2a b d - 2b c d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 3 3 2 2 +--R - 2b c log(d x + c) + 2a d log(b x + a) + (a b d - b c d )x +--R + +--R 2 3 3 2 +--R (- 2a b d + 2b c d)x +--R / +--R 3 4 4 3 +--R 2a b d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1092 +r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) +--R +--R +--R 2 2 2 2 2 2 +--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x +--R (2) ------------------------------------------------------- +--R 2 3 3 2 +--R a b d - b c d +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 +--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x +--R (3) ------------------------------------------------------- +--R 2 3 3 2 +--R a b d - b c d +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1092 +t0:=x/((a+b*x)*(c+d*x)) +--R +--R +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1092 +r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) +--R +--R +--R - b c log(d x + c) + a d log(b x + a) +--R (2) ------------------------------------- +--R 2 2 +--R a b d - b c d +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1092 +a0:=integrate(t0,x) +--R +--R +--R - b c log(d x + c) + a d log(b x + a) +--R (3) ------------------------------------- +--R 2 2 +--R a b d - b c d +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1092 +t0:=1/((a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1092 +r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) +--R +--R +--R log(d x + c) - log(b x + a) +--R (2) --------------------------- +--R a d - b c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1092 +a0:=integrate(t0,x) +--R +--R +--R log(d x + c) - log(b x + a) +--R (3) --------------------------- +--R a d - b c +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1092 +r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) +--R +--R +--R - a d log(d x + c) + b c log(b x + a) + (a d - b c)log(x) +--R (2) --------------------------------------------------------- +--R 2 2 +--R a c d - a b c +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1092 +a0:=integrate(t0,x) +--R +--R +--R - a d log(d x + c) + b c log(b x + a) + (a d - b c)log(x) +--R (3) --------------------------------------------------------- +--R 2 2 +--R a c d - a b c +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 4 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 1092 +r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ + b^2*log(a+b*x)/(a^2*(b*c-a*d))-d^2*log(c+d*x)/(c^2*(b*c-a*d)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R a d x log(d x + c) - b c x log(b x + a) + (- a d + b c )x log(x) - a c d +--R + +--R 2 +--R a b c +--R / +--R 3 2 2 3 +--R (a c d - a b c )x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R a d x log(d x + c) - b c x log(b x + a) + (- a d + b c )x log(x) - a c d +--R + +--R 2 +--R a b c +--R / +--R 3 2 2 3 +--R (a c d - a b c )x +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 5 4 3 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1092 +r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ + log(x)/(a^3*c^3)-b^3*log(a+b*x)/(a^3*(b*c-a*d))+_ + d^3*log(c+d*x)/(c^3*(b*c-a*d)) +--R +--R +--R (2) +--R 3 3 2 3 3 2 3 3 3 3 2 +--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (2a d - 2b c )x log(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (2a c d - 2a b c )x - a c d + a b c +--R / +--R 4 3 3 4 2 +--R (2a c d - 2a b c )x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 3 3 2 3 3 3 3 2 +--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (2a d - 2b c )x log(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (2a c d - 2a b c )x - a c d + a b c +--R / +--R 4 3 3 4 2 +--R (2a c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1092 +t0:=1/(x^4*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 6 5 4 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1092 +r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ + (-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*_ + log(x)/(a^4*c^4)+b^4*log(a+b*x)/(a^4*(b*c-a*d))-_ + d^4*log(c+d*x)/(c^4*(b*c-a*d)) +--R +--R +--R (2) +--R 4 4 3 4 4 3 4 4 4 4 3 +--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 6a d + 6b c )x log(x) +--R + +--R 4 3 3 4 2 4 2 2 2 2 4 4 3 3 4 +--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c +--R / +--R 5 4 4 5 3 +--R (6a c d - 6a b c )x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 4 4 3 4 4 4 4 3 +--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 6a d + 6b c )x log(x) +--R + +--R 4 3 3 4 2 4 2 2 2 2 4 4 3 3 4 +--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c +--R / +--R 5 4 4 5 3 +--R (6a c d - 6a b c )x +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)^2) +--R +--R +--R m +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1092 +--r0:=-d*x^(1+m)/(c*(b*c-a*d)*(c+d*x))+b^2*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^2*(1+m))-b*d*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^2*(1+m))+d*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)*(1+m)) +--E 377 + +--S 378 of 1092 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 1092 +--m0:=a0-r0 +--E 379 + +--S 380 of 1092 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 1092 +t0:=x^m/((1-a*x)^2*(1+a*x)) +--R +--R +--R m +--R x +--R (1) --------------------- +--R 3 3 2 2 +--R a x - a x - a x + 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1092 +--r0:=1/2*x^(1+m)/(1-a*x)+1/4*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-a*x)/(1+m)+1/4*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,a*x)/(1+m)-1/2*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,a*x)/(1+m) +--E 382 + +--S 383 of 1092 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 1092 +--m0:=a0-r0 +--E 384 + +--S 385 of 1092 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)^2) +--R +--R +--R 5 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1092 +r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ + 1/2*(2*b*c+a*d)*x^2/(b^2*d^3)+1/3*x^3/(b*d^2)-_ + c^5/(d^5*(b*c-a*d)*(c+d*x))-a^5*log(a+b*x)/(b^4*(b*c-a*d)^2)-_ + c^4*(4*b*c-5*a*d)*log(c+d*x)/(d^5*(b*c-a*d)^2) +--R +--R +--R (2) +--R 4 4 2 5 5 4 5 5 6 +--R ((30a b c d - 24b c d)x + 30a b c d - 24b c )log(d x + c) +--R + +--R 5 6 5 5 2 3 6 4 5 5 2 4 4 +--R (- 6a d x - 6a c d )log(b x + a) + (2a b d - 4a b c d + 2b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (- 3a b d + 2a b c d + 5a b c d - 4b c d )x +--R + +--R 4 6 3 2 5 4 3 3 5 4 2 2 +--R (6a b d - 3a b c d - 15a b c d + 12b c d )x +--R + +--R 4 5 4 4 2 5 5 4 5 5 6 +--R (6a b c d - 24a b c d + 18b c d)x + 6a b c d - 6b c +--R / +--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 +--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 2 5 5 4 5 5 6 +--R ((30a b c d - 24b c d)x + 30a b c d - 24b c )log(d x + c) +--R + +--R 5 6 5 5 2 3 6 4 5 5 2 4 4 +--R (- 6a d x - 6a c d )log(b x + a) + (2a b d - 4a b c d + 2b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (- 3a b d + 2a b c d + 5a b c d - 4b c d )x +--R + +--R 4 6 3 2 5 4 3 3 5 4 2 2 +--R (6a b d - 3a b c d - 15a b c d + 12b c d )x +--R + +--R 4 5 4 4 2 5 5 4 5 5 6 +--R (6a b c d - 24a b c d + 18b c d)x + 6a b c d - 6b c +--R / +--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 +--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)^2) +--R +--R +--R 4 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1092 +r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ + c^4/(d^4*(b*c-a*d)*(c+d*x))+a^4*log(a+b*x)/(b^3*(b*c-a*d)^2)+_ + c^3*(3*b*c-4*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^2) +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 4 5 +--R ((- 8a b c d + 6b c d)x - 8a b c d + 6b c )log(d x + c) +--R + +--R 4 5 4 4 2 2 5 3 4 4 2 3 3 +--R (2a d x + 2a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 2a b d + a b c d + 4a b c d - 3b c d )x +--R + +--R 3 4 3 3 2 4 4 3 4 4 5 +--R (- 2a b c d + 6a b c d - 4b c d)x - 2a b c d + 2b c +--R / +--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 +--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 4 4 3 4 4 5 +--R ((- 8a b c d + 6b c d)x - 8a b c d + 6b c )log(d x + c) +--R + +--R 4 5 4 4 2 2 5 3 4 4 2 3 3 +--R (2a d x + 2a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 2a b d + a b c d + 4a b c d - 3b c d )x +--R + +--R 3 4 3 3 2 4 4 3 4 4 5 +--R (- 2a b c d + 6a b c d - 4b c d)x - 2a b c d + 2b c +--R / +--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 +--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)^2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1092 +r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ + a^3*log(a+b*x)/(b^2*(b*c-a*d)^2)-c^2*(2*b*c-3*a*d)*log(c+d*x)/_ + (d^3*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 2 2 3 3 2 3 3 4 +--R ((3a b c d - 2b c d)x + 3a b c d - 2b c )log(d x + c) +--R + +--R 3 4 3 3 2 4 2 3 3 2 2 2 +--R (- a d x - a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 2 3 2 2 2 3 3 2 3 3 4 +--R (a b c d - 2a b c d + b c d)x + a b c d - b c +--R / +--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 3 2 3 3 4 +--R ((3a b c d - 2b c d)x + 3a b c d - 2b c )log(d x + c) +--R + +--R 3 4 3 3 2 4 2 3 3 2 2 2 +--R (- a d x - a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 2 3 2 2 2 3 3 2 3 3 4 +--R (a b c d - 2a b c d + b c d)x + a b c d - b c +--R / +--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)^2) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1092 +r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ + c*(b*c-2*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 2 2 2 2 3 +--R ((- 2a b c d + b c d)x - 2a b c d + b c )log(d x + c) +--R + +--R 2 3 2 2 2 2 3 +--R (a d x + a c d )log(b x + a) - a b c d + b c +--R / +--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 3 +--R ((- 2a b c d + b c d)x - 2a b c d + b c )log(d x + c) +--R + +--R 2 3 2 2 2 2 3 +--R (a d x + a c d )log(b x + a) - a b c d + b c +--R / +--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1092 +t0:=x/((a+b*x)*(c+d*x)^2) +--R +--R +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1092 +r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (2) +--R 2 2 2 +--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d - b c +--R -------------------------------------------------------------------------- +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d - b c +--R -------------------------------------------------------------------------- +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1092 +t0:=1/((a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1092 +r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1092 +r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ + b^2*log(a+b*x)/(a*(b*c-a*d)^2)+d*(2*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c) +--R + +--R 2 2 2 3 +--R (- b c d x - b c )log(b x + a) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c )log(x) + a c d +--R + +--R 2 +--R - a b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c) +--R + +--R 2 2 2 3 +--R (- b c d x - b c )log(b x + a) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c )log(x) + a c d +--R + +--R 2 +--R - a b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1092 +r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ + (b*c+2*a*d)*log(x)/(a^2*c^3)+b^3*log(a+b*x)/(a^2*(b*c-a*d)^2)-_ + d^2*(3*b*c-2*a*d)*log(c+d*x)/(c^3*(b*c-a*d)^2) +--R +--R +--R (2) +--R 3 4 2 3 2 3 3 2 2 2 +--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x)log(d x + c) +--R + +--R 3 3 2 3 4 +--R (b c d x + b c x)log(b x + a) +--R + +--R 3 4 2 3 3 3 2 3 3 2 2 2 3 4 +--R ((- 2a d + 3a b c d - b c d)x + (- 2a c d + 3a b c d - b c )x)log(x) +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 2 4 +--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c +--R / +--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 +--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 3 2 3 3 2 2 2 +--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x)log(d x + c) +--R + +--R 3 3 2 3 4 +--R (b c d x + b c x)log(b x + a) +--R + +--R 3 4 2 3 3 3 2 3 3 2 2 2 3 4 +--R ((- 2a d + 3a b c d - b c d)x + (- 2a c d + 3a b c d - b c )x)log(x) +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 2 4 +--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c +--R / +--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 +--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 2 6 2 5 2 4 2 3 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1092 +r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ + d^3/(c^3*(b*c-a*d)*(c+d*x))+(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*log(x)/_ + (a^3*c^4)-b^4*log(a+b*x)/(a^3*(b*c-a*d)^2)+d^3*(4*b*c-3*a*d)*_ + log(c+d*x)/(c^4*(b*c-a*d)^2) +--R +--R +--R (2) +--R 4 5 3 4 3 4 4 3 2 3 2 +--R ((- 6a d + 8a b c d )x + (- 6a c d + 8a b c d )x )log(d x + c) +--R + +--R 4 4 3 4 5 2 +--R (- 2b c d x - 2b c x )log(b x + a) +--R + +--R 4 5 3 4 4 4 3 4 4 3 2 3 4 5 2 +--R ((6a d - 8a b c d + 2b c d)x + (6a c d - 8a b c d + 2b c )x )log(x) +--R + +--R 4 4 3 2 3 3 4 2 +--R (6a c d - 8a b c d + 2a b c d)x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 3 2 3 4 2 2 5 +--R (3a c d - 4a b c d - a b c d + 2a b c )x - a c d + 2a b c d - a b c +--R / +--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 +--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 4 3 4 4 3 2 3 2 +--R ((- 6a d + 8a b c d )x + (- 6a c d + 8a b c d )x )log(d x + c) +--R + +--R 4 4 3 4 5 2 +--R (- 2b c d x - 2b c x )log(b x + a) +--R + +--R 4 5 3 4 4 4 3 4 4 3 2 3 4 5 2 +--R ((6a d - 8a b c d + 2b c d)x + (6a c d - 8a b c d + 2b c )x )log(x) +--R + +--R 4 4 3 2 3 3 4 2 +--R (6a c d - 8a b c d + 2a b c d)x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 3 2 3 4 2 2 5 +--R (3a c d - 4a b c d - a b c d + 2a b c )x - a c d + 2a b c d - a b c +--R / +--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 +--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R m +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1092 +--r0:=-1/2*d*x^(1+m)/(c*(b*c-a*d)*(c+d*x)^2)-_ +-- b*d*x^(1+m)/(c*(b*c-a*d)^2*(c+d*x))-_ +-- 1/2*d*(1-m)*x^(1+m)/(c^2*(b*c-a*d)*(c+d*x))+_ +-- b^3*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^3*(1+m))-b^2*d*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^3*(1+m))+b*d*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)^2*(1+m))+_ +-- 1/2*d*(1-m)*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^3*(b*c-a*d)*(1+m)) +--E 432 + +--S 433 of 1092 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 1092 +--m0:=a0-r0 +--E 434 + +--S 435 of 1092 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 1092 +t0:=x^6/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 1092 +r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ + 1/2*(3*b*c+a*d)*x^2/(b^2*d^4)+1/3*x^3/(b*d^3)+_ + 1/2*c^6/(d^6*(b*c-a*d)*(c+d*x)^2)-_ + c^5*(5*b*c-6*a*d)/(d^6*(b*c-a*d)^2*(c+d*x))+_ + a^6*log(a+b*x)/(b^4*(b*c-a*d)^3)-_ + c^4*(10*b^2*c^2-24*a*b*c*d+15*a^2*d^2)*log(c+d*x)/(d^6*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 4 4 4 5 5 3 6 6 2 2 +--R (90a b c d - 144a b c d + 60b c d )x +--R + +--R 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (180a b c d - 288a b c d + 120b c d)x + 90a b c d - 144a b c d +--R + +--R 6 8 +--R 60b c +--R * +--R log(d x + c) +--R + +--R 6 8 2 6 7 6 2 6 +--R (- 6a d x - 12a c d x - 6a c d )log(b x + a) +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 4 +--R (- 3a b d + 4a b c d + 6a b c d - 12a b c d + 5b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 3 +--R (6a b d - 6a b c d + 2a b c d - 30a b c d + 48a b c d - 20b c d )x +--R + +--R 5 7 4 2 2 6 2 4 4 4 5 5 3 6 6 2 2 +--R (12a b c d - 3a b c d - 102a b c d + 156a b c d - 63b c d )x +--R + +--R 5 2 6 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (6a b c d - 24a b c d + 24a b c d - 6b c d)x + 33a b c d - 60a b c d +--R + +--R 6 8 +--R 27b c +--R / +--R 3 4 11 2 5 10 6 2 9 7 3 8 2 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 3 4 10 2 5 2 9 6 3 8 7 4 7 3 4 2 9 +--R (12a b c d - 36a b c d + 36a b c d - 12b c d )x + 6a b c d +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R - 18a b c d + 18a b c d - 6b c d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 5 5 3 6 6 2 2 +--R (90a b c d - 144a b c d + 60b c d )x +--R + +--R 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (180a b c d - 288a b c d + 120b c d)x + 90a b c d - 144a b c d +--R + +--R 6 8 +--R 60b c +--R * +--R log(d x + c) +--R + +--R 6 8 2 6 7 6 2 6 +--R (- 6a d x - 12a c d x - 6a c d )log(b x + a) +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 4 +--R (- 3a b d + 4a b c d + 6a b c d - 12a b c d + 5b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 3 +--R (6a b d - 6a b c d + 2a b c d - 30a b c d + 48a b c d - 20b c d )x +--R + +--R 5 7 4 2 2 6 2 4 4 4 5 5 3 6 6 2 2 +--R (12a b c d - 3a b c d - 102a b c d + 156a b c d - 63b c d )x +--R + +--R 5 2 6 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (6a b c d - 24a b c d + 24a b c d - 6b c d)x + 33a b c d - 60a b c d +--R + +--R 6 8 +--R 27b c +--R / +--R 3 4 11 2 5 10 6 2 9 7 3 8 2 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 3 4 10 2 5 2 9 6 3 8 7 4 7 3 4 2 9 +--R (12a b c d - 36a b c d + 36a b c d - 12b c d )x + 6a b c d +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R - 18a b c d + 18a b c d - 6b c d +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1092 +r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ + 1/2*c^5/(d^5*(b*c-a*d)*(c+d*x)^2)+c^4*(4*b*c-5*a*d)/_ + (d^5*(b*c-a*d)^2*(c+d*x))-a^5*log(a+b*x)/(b^3*(b*c-a*d)^3)+_ + c^3*(6*b^2*c^2-15*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 3 3 4 4 4 3 5 5 2 2 +--R (- 20a b c d + 30a b c d - 12b c d )x +--R + +--R 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 40a b c d + 60a b c d - 24b c d)x - 20a b c d + 30a b c d +--R + +--R 5 7 +--R - 12b c +--R * +--R log(d x + c) +--R + +--R 5 7 2 5 6 5 2 5 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (- 2a b d + 2a b c d + 6a b c d - 10a b c d + 4b c d )x +--R + +--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (- 4a b c d + a b c d + 21a b c d - 29a b c d + 11b c d )x +--R + +--R 4 2 5 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 2a b c d + 2a b c d + 2a b c d - 2b c d)x - 9a b c d + 16a b c d +--R + +--R 5 7 +--R - 7b c +--R / +--R 3 3 10 2 4 9 5 2 8 6 3 7 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 3 9 2 4 2 8 5 3 7 6 4 6 3 3 2 8 2 4 3 7 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 5 4 6 6 5 5 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 4 4 4 3 5 5 2 2 +--R (- 20a b c d + 30a b c d - 12b c d )x +--R + +--R 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 40a b c d + 60a b c d - 24b c d)x - 20a b c d + 30a b c d +--R + +--R 5 7 +--R - 12b c +--R * +--R log(d x + c) +--R + +--R 5 7 2 5 6 5 2 5 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (- 2a b d + 2a b c d + 6a b c d - 10a b c d + 4b c d )x +--R + +--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (- 4a b c d + a b c d + 21a b c d - 29a b c d + 11b c d )x +--R + +--R 4 2 5 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 2a b c d + 2a b c d + 2a b c d - 2b c d)x - 9a b c d + 16a b c d +--R + +--R 5 7 +--R - 7b c +--R / +--R 3 3 10 2 4 9 5 2 8 6 3 7 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 3 9 2 4 2 8 5 3 7 6 4 6 3 3 2 8 2 4 3 7 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 5 4 6 6 5 5 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 1092 +r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ + c^3*(3*b*c-4*a*d)/(d^4*(b*c-a*d)^2*(c+d*x))+_ + a^4*log(a+b*x)/(b^2*(b*c-a*d)^3)-_ + c^2*(3*b^2*c^2-8*a*b*c*d+6*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 2 2 4 3 3 3 4 4 2 2 +--R (12a b c d - 16a b c d + 6b c d )x +--R + +--R 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 4 6 +--R (24a b c d - 32a b c d + 12b c d)x + 12a b c d - 16a b c d + 6b c +--R * +--R log(d x + c) +--R + +--R 4 6 2 4 5 4 2 4 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x +--R + +--R 3 2 4 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 +--R (2a b c d + 2a b c d - 8a b c d + 4b c d)x + 7a b c d - 12a b c d +--R + +--R 4 6 +--R 5b c +--R / +--R 3 2 9 2 3 8 4 2 7 5 3 6 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 2 8 2 3 2 7 4 3 6 5 4 5 3 2 2 7 2 3 3 6 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 4 4 5 5 5 4 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 3 3 3 4 4 2 2 +--R (12a b c d - 16a b c d + 6b c d )x +--R + +--R 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 4 6 +--R (24a b c d - 32a b c d + 12b c d)x + 12a b c d - 16a b c d + 6b c +--R * +--R log(d x + c) +--R + +--R 4 6 2 4 5 4 2 4 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x +--R + +--R 3 2 4 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 +--R (2a b c d + 2a b c d - 8a b c d + 4b c d)x + 7a b c d - 12a b c d +--R + +--R 4 6 +--R 5b c +--R / +--R 3 2 9 2 3 8 4 2 7 5 3 6 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 2 8 2 3 2 7 4 3 6 5 4 5 3 2 2 7 2 3 3 6 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 4 4 5 5 5 4 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 1092 +r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ + (d^3*(b*c-a*d)^2*(c+d*x))-a^3*log(a+b*x)/(b*(b*c-a*d)^3)+_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 4 2 2 3 3 3 2 2 +--R (- 6a b c d + 6a b c d - 2b c d )x +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 12a b c d + 12a b c d - 4b c d)x - 6a b c d + 6a b c d - 2b c +--R * +--R log(d x + c) +--R + +--R 3 5 2 3 4 3 2 3 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 6a b c d + 10a b c d - 4b c d)x - 5a b c d + 8a b c d - 3b c +--R / +--R 3 8 2 2 7 3 2 6 4 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 7 2 2 2 6 3 3 5 4 4 4 3 2 6 2 2 3 5 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 3 4 4 4 5 3 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 3 3 2 2 +--R (- 6a b c d + 6a b c d - 2b c d )x +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 12a b c d + 12a b c d - 4b c d)x - 6a b c d + 6a b c d - 2b c +--R * +--R log(d x + c) +--R + +--R 3 5 2 3 4 3 2 3 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 6a b c d + 10a b c d - 4b c d)x - 5a b c d + 8a b c d - 3b c +--R / +--R 3 8 2 2 7 3 2 6 4 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 7 2 2 2 6 3 3 5 4 4 4 3 2 6 2 2 3 5 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 3 4 4 4 5 3 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 1092 +r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ + (d^2*(b*c-a*d)^2*(c+d*x))+a^2*log(a+b*x)/(b*c-a*d)^3-_ + a^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 4 2 2 3 2 2 2 +--R (2a d x + 4a c d x + 2a c d )log(d x + c) +--R + +--R 2 4 2 2 3 2 2 2 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4a c d - 6a b c d + 2b c d)x + 3a c d - 4a b c d + b c +--R / +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 2 5 2 3 4 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 3 3 5 2 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 2 2 +--R (2a d x + 4a c d x + 2a c d )log(d x + c) +--R + +--R 2 4 2 2 3 2 2 2 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4a c d - 6a b c d + 2b c d)x + 3a c d - 4a b c d + b c +--R / +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 2 5 2 3 4 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 3 3 5 2 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1092 +t0:=x/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 1092 +r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ + a*b*log(a+b*x)/(b*c-a*d)^3+a*b*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 3 2 2 2 +--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c) +--R + +--R 3 2 2 2 2 3 2 +--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a) + (- 2a d + 2a b c d )x +--R + +--R 2 2 2 3 +--R - a c d + b c +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 2 3 5 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 +--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c) +--R + +--R 3 2 2 2 2 3 2 +--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a) + (- 2a d + 2a b c d )x +--R + +--R 2 2 2 3 +--R - a c d + b c +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 2 3 5 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1092 +t0:=1/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 1092 +r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ + b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 1092 +r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ + (c^2*(b*c-a*d)^2*(c+d*x))+log(x)/(a*c^3)-_ + b^3*log(a+b*x)/(a*(b*c-a*d)^3)+d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_ + log(c+d*x)/(c^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 +--R (- 2a d + 6a b c d - 6a b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2b c d x + 4b c d x + 2b c )log(b x + a) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x + 2a c d - 6a b c d +--R + +--R 2 2 7 3 8 +--R 6a b c d - 2a b c +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 4 2 2 3 2 +--R (- 2a d + 6a b c d - 6a b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2b c d x + 4b c d x + 2b c )log(b x + a) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x + 2a c d - 6a b c d +--R + +--R 2 2 7 3 8 +--R 6a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 6 3 2 5 2 2 4 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 2 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1092 +r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ + d^2*(3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x))-(b*c+3*a*d)*_ + log(x)/(a^2*c^4)+b^4*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ + d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 6 3 5 2 2 2 4 3 +--R (6a d - 16a b c d + 12a b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 2 +--R (12a c d - 32a b c d + 24a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 +--R (6a c d - 16a b c d + 12a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 4 2 3 4 5 2 4 6 +--R (- 2b c d x - 4b c d x - 2b c x)log(b x + a) +--R + +--R 4 6 3 5 2 2 2 4 4 4 2 3 +--R (- 6a d + 16a b c d - 12a b c d + 2b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 5 2 +--R (- 12a c d + 32a b c d - 24a b c d + 4b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 4 6 +--R (- 6a c d + 16a b c d - 12a b c d + 2b c )x +--R * +--R log(x) +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 2 +--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d +--R + +--R 2 2 5 3 6 +--R - 6a b c d + 2a b c +--R / +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 3 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 5 2 2 2 4 3 +--R (6a d - 16a b c d + 12a b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 2 +--R (12a c d - 32a b c d + 24a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 +--R (6a c d - 16a b c d + 12a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 4 2 3 4 5 2 4 6 +--R (- 2b c d x - 4b c d x - 2b c x)log(b x + a) +--R + +--R 4 6 3 5 2 2 2 4 4 4 2 3 +--R (- 6a d + 16a b c d - 12a b c d + 2b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 5 2 +--R (- 12a c d + 32a b c d - 24a b c d + 4b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 4 6 +--R (- 6a c d + 16a b c d - 12a b c d + 2b c )x +--R * +--R log(x) +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 2 +--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d +--R + +--R 2 2 5 3 6 +--R - 6a b c d + 2a b c +--R / +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 3 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 7 3 2 6 2 2 5 2 3 4 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 3 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1092 +r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ + (c+d*x)^2)-d^3*(4*b*c-3*a*d)/(c^4*(b*c-a*d)^2*(c+d*x))+_ + (b^2*c^2+3*a*b*c*d+6*a^2*d^2)*log(x)/(a^3*c^5)-b^5*_ + log(a+b*x)/(a^3*(b*c-a*d)^3)+d^3*(10*b^2*c^2-15*a*b*c*d+6*a^2*d^2)*_ + log(c+d*x)/(c^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 7 4 6 3 2 2 5 4 +--R (- 12a d + 30a b c d - 20a b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 3 +--R (- 24a c d + 60a b c d - 40a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 +--R (- 12a c d + 30a b c d - 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 5 2 4 5 6 3 5 7 2 +--R (2b c d x + 4b c d x + 2b c x )log(b x + a) +--R + +--R 5 7 4 6 3 2 2 5 5 5 2 4 +--R (12a d - 30a b c d + 20a b c d - 2b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 5 6 3 +--R (24a c d - 60a b c d + 40a b c d - 4b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 5 7 2 +--R (12a c d - 30a b c d + 20a b c d - 2b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 3 2 3 4 4 5 2 3 +--R (12a c d - 30a b c d + 20a b c d - 2a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (18a c d - 45a b c d + 30a b c d + a b c d - 4a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (4a c d - 10a b c d + 6a b c d + 2a b c d - 2a b c )x - a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R 3a b c d - 3a b c d + a b c +--R / +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 4 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 3 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 6 7 3 5 8 2 4 2 9 3 3 10 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 4 6 3 2 2 5 4 +--R (- 12a d + 30a b c d - 20a b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 3 +--R (- 24a c d + 60a b c d - 40a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 +--R (- 12a c d + 30a b c d - 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 5 2 4 5 6 3 5 7 2 +--R (2b c d x + 4b c d x + 2b c x )log(b x + a) +--R + +--R 5 7 4 6 3 2 2 5 5 5 2 4 +--R (12a d - 30a b c d + 20a b c d - 2b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 5 6 3 +--R (24a c d - 60a b c d + 40a b c d - 4b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 5 7 2 +--R (12a c d - 30a b c d + 20a b c d - 2b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 3 2 3 4 4 5 2 3 +--R (12a c d - 30a b c d + 20a b c d - 2a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (18a c d - 45a b c d + 30a b c d + a b c d - 4a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (4a c d - 10a b c d + 6a b c d + 2a b c d - 2a b c )x - a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R 3a b c d - 3a b c d + a b c +--R / +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 4 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 3 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 6 7 3 5 8 2 4 2 9 3 3 10 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1092 +t0:=x^4*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 6 5 2 4 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1092 +r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ + 1/3*(b*c-3*a*d)*(b*c-a*d)*x^3/b^4+1/2*d*(b*c-a*d)*x^4/b^3+_ + 1/5*d^2*x^5/b^2-a^4*(b*c-a*d)^2/(b^7*(a+b*x))-_ + 2*a^3*(2*b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 180a b d + 300a b c d - 120a b c )x - 180a d + 300a b c d +--R + +--R 4 2 2 +--R - 120a b c +--R * +--R log(b x + a) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6b d x + (- 9a b d + 15b c d)x + (15a b d - 25a b c d + 10b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 30a b d + 50a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (90a b d - 150a b c d + 60a b c )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (150a b d - 240a b c d + 90a b c )x - 30a d + 60a b c d - 30a b c +--R / +--R 8 7 +--R 30b x + 30a b +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 180a b d + 300a b c d - 120a b c )x - 180a d + 300a b c d +--R + +--R 4 2 2 +--R - 120a b c +--R * +--R log(b x + a) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6b d x + (- 9a b d + 15b c d)x + (15a b d - 25a b c d + 10b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 30a b d + 50a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (90a b d - 150a b c d + 60a b c )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (150a b d - 240a b c d + 90a b c )x - 30a d + 60a b c d - 30a b c +--R / +--R 8 7 +--R 30b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1092 +t0:=x^3*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1092 +r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ + 2/3*d*(b*c-a*d)*x^3/b^3+1/4*d^2*x^4/b^2+_ + a^3*(b*c-a*d)^2/(b^6*(a+b*x))+a^2*(3*b*c-5*a*d)*(b*c-a*d)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R ((60a b d - 96a b c d + 36a b c )x + 60a d - 96a b c d + 36a b c ) +--R * +--R log(b x + a) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3b d x + (- 5a b d + 8b c d)x + (10a b d - 16a b c d + 6b c )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 30a b d + 48a b c d - 18a b c )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 48a b d + 72a b c d - 24a b c )x + 12a d - 24a b c d + 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R ((60a b d - 96a b c d + 36a b c )x + 60a d - 96a b c d + 36a b c ) +--R * +--R log(b x + a) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3b d x + (- 5a b d + 8b c d)x + (10a b d - 16a b c d + 6b c )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 30a b d + 48a b c d - 18a b c )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 48a b d + 72a b c d - 24a b c )x + 12a d - 24a b c d + 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1092 +t0:=x^2*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1092 +r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ + a^2*(b*c-a*d)^2/(b^5*(a+b*x))-2*a*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((- 12a b d + 18a b c d - 6a b c )x - 12a d + 18a b c d - 6a b c ) +--R * +--R log(b x + a) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R b d x + (- 2a b d + 3b c d)x + (6a b d - 9a b c d + 3b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (9a b d - 12a b c d + 3a b c )x - 3a d + 6a b c d - 3a b c +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((- 12a b d + 18a b c d - 6a b c )x - 12a d + 18a b c d - 6a b c ) +--R * +--R log(b x + a) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R b d x + (- 2a b d + 3b c d)x + (6a b d - 9a b c d + 3b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (9a b d - 12a b c d + 3a b c )x - 3a d + 6a b c d - 3a b c +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1092 +t0:=x*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 3 2 2 +--R d x + 2c d x + c x +--R (1) -------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1092 +r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ + (b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d +--R + +--R 2 2 2 +--R - 4a b c d + 2a b c +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d +--R + +--R 2 2 2 +--R - 4a b c d + 2a b c +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1092 +t0:=(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1092 +r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1092 +t0:=(c+d*x)^2/(x*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) -------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1092 +r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 2 3 2 2 2 +--R ((a b d - b c )x + a d - a b c )log(b x + a) + (b c x + a b c )log(x) +--R + +--R 3 2 2 2 2 +--R a d - 2a b c d + a b c +--R / +--R 2 3 3 2 +--R a b x + a b +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 2 2 2 3 2 2 2 +--R ((a b d - b c )x + a d - a b c )log(b x + a) + (b c x + a b c )log(x) +--R + +--R 3 2 2 2 2 +--R a d - 2a b c d + a b c +--R / +--R 2 3 3 2 +--R a b x + a b +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1092 +t0:=(c+d*x)^2/(x^2*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1092 +r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ + log(x)/a^3+2*c*(b*c-a*d)*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x)log(b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((2a b c d - 2b c )x + (2a b c d - 2a b c )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- a d + 2a b c d - 2a b c )x - a b c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x)log(b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((2a b c d - 2b c )x + (2a b c d - 2a b c )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- a d + 2a b c d - 2a b c )x - a b c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1092 +t0:=(c+d*x)^2/(x^3*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1092 +r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ + (b*c-a*d)*(3*b*c-a*d)*log(x)/a^4-(b*c-a*d)*(3*b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((- 2a b d + 8a b c d - 6b c )x + (- 2a d + 8a b c d - 6a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 8a b c d + 6b c )x + (2a d - 8a b c d + 6a b c )x )log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (2a d - 8a b c d + 6a b c )x + (- 4a c d + 3a b c )x - a c +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((- 2a b d + 8a b c d - 6b c )x + (- 2a d + 8a b c d - 6a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 8a b c d + 6b c )x + (2a d - 8a b c d + 6a b c )x )log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (2a d - 8a b c d + 6a b c )x + (- 4a c d + 3a b c )x - a c +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1092 +t0:=(c+d*x)^2/(x^4*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1092 +r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ + (a^4*x)-b*(b*c-a*d)^2/(a^4*(a+b*x))-2*b*(b*c-a*d)*(2*b*c-a*d)*_ + log(x)/a^5+2*b*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R ((6a b d - 18a b c d + 12b c )x + (6a b d - 18a b c d + 12a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (- 6a b d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6a b d + 18a b c d - 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 6a b d + 18a b c d - 12a b c )x + (- 3a d + 9a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 3a c d + 2a b c )x - a c +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R ((6a b d - 18a b c d + 12b c )x + (6a b d - 18a b c d + 12a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (- 6a b d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6a b d + 18a b c d - 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 6a b d + 18a b c d - 12a b c )x + (- 3a d + 9a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 3a c d + 2a b c )x - a c +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1092 +t0:=(c+d*x)^2/(x^5*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1092 +r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ + (3*b*c-a*d)/(a^4*x^2)+2*b*(b*c-a*d)*(2*b*c-a*d)/(a^5*x)+_ + b^2*(b*c-a*d)^2/(a^5*(a+b*x))+b^2*(5*b*c-3*a*d)*(b*c-a*d)*_ + log(x)/a^6-b^2*(5*b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 2 5 +--R (- 36a b d + 96a b c d - 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 36a b d + 96a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (36a b d - 96a b c d + 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (36a b d - 96a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (36a b d - 96a b c d + 60a b c )x + (18a b d - 48a b c d + 30a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (- 6a d + 16a b c d - 10a b c )x + (- 8a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 5 +--R (- 36a b d + 96a b c d - 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 36a b d + 96a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (36a b d - 96a b c d + 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (36a b d - 96a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (36a b d - 96a b c d + 60a b c )x + (18a b d - 48a b c d + 30a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (- 6a d + 16a b c d - 10a b c )x + (- 8a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1092 +t0:=x^4*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 7 2 6 2 5 3 4 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1092 +r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ + (b*c-a*d)^2*x^2/b^6+1/3*(b*c-4*a*d)*(b*c-a*d)^2*x^3/b^5+_ + 3/4*d*(b*c-a*d)^2*x^4/b^4+1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+_ + 1/6*d^3*x^6/b^2-a^4*(b*c-a*d)^3/(b^8*(a+b*x))-_ + a^3*(4*b*c-7*a*d)*(b*c-a*d)^2*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (420a b d - 1080a b c d + 900a b c d - 240a b c )x + 420a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 1080a b c d + 900a b c d - 240a b c +--R * +--R log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 10b d x + (- 14a b d + 36b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (21a b d - 54a b c d + 45b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 35a b d + 90a b c d - 75a b c d + 20b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (70a b d - 180a b c d + 150a b c d - 40a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 540a b c d - 450a b c d + 120a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 360a b d + 900a b c d - 720a b c d + 180a b c )x + 60a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 180a b c d + 180a b c d - 60a b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (420a b d - 1080a b c d + 900a b c d - 240a b c )x + 420a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 1080a b c d + 900a b c d - 240a b c +--R * +--R log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 10b d x + (- 14a b d + 36b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (21a b d - 54a b c d + 45b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 35a b d + 90a b c d - 75a b c d + 20b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (70a b d - 180a b c d + 150a b c d - 40a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 540a b c d - 450a b c d + 120a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 360a b d + 900a b c d - 720a b c d + 180a b c )x + 60a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 180a b c d + 180a b c d - 60a b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1092 +r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ + x^2/b^5+d*(b*c-a*d)^2*x^3/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_ + 1/5*d^3*x^5/b^2+a^3*(b*c-a*d)^3/(b^7*(a+b*x))+_ + 3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 120a b d + 300a b c d - 240a b c d + 60a b c )x - 120a d +--R + +--R 5 2 4 2 2 3 3 3 +--R 300a b c d - 240a b c d + 60a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R 4b d x + (- 6a b d + 15b c d )x + (10a b d - 25a b c d + 20b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 50a b c d - 40a b c d + 10b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 150a b c d + 120a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (100a b d - 240a b c d + 180a b c d - 40a b c )x - 20a d + 60a b c d +--R + +--R 4 2 2 3 3 3 +--R - 60a b c d + 20a b c +--R / +--R 8 7 +--R 20b x + 20a b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 120a b d + 300a b c d - 240a b c d + 60a b c )x - 120a d +--R + +--R 5 2 4 2 2 3 3 3 +--R 300a b c d - 240a b c d + 60a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R 4b d x + (- 6a b d + 15b c d )x + (10a b d - 25a b c d + 20b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 50a b c d - 40a b c d + 10b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 150a b c d + 120a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (100a b d - 240a b c d + 180a b c d - 40a b c )x - 20a d + 60a b c d +--R + +--R 4 2 2 3 3 3 +--R - 60a b c d + 20a b c +--R / +--R 8 7 +--R 20b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1092 +r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ + 1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/4*d^3*x^4/b^2-a^2*_ + (b*c-a*d)^3/(b^6*(a+b*x))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (60a b d - 144a b c d + 108a b c d - 24a b c )x + 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 144a b c d + 108a b c d - 24a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 3b d x + (- 5a b d + 12b c d )x + (10a b d - 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 72a b c d - 54a b c d + 12b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (- 48a b d + 108a b c d - 72a b c d + 12a b c )x + 12a d - 36a b c d +--R + +--R 3 2 2 2 3 3 +--R 36a b c d - 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (60a b d - 144a b c d + 108a b c d - 24a b c )x + 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 144a b c d + 108a b c d - 24a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 3b d x + (- 5a b d + 12b c d )x + (10a b d - 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 72a b c d - 54a b c d + 12b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (- 48a b d + 108a b c d - 72a b c d + 12a b c )x + 12a d - 36a b c d +--R + +--R 3 2 2 2 3 3 +--R 36a b c d - 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1092 +t0:=x*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1092 +r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ + a*(b*c-a*d)^3/(b^5*(a+b*x))+(b*c-4*a*d)*(b*c-a*d)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d +--R + +--R 2 2 2 3 3 +--R - 36a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d +--R + +--R 3 3 +--R 6a b c +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d +--R + +--R 2 2 2 3 3 +--R - 36a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d +--R + +--R 3 3 +--R 6a b c +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1092 +t0:=(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1092 +r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ + 3*d*(b*c-a*d)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b 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 2b x + 2a b +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b 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 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1092 +r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ + (b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x)/(a^2*b^3) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 4 3 3 2 3 3 +--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 2 2 3 2 3 3 4 3 3 2 2 2 2 +--R (b c x + a b c )log(x) + a b d x + a b d x - a d + 3a b c d - 3a b c d +--R + +--R 3 3 +--R a b c +--R / +--R 2 4 3 3 +--R a b x + a b +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 4 3 4 3 3 2 3 3 +--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 2 2 3 2 3 3 4 3 3 2 2 2 2 +--R (b c x + a b c )log(x) + a b d x + a b d x - a d + 3a b c d - 3a b c d +--R + +--R 3 3 +--R a b c +--R / +--R 2 4 3 3 +--R a b x + a b +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1092 +r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ + log(x)/a^3+(b*c-a*d)^2*(2*b*c+a*d)*log(a+b*x)/(a^3*b^2) +--R +--R +--R (2) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x) +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3a b c d - 2b c )x + (3a b c d - 2a b c )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c +--R / +--R 3 3 2 4 2 +--R a b x + a b x +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x) +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3a b c d - 2b c )x + (3a b c d - 2a b c )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c +--R / +--R 3 3 2 4 2 +--R a b x + a b x +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1092 +r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ + (a^3*b*(a+b*x))+3*c*(b*c-a*d)^2*log(x)/a^4-3*c*(b*c-a*d)^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 4 3 3 +--R (- 6a b c d + 12a b c d - 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- 6a b c d + 12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 4 3 3 +--R (6a b c d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (6a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- 2a d + 6a b c d - 12a b c d + 6a b c )x + (- 6a b c d + 3a b c )x +--R + +--R 3 3 +--R - a b c +--R / +--R 4 2 3 5 2 +--R 2a b x + 2a b x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 4 3 3 +--R (- 6a b c d + 12a b c d - 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- 6a b c d + 12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 4 3 3 +--R (6a b c d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (6a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- 2a d + 6a b c d - 12a b c d + 6a b c )x + (- 6a b c d + 3a b c )x +--R + +--R 3 3 +--R - a b c +--R / +--R 4 2 3 5 2 +--R 2a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1092 +r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ + (a^4*x)-(b*c-a*d)^3/(a^4*(a+b*x))-(b*c-a*d)^2*(4*b*c-a*d)*log(x)/_ + a^5+(b*c-a*d)^2*(4*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 6a b d + 36a b c d - 54a b c d + 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 36a b c d - 54a b c d + 24a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 36a b c d + 54a b c d - 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 27a b c d - 12a b c )x + (- 9a c d + 4a b c )x - 2a c +--R / +--R 5 4 6 3 +--R 6a b x + 6a x +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 6a b d + 36a b c d - 54a b c d + 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 36a b c d - 54a b c d + 24a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 36a b c d + 54a b c d - 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 27a b c d - 12a b c )x + (- 9a c d + 4a b c )x - 2a c +--R / +--R 5 4 6 3 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1092 +t0:=(c+d*x)^3/(x^5*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1092 +r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ + 3/2*c*(b*c-a*d)^2/(a^4*x^2)+(b*c-a*d)^2*(4*b*c-a*d)/_ + (a^5*x)+b*(b*c-a*d)^3/(a^5*(a+b*x))+b*(5*b*c-2*a*d)*_ + (b*c-a*d)^2*log(x)/a^6-b*(5*b*c-2*a*d)*(b*c-a*d)^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (24a b d - 108a b c d + 144a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (24a b d - 108a b c d + 144a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 24a b d + 108a b c d - 144a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 12a d + 54a b c d - 72a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 24a b c d - 10a b c )x + (- 12a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (24a b d - 108a b c d + 144a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (24a b d - 108a b c d + 144a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 24a b d + 108a b c d - 144a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 12a d + 54a b c d - 72a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 24a b c d - 10a b c )x + (- 12a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1092 +t0:=(c+d*x)^3/(x^6*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 8 7 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1092 +r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ + (a^4*x^3)+1/2*(b*c-a*d)^2*(4*b*c-a*d)/(a^5*x^2)-_ + b*(5*b*c-2*a*d)*(b*c-a*d)^2/(a^6*x)-b^2*(b*c-a*d)^3/_ + (a^6*(a+b*x))-3*b^2*(b*c-a*d)^2*(2*b*c-a*d)*log(x)/a^7+_ + 3*b^2*(b*c-a*d)^2*(2*b*c-a*d)*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 240a b c d - 300a b c d + 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 240a b c d - 300a b c d + 120a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 240a b c d + 300a b c d - 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R * +--R log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 120a b c d + 150a b c d - 60a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 10a d + 40a b c d - 50a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 20a c d + 25a b c d - 10a b c )x + (- 15a c d + 6a b c )x - 4a c +--R / +--R 7 6 8 5 +--R 20a b x + 20a x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 240a b c d - 300a b c d + 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 240a b c d - 300a b c d + 120a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 240a b c d + 300a b c d - 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R * +--R log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 120a b c d + 150a b c d - 60a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 10a d + 40a b c d - 50a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 20a c d + 25a b c d - 10a b c )x + (- 15a c d + 6a b c )x - 4a c +--R / +--R 7 6 8 5 +--R 20a b x + 20a x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1092 +t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 +--R +--R +--R 3 2 +-+ +--R (- 27x + 54x - 36x + 8)\|x +--R (1) ----------------------------- +--R 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1092 +r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ + 125*sqrt(x)/(1+x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (2) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1092 +r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ + 1/5*(62-513*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (3) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1092 +a0:=integrate(t0,x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (4) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Union(Expression(Integer),...) +--E 594 + +--S 595 of 1092 +m0a:=a0-r0a +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1092 +d0:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1092 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1092 +d0:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1092 +t0:=x^6/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 6 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 599 + +--S 600 of 1092 +r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ + 1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-_ + c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/_ + (b^5*(b*c-a*d)^3)-2*c^5*(2*b*c-3*a*d)*log(c+d*x)/(d^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 6 5 2 7 6 2 2 5 5 2 6 6 7 7 +--R (- 18a b c d + 12b c d)x + (- 18a b c d - 6a b c d + 12b c )x +--R + +--R 2 5 6 6 7 +--R - 18a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 7 5 2 6 2 7 7 6 6 5 2 2 5 +--R (- 12a b d + 18a b c d )x + (- 12a d + 6a b c d + 18a b c d )x +--R + +--R 7 6 6 2 5 +--R - 12a c d + 18a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 3 +--R (6a b d - 11a b c d + 3a b c d - 3a b c d + 11a b c d - 6b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 2 +--R (9a b d - 9a b c d - 9a b c d + 9a b c d + 9a b c d - 9b c d)x +--R + +--R 7 7 6 6 5 2 2 5 2 5 5 2 6 6 7 7 +--R (- 3a d + 12a b c d - 15a b c d + 15a b c d - 12a b c d + 3b c )x +--R + +--R 7 6 6 2 5 2 5 6 6 7 +--R - 3a c d + 3a b c d - 3a b c d + 3a b c +--R / +--R 3 6 9 2 7 8 8 2 7 9 3 6 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 9 3 6 8 8 3 6 9 4 5 4 5 8 3 6 2 7 +--R (3a b d - 6a b c d + 6a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 2 7 3 6 8 4 5 +--R 9a b c d - 3a b c d +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 2 7 6 2 2 5 5 2 6 6 7 7 +--R (- 18a b c d + 12b c d)x + (- 18a b c d - 6a b c d + 12b c )x +--R + +--R 2 5 6 6 7 +--R - 18a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 7 5 2 6 2 7 7 6 6 5 2 2 5 +--R (- 12a b d + 18a b c d )x + (- 12a d + 6a b c d + 18a b c d )x +--R + +--R 7 6 6 2 5 +--R - 12a c d + 18a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 3 +--R (6a b d - 11a b c d + 3a b c d - 3a b c d + 11a b c d - 6b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 2 +--R (9a b d - 9a b c d - 9a b c d + 9a b c d + 9a b c d - 9b c d)x +--R + +--R 7 7 6 6 5 2 2 5 2 5 5 2 6 6 7 7 +--R (- 3a d + 12a b c d - 15a b c d + 15a b c d - 12a b c d + 3b c )x +--R + +--R 7 6 6 2 5 2 5 6 6 7 +--R - 3a c d + 3a b c d - 3a b c d + 3a b c +--R / +--R 3 6 9 2 7 8 8 2 7 9 3 6 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 9 3 6 8 8 3 6 9 4 5 4 5 8 3 6 2 7 +--R (3a b d - 6a b c d + 6a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 2 7 3 6 8 4 5 +--R 9a b c d - 3a b c d +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1092 +t0:=x^5/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 5 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 604 + +--S 605 of 1092 +r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ + (a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*_ + log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/_ + (d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 4 2 6 5 2 2 4 4 2 5 5 6 6 +--R (10a b c d - 6b c d)x + (10a b c d + 4a b c d - 6b c )x +--R + +--R 2 4 5 5 6 +--R 10a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 6 4 2 5 2 6 6 5 5 4 2 2 4 +--R (6a b d - 10a b c d )x + (6a d - 4a b c d - 10a b c d )x +--R + +--R 6 5 5 2 4 +--R 6a c d - 10a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 3 +--R (- 3a b d + 6a b c d - 6a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 2 +--R (- 4a b d + 5a b c d + 5a b c d - 5a b c d - 5a b c d + 4b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 6 5 +--R (2a d - 6a b c d + 8a b c d - 8a b c d + 6a b c d - 2b c )x + 2a c d +--R + +--R 5 2 4 2 4 5 5 6 +--R - 2a b c d + 2a b c d - 2a b c +--R / +--R 3 5 8 2 6 7 7 2 6 8 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 4 8 3 5 7 7 3 5 8 4 4 4 4 7 3 5 2 6 +--R (2a b d - 4a b c d + 4a b c d - 2b c d )x + 2a b c d - 6a b c d +--R + +--R 2 6 3 5 7 4 4 +--R 6a b c d - 2a b c d +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 2 6 5 2 2 4 4 2 5 5 6 6 +--R (10a b c d - 6b c d)x + (10a b c d + 4a b c d - 6b c )x +--R + +--R 2 4 5 5 6 +--R 10a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 6 4 2 5 2 6 6 5 5 4 2 2 4 +--R (6a b d - 10a b c d )x + (6a d - 4a b c d - 10a b c d )x +--R + +--R 6 5 5 2 4 +--R 6a c d - 10a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 3 +--R (- 3a b d + 6a b c d - 6a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 2 +--R (- 4a b d + 5a b c d + 5a b c d - 5a b c d - 5a b c d + 4b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 6 5 +--R (2a d - 6a b c d + 8a b c d - 8a b c d + 6a b c d - 2b c )x + 2a c d +--R + +--R 5 2 4 2 4 5 5 6 +--R - 2a b c d + 2a b c d - 2a b c +--R / +--R 3 5 8 2 6 7 7 2 6 8 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 4 8 3 5 7 7 3 5 8 4 4 4 4 7 3 5 2 6 +--R (2a b d - 4a b c d + 4a b c d - 2b c d )x + 2a b c d - 6a b c d +--R + +--R 2 6 3 5 7 4 4 +--R 6a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1092 +t0:=x^4/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 4 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 609 + +--S 610 of 1092 +r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ + 2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-_ + 2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 3 2 5 4 2 2 3 3 2 4 4 5 5 +--R (- 4a b c d + 2b c d)x + (- 4a b c d - 2a b c d + 2b c )x +--R + +--R 2 3 4 4 5 +--R - 4a b c d + 2a b c +--R * +--R log(d x + c) +--R + +--R 4 5 3 2 4 2 5 5 4 4 3 2 2 3 +--R (- 2a b d + 4a b c d )x + (- 2a d + 2a b c d + 4a b c d )x +--R + +--R 5 4 4 2 3 +--R - 2a c d + 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 2 +--R (a b d - 2a b c d + 2a b c d - b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 4 +--R (- a d + 2a b c d - 3a b c d + 3a b c d - 2a b c d + b c )x - a c d +--R + +--R 4 2 3 2 3 4 4 5 +--R a b c d - a b c d + a b c +--R / +--R 3 4 7 2 5 6 6 2 5 7 3 4 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 3 6 3 4 2 5 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 5 3 4 6 4 3 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 5 4 2 2 3 3 2 4 4 5 5 +--R (- 4a b c d + 2b c d)x + (- 4a b c d - 2a b c d + 2b c )x +--R + +--R 2 3 4 4 5 +--R - 4a b c d + 2a b c +--R * +--R log(d x + c) +--R + +--R 4 5 3 2 4 2 5 5 4 4 3 2 2 3 +--R (- 2a b d + 4a b c d )x + (- 2a d + 2a b c d + 4a b c d )x +--R + +--R 5 4 4 2 3 +--R - 2a c d + 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 2 +--R (a b d - 2a b c d + 2a b c d - b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 4 +--R (- a d + 2a b c d - 3a b c d + 3a b c d - 2a b c d + b c )x - a c d +--R + +--R 4 2 3 2 3 4 4 5 +--R a b c d - a b c d + a b c +--R / +--R 3 4 7 2 5 6 6 2 5 7 3 4 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 3 6 3 4 2 5 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 5 3 4 6 4 3 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1092 +t0:=x^3/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 3 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 614 + +--S 615 of 1092 +r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ + a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+_ + c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (3a b c d - b c d)x + (3a b c d + 2a b c d - b c )x + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(d x + c) +--R + +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (a b d - 3a b c d )x + (a d - 2a b c d - 3a b c d )x + a c d +--R + +--R 3 2 2 +--R - 3a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 3 4 +--R (a d - a b c d + a b c d - b c )x + a c d - a b c d + a b c d - a b c +--R / +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 4 2 5 3 3 2 4 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 4 3 3 5 4 2 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (3a b c d - b c d)x + (3a b c d + 2a b c d - b c )x + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(d x + c) +--R + +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (a b d - 3a b c d )x + (a d - 2a b c d - 3a b c d )x + a c d +--R + +--R 3 2 2 +--R - 3a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 3 4 +--R (a d - a b c d + a b c d - b c )x + a c d - a b c d + a b c d - a b c +--R / +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 4 2 5 3 3 2 4 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 4 3 3 5 4 2 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1092 +t0:=x^2/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 2 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 619 + +--S 620 of 1092 +r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ + 2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b c d x + (- 2a b c d - 2a b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b c d x + (2a b c d + 2a b c d)x + 2a b c d)log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 3 +--R (- a d + a b c d - a b c d + b c )x - a c d + a b c +--R / +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 4 4 3 2 2 3 +--R (a b d - 2a b c d + 2a b c d - b c d)x + a b c d - 3a b c d +--R + +--R 2 3 3 2 4 4 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b c d x + (- 2a b c d - 2a b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b c d x + (2a b c d + 2a b c d)x + 2a b c d)log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 3 +--R (- a d + a b c d - a b c d + b c )x - a c d + a b c +--R / +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 4 4 3 2 2 3 +--R (a b d - 2a b c d + 2a b c d - b c d)x + a b c d - 3a b c d +--R + +--R 2 3 3 2 4 4 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1092 +t0:=x/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 624 + +--S 625 of 1092 +r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ + (b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c ) +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (a d - b c )x + 2a c d - 2a b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c ) +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (a d - b c )x + 2a c d - 2a b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1092 +t0:=1/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--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: Fraction(Polynomial(Integer)) +--E 629 + +--S 630 of 1092 +r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ + 2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 +--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 +--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1092 +t0:=1/(x*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--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 2 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 634 + +--S 635 of 1092 +r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ + log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ + d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x - a c d +--R + +--R 3 2 2 +--R 3a b c d +--R * +--R log(d x + c) +--R + +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x - 3a b c d +--R + +--R 3 4 +--R a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(x) +--R + +--R 3 3 3 3 4 3 3 2 2 2 2 3 3 4 +--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c +--R / +--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 2 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 4 2 5 +--R (a c d - 2a b c d + 2a b c d - a b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 3 6 +--R - a b c +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x - a c d +--R + +--R 3 2 2 +--R 3a b c d +--R * +--R log(d x + c) +--R + +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x - 3a b c d +--R + +--R 3 4 +--R a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(x) +--R + +--R 3 3 3 3 4 3 3 2 2 2 2 3 3 4 +--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c +--R / +--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 2 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 4 2 5 +--R (a c d - 2a b c d + 2a b c d - a b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 3 6 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 639 + +--S 640 of 1092 +r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ + d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_ + 2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+_ + 2*d^3*(2*b*c-a*d)*log(c+d*x)/(c^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x +--R + +--R 5 4 4 2 3 +--R (2a c d - 4a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x +--R + +--R 2 3 4 4 5 +--R (4a b c d - 2a b c )x +--R * +--R log(b x + a) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2a d + 2a b c d + 4a b c d - 4a b c d - 2a b c d + 2b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2a c d + 4a b c d - 4a b c d + 2a b c )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d +--R + +--R 3 2 4 2 3 5 +--R - 3a b c d + a b c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (a c d - 2a b c d + 2a b c d - a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (a c d - 3a b c d + 3a b c d - a b c )x +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x +--R + +--R 5 4 4 2 3 +--R (2a c d - 4a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x +--R + +--R 2 3 4 4 5 +--R (4a b c d - 2a b c )x +--R * +--R log(b x + a) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2a d + 2a b c d + 4a b c d - 4a b c d - 2a b c d + 2b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2a c d + 4a b c d - 4a b c d + 2a b c )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d +--R + +--R 3 2 4 2 3 5 +--R - 3a b c d + a b c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (a c d - 2a b c d + 2a b c d - a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (a c d - 3a b c d + 3a b c d - a b c )x +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +)clear all + +--S 644 of 1092 +t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 7 2 2 6 2 2 2 2 5 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 4 2 2 3 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 644 + +--S 645 of 1092 +r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ + b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+_ + (3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*_ + log(a+b*x)/(a^4*(b*c-a*d)^3)-d^4*(5*b*c-3*a*d)*_ + log(c+d*x)/(c^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 6 4 2 5 4 6 6 5 5 4 2 2 4 3 +--R (- 6a b d + 10a b c d )x + (- 6a d + 4a b c d + 10a b c d )x +--R + +--R 6 5 5 2 4 2 +--R (- 6a c d + 10a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 2 6 5 4 2 4 4 2 5 5 6 6 3 +--R (- 10a b c d + 6b c d)x + (- 10a b c d - 4a b c d + 6b c )x +--R + +--R 2 4 5 5 6 2 +--R (- 10a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 5 4 2 6 5 4 +--R (6a b d - 10a b c d + 10a b c d - 6b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3 +--R (6a d - 4a b c d - 10a b c d + 10a b c d + 4a b c d - 6b c )x +--R + +--R 6 5 5 2 4 2 4 5 5 6 2 +--R (6a c d - 10a b c d + 10a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 5 5 4 2 2 4 2 4 4 2 5 5 3 +--R (6a b c d - 10a b c d + 10a b c d - 6a b c d)x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 2 +--R (6a c d - 7a b c d - 5a b c d + 5a b c d + 7a b c d - 6a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x - a c d + 3a b c d +--R + +--R 4 2 5 3 3 6 +--R - 3a b c d + a b c +--R / +--R 7 4 4 6 2 5 3 5 3 6 2 4 4 7 4 +--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x +--R + +--R 8 4 4 7 5 3 5 3 7 4 4 8 3 +--R (2a c d - 4a b c d + 4a b c d - 2a b c )x +--R + +--R 8 5 3 7 6 2 6 2 7 5 3 8 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 2 5 4 6 6 5 5 4 2 2 4 3 +--R (- 6a b d + 10a b c d )x + (- 6a d + 4a b c d + 10a b c d )x +--R + +--R 6 5 5 2 4 2 +--R (- 6a c d + 10a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 2 6 5 4 2 4 4 2 5 5 6 6 3 +--R (- 10a b c d + 6b c d)x + (- 10a b c d - 4a b c d + 6b c )x +--R + +--R 2 4 5 5 6 2 +--R (- 10a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 5 4 2 6 5 4 +--R (6a b d - 10a b c d + 10a b c d - 6b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3 +--R (6a d - 4a b c d - 10a b c d + 10a b c d + 4a b c d - 6b c )x +--R + +--R 6 5 5 2 4 2 4 5 5 6 2 +--R (6a c d - 10a b c d + 10a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 5 5 4 2 2 4 2 4 4 2 5 5 3 +--R (6a b c d - 10a b c d + 10a b c d - 6a b c d)x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 2 +--R (6a c d - 7a b c d - 5a b c d + 5a b c d + 7a b c d - 6a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x - a c d + 3a b c d +--R + +--R 4 2 5 3 3 6 +--R - 3a b c d + a b c +--R / +--R 7 4 4 6 2 5 3 5 3 6 2 4 4 7 4 +--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x +--R + +--R 8 4 4 7 5 3 5 3 7 4 4 8 3 +--R (2a c d - 4a b c d + 4a b c d - 2a b c )x +--R + +--R 8 5 3 7 6 2 6 2 7 5 3 8 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 646 + +--S 647 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1092 +t0:=x^7/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 649 + +--S 650 of 1092 +r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ + (b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/_ + (d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*_ + (c+d*x))+a^6*(7*b*c-4*a*d)*log(a+b*x)/(b^5*(b*c-a*d)^4)-_ + c^5*(10*b^2*c^2-28*a*b*c*d+21*a^2*d^2)*log(c+d*x)/(d^6*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 6 5 4 7 6 3 8 7 2 3 +--R (- 126a b c d + 168a b c d - 60b c d )x +--R + +--R 3 5 5 4 2 6 6 3 7 7 2 8 8 2 +--R (- 126a b c d - 84a b c d + 276a b c d - 120b c d)x +--R + +--R 3 5 6 3 2 6 7 2 7 8 8 9 3 5 7 2 +--R (- 252a b c d + 210a b c d + 48a b c d - 60b c )x - 126a b c d +--R + +--R 2 6 8 7 9 +--R 168a b c d - 60a b c +--R * +--R log(d x + c) +--R + +--R 7 9 6 2 8 3 8 9 7 8 6 2 2 7 2 +--R (- 24a b d + 42a b c d )x + (- 24a d - 6a b c d + 84a b c d )x +--R + +--R 8 8 7 2 7 6 2 3 6 8 2 7 7 3 6 +--R (- 48a c d + 60a b c d + 42a b c d )x - 24a c d + 42a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 6 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 7 4 5 +--R - 4a b d + 11a b c d - 4a b c d - 14a b c d + 16a b c d +--R + +--R 8 5 4 +--R - 5b c d +--R * +--R 5 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 12a b d - 29a b c d + 16a b c d - 14a b c d + 56a b c d +--R + +--R 7 5 4 8 6 3 +--R - 61a b c d + 20b c d +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 18a b d - 12a b c d - 46a b c d + 7a b c d + 42a b c d +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 94a b c d - 166a b c d + 63b c d +--R * +--R 3 +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 3 5 5 4 +--R - 6a d + 42a b c d - 60a b c d - 21a b c d + 150a b c d +--R + +--R 2 6 6 3 7 7 2 8 8 +--R - 138a b c d + 27a b c d + 6b c d +--R * +--R 2 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 3 5 6 3 2 6 7 2 +--R - 12a c d + 30a b c d - 36a b c d + 48a b c d - 75a b c d +--R + +--R 7 8 8 9 +--R 72a b c d - 27b c +--R * +--R x +--R + +--R 8 2 7 7 3 6 3 5 7 2 2 6 8 7 9 +--R - 6a c d + 6a b c d - 39a b c d + 66a b c d - 27a b c +--R / +--R 4 6 12 3 7 11 2 8 2 10 9 3 9 10 4 8 3 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 5 12 4 6 11 3 7 2 10 2 8 3 9 9 4 8 +--R 6a b d - 12a b c d - 12a b c d + 48a b c d - 42a b c d +--R + +--R 10 5 7 +--R 12b c d +--R * +--R 2 +--R x +--R + +--R 5 5 11 4 6 2 10 3 7 3 9 2 8 4 8 9 5 7 +--R 12a b c d - 42a b c d + 48a b c d - 12a b c d - 12a b c d +--R + +--R 10 6 6 +--R 6b c d +--R * +--R x +--R + +--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 +--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 4 7 6 3 8 7 2 3 +--R (- 126a b c d + 168a b c d - 60b c d )x +--R + +--R 3 5 5 4 2 6 6 3 7 7 2 8 8 2 +--R (- 126a b c d - 84a b c d + 276a b c d - 120b c d)x +--R + +--R 3 5 6 3 2 6 7 2 7 8 8 9 3 5 7 2 +--R (- 252a b c d + 210a b c d + 48a b c d - 60b c )x - 126a b c d +--R + +--R 2 6 8 7 9 +--R 168a b c d - 60a b c +--R * +--R log(d x + c) +--R + +--R 7 9 6 2 8 3 8 9 7 8 6 2 2 7 2 +--R (- 24a b d + 42a b c d )x + (- 24a d - 6a b c d + 84a b c d )x +--R + +--R 8 8 7 2 7 6 2 3 6 8 2 7 7 3 6 +--R (- 48a c d + 60a b c d + 42a b c d )x - 24a c d + 42a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 6 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 7 4 5 +--R - 4a b d + 11a b c d - 4a b c d - 14a b c d + 16a b c d +--R + +--R 8 5 4 +--R - 5b c d +--R * +--R 5 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 12a b d - 29a b c d + 16a b c d - 14a b c d + 56a b c d +--R + +--R 7 5 4 8 6 3 +--R - 61a b c d + 20b c d +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 18a b d - 12a b c d - 46a b c d + 7a b c d + 42a b c d +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 94a b c d - 166a b c d + 63b c d +--R * +--R 3 +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 3 5 5 4 +--R - 6a d + 42a b c d - 60a b c d - 21a b c d + 150a b c d +--R + +--R 2 6 6 3 7 7 2 8 8 +--R - 138a b c d + 27a b c d + 6b c d +--R * +--R 2 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 3 5 6 3 2 6 7 2 +--R - 12a c d + 30a b c d - 36a b c d + 48a b c d - 75a b c d +--R + +--R 7 8 8 9 +--R 72a b c d - 27b c +--R * +--R x +--R + +--R 8 2 7 7 3 6 3 5 7 2 2 6 8 7 9 +--R - 6a c d + 6a b c d - 39a b c d + 66a b c d - 27a b c +--R / +--R 4 6 12 3 7 11 2 8 2 10 9 3 9 10 4 8 3 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 5 12 4 6 11 3 7 2 10 2 8 3 9 9 4 8 +--R 6a b d - 12a b c d - 12a b c d + 48a b c d - 42a b c d +--R + +--R 10 5 7 +--R 12b c d +--R * +--R 2 +--R x +--R + +--R 5 5 11 4 6 2 10 3 7 3 9 2 8 4 8 9 5 7 +--R 12a b c d - 42a b c d + 48a b c d - 12a b c d - 12a b c d +--R + +--R 10 6 6 +--R 6b c d +--R * +--R x +--R + +--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 +--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d +--R Type: Union(Expression(Integer),...) +--E 651 + +--S 652 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 653 + +)clear all + +--S 654 of 1092 +t0:=x^6/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 654 + +--S 655 of 1092 +r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ + (a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/_ + (d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/_ + (b^4*(b*c-a*d)^4)+3*c^4*(2*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*_ + log(c+d*x)/(d^5*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 5 4 4 6 5 3 7 6 2 3 +--R (30a b c d - 36a b c d + 12b c d )x +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 2 +--R (30a b c d + 24a b c d - 60a b c d + 24b c d)x +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 3 4 6 2 +--R (60a b c d - 42a b c d - 12a b c d + 12b c )x + 30a b c d +--R + +--R 2 5 7 6 8 +--R - 36a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 8 5 2 7 3 7 8 5 2 2 6 2 +--R (6a b d - 12a b c d )x + (6a d - 24a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 7 2 6 6 3 5 +--R (12a c d - 18a b c d - 12a b c d )x + 6a c d - 12a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 5 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c d )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 7 5 3 4 +--R (- 3a b d + 8a b c d - 2a b c d - 12a b c d + 13a b c d - 4b c d )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 4a b d + 4a b c d + 13a b c d - 12a b c d - 22a b c d +--R + +--R 6 5 3 7 6 2 +--R 32a b c d - 11b c d +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 2 5 5 3 +--R 2a d - 10a b c d + 17a b c d + 6a b c d - 34a b c d + 28a b c d +--R + +--R 6 6 2 7 7 +--R - 11a b c d + 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 3 4 5 3 2 5 6 2 6 7 +--R 4a c d - 8a b c d + 10a b c d - 8a b c d + 11a b c d - 16a b c d +--R + +--R 7 8 +--R 7b c +--R * +--R x +--R + +--R 7 2 6 6 3 5 3 4 6 2 2 5 7 6 8 +--R 2a c d - 2a b c d + 11a b c d - 18a b c d + 7a b c +--R / +--R 4 5 11 3 6 10 2 7 2 9 8 3 8 9 4 7 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 4 11 4 5 10 3 6 2 9 2 7 3 8 8 4 7 9 5 6 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 4 10 4 5 2 9 3 6 3 8 2 7 4 7 8 5 6 9 6 5 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 4 6 5 3 7 6 2 3 +--R (30a b c d - 36a b c d + 12b c d )x +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 2 +--R (30a b c d + 24a b c d - 60a b c d + 24b c d)x +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 3 4 6 2 +--R (60a b c d - 42a b c d - 12a b c d + 12b c )x + 30a b c d +--R + +--R 2 5 7 6 8 +--R - 36a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 8 5 2 7 3 7 8 5 2 2 6 2 +--R (6a b d - 12a b c d )x + (6a d - 24a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 7 2 6 6 3 5 +--R (12a c d - 18a b c d - 12a b c d )x + 6a c d - 12a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 5 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c d )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 7 5 3 4 +--R (- 3a b d + 8a b c d - 2a b c d - 12a b c d + 13a b c d - 4b c d )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 4a b d + 4a b c d + 13a b c d - 12a b c d - 22a b c d +--R + +--R 6 5 3 7 6 2 +--R 32a b c d - 11b c d +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 2 5 5 3 +--R 2a d - 10a b c d + 17a b c d + 6a b c d - 34a b c d + 28a b c d +--R + +--R 6 6 2 7 7 +--R - 11a b c d + 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 3 4 5 3 2 5 6 2 6 7 +--R 4a c d - 8a b c d + 10a b c d - 8a b c d + 11a b c d - 16a b c d +--R + +--R 7 8 +--R 7b c +--R * +--R x +--R + +--R 7 2 6 6 3 5 3 4 6 2 2 5 7 6 8 +--R 2a c d - 2a b c d + 11a b c d - 18a b c d + 7a b c +--R / +--R 4 5 11 3 6 10 2 7 2 9 8 3 8 9 4 7 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 4 11 4 5 10 3 6 2 9 2 7 3 8 8 4 7 9 5 6 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 4 10 4 5 2 9 3 6 3 8 2 7 4 7 8 5 6 9 6 5 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 656 + +--S 657 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 658 + +)clear all + +--S 659 of 1092 +t0:=x^5/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 659 + +--S 660 of 1092 +r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ + (c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+_ + a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*_ + (3*b^2*c^2-10*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 4 3 4 5 4 3 6 5 2 3 +--R (- 20a b c d + 20a b c d - 6b c d )x +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (- 20a b c d - 20a b c d + 34a b c d - 12b c d)x +--R + +--R 3 3 4 3 2 4 5 2 5 6 6 7 3 3 5 2 +--R (- 40a b c d + 20a b c d + 8a b c d - 6b c )x - 20a b c d +--R + +--R 2 4 6 5 7 +--R 20a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 7 4 2 6 3 6 7 5 6 4 2 2 5 2 +--R (- 4a b d + 10a b c d )x + (- 4a d + 2a b c d + 20a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 6 2 5 5 3 4 +--R (- 8a c d + 16a b c d + 10a b c d )x - 4a c d + 10a b c d +--R * +--R log(b x + a) +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 4 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 6 5 2 3 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 2a d + 6a b c d - 14a b c d + 16a b c d - 14a b c d +--R + +--R 5 5 2 6 6 +--R 12a b c d - 4b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 5 6 +--R - 4a c d + 6a b c d - 8a b c d + 2a b c d - a b c d + 10a b c d +--R + +--R 6 7 +--R - 5b c +--R * +--R x +--R + +--R 6 2 5 5 3 4 3 3 5 2 2 4 6 5 7 +--R - 2a c d + 2a b c d - 9a b c d + 14a b c d - 5a b c +--R / +--R 4 4 10 3 5 9 2 6 2 8 7 3 7 8 4 6 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 8 5 5 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 3 9 4 4 2 8 3 5 3 7 2 6 4 6 7 5 5 8 6 4 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 4 5 4 3 6 5 2 3 +--R (- 20a b c d + 20a b c d - 6b c d )x +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (- 20a b c d - 20a b c d + 34a b c d - 12b c d)x +--R + +--R 3 3 4 3 2 4 5 2 5 6 6 7 3 3 5 2 +--R (- 40a b c d + 20a b c d + 8a b c d - 6b c )x - 20a b c d +--R + +--R 2 4 6 5 7 +--R 20a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 7 4 2 6 3 6 7 5 6 4 2 2 5 2 +--R (- 4a b d + 10a b c d )x + (- 4a d + 2a b c d + 20a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 6 2 5 5 3 4 +--R (- 8a c d + 16a b c d + 10a b c d )x - 4a c d + 10a b c d +--R * +--R log(b x + a) +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 4 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 6 5 2 3 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 2a d + 6a b c d - 14a b c d + 16a b c d - 14a b c d +--R + +--R 5 5 2 6 6 +--R 12a b c d - 4b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 5 6 +--R - 4a c d + 6a b c d - 8a b c d + 2a b c d - a b c d + 10a b c d +--R + +--R 6 7 +--R - 5b c +--R * +--R x +--R + +--R 6 2 5 5 3 4 3 3 5 2 2 4 6 5 7 +--R - 2a c d + 2a b c d - 9a b c d + 14a b c d - 5a b c +--R / +--R 4 4 10 3 5 9 2 6 2 8 7 3 7 8 4 6 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 8 5 5 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 3 9 4 4 2 8 3 5 3 7 2 6 4 6 7 5 5 8 6 4 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1092 +t0:=x^4/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 664 + +--S 665 of 1092 +r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ + 2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*_ + log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*_ + log(c+d*x)/(d^3*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 3 2 4 4 3 3 5 4 2 3 +--R (12a b c d - 8a b c d + 2b c d )x +--R + +--R 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (12a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 3 2 3 3 2 3 4 2 4 5 5 6 3 2 4 2 2 3 5 +--R (24a b c d - 4a b c d - 4a b c d + 2b c )x + 12a b c d - 8a b c d +--R + +--R 4 6 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 4 6 3 2 5 3 5 6 4 5 3 2 2 4 2 +--R (2a b d - 8a b c d )x + (2a d - 4a b c d - 16a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 5 2 4 4 3 3 +--R (4a c d - 14a b c d - 8a b c d )x + 2a c d - 8a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 5 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 2a b c d + 8a b c d - 12a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 4a b c d + 8a b c d - 5a b c d - 6a b c d + 3b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 2a b c d + 7a b c d - 10a b c d + 3a b c +--R / +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 7 5 4 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 4 3 3 5 4 2 3 +--R (12a b c d - 8a b c d + 2b c d )x +--R + +--R 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (12a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 3 2 3 3 2 3 4 2 4 5 5 6 3 2 4 2 2 3 5 +--R (24a b c d - 4a b c d - 4a b c d + 2b c )x + 12a b c d - 8a b c d +--R + +--R 4 6 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 4 6 3 2 5 3 5 6 4 5 3 2 2 4 2 +--R (2a b d - 8a b c d )x + (2a d - 4a b c d - 16a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 5 2 4 4 3 3 +--R (4a c d - 14a b c d - 8a b c d )x + 2a c d - 8a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 5 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 2a b c d + 8a b c d - 12a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 4a b c d + 8a b c d - 5a b c d - 6a b c d + 3b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 2a b c d + 7a b c d - 10a b c d + 3a b c +--R / +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 7 5 4 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 668 + +)clear all + +--S 669 of 1092 +t0:=x^3/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 669 + +--S 670 of 1092 +r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ + c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/_ + (b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 3 2 +--R - 6a b c d x + (- 6a b c d - 12a b c d )x +--R + +--R 3 2 3 2 2 3 2 3 3 2 +--R (- 12a b c d - 6a b c d )x - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 3 2 3 2 2 3 2 +--R 6a b c d x + (6a b c d + 12a b c d )x + (12a b c d + 6a b c d )x +--R + +--R 3 3 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 2a d + 2a b c d - 6a b c d + 8a b c d - 2b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 4a c d - 2a b c d + 3a b c d + 4a b c d - b c )x - 2a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 3a b c d + 6a b c d - a b c +--R / +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 7 4 2 2 6 3 3 3 5 2 4 4 4 5 5 3 6 6 2 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 3 2 +--R - 6a b c d x + (- 6a b c d - 12a b c d )x +--R + +--R 3 2 3 2 2 3 2 3 3 2 +--R (- 12a b c d - 6a b c d )x - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 3 2 3 2 2 3 2 +--R 6a b c d x + (6a b c d + 12a b c d )x + (12a b c d + 6a b c d )x +--R + +--R 3 3 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 2a d + 2a b c d - 6a b c d + 8a b c d - 2b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 4a c d - 2a b c d + 3a b c d + 4a b c d - b c )x - 2a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 3a b c d + 6a b c d - a b c +--R / +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 7 4 2 2 6 3 3 3 5 2 4 4 4 5 5 3 6 6 2 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 673 + +)clear all + +--S 674 of 1092 +t0:=x^2/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 674 + +--S 675 of 1092 +r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ + 2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+_ + a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (2a b d + 4a b c d )x + (2a d + 8a b c d + 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (4a c d + 10a b c d + 4a b c d)x + 2a c d + 4a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (- 2a b d - 4a b c d )x + (- 2a d - 8a b c d - 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (- 4a c d - 10a b c d - 4a b c d)x - 2a c d - 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 2 3 2 2 2 2 +--R (2a d + 2a b c d - 4a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 2 4 +--R (8a c d - 5a b c d - 2a b c d - b c )x + 5a c d - 4a b c d - a b c +--R / +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (2a b d + 4a b c d )x + (2a d + 8a b c d + 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (4a c d + 10a b c d + 4a b c d)x + 2a c d + 4a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (- 2a b d - 4a b c d )x + (- 2a d - 8a b c d - 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (- 4a c d - 10a b c d - 4a b c d)x - 2a c d - 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 2 3 2 2 2 2 +--R (2a d + 2a b c d - 4a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 2 4 +--R (8a c d - 5a b c d - 2a b c d - b c )x + 5a c d - 4a b c d - a b c +--R / +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 676 + +--S 677 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 1092 +t0:=x/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 679 + +--S 680 of 1092 +r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ + ((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-_ + b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 3 2 2 +--R (- 4a b d + 2a b c d + 2b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 3 2 2 +--R (- 4a b d + 2a b c d + 2b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 681 + +--S 682 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 683 + +)clear all + +--S 684 of 1092 +t0:=1/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 684 + +--S 685 of 1092 +r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ + 2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_ + 3*b^2*d*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 3a b c d - 2b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 3a b c d - 2b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 686 + +--S 687 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1092 +t0:=1/(x*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 3 2 2 3 2 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1092 +r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ + d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-_ + b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^4) +--R +--R +--R (2) +--R 4 6 3 2 5 2 3 2 4 3 +--R (- 2a b d + 8a b c d - 12a b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 2 +--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 2 4 +--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d +--R + +--R 4 3 3 3 2 4 2 +--R 8a b c d - 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 3 3 5 4 2 3 2 3 3 3 4 4 2 5 5 2 +--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x +--R + +--R 2 3 4 2 4 5 5 6 2 3 5 4 6 +--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c +--R * +--R log(b x + a) +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R * +--R log(x) +--R + +--R 4 5 3 2 2 4 2 3 3 3 4 4 2 2 +--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 2 4 +--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d +--R + +--R 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 10a b c d + 7a b c d - 2a b c d + 2a b c +--R / +--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 3 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 2 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 2 5 2 3 2 4 3 +--R (- 2a b d + 8a b c d - 12a b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 2 +--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 2 4 +--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d +--R + +--R 4 3 3 3 2 4 2 +--R 8a b c d - 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 3 3 5 4 2 3 2 3 3 3 4 4 2 5 5 2 +--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x +--R + +--R 2 3 4 2 4 5 5 6 2 3 5 4 6 +--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c +--R * +--R log(b x + a) +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R * +--R log(x) +--R + +--R 4 5 3 2 2 4 2 3 3 3 4 4 2 2 +--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 2 4 +--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d +--R + +--R 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 10a b c d + 7a b c d - 2a b c d + 2a b c +--R / +--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 3 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 2 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1092 +r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ + 1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/_ + (c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+_ + b^4*(2*b*c-5*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^4)+_ + d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 5 7 4 2 6 3 3 2 5 4 +--R (6a b d - 20a b c d + 20a b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 3 +--R (6a d - 8a b c d - 20a b c d + 40a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 +--R (12a c d - 34a b c d + 20a b c d + 20a b c d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 +--R (6a c d - 20a b c d + 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 +--R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x +--R * +--R log(b x + a) +--R + +--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 +--R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d +--R + +--R 5 5 2 6 6 +--R 16a b c d - 8b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d +--R + +--R 5 6 6 7 +--R 2a b c d - 4b c +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 +--R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 +--R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d +--R + +--R 5 6 +--R - 8a b c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 4 2 6 3 3 2 5 4 +--R (6a b d - 20a b c d + 20a b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 3 +--R (6a d - 8a b c d - 20a b c d + 40a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 +--R (12a c d - 34a b c d + 20a b c d + 20a b c d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 +--R (6a c d - 20a b c d + 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 +--R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x +--R * +--R log(b x + a) +--R + +--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 +--R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d +--R + +--R 5 5 2 6 6 +--R 16a b c d - 8b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d +--R + +--R 5 6 6 7 +--R 2a b c d - 4b c +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 +--R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 +--R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d +--R + +--R 5 6 +--R - 8a b c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 696 + +--S 697 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +)clear all + +--S 699 of 1092 +t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 8 3 2 2 7 2 3 2 2 2 6 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 5 2 2 3 4 2 3 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 699 + +--S 700 of 1092 +r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ + (a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/_ + (c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/_ + (a^4*c^5)-3*b^5*(b*c-2*a*d)*log(a+b*x)/(a^4*(b*c-a*d)^4)-_ + 3*d^4*(5*b^2*c^2-6*a*b*c*d+2*a^2*d^2)*log(c+d*x)/(c^5*(b*c-a*d)^4) +--R +--R +--R (2) +--R 6 8 5 2 7 4 3 2 6 5 +--R (- 12a b d + 36a b c d - 30a b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 4 +--R (- 12a d + 12a b c d + 42a b c d - 60a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 +--R (- 24a c d + 60a b c d - 24a b c d - 30a b c d )x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 +--R (- 12a c d + 36a b c d - 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 6 5 3 7 6 2 5 2 5 5 3 6 6 2 7 7 4 +--R (12a b c d - 6b c d )x + (12a b c d + 18a b c d - 12b c d)x +--R + +--R 2 5 6 2 7 8 3 2 5 7 6 8 2 +--R (24a b c d - 6b c )x + (12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 8 5 2 7 4 3 2 6 6 5 3 7 6 2 5 +--R (12a b d - 36a b c d + 30a b c d - 12a b c d + 6b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 2 5 5 3 +--R 12a d - 12a b c d - 42a b c d + 60a b c d - 12a b c d +--R + +--R 6 6 2 7 7 +--R - 18a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 2 5 6 2 +--R 24a c d - 60a b c d + 24a b c d + 30a b c d - 24a b c d +--R + +--R 7 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 5 7 6 8 2 +--R (12a c d - 36a b c d + 30a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 6 7 5 2 2 6 4 3 3 5 2 5 5 3 6 6 2 4 +--R (12a b c d - 36a b c d + 30a b c d - 12a b c d + 6a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R 12a c d - 18a b c d - 24a b c d + 45a b c d - 6a b c d +--R + +--R 2 5 6 2 6 7 +--R - 21a b c d + 12a b c d +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R 18a c d - 50a b c d + 33a b c d + 12a b c d - 13a b c d +--R + +--R 2 5 7 6 8 +--R - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R (4a c d - 13a b c d + 12a b c d + 2a b c d - 8a b c d + 3a b c )x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +--R - a c d + 4a b c d - 6a b c d + 4a b c d - a b c +--R / +--R 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 4 5 9 2 5 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 4 5 10 4 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 4 5 11 3 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 5 2 7 4 3 2 6 5 +--R (- 12a b d + 36a b c d - 30a b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 4 +--R (- 12a d + 12a b c d + 42a b c d - 60a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 +--R (- 24a c d + 60a b c d - 24a b c d - 30a b c d )x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 +--R (- 12a c d + 36a b c d - 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 6 5 3 7 6 2 5 2 5 5 3 6 6 2 7 7 4 +--R (12a b c d - 6b c d )x + (12a b c d + 18a b c d - 12b c d)x +--R + +--R 2 5 6 2 7 8 3 2 5 7 6 8 2 +--R (24a b c d - 6b c )x + (12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 8 5 2 7 4 3 2 6 6 5 3 7 6 2 5 +--R (12a b d - 36a b c d + 30a b c d - 12a b c d + 6b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 2 5 5 3 +--R 12a d - 12a b c d - 42a b c d + 60a b c d - 12a b c d +--R + +--R 6 6 2 7 7 +--R - 18a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 2 5 6 2 +--R 24a c d - 60a b c d + 24a b c d + 30a b c d - 24a b c d +--R + +--R 7 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 5 7 6 8 2 +--R (12a c d - 36a b c d + 30a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 6 7 5 2 2 6 4 3 3 5 2 5 5 3 6 6 2 4 +--R (12a b c d - 36a b c d + 30a b c d - 12a b c d + 6a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R 12a c d - 18a b c d - 24a b c d + 45a b c d - 6a b c d +--R + +--R 2 5 6 2 6 7 +--R - 21a b c d + 12a b c d +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R 18a c d - 50a b c d + 33a b c d + 12a b c d - 13a b c d +--R + +--R 2 5 7 6 8 +--R - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R (4a c d - 13a b c d + 12a b c d + 2a b c d - 8a b c d + 3a b c )x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +--R - a c d + 4a b c d - 6a b c d + 4a b c d - a b c +--R / +--R 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 4 5 9 2 5 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 4 5 10 4 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 4 5 11 3 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 701 + +--S 702 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 703 + +)clear all + +--S 704 of 1092 +t0:=x^2/((-1+x)^2*(1+x)^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 704 + +--S 705 of 1092 +r0:=1/2*x/(1-x^2)-1/2*atanh(x) +--R +--R +--R 2 +--R (- x + 1)atanh(x) - x +--R (2) ---------------------- +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (- x + 1)log(x + 1) + (x - 1)log(x - 1) - 2x +--R (3) ---------------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1092 +m0:=a0-r0 +--R +--R +--R - log(x + 1) + log(x - 1) + 2atanh(x) +--R (4) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1092 +t0:=b^2*x^m/(b+a*x^2)^2 +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1092 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 710 + +--S 711 of 1092 +--a0:=integrate(t0,x) +--E 711 + +--S 712 of 1092 +--m0:=a0-r0 +--E 712 + +--S 713 of 1092 +--d0:=D(m0,x) +--E 713 + +)clear all + +--S 714 of 1092 +t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1092 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 715 + +--S 716 of 1092 +--a0:=integrate(t0,x) +--E 716 + +--S 717 of 1092 +--m0:=a0-r0 +--E 717 + +--S 718 of 1092 +--d0:=D(m0,x) +--E 718 + +)clear all + +--S 719 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 719 + +--S 720 of 1092 +r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ + 3/2*d*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+d^2*(b*c-a*d)*x^3/b^4+_ + 1/4*d^3*x^4/b^3+1/2*a^3*(b*c-a*d)^3/(b^7*(a+b*x)^2)-_ + 3*a^2*(b*c-2*a*d)*(b*c-a*d)^2/(b^7*(a+b*x))-_ + 3*a*(b*c-a*d)*(b^2*c^2-5*a*b*c*d+5*a^2*d^2)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 120a b c d + 72a b c d - 12a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (120a b d - 240a b c d + 144a b c d - 24a b c )x + 60a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 120a b c d + 72a b c d - 12a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R b d x + (- 2a b d + 4b c d )x + (5a b d - 10a b c d + 6b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 40a b c d - 24a b c d + 4b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 68a b d + 126a b c d - 66a b c d + 8a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (- 16a b d + 12a b c d + 12a b c d - 8a b c )x + 22a d - 54a b c d +--R + +--R 4 2 2 3 3 3 +--R 42a b c d - 10a b c +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 120a b c d + 72a b c d - 12a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (120a b d - 240a b c d + 144a b c d - 24a b c )x + 60a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 120a b c d + 72a b c d - 12a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R b d x + (- 2a b d + 4b c d )x + (5a b d - 10a b c d + 6b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 40a b c d - 24a b c d + 4b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 68a b d + 126a b c d - 66a b c d + 8a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (- 16a b d + 12a b c d + 12a b c d - 8a b c )x + 22a d - 54a b c d +--R + +--R 4 2 2 3 3 3 +--R 42a b c d - 10a b c +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 724 + +--S 725 of 1092 +r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ + 1/3*d^3*x^3/b^3-1/2*a^2*(b*c-a*d)^3/(b^6*(a+b*x)^2)+_ + a*(2*b*c-5*a*d)*(b*c-a*d)^2/(b^6*(a+b*x))+(b*c-a*d)*_ + (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 60a b d + 108a b c d - 54a b c d + 6b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 120a b d + 216a b c d - 108a b c d + 12a b c )x - 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 108a b c d - 54a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 2b d x + (- 5a b d + 9b c d )x + (20a b d - 36a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 2 +--R (63a b d - 99a b c d + 36a b c d)x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (6a b d + 18a b c d - 36a b c d + 12a b c )x - 27a d + 63a b c d +--R + +--R 3 2 2 2 3 3 +--R - 45a b c d + 9a b c +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 60a b d + 108a b c d - 54a b c d + 6b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 120a b d + 216a b c d - 108a b c d + 12a b c )x - 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 108a b c d - 54a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 2b d x + (- 5a b d + 9b c d )x + (20a b d - 36a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 2 +--R (63a b d - 99a b c d + 36a b c d)x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (6a b d + 18a b c d - 36a b c d + 12a b c )x - 27a d + 63a b c d +--R + +--R 3 2 2 2 3 3 +--R - 45a b c d + 9a b c +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1092 +t0:=x*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 729 + +--S 730 of 1092 +r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ + (b^5*(a+b*x)^2)-(b*c-4*a*d)*(b*c-a*d)^2/(b^5*(a+b*x))+_ + 3*d*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 2 4 2 2 +--R (12a b d - 18a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (24a b d - 36a b c d + 12a b c d)x + 12a d - 18a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 2 +--R b d x + (- 4a b d + 6b c d )x + (- 11a b d + 12a b c d )x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (2a b d - 12a b c d + 12a b c d - 2b c )x + 7a d - 15a b c d +--R + +--R 2 2 2 3 3 +--R 9a b c d - a b c +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 2 4 2 2 +--R (12a b d - 18a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (24a b d - 36a b c d + 12a b c d)x + 12a d - 18a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 2 +--R b d x + (- 4a b d + 6b c d )x + (- 11a b d + 12a b c d )x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (2a b d - 12a b c d + 12a b c d - 2b c )x + 7a d - 15a b c d +--R + +--R 2 2 2 3 3 +--R 9a b c d - a b c +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 731 + +--S 732 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 733 + +)clear all + +--S 734 of 1092 +t0:=(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 734 + +--S 735 of 1092 +r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ + (b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 739 + +--S 740 of 1092 +r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ + (a^2*b^3*(a+b*x))+c^3*log(x)/a^3-(c^3/a^3-d^3/b^3)*log(a+b*x) +--R +--R +--R (2) +--R 3 2 3 5 3 2 4 3 4 3 5 3 2 3 3 +--R ((2a b d - 2b c )x + (4a b d - 4a b c )x + 2a d - 2a b c ) +--R * +--R log(b x + a) +--R + +--R 5 3 2 4 3 2 3 3 4 3 3 2 2 4 3 +--R (2b c x + 4a b c x + 2a b c )log(x) + (4a b d - 6a b c d + 2a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 +--R 3a d - 3a b c d - 3a b c d + 3a b c +--R / +--R 3 5 2 4 4 5 3 +--R 2a b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 5 3 2 4 3 4 3 5 3 2 3 3 +--R ((2a b d - 2b c )x + (4a b d - 4a b c )x + 2a d - 2a b c ) +--R * +--R log(b x + a) +--R + +--R 5 3 2 4 3 2 3 3 4 3 3 2 2 4 3 +--R (2b c x + 4a b c x + 2a b c )log(x) + (4a b d - 6a b c d + 2a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 +--R 3a d - 3a b c d - 3a b c d + 3a b c +--R / +--R 3 5 2 4 4 5 3 +--R 2a b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 741 + +--S 742 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 744 + +--S 745 of 1092 +r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ + (2*b*c+a*d)/(a^3*b^2*(a+b*x))-3*c^2*(b*c-a*d)*log(x)/a^4+_ + 3*c^2*(b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (- 6a b c d + 6b c )x + (- 12a b c d + 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (- 6a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (6a b c d - 6b c )x + (12a b c d - 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (6a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R (- 2a b d + 6a b c d - 6a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 2 3 +--R (- a d - 3a b c d + 9a b c d - 9a b c )x - 2a b c +--R / +--R 4 4 3 5 3 2 6 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (- 6a b c d + 6b c )x + (- 12a b c d + 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (- 6a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (6a b c d - 6b c )x + (12a b c d - 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (6a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R (- 2a b d + 6a b c d - 6a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 2 3 +--R (- a d - 3a b c d + 9a b c d - 9a b c )x - 2a b c +--R / +--R 4 4 3 5 3 2 6 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 749 + +--S 750 of 1092 +r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ + (a^3*b*(a+b*x)^2)+3*c*(b*c-a*d)^2/(a^4*(a+b*x))+3*c*(b*c-a*d)*_ + (2*b*c-a*d)*log(x)/a^5-3*c*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 3 2 4 2 5 3 4 +--R (- 6a b c d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12a b c d + 36a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6a b c d + 18a b c d - 12a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6a b c d - 18a b c d + 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12a b c d - 36a b c d + 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6a b c d - 18a b c d + 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6a b c d - 18a b c d + 12a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- a d + 9a b c d - 27a b c d + 18a b c )x + (- 6a b c d + 4a b c )x +--R + +--R 4 3 +--R - a b c +--R / +--R 5 3 4 6 2 3 7 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 5 3 4 +--R (- 6a b c d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12a b c d + 36a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6a b c d + 18a b c d - 12a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6a b c d - 18a b c d + 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12a b c d - 36a b c d + 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6a b c d - 18a b c d + 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6a b c d - 18a b c d + 12a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- a d + 9a b c d - 27a b c d + 18a b c )x + (- 6a b c d + 4a b c )x +--R + +--R 4 3 +--R - a b c +--R / +--R 5 3 4 6 2 3 7 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1092 +r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ + (2*b*c-a*d)/(a^5*x)-1/2*(b*c-a*d)^3/(a^4*(a+b*x)^2)-(b*c-a*d)^2*_ + (4*b*c-a*d)/(a^5*(a+b*x))-(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ + log(x)/a^6+(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 6a b d + 54a b c d - 108a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 108a b c d - 216a b c d + 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 6a d + 54a b c d - 108a b c d + 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (6a b d - 54a b c d + 108a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 108a b c d + 216a b c d - 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (6a d - 54a b c d + 108a b c d - 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 54a b c d + 108a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (9a d - 81a b c d + 162a b c d - 90a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 36a b c d - 20a b c )x + (- 9a c d + 5a b c )x - 2a c +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 6a b d + 54a b c d - 108a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 108a b c d - 216a b c d + 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 6a d + 54a b c d - 108a b c d + 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (6a b d - 54a b c d + 108a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 108a b c d + 216a b c d - 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (6a d - 54a b c d + 108a b c d - 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 54a b c d + 108a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (9a d - 81a b c d + 162a b c d - 90a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 36a b c d - 20a b c )x + (- 9a c d + 5a b c )x - 2a c +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1092 +t0:=x^7/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 7 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 759 + +--S 760 of 1092 +r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ + (a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/_ + (d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-_ + 3*a^5*(7*b^2*c^2-7*a*b*c*d+2*a^2*d^2)*log(a+b*x)/(b^5*(b*c-a*d)^5)+_ + 3*c^5*(2*b^2*c^2-7*a*b*c*d+7*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 7 5 4 8 6 3 9 7 2 4 +--R (- 42a b c d + 42a b c d - 12b c d )x +--R + +--R 3 6 5 4 8 7 2 9 8 3 +--R (- 84a b c d + 60a b c d - 24b c d)x +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 2 +--R (- 42a b c d - 126a b c d + 114a b c d - 6a b c d - 12b c )x +--R + +--R 4 5 6 3 2 7 8 8 9 4 5 7 2 3 6 8 +--R (- 84a b c d + 60a b c d - 24a b c )x - 42a b c d + 42a b c d +--R + +--R 2 7 9 +--R - 12a b c +--R * +--R log(d x + c) +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 +--R (12a b d - 42a b c d + 42a b c d )x +--R + +--R 8 9 7 2 8 5 4 3 6 3 +--R (24a b d - 60a b c d + 84a b c d )x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 2 +--R (12a d + 6a b c d - 114a b c d + 126a b c d + 42a b c d )x +--R + +--R 9 8 8 2 7 6 3 4 5 9 2 7 8 3 6 +--R (24a c d - 60a b c d + 84a b c d )x + 12a c d - 42a b c d +--R + +--R 7 2 4 5 +--R 42a b c d +--R * +--R log(b x + a) +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 6 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 +--R - 4a b d + 16a b c d - 20a b c d + 20a b c d - 16a b c d +--R + +--R 9 6 3 +--R 4b c d +--R * +--R 5 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R - 11a b d + 35a b c d - 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 21a b c d - 35a b c d + 11b c d +--R * +--R 4 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 +--R 2a b d - 20a b c d + 66a b c d - 86a b c d + 86a b c d +--R + +--R 2 7 6 3 8 7 2 9 8 +--R - 66a b c d + 20a b c d - 2b c d +--R * +--R 3 +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 +--R 7a d - 16a b c d + 6a b c d + 11a b c d - 50a b c d + 50a b c d +--R + +--R 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 11a b c d - 6a b c d + 16a b c d - 7b c +--R * +--R 2 +--R x +--R + +--R 9 8 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 +--R 14a c d - 38a b c d + 28a b c d - 16a b c d + 16a b c d +--R + +--R 3 6 7 2 2 7 8 8 9 +--R - 28a b c d + 38a b c d - 14a b c +--R * +--R x +--R + +--R 9 2 7 8 3 6 7 2 4 5 4 5 7 2 3 6 8 2 7 9 +--R 7a c d - 20a b c d + 13a b c d - 13a b c d + 20a b c d - 7a b c +--R / +--R 5 7 12 4 8 11 3 9 2 10 2 10 3 9 11 4 8 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 12 5 7 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 6 12 5 7 11 4 8 2 10 2 10 4 8 11 5 7 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 12 6 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 5 12 6 6 11 5 7 2 10 4 8 3 9 3 9 4 8 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 10 5 7 11 6 6 12 7 5 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 5 11 6 6 2 10 5 7 3 9 3 9 5 7 2 10 6 6 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 7 5 +--R - 4a b c d +--R * +--R x +--R + +--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 5 4 8 6 3 9 7 2 4 +--R (- 42a b c d + 42a b c d - 12b c d )x +--R + +--R 3 6 5 4 8 7 2 9 8 3 +--R (- 84a b c d + 60a b c d - 24b c d)x +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 2 +--R (- 42a b c d - 126a b c d + 114a b c d - 6a b c d - 12b c )x +--R + +--R 4 5 6 3 2 7 8 8 9 4 5 7 2 3 6 8 +--R (- 84a b c d + 60a b c d - 24a b c )x - 42a b c d + 42a b c d +--R + +--R 2 7 9 +--R - 12a b c +--R * +--R log(d x + c) +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 +--R (12a b d - 42a b c d + 42a b c d )x +--R + +--R 8 9 7 2 8 5 4 3 6 3 +--R (24a b d - 60a b c d + 84a b c d )x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 2 +--R (12a d + 6a b c d - 114a b c d + 126a b c d + 42a b c d )x +--R + +--R 9 8 8 2 7 6 3 4 5 9 2 7 8 3 6 +--R (24a c d - 60a b c d + 84a b c d )x + 12a c d - 42a b c d +--R + +--R 7 2 4 5 +--R 42a b c d +--R * +--R log(b x + a) +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 6 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 +--R - 4a b d + 16a b c d - 20a b c d + 20a b c d - 16a b c d +--R + +--R 9 6 3 +--R 4b c d +--R * +--R 5 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R - 11a b d + 35a b c d - 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 21a b c d - 35a b c d + 11b c d +--R * +--R 4 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 +--R 2a b d - 20a b c d + 66a b c d - 86a b c d + 86a b c d +--R + +--R 2 7 6 3 8 7 2 9 8 +--R - 66a b c d + 20a b c d - 2b c d +--R * +--R 3 +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 +--R 7a d - 16a b c d + 6a b c d + 11a b c d - 50a b c d + 50a b c d +--R + +--R 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 11a b c d - 6a b c d + 16a b c d - 7b c +--R * +--R 2 +--R x +--R + +--R 9 8 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 +--R 14a c d - 38a b c d + 28a b c d - 16a b c d + 16a b c d +--R + +--R 3 6 7 2 2 7 8 8 9 +--R - 28a b c d + 38a b c d - 14a b c +--R * +--R x +--R + +--R 9 2 7 8 3 6 7 2 4 5 4 5 7 2 3 6 8 2 7 9 +--R 7a c d - 20a b c d + 13a b c d - 13a b c d + 20a b c d - 7a b c +--R / +--R 5 7 12 4 8 11 3 9 2 10 2 10 3 9 11 4 8 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 12 5 7 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 6 12 5 7 11 4 8 2 10 2 10 4 8 11 5 7 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 12 6 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 5 12 6 6 11 5 7 2 10 4 8 3 9 3 9 4 8 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 10 5 7 11 6 6 12 7 5 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 5 11 6 6 2 10 5 7 3 9 3 9 5 7 2 10 6 6 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 7 5 +--R - 4a b c d +--R * +--R x +--R + +--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 761 + +--S 762 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +)clear all + +--S 764 of 1092 +t0:=x^6/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 764 + +--S 765 of 1092 +r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ + (b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-_ + 3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^4*(b*c-a*d)^5)-3*c^4*_ + (b^2*c^2-4*a*b*c*d+5*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 6 4 4 7 5 3 8 6 2 4 +--R (30a b c d - 24a b c d + 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 3 +--R (60a b c d + 12a b c d - 36a b c d + 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 2 +--R (30a b c d + 96a b c d - 60a b c d + 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 4 4 6 2 +--R (60a b c d + 12a b c d - 36a b c d + 12a b c )x + 30a b c d +--R + +--R 3 5 7 2 6 8 +--R - 24a b c d + 6a b c +--R * +--R log(d x + c) +--R + +--R 6 2 8 5 3 7 4 4 2 6 4 +--R (- 6a b d + 24a b c d - 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 +--R (- 12a b d + 36a b c d - 12a b c d - 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 2 +--R (- 6a d + 60a b c d - 96a b c d - 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 8 2 6 +--R (- 12a c d + 36a b c d - 12a b c d - 60a b c d )x - 6a c d +--R + +--R 7 3 5 6 2 4 4 +--R 24a b c d - 30a b c d +--R * +--R log(b x + a) +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 5 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 4 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 4a b d + 16a b c d - 30a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 30a b c d - 16a b c d + 4b c d +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 5a d + 8a b c d + 9a b c d - 4a b c d + 4a b c d - 9a b c d +--R + +--R 7 7 8 8 +--R - 8a b c d + 5b c +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 10a c d + 28a b c d - 14a b c d + 8a b c d - 8a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 14a b c d - 28a b c d + 10a b c +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R - 5a c d + 16a b c d - 11a b c d + 11a b c d - 16a b c d + 5a b c +--R / +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 10 4 7 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 11 5 6 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 2 9 4 7 10 5 6 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 6 5 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 3 8 4 7 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 9 5 6 10 6 5 11 7 4 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 4 10 6 5 2 9 5 6 3 8 3 8 5 6 2 9 6 5 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 7 4 +--R - 4a b c d +--R * +--R x +--R + +--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 4 4 7 5 3 8 6 2 4 +--R (30a b c d - 24a b c d + 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 3 +--R (60a b c d + 12a b c d - 36a b c d + 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 2 +--R (30a b c d + 96a b c d - 60a b c d + 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 4 4 6 2 +--R (60a b c d + 12a b c d - 36a b c d + 12a b c )x + 30a b c d +--R + +--R 3 5 7 2 6 8 +--R - 24a b c d + 6a b c +--R * +--R log(d x + c) +--R + +--R 6 2 8 5 3 7 4 4 2 6 4 +--R (- 6a b d + 24a b c d - 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 +--R (- 12a b d + 36a b c d - 12a b c d - 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 2 +--R (- 6a d + 60a b c d - 96a b c d - 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 8 2 6 +--R (- 12a c d + 36a b c d - 12a b c d - 60a b c d )x - 6a c d +--R + +--R 7 3 5 6 2 4 4 +--R 24a b c d - 30a b c d +--R * +--R log(b x + a) +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 5 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 4 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 4a b d + 16a b c d - 30a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 30a b c d - 16a b c d + 4b c d +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 5a d + 8a b c d + 9a b c d - 4a b c d + 4a b c d - 9a b c d +--R + +--R 7 7 8 8 +--R - 8a b c d + 5b c +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 10a c d + 28a b c d - 14a b c d + 8a b c d - 8a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 14a b c d - 28a b c d + 10a b c +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R - 5a c d + 16a b c d - 11a b c d + 11a b c d - 16a b c d + 5a b c +--R / +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 10 4 7 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 11 5 6 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 2 9 4 7 10 5 6 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 6 5 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 3 8 4 7 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 9 5 6 10 6 5 11 7 4 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 4 10 6 5 2 9 5 6 3 8 3 8 5 6 2 9 6 5 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 7 4 +--R - 4a b c d +--R * +--R x +--R + +--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 768 + +)clear all + +--S 769 of 1092 +t0:=x^5/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 769 + +--S 770 of 1092 +r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ + (b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+_ + c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-_ + 5*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^3*(b*c-a*d)^5)+c^3*(b^2*c^2-_ + 5*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (- 20a b c d + 10a b c d - 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (- 40a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (- 20a b c d - 70a b c d + 18a b c d + 2a b c d - 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (- 40a b c d - 20a b c d + 16a b c d - 4a b c )x - 20a b c d +--R + +--R 3 4 6 2 5 7 +--R 10a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (2a b d - 10a b c d + 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (4a b d - 16a b c d + 20a b c d + 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (2a d - 2a b c d - 18a b c d + 70a b c d + 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (4a c d - 16a b c d + 20a b c d + 40a b c d )x + 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R - 10a b c d + 20a b c d +--R * +--R log(b x + a) +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 14a b c d + 10a b c d - 10a b c d + 14a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 3a d - 4a b c d - 19a b c d + 20a b c d - 20a b c d + 19a b c d +--R + +--R 6 6 7 7 +--R 4a b c d - 3b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (6a c d - 20a b c d + 4a b c d - 4a b c d + 20a b c d - 6a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 10 5 5 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 2 8 4 6 9 5 5 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 6 4 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 3 9 6 4 2 8 5 5 3 7 3 7 5 5 2 8 6 4 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 9 7 3 +--R - 4a b c d +--R * +--R x +--R + +--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (- 20a b c d + 10a b c d - 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (- 40a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (- 20a b c d - 70a b c d + 18a b c d + 2a b c d - 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (- 40a b c d - 20a b c d + 16a b c d - 4a b c )x - 20a b c d +--R + +--R 3 4 6 2 5 7 +--R 10a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (2a b d - 10a b c d + 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (4a b d - 16a b c d + 20a b c d + 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (2a d - 2a b c d - 18a b c d + 70a b c d + 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (4a c d - 16a b c d + 20a b c d + 40a b c d )x + 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R - 10a b c d + 20a b c d +--R * +--R log(b x + a) +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 14a b c d + 10a b c d - 10a b c d + 14a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 3a d - 4a b c d - 19a b c d + 20a b c d - 20a b c d + 19a b c d +--R + +--R 6 6 7 7 +--R 4a b c d - 3b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (6a c d - 20a b c d + 4a b c d - 4a b c d + 20a b c d - 6a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 10 5 5 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 2 8 4 6 9 5 5 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 6 4 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 3 9 6 4 2 8 5 5 3 7 3 7 5 5 2 8 6 4 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 9 7 3 +--R - 4a b c d +--R * +--R x +--R + +--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 771 + +--S 772 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 773 + +)clear all + +--S 774 of 1092 +t0:=x^4/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 774 + +--S 775 of 1092 +r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ + (a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/_ + (d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-_ + 6*a^2*c^2*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R 12a b c d x + (24a b c d + 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 4 2 3 3 3 3 4 2 +--R (12a b c d + 48a b c d + 12a b c d )x + (24a b c d + 24a b c d )x +--R + +--R 4 2 4 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R - 12a b c d x + (- 24a b c d - 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (- 12a b c d - 48a b c d - 12a b c d )x +--R + +--R 4 2 3 3 3 3 4 2 4 2 4 2 +--R (- 24a b c d - 24a b c d )x - 12a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (- 2a b d + 10a b c d - 8a b c d + 8a b c d - 10a b c d + 2b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 2 +--R (- a d + 4a b c d + 13a b c d - 13a b c d - 4a b c d + b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (- 2a c d + 14a b c d + 4a b c d - 4a b c d - 14a b c d + 2a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 +--R - a c d + 8a b c d - 8a b c d + a b c +--R / +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 9 6 3 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 2 7 6 3 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 8 7 2 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R 12a b c d x + (24a b c d + 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 4 2 3 3 3 3 4 2 +--R (12a b c d + 48a b c d + 12a b c d )x + (24a b c d + 24a b c d )x +--R + +--R 4 2 4 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R - 12a b c d x + (- 24a b c d - 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (- 12a b c d - 48a b c d - 12a b c d )x +--R + +--R 4 2 3 3 3 3 4 2 4 2 4 2 +--R (- 24a b c d - 24a b c d )x - 12a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (- 2a b d + 10a b c d - 8a b c d + 8a b c d - 10a b c d + 2b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 2 +--R (- a d + 4a b c d + 13a b c d - 13a b c d - 4a b c d + b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (- 2a c d + 14a b c d + 4a b c d - 4a b c d - 14a b c d + 2a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 +--R - a c d + 8a b c d - 8a b c d + a b c +--R / +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 9 6 3 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 2 7 6 3 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 8 7 2 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 776 + +--S 777 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1092 +t0:=x^3/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 779 + +--S 780 of 1092 +r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ + 1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-_ + 3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/_ + (b*c-a*d)^5 +--R +--R +--R (2) +--R 2 3 4 4 2 3 4 +--R (- 6a b c d - 6a b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 6a b c d - 30a b c d - 30a b c d - 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 3 4 4 2 3 4 3 2 4 2 3 2 3 4 3 2 3 +--R (6a b c d + 6a b c d )x + (12a b c d + 24a b c d + 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (6a b c d + 30a b c d + 30a b c d + 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 4 4 3 2 3 +--R (- 6a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- a d - 4a b c d - 19a b c d + 19a b c d + 4a b c d + b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d - 14a b c d + 14a b c d + 2a b c )x - a c d - 9a b c d +--R + +--R 3 2 4 2 3 5 +--R 9a b c d + a b c +--R / +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 7 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 4 2 3 4 +--R (- 6a b c d - 6a b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 6a b c d - 30a b c d - 30a b c d - 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 3 4 4 2 3 4 3 2 4 2 3 2 3 4 3 2 3 +--R (6a b c d + 6a b c d )x + (12a b c d + 24a b c d + 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (6a b c d + 30a b c d + 30a b c d + 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 4 4 3 2 3 +--R (- 6a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- a d - 4a b c d - 19a b c d + 19a b c d + 4a b c d + b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d - 14a b c d + 14a b c d + 2a b c )x - a c d - 9a b c d +--R + +--R 3 2 4 2 3 5 +--R 9a b c d + a b c +--R / +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 7 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 781 + +--S 782 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +)clear all + +--S 784 of 1092 +t0:=x^2/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 784 + +--S 785 of 1092 +r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ + 1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+_ + (b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+_ + a^2*d^2)*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 4 +--R (2a b d + 8a b c d + 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (4a b d + 20a b c d + 20a b c d + 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (2a d + 16a b c d + 36a b c d + 16a b c d + 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (4a c d + 20a b c d + 20a b c d + 4a b c )x + 2a c d + 8a b c d +--R + +--R 2 2 4 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 4 +--R (- 2a b d - 8a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- 4a b d - 20a b c d - 20a b c d - 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 2a d - 16a b c d - 36a b c d - 16a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (- 4a c d - 20a b c d - 20a b c d - 4a b c )x - 2a c d - 8a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (2a b d + 6a b c d - 6a b c d - 2b c d)x +--R + +--R 4 4 3 3 3 3 4 4 2 +--R (3a d + 12a b c d - 12a b c d - 3b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 2 2 4 +--R (10a c d + 6a b c d - 6a b c d - 10a b c )x + 6a c d - 6a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 4 +--R (2a b d + 8a b c d + 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (4a b d + 20a b c d + 20a b c d + 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (2a d + 16a b c d + 36a b c d + 16a b c d + 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (4a c d + 20a b c d + 20a b c d + 4a b c )x + 2a c d + 8a b c d +--R + +--R 2 2 4 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 4 +--R (- 2a b d - 8a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- 4a b d - 20a b c d - 20a b c d - 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 2a d - 16a b c d - 36a b c d - 16a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (- 4a c d - 20a b c d - 20a b c d - 4a b c )x - 2a c d - 8a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (2a b d + 6a b c d - 6a b c d - 2b c d)x +--R + +--R 4 4 3 3 3 3 4 4 2 +--R (3a d + 12a b c d - 12a b c d - 3b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 2 2 4 +--R (10a c d + 6a b c d - 6a b c d - 10a b c )x + 6a c d - 6a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 786 + +--S 787 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 788 + +)clear all + +--S 789 of 1092 +t0:=x/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 789 + +--S 790 of 1092 +r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ + 1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-_ + 3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*_ + log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (- 6a b d - 6b c d )x + (- 12a b d - 24a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d - 30a b c d - 30a b c d - 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (6a b d + 6b c d )x + (12a b d + 24a b c d + 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b d + 30a b c d + 30a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 2 4 4 2 2 3 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d + 6b c d )x + (- 9a b d - 9a b c d + 9a b c d + 9b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (- 2a d - 14a b c d + 14a b c d + 2b c )x - a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d + a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (- 6a b d - 6b c d )x + (- 12a b d - 24a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d - 30a b c d - 30a b c d - 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (6a b d + 6b c d )x + (12a b d + 24a b c d + 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b d + 30a b c d + 30a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 2 4 4 2 2 3 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d + 6b c d )x + (- 9a b d - 9a b c d + 9a b c d + 9b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (- 2a d - 14a b c d + 14a b c d + 2b c )x - a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d + a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 791 + +--S 792 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 793 + +)clear all + +--S 794 of 1092 +t0:=1/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--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: Fraction(Polynomial(Integer)) +--E 794 + +--S 795 of 1092 +r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ + 1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_ + 6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 796 + +--S 797 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 798 + +)clear all + +--S 799 of 1092 +t0:=1/(x*(a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 7 2 3 3 2 6 2 3 2 2 3 2 5 +--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 4 3 2 2 2 2 3 3 +--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 2 3 3 +--R (3a c d + 3a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 799 + +--S 800 of 1092 +r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ + (a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/_ + (c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-_ + 5*a*b*c*d+10*a^2*d^2)*log(a+b*x)/(a^3*(b*c-a*d)^5)+_ + d^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^5) +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (- 2a b d + 10a b c d - 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (- 4a b d + 16a b c d - 20a b c d - 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (- 2a d + 2a b c d + 18a b c d - 70a b c d - 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (- 4a c d + 16a b c d - 20a b c d - 40a b c d )x - 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R 10a b c d - 20a b c d +--R * +--R log(d x + c) +--R + +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (20a b c d - 10a b c d + 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (40a b c d + 20a b c d - 16a b c d + 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (20a b c d + 70a b c d - 18a b c d - 2a b c d + 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (40a b c d + 20a b c d - 16a b c d + 4a b c )x + 20a b c d +--R + +--R 3 4 6 2 5 7 +--R - 10a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 7 5 2 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b c d + 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 6 7 +--R - 4a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R * +--R log(x) +--R + +--R 5 2 6 4 3 2 5 2 5 4 3 6 5 2 3 +--R (2a b c d - 10a b c d + 10a b c d - 2a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 4a b c d - 17a b c d - 5a b c d + 5a b c d + 17a b c d +--R + +--R 6 6 +--R - 4a b c d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (2a c d - 4a b c d - 16a b c d + 16a b c d + 4a b c d - 2a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 8 2 3 7 7 3 4 6 6 4 5 5 5 5 6 4 4 6 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 3 7 8 2 +--R - 2a b c d +--R * +--R 4 +--R x +--R + +--R 9 3 7 8 2 4 6 7 3 5 5 5 5 7 3 4 6 8 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 3 7 9 +--R - 4a b c d +--R * +--R 3 +--R x +--R + +--R 10 3 7 9 4 6 8 2 5 5 7 3 6 4 6 4 7 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 5 5 8 2 4 6 9 3 7 10 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 2 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 6 4 8 2 5 5 9 4 6 10 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (- 2a b d + 10a b c d - 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (- 4a b d + 16a b c d - 20a b c d - 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (- 2a d + 2a b c d + 18a b c d - 70a b c d - 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (- 4a c d + 16a b c d - 20a b c d - 40a b c d )x - 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R 10a b c d - 20a b c d +--R * +--R log(d x + c) +--R + +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (20a b c d - 10a b c d + 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (40a b c d + 20a b c d - 16a b c d + 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (20a b c d + 70a b c d - 18a b c d - 2a b c d + 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (40a b c d + 20a b c d - 16a b c d + 4a b c )x + 20a b c d +--R + +--R 3 4 6 2 5 7 +--R - 10a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 7 5 2 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b c d + 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 6 7 +--R - 4a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R * +--R log(x) +--R + +--R 5 2 6 4 3 2 5 2 5 4 3 6 5 2 3 +--R (2a b c d - 10a b c d + 10a b c d - 2a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 4a b c d - 17a b c d - 5a b c d + 5a b c d + 17a b c d +--R + +--R 6 6 +--R - 4a b c d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (2a c d - 4a b c d - 16a b c d + 16a b c d + 4a b c d - 2a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 8 2 3 7 7 3 4 6 6 4 5 5 5 5 6 4 4 6 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 3 7 8 2 +--R - 2a b c d +--R * +--R 4 +--R x +--R + +--R 9 3 7 8 2 4 6 7 3 5 5 5 5 7 3 4 6 8 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 3 7 9 +--R - 4a b c d +--R * +--R 3 +--R x +--R + +--R 10 3 7 9 4 6 8 2 5 5 7 3 6 4 6 4 7 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 5 5 8 2 4 6 9 3 7 10 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 2 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 6 4 8 2 5 5 9 4 6 10 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 801 + +--S 802 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 803 + +)clear all + +--S 804 of 1092 +t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 8 2 3 3 2 7 2 3 2 2 3 2 6 +--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 5 3 2 2 2 2 3 4 +--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 3 2 +--R (3a c d + 3a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 804 + +--S 805 of 1092 +r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ + (a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*_ + (c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-_ + 3*(b*c+a*d)*log(x)/(a^4*c^4)+3*b^4*(b^2*c^2-4*a*b*c*d+_ + 5*a^2*d^2)*log(a+b*x)/(a^4*(b*c-a*d)^5)-3*d^4*(5*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^5) +--R +--R +--R (2) +--R 6 2 8 5 3 7 4 4 2 6 5 +--R (6a b d - 24a b c d + 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 4 +--R (12a b d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 3 +--R (6a d - 60a b c d + 96a b c d + 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 2 +--R (12a c d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 2 6 7 3 5 6 2 4 4 +--R (6a c d - 24a b c d + 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 2 6 4 4 7 5 3 8 6 2 5 +--R (- 30a b c d + 24a b c d - 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 4 +--R (- 60a b c d - 12a b c d + 36a b c d - 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 3 +--R (- 30a b c d - 96a b c d + 60a b c d - 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 2 +--R (- 60a b c d - 12a b c d + 36a b c d - 12a b c )x +--R + +--R 4 4 6 2 3 5 7 2 6 8 +--R (- 30a b c d + 24a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 +--R - 6a b d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 8 6 2 +--R 6b c d +--R * +--R 5 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 12a b d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 12a b c d - 36a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 8 8 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 6a d + 60a b c d - 96a b c d + 96a b c d - 60a b c d +--R + +--R 8 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 12a c d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 12a b c d - 36a b c d + 12a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 +--R - 6a c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 2 6 8 +--R 6a b c +--R * +--R x +--R * +--R log(x) +--R + +--R 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 2 6 5 3 +--R - 6a b c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 7 6 2 +--R 6a b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 12a b c d + 39a b c d - 24a b c d + 24a b c d - 39a b c d +--R + +--R 7 7 +--R 12a b c d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 6a c d + 6a b c d + 40a b c d - 72a b c d + 72a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R - 40a b c d - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R (- 9a c d + 32a b c d - 31a b c d + 31a b c d - 32a b c d + 9a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R - 2a c d + 10a b c d - 20a b c d + 20a b c d - 10a b c d + 2a b c +--R / +--R 9 2 4 7 8 3 5 6 7 4 6 5 6 5 7 4 5 6 8 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 4 7 9 2 +--R - 2a b c d +--R * +--R 5 +--R x +--R + +--R 10 4 7 9 2 5 6 8 3 6 5 6 5 8 3 5 6 9 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 4 7 10 +--R - 4a b c d +--R * +--R 4 +--R x +--R + +--R 11 4 7 10 5 6 9 2 6 5 8 3 7 4 7 4 8 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 6 5 9 2 5 6 10 4 7 11 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 3 +--R x +--R + +--R 11 5 6 10 6 5 9 2 7 4 7 4 9 2 6 5 10 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 5 6 11 +--R - 4a b c +--R * +--R 2 +--R x +--R + +--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 +--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 8 5 3 7 4 4 2 6 5 +--R (6a b d - 24a b c d + 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 4 +--R (12a b d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 3 +--R (6a d - 60a b c d + 96a b c d + 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 2 +--R (12a c d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 2 6 7 3 5 6 2 4 4 +--R (6a c d - 24a b c d + 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 2 6 4 4 7 5 3 8 6 2 5 +--R (- 30a b c d + 24a b c d - 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 4 +--R (- 60a b c d - 12a b c d + 36a b c d - 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 3 +--R (- 30a b c d - 96a b c d + 60a b c d - 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 2 +--R (- 60a b c d - 12a b c d + 36a b c d - 12a b c )x +--R + +--R 4 4 6 2 3 5 7 2 6 8 +--R (- 30a b c d + 24a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 +--R - 6a b d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 8 6 2 +--R 6b c d +--R * +--R 5 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 12a b d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 12a b c d - 36a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 8 8 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 6a d + 60a b c d - 96a b c d + 96a b c d - 60a b c d +--R + +--R 8 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 12a c d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 12a b c d - 36a b c d + 12a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 +--R - 6a c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 2 6 8 +--R 6a b c +--R * +--R x +--R * +--R log(x) +--R + +--R 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 2 6 5 3 +--R - 6a b c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 7 6 2 +--R 6a b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 12a b c d + 39a b c d - 24a b c d + 24a b c d - 39a b c d +--R + +--R 7 7 +--R 12a b c d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 6a c d + 6a b c d + 40a b c d - 72a b c d + 72a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R - 40a b c d - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R (- 9a c d + 32a b c d - 31a b c d + 31a b c d - 32a b c d + 9a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R - 2a c d + 10a b c d - 20a b c d + 20a b c d - 10a b c d + 2a b c +--R / +--R 9 2 4 7 8 3 5 6 7 4 6 5 6 5 7 4 5 6 8 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 4 7 9 2 +--R - 2a b c d +--R * +--R 5 +--R x +--R + +--R 10 4 7 9 2 5 6 8 3 6 5 6 5 8 3 5 6 9 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 4 7 10 +--R - 4a b c d +--R * +--R 4 +--R x +--R + +--R 11 4 7 10 5 6 9 2 6 5 8 3 7 4 7 4 8 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 6 5 9 2 5 6 10 4 7 11 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 3 +--R x +--R + +--R 11 5 6 10 6 5 9 2 7 4 7 4 9 2 6 5 10 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 5 6 11 +--R - 4a b c +--R * +--R 2 +--R x +--R + +--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 +--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 806 + +--S 807 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 808 + +)clear all + +--S 809 of 1092 +t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1092 +r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ + a^2*sqrt(c+d*x)/(c*x) +--R +--R +--R +-------+ +--R 2 2 \|d x + c 2 2 +-+ +-------+ +--R (a d - 4a b c d)x atanh(----------) + (2b c x - a d)\|c \|d x + c +--R +-+ +--R \|c +--R (2) ------------------------------------------------------------------- +--R +-+ +--R c d x\|c +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4a b c d)x log(-----------------------------) +--R x +--R + +--R 2 2 +-+ +-------+ +--R (4b c x - 2a d)\|c \|d x + c +--R / +--R +-+ +--R 2c d x\|c +--R , +--R +---+ +-------+ +--R 2 2 \|- c \|d x + c 2 2 +---+ +-------+ +--R (a d - 4a b c d)x atan(----------------) + (2b c x - a d)\|- c \|d x + c +--R c +--R --------------------------------------------------------------------------] +--R +---+ +--R c d x\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 811 + +--S 812 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R 2 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4a b c)log(-----------------------------) +--R x +--R + +--R +-------+ +--R 2 \|d x + c +--R (- 2a d + 8a b c)atanh(----------) +--R +-+ +--R \|c +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +--R 2 +---+ \|d x + c +--R (- a d + 4a b c)\|- c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---+ +-------+ +--R 2 +-+ \|- c \|d x + c +--R (a d - 4a b c)\|c atan(----------------) +--R c +--R / +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 1092 +t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1092 +r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ + sqrt(c)/a^3-(4*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b*c-a*d)/(a^3*sqrt(b))-2*(b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|d x + c +--R ((a b d - 4b c)x + (a d - 4a b c)x)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 +-+ +-+ \|d x + c +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 +-+ +-------+ +--R ((a d - 2a b c)x - a c)\|b \|d x + c +--R / +--R 3 2 4 +-+ +--R (a b x + a x)\|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- a d + b c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R 2 2 2 +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 |a d - b c \|d x + c +--R ((2a b d - 8b c)x + (2a d - 8a b c)x) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R +-----------+ +--R 2 2 2 |- a d + b c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 2 +---+ \|d x + c +--R ((- 6a b d + 8b c)x + (- 6a d + 8a b c)x)\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R +-------+ +--R 2 2 2 +---+ \|d x + c +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 |a d - b c \|d x + c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 +-------+ +--R ((a d - 2a b c)x - a c)\|d x + c +--R / +--R 3 2 4 +--R a b x + a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 818 + +--S 819 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a d + b c +-+ +--R (a d - 4b c) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (3a d - 4b c)\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 8b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-+ +-+ \|d x + c +--R (6a d - 8b c)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a \|b +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (3a d - 4b c)\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 8b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-+ +-+ \|d x + c +--R (6a d - 8b c)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R +-+ |a d - b c \|d x + c +--R (2a d - 8b c)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a \|b +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1092 +t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1092 +r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-_ + 2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-+ +-+ \|b \|d x + c +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 +-----------+ \|d x + c +--R ((- a b d + 4b c)x + (- a d + 4a b c)x)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 +-----------+ +-+ +-------+ +--R (- 2a b x - a )\|- a d + b c \|c \|d x + c +--R / +--R 3 2 4 +-----------+ +-+ +--R (a b x + a x)\|- a d + b c \|c +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R ((a b d - 4b c)x + (a d - 4a b c)x) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 | b +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x) |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 +-+ +-------+ +--R (- 4a b x - 2a )\|c \|d x + c +--R / +--R 3 2 4 +-+ +--R (2a b x + 2a x)\|c +--R , +--R +--R 2 2 2 +--R ((a b d - 4b c)x + (a d - 4a b c)x) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 | b +-+ +--R ((- 6a b d + 8b c)x + (- 6a d + 8a b c)x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 +-+ +-------+ +--R (- 4a b x - 2a )\|c \|d x + c +--R / +--R 3 2 4 +-+ +--R (2a b x + 2a x)\|c +--R , +--R +--R +-----------+ +--R 2 2 2 +---+ | b +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +---+ +-------+ +--R 2 2 2 \|- c \|d x + c +--R ((- 2a b d + 8b c)x + (- 2a d + 8a b c)x)atan(----------------) +--R c +--R + +--R 2 +---+ +-------+ +--R (- 4a b x - 2a )\|- c \|d x + c +--R / +--R 3 2 4 +---+ +--R (2a b x + 2a x)\|- c +--R , +--R +--R +---+ +-------+ +--R 2 2 2 \|- c \|d x + c +--R ((- a b d + 4b c)x + (- a d + 4a b c)x)atan(----------------) +--R c +--R + +--R +---------+ +--R 2 2 2 +---+ | b +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 +---+ +-------+ +--R (- 2a b x - a )\|- c \|d x + c +--R / +--R 3 2 4 +---+ +--R (a b x + a x)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 825 + +--S 826 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4b c)\|- a d + b c log(-------------------------------) +--R x +--R + +--R +-----------+ +--R +-----------+ | b +-+ +--R (3a d - 4b c)\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ +-+ \|b \|d x + c +--R (- 6a d + 8b c)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-----------+ \|d x + c +--R (2a d - 8b c)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-----------+ +-+ +--R 2a \|- a d + b c \|c +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4b c)\|- a d + b c log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|b \|d x + c +--R (- 6a d + 8b c)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-----------+ \|d x + c +--R (2a d - 8b c)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R +-----------+ | b +-+ b\|d x + c +--R (- 6a d + 8b c)\|- a d + b c |--------- \|c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 3 +-----------+ +-+ +--R 2a \|- a d + b c \|c +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 829 + +)clear all + +--S 830 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|d x + c +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1092 +r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ + (4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*_ + (b*c-a*d)^(3/2))-b*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*c*(b*c-a*d)*(a+b*x))-_ + sqrt(c+d*x)/(a*c*x*(a+b*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +--R +-----------+ \|d x + c +--R \|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 3 2 +-----------+ +-+ +-------+ +--R ((- a b d + 2a b c)x - a d + a b c)\|- a d + b c \|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((a b c d - a b c )x + (a c d - a b c )x)\|- a d + b c \|c +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 3 2 2 2 2 2 | b +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x) |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|c +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 | b +-+ +--R ((10a b c d - 8b c )x + (10a b c d - 8a b c )x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|c +--R , +--R +--R +-----------+ +--R 2 3 2 2 2 2 2 +---+ | b +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2a b d + 6a b c d - 8b c )x + (2a d + 6a b c d - 8a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|- c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|- c +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 +---+ | b +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- a b d + 2a b c)x - a d + a b c)\|- c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((a b c d - a b c )x + (a c d - a b c )x)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 832 + +--S 833 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +-+ +--R (5a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2c\|d x + c + (d x + 2c)\|c +--R (a d + 3a b c d - 4b c )\|- a d + b c log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|b \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 3 2 +-----------+ +-+ +--R (2a c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2c\|d x + c + (d x + 2c)\|c +--R (a d + 3a b c d - 4b c )\|- a d + b c log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|b \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 2 2 +-----------+ | b +-+ +--R (10a b c d - 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 4 3 2 +-----------+ +-+ +--R (2a c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 836 + +)clear all + +--S 837 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1092 +r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ + (4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a^3*(b*c-a*d)^(5/2))-d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/_ + (a^2*c^2*(b*c-a*d)^2*sqrt(c+d*x))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*_ + (a+b*x)*sqrt(c+d*x))+(-1)/(a*c*x*(a+b*x)*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 2 4 3 2 2 2 2 3 3 +-+ +-+ +-------+ +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x)\|b \|c \|d x + c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|d x + c +--R \|- a d + b c \|d x + c atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 2a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3 +--R (- 3a d + a b c d + a b c d - 2a b c )x - a c d + 2a b c d - a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((a b c d - 2a b c d + a b c )x + (a c d - 2a b c d + a b c )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|c \|d x + c +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 | b +-+ +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x) |- --------- \|c +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +-+ +--R \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 | b +-+ +--R ((- 14a b c d + 8b c )x + (- 14a b c d + 8a b c )x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R +-------+ b\|d x + c +--R \|d x + c atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +-+ +--R \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | b +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (6a b d - 4a b c d - 10a b c d + 8b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (6a d - 4a b c d - 10a b c d + 8a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +---+ +--R \|- c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | b +--R ((- 7a b c d + 4b c )x + (- 7a b c d + 4a b c )x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R +-------+ b\|d x + c +--R \|d x + c atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 2a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 3a d + a b c d + a b c d - 2a b c )x - a c d + 2a b c d +--R + +--R 2 2 3 +--R - a b c +--R * +--R +---+ +--R \|- c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((a b c d - 2a b c d + a b c )x + (a c d - 2a b c d + a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 839 + +--S 840 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3a d - 2a b c d - 5a b c d + 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 3 3 +-----------+ | b +-+ +--R (7a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|b \|d x + c +--R (- 14a b c d + 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|d x + c +--R (- 6a d + 4a b c d + 10a b c d - 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3a d - 2a b c d - 5a b c d + 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|b \|d x + c +--R (- 14a b c d + 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|d x + c +--R (- 6a d + 4a b c d + 10a b c d - 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 2 2 3 3 +-----------+ | b +-+ +--R (- 14a b c d + 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 843 + +)clear all + +--S 844 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1092 +r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ + (c+d*x)^(3/2))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+_ + (-1)/(a*c*x*(a+b*x)*(c+d*x)^(3/2))+(4*b*c+5*a*d)*atanh(sqrt(c+d*x)/_ + sqrt(c))/(a^3*c^(7/2))-b^(7/2)*(4*b*c-9*a*d)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(7/2))-d*(2*b*c-a*d)*_ + (b^2*c^2-a*b*c*d+5*a^2*d^2)/(a^2*c^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (- 27a b c d + 12b c d)x + (- 27a b c d - 15a b c d + 12b c )x +--R + +--R 2 3 4 4 5 +--R (- 27a b c d + 12a b c )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|b \|d x + c +--R \|b \|c \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d - 12b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|d x + c +--R \|- a d + b c \|d x + c atanh(----------) +--R +-+ +--R \|c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15a b d + 33a b c d - 9a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15a d + 13a b c d + 35a b c d - 15a b c d + 12a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 5 2 3 +--R (- 20a c d + 41a b c d - 9a b c d - 3a b c d + 6a b c )x - 3a c d +--R + +--R 4 3 2 3 2 4 2 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3a b c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|c \|d x + c +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +-----------+ +--R | b +-+ +-------+ +--R |- --------- \|c \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +--R \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (54a b c d - 24b c d)x + (54a b c d + 30a b c d - 24b c )x +--R + +--R 2 3 4 4 5 +--R (54a b c d - 24a b c )x +--R * +--R +---------+ +-------+ +--R | b +-+ +-------+ b\|d x + c +--R |--------- \|c \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +--R \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +-----------+ +--R +---+ | b +-------+ +--R \|- c |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (30a b d - 66a b c d + 18a b c d + 42a b c d - 24b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 30a d - 36a b c d - 48a b c d + 60a b c d + 18a b c d +--R + +--R 5 5 +--R - 24b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (30a c d - 66a b c d + 18a b c d + 42a b c d - 24a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +---+ +--R \|- c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +---------+ +-------+ +--R +---+ | b +-------+ b\|d x + c +--R \|- c |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15a b d + 33a b c d - 9a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15a d + 13a b c d + 35a b c d - 15a b c d + 12a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 20a c d + 41a b c d - 9a b c d - 3a b c d + 6a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3a c d + 9a b c d - 9a b c d + 3a b c +--R * +--R +---+ +--R \|- c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3a b c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 846 + +--S 847 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 4 4 +-----------+ | b +-+ +--R (9a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5a d - 11a b c d + 3a b c d + 7a b c d - 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|b \|d x + c +--R (18a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10a d + 22a b c d - 6a b c d - 14a b c d + 8b c )\|- a d + b c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5a d - 11a b c d + 3a b c d + 7a b c d - 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|b \|d x + c +--R (18a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10a d + 22a b c d - 6a b c d - 14a b c d + 8b c )\|- a d + b c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 3 3 4 4 +-----------+ | b +-+ +--R (18a b c d - 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1092 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1092 +r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ + 495*a^2*b*c*d^2-693*a^3*d^3)*(c+d*x)^(5/2)/(b^4*d^3)-2/693*_ + (20*b^2*c^2+55*a*b*c*d-99*a^2*d^2)*x*(c+d*x)^(5/2)/(b^3*d^2)+_ + 2/99*(5*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*d)+2/11*x^3*(c+d*x)^(5/2)/b+_ + 2*a^3*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)-_ + 2*a^3*(b*c-a*d)^2*sqrt(c+d*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 +-----------+ +--R (6930a d - 13860a b c d + 6930a b c d )\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d + 220a b c d +--R + +--R 5 5 +--R 80b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 6 3 +-+ +--R 3465b d \|b +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 5 5 4 4 3 2 2 3 |- a d + b c +--R (3465a d - 6930a b c d + 3465a b c d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d +--R + +--R 4 4 5 5 +--R 220a b c d + 80b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 3 +--R 3465b d +--R , +--R +--R +---------+ +-------+ +--R 5 5 4 4 3 2 2 3 |a d - b c \|d x + c +--R (6930a d - 13860a b c d + 6930a b c d ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d +--R + +--R 4 4 5 5 +--R 220a b c d + 80b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 3 +--R 3465b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 853 + +--S 854 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 2 4 3 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 2 4 3 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 2 4 3 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 5 2 4 3 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1092 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1092 +r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ + 2/63*(2*b*c+9*a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*x*(c+d*x)^(7/2)/(b*d)-_ + 2*a^2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/b^(11/2)+2*a^2*(b*c-a*d)^2*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 +-----------+ +--R (- 630a d + 1260a b c d - 630a b c d )\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 2 +-+ +--R 315b d \|b +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 4 4 3 3 2 2 2 2 |- a d + b c +--R (315a d - 630a b c d + 315a b c d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 2 +--R 315b d +--R , +--R +--R +---------+ +-------+ +--R 4 4 3 3 2 2 2 2 |a d - b c \|d x + c +--R (- 630a d + 1260a b c d - 630a b c d ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 2 +--R 315b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 860 + +--S 861 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 2 3 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 4 2 3 2 2 2 +-+ |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1092 +t0:=x*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1092 +r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ + 2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (210a d - 420a b c d + 210a b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 4 +-+ +--R 105b d\|b +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 2 2 |- a d + b c +--R (105a d - 210a b c d + 105a b c d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 105b d +--R , +--R +--R +---------+ +-------+ +--R 3 3 2 2 2 2 |a d - b c \|d x + c +--R (210a d - 420a b c d + 210a b c d) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 105b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 867 + +--S 868 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1092 +t0:=(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1092 +r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*_ + sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 30a d + 60a b c d - 30b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (15a d - 30a b c d + 15b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 30a d + 60a b c d - 30b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 874 + +--S 875 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 878 + +)clear all + +--S 879 of 1092 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 +--R b x + a x +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1092 +r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (6a d - 12a b c d + 6b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R - 6b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 +-+ +-------+ +--R (2a b d x - 6a d + 14a b c d)\|b \|d x + c +--R / +--R 2 +-+ +--R 3a b \|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (3a d - 6a b c d + 3b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R 3b c \|c log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R 3b c \|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (6a d - 12a b c d + 6b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (3a d - 6a b c d + 3b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 +---+ \|d x + c 2 2 2 +-------+ +--R - 6b c \|- c atan(----------) + (2a b d x - 6a d + 14a b c d)\|d x + c +--R +---+ +--R \|- c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-------+ +--R 2 2 +---+ \|d x + c +--R - 6b c \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (6a d - 12a b c d + 6b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 881 + +--S 882 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1092 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 3 2 +--R b x + a x +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1092 +r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ + atanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+_ + d*(b*c+2*a*d)*sqrt(c+d*x)/(a*b) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )x\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (- 5a b c d + 2b c )x\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 +-+ +-------+ +--R (2a d x - a b c )\|b \|d x + c +--R / +--R 2 +-+ +--R a b x\|b +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (2a d - 4a b c d + 2b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )x\|c log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4a d x - 2a b c )\|d x + c +--R / +--R 2 +--R 2a b x +--R , +--R +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )x\|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 4a d + 8a b c d - 4b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (4a d x - 2a b c )\|d x + c +--R / +--R 2 +--R 2a b x +--R , +--R +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (a d - 2a b c d + b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 +---+ \|d x + c 2 2 2 +-------+ +--R (- 5a b c d + 2b c )x\|- c atan(----------) + (2a d x - a b c )\|d x + c +--R +---+ +--R \|- c +--R / +--R 2 +--R a b x +--R , +--R +--R +-------+ +--R 2 2 +---+ \|d x + c +--R (- 5a b c d + 2b c )x\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a d x - a b c )\|d x + c +--R / +--R 2 +--R a b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 888 + +--S 889 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (2a d - 4a b c d + 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (4a d - 8a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 4b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (4a d - 8a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 4b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 4a d + 8a b c d - 4b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1092 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 4 3 +--R b x + a x +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1092 +r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*_ + atanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^3-1/4*d*(4*b*c-7*a*d)*_ + sqrt(c+d*x)/a^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 +-----------+ \|b \|d x + c +--R (8a d - 16a b c d + 8b c )x \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 2 +-+ +-+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 2 +-+ +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|b \|d x + c +--R / +--R 3 2 +-+ +--R 4a x \|b +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 |- a d + b c +--R (8a d - 16a b c d + 8b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )x \|c log(----------------------------) +--R x +--R + +--R 2 2 2 2 +-------+ +--R ((- 18a c d + 8a b c )x - 4a c )\|d x + c +--R / +--R 3 2 +--R 8a x +--R , +--R +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )x \|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 |a d - b c \|d x + c +--R (16a d - 32a b c d + 16b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 +-------+ +--R ((- 18a c d + 8a b c )x - 4a c )\|d x + c +--R / +--R 3 2 +--R 8a x +--R , +--R +--R +-----------+ +--R 2 2 2 2 2 |- a d + b c +--R (4a d - 8a b c d + 4b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 2 2 2 +---+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 2 +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|d x + c +--R / +--R 3 2 +--R 4a x +--R , +--R +--R +-------+ +--R 2 2 2 2 2 +---+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 |a d - b c \|d x + c +--R (8a d - 16a b c d + 8b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|d x + c +--R / +--R 3 2 +--R 4a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 895 + +--S 896 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (8a d - 16a b c d + 8b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 16a d + 32a b c d - 16b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 40a b c d + 16b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 16a d + 32a b c d - 16b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 40a b c d + 16b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (16a d - 32a b c d + 16b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1092 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 5 4 +--R b x + a x +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1092 +r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*_ + atanh(sqrt(c+d*x)/sqrt(c))/(a^4*sqrt(c))-1/8*(4*b*c-5*a*d)*_ + (2*b*c-a*d)*sqrt(c+d*x)/(a^3*x) +--R +--R +--R (2) +--R 2 2 2 2 3 +-----------+ +-+ +-+ +--R (- 48a d + 96a b c d - 48b c )x \|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 3 \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x - 8a c ) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 24a x \|c +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 3 3 +--R (15a d - 90a b c d + 120a b c d - 48b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 3 | 2 +-+ +--R (48a d - 96a b c d + 48b c )x \|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 66a d + 108a b c d - 48a b c )x + (- 52a c d + 24a b c )x +--R + +--R 3 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 48a x \|c +--R , +--R +--R 3 3 2 2 2 2 3 3 3 +--R (15a d - 90a b c d + 120a b c d - 48b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 2 3 +-+ | 2 +--R (- 96a d + 192a b c d - 96b c )x \|c \|a b d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 66a d + 108a b c d - 48a b c )x + (- 52a c d + 24a b c )x +--R + +--R 3 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 48a x \|c +--R , +--R +--R +-------------+ +--R 2 2 2 2 3 | 2 +---+ +--R (24a d - 48a b c d + 24b c )x \|- a b d + b c \|- c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R +---+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|- c \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atan(----------------) +--R c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x +--R + +--R 3 2 +--R - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 4 3 +---+ +--R 24a x \|- c +--R , +--R +--R +---+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|- c \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atan(----------------) +--R c +--R + +--R +-----------+ +--R 2 2 2 2 3 +---+ | 2 +--R (- 48a d + 96a b c d - 48b c )x \|- c \|a b d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x +--R + +--R 3 2 +--R - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 4 3 +---+ +--R 24a x \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 902 + +--S 903 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 30a b c d + 40a b c d - 16b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +-+ +--R (16a d - 32a b c d + 16b c )\|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ +-+ +-+ \|b \|d x + c +--R (32a d - 64a b c d + 32b c )\|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 60a b c d + 80a b c d - 32b c )atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 30a b c d + 40a b c d - 16b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ +-+ +-+ \|b \|d x + c +--R (32a d - 64a b c d + 32b c )\|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 60a b c d + 80a b c d - 32b c )atanh(----------) +--R +-+ +--R \|c +--R + +--R +-----------+ +-------+ +--R 2 2 2 2 +-+ | 2 b\|d x + c +--R (- 32a d + 64a b c d - 32b c )\|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R / +--R 4 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1092 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1092 +r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ + 180*a*b*c*d-693*a^2*d^2)*(c+d*x)^(5/2)/(b^4*d^2)+_ + 1/63*(10*b*c-99*a*d)*x*(c+d*x)^(5/2)/(b^3*d)+11/9*x^2*(c+d*x)^(5/2)/_ + b^2-x^3*(c+d*x)^(5/2)/(b*(a+b*x))-a^2*(6*b*c-11*a*d)*(b*c-a*d)^(3/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)+a^2*(6*b*c-11*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/b^6 +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (- 3465a b d + 5355a b c d - 1890a b c d )x - 3465a d +--R + +--R 4 3 3 2 2 2 +--R 5355a b c d - 1890a b c d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b d x + (- 110a b d + 190b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (198a b d - 350a b c d + 150b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 462a b d + 846a b c d - 390a b c d + 10b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (2310a b d - 4494a b c d + 2358a b c d - 170a b c d - 20b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6510a b c d + 3213a b c d - 180a b c d - 20a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 7 2 6 2 +-+ +--R (315b d x + 315a b d )\|b +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (3465a b d - 5355a b c d + 1890a b c d )x + 3465a d +--R + +--R 4 3 3 2 2 2 +--R - 5355a b c d + 1890a b c d +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 140b d x + (- 220a b d + 380b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (396a b d - 700a b c d + 300b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 924a b d + 1692a b c d - 780a b c d + 20b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (4620a b d - 8988a b c d + 4716a b c d - 340a b c d - 40b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 6930a d - 13020a b c d + 6426a b c d - 360a b c d - 40a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 7 2 6 2 +--R 630b d x + 630a b d +--R , +--R +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (- 3465a b d + 5355a b c d - 1890a b c d )x - 3465a d +--R + +--R 4 3 3 2 2 2 +--R 5355a b c d - 1890a b c d +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b d x + (- 110a b d + 190b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (198a b d - 350a b c d + 150b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 462a b d + 846a b c d - 390a b c d + 10b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (2310a b d - 4494a b c d + 2358a b c d - 170a b c d - 20b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6510a b c d + 3213a b c d - 180a b c d - 20a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 7 2 6 2 +--R 315b d x + 315a b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 909 + +--S 910 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 2 3 2 2 2 |- a d + b c +-+ +--R (11a d - 17a b c d + 6a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (22a d - 34a b c d + 12a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 6 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (11a d - 17a b c d + 6a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 4 2 3 2 2 2 +-+ |a d - b c \|d x + c +--R (- 11a d + 17a b c d - 6a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 913 + +)clear all + +--S 914 of 1092 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1092 +r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ + (c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-_ + a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*_ + (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(11/2)-_ + a*(4*b*c-9*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 3 4 3 3 4 2 3 +--R 30b d x + (- 54a b d + 90b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (126a b d - 218a b c d + 90b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 630a b d + 1162a b c d - 554a b c d + 30b c )x - 945a d +--R + +--R 3 2 2 2 2 3 3 +--R 1680a b c d - 749a b c d + 30a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 6 5 +-+ +--R (105b d x + 105a b d)\|b +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 60b d x + (- 108a b d + 180b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (252a b d - 436a b c d + 180b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 1260a b d + 2324a b c d - 1108a b c d + 60b c )x - 1890a d +--R + +--R 3 2 2 2 2 3 3 +--R 3360a b c d - 1498a b c d + 60a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 5 +--R 210b d x + 210a b d +--R , +--R +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 4 3 4 3 3 4 2 3 +--R 30b d x + (- 54a b d + 90b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (126a b d - 218a b c d + 90b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 630a b d + 1162a b c d - 554a b c d + 30b c )x - 945a d +--R + +--R 3 2 2 2 2 3 3 +--R 1680a b c d - 749a b c d + 30a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 5 +--R 105b d x + 105a b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 916 + +--S 917 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 2 2 2 |- a d + b c +-+ +--R (9a d - 13a b c d + 4a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 18a d + 26a b c d - 8a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 9a d + 13a b c d - 4a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 2 2 2 2 +-+ |a d - b c \|d x + c +--R (9a d - 13a b c d + 4a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 1092 +t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1092 +r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ + (b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*_ + (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+_ + (2*b*c-7*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 +--R (- 105a b d + 135a b c d - 30b c )x - 105a d + 135a b c d +--R + +--R 2 2 +--R - 30a b c +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 14a b d + 22b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (70a b d - 118a b c d + 46b c )x + 105a d - 170a b c d + 61a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 2 +--R (105a b d - 135a b c d + 30b c )x + 105a d - 135a b c d +--R + +--R 2 2 +--R 30a b c +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 2 2 3 2 +--R 12b d x + (- 28a b d + 44b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (140a b d - 236a b c d + 92b c )x + 210a d - 340a b c d + 122a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 2 +--R (- 105a b d + 135a b c d - 30b c )x - 105a d + 135a b c d +--R + +--R 2 2 +--R - 30a b c +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 14a b d + 22b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (70a b d - 118a b c d + 46b c )x + 105a d - 170a b c d + 61a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 923 + +--S 924 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (7a d - 9a b c d + 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (14a d - 18a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (7a d - 9a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 7a d + 9a b c d - 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1092 +t0:=(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1092 +r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*_ + sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b d - 15b c d)x + 15a d - 15a b c d)\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b d x + (- 10a b d + 14b c d)x - 15a d + 20a b c d - 3b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d x + (- 20a b d + 28b c d)x - 30a d + 40a b c d - 6b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R +---------+ +--R 2 2 2 2 |a d - b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |--------- +--R \| b +--R * +--R +-------+ +--R \|d x + c +--R atan(------------) +--R +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2b d x + (- 10a b d + 14b c d)x - 15a d + 20a b c d - 3b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 930 + +--S 931 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a d + b c +-+ +--R (5a d - 5b c d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 10a d + 10b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 5a d + 5b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-+ |a d - b c \|d x + c +--R (5a d - 5b c d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1092 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1092 +r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ + atanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_ + d*(b*c-3*a*d)*sqrt(c+d*x)/(a*b^2) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 2 2 2 +-+ +-+ \|d x + c +--R (- 2b c x - 2a b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 3 2 2 2 2 +-+ +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|b \|d x + c +--R / +--R 2 3 3 2 +-+ +--R (a b x + a b )\|b +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3a b d - a b c d - 2b c )x + 3a d - a b c d - 2a b c ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (2b c x + 2a b c )\|c log(----------------------------) +--R x +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (4a b d x + 6a d - 4a b c d + 2a b c )\|d x + c +--R / +--R 2 3 3 2 +--R 2a b x + 2a b +--R , +--R +--R +-+ +-------+ +--R 3 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (b c x + a b c )\|c log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|d x + c +--R / +--R 2 3 3 2 +--R a b x + a b +--R , +--R +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3a b d - a b c d - 2b c )x + 3a d - a b c d - 2a b c ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-------+ +--R 3 2 2 2 +---+ \|d x + c +--R (- 4b c x - 4a b c )\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (4a b d x + 6a d - 4a b c d + 2a b c )\|d x + c +--R / +--R 2 3 3 2 +--R 2a b x + 2a b +--R , +--R +--R +-------+ +--R 3 2 2 2 +---+ \|d x + c +--R (- 2b c x - 2a b c )\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|d x + c +--R / +--R 2 3 3 2 +--R a b x + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 937 + +--S 938 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (3a d - a b c d - 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R 2b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (6a d - 2a b c d - 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 4b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 2 +-+ +--R 2a b \|b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (3a d - a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 3a d + a b c d + 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 941 + +)clear all + +--S 942 of 1092 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1092 +r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ + (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-_ + c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 2 +-+ +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c +--R / +--R 3 2 2 4 +-+ +--R (a b x + a b x)\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1092 +r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ + c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ + (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))+_ + d*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*b) +--R +--R +--R (3) +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 2 +-+ +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c +--R / +--R 3 2 2 4 +-+ +--R (a b x + a b x)\|b +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R [ +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 2 +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 3 2 2 2 2 2 +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2a b d + 6a b c d - 8b c )x + (2a d + 6a b c d - 8a b c )x) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 2 +---+ +--R ((- 10a b c d + 8b c )x + (- 10a b c d + 8a b c )x)\|- c +--R * +--R +-------+ +--R \|d x + c +--R atan(----------) +--R +---+ +--R \|- c +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 3 2 2 2 2 2 +---+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|- c +--R * +--R +-------+ +--R \|d x + c +--R atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|d x + c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 945 + +--S 946 of 1092 +m0a:=a0.1-r0a +--R +--R +--R (5) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d + 3a b c d - 4b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1092 +m0b:=a0.1-r0b +--R +--R +--R (7) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d + 3a b c d - 4b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1092 +m0c:=a0.2-r0a +--R +--R +--R (9) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d + 6a b c d - 8b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1092 +d0c:=D(m0c,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1092 +m0d:=a0.2-r0b +--R +--R +--R (11) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d + 6a b c d - 8b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1092 +d0d:=D(m0d,x) +--R +--R +--R (12) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1092 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1092 +r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ + (a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*_ + atanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^4+1/4*(12*b*c-11*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +-+ +-+ \|d x + c +--R \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +-+ +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +-+ +--R (4a b x + 4a x )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 3 2 3 +--R (15a b d - 40a b c d + 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (15a d - 40a b c d + 24a b c )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|c \|d x + c + d x + 2c +--R \|c log(----------------------------) +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((8a d - 34a b c d + 24a b c )x + (- 18a c d + 12a b c )x - 4a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 8a b x + 8a x +--R , +--R +--R 2 2 2 3 2 3 +--R (15a b d - 40a b c d + 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (15a d - 40a b c d + 24a b c )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|c \|d x + c + d x + 2c +--R \|c log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((8a b d - 56a b c d + 48b c )x + (8a d - 56a b c d + 48a b c )x ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((8a d - 34a b c d + 24a b c )x + (- 18a c d + 12a b c )x - 4a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 8a b x + 8a x +--R , +--R +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 14a b c d + 12b c )x + (2a d - 14a b c d + 12a b c )x ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +---+ \|d x + c +--R \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 4a b x + 4a x +--R , +--R +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +---+ \|d x + c +--R \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 4a b x + 4a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (4a d - 28a b c d + 24b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 40a b c d + 24b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 8a d + 56a b c d - 48b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 80a b c d + 48b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 40a b c d + 24b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 8a d + 56a b c d - 48b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 80a b c d + 48b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (8a d - 56a b c d + 48b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1092 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1092 +r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ + (a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-_ + 120*a*b^2*c^2*d+60*a^2*b*c*d^2-5*a^3*d^3)*atanh(sqrt(c+d*x)/_ + sqrt(c))/(a^5*sqrt(c))-1/8*b*(32*b^2*c^2-52*a*b*c*d+19*a^2*d^2)*_ + sqrt(c+d*x)/(a^4*(a+b*x))-1/8*(16*b^2*c^2-22*a*b*c*d+5*a^2*d^2)*_ + sqrt(c+d*x)/(a^3*x*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (- 72a b d + 264a b c d - 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 72a d + 264a b c d - 192a b c )x +--R * +--R +-+ +-------+ +--R +-----------+ +-+ +-+ \|b \|d x + c +--R \|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (24a b x + 24a x )\|c +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 4 +--R (15a b d - 180a b c d + 360a b c d - 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (15a d - 180a b c d + 360a b c d - 192a b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 2 4 +--R (72a b d - 264a b c d + 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (72a d - 264a b c d + 192a b c )x +--R * +--R +-------------+ +--R | 2 +-+ +--R \|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 2 3 2 3 +--R (- 114a b d + 312a b c d - 192a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 +--R (- 66a d + 164a b c d - 96a b c )x + (- 52a c d + 32a b c )x +--R + +--R 4 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (48a b x + 48a x )\|c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 4 +--R (15a b d - 180a b c d + 360a b c d - 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (15a d - 180a b c d + 360a b c d - 192a b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 2 4 +--R (- 144a b d + 528a b c d - 384b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 144a d + 528a b c d - 384a b c )x +--R * +--R +-----------+ +-------+ +--R +-+ | 2 b\|d x + c +--R \|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 3 2 3 +--R (- 114a b d + 312a b c d - 192a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 +--R (- 66a d + 164a b c d - 96a b c )x + (- 52a c d + 32a b c )x +--R + +--R 4 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (48a b x + 48a x )\|c +--R , +--R +--R 2 2 2 3 2 4 +--R (36a b d - 132a b c d + 96b c )x +--R + +--R 3 2 2 2 2 3 +--R (36a d - 132a b c d + 96a b c )x +--R * +--R +-------------+ +--R | 2 +---+ +--R \|- a b d + b c \|- c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 5 4 6 3 +---+ +--R (24a b x + 24a x )\|- c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 2 2 2 3 2 4 +--R (- 72a b d + 264a b c d - 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 72a d + 264a b c d - 192a b c )x +--R * +--R +-----------+ +-------+ +--R +---+ | 2 b\|d x + c +--R \|- c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 5 4 6 3 +---+ +--R (24a b x + 24a x )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 60a b c d + 120a b c d - 64b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +-+ +--R (24a d - 88a b c d + 64b c )\|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (48a d - 176a b c d + 128b c )\|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 120a b c d + 240a b c d - 128b c )atanh(----------) +--R +-+ +--R \|c +--R / +--R 5 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 60a b c d + 120a b c d - 64b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (48a d - 176a b c d + 128b c )\|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 120a b c d + 240a b c d - 128b c )atanh(----------) +--R +-+ +--R \|c +--R + +--R +-----------+ +-------+ +--R 2 2 2 2 +-+ | 2 b\|d x + c +--R (- 48a d + 176a b c d - 128b c )\|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R / +--R 5 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1092 +t0:=x^3*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R 3 +-------+ +-------+ +--R (1) x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1092 +r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-_ + 1/960*(105*b^3*c^3-5*a*b^2*c^2*d-17*a^2*b*c*d^2-35*a^3*d^3)*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d^4)-1/240*(4*a*c-35*b*c^2/d+_ + 7*a^2*d/b)*x*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)-1/40*(7*b*c-a*d)*x^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)+1/5*x^3*(c+d*x)^(3/2)*_ + sqrt(a+b*x)/d+1/128*(7*b^4*c^4+2*a*b^3*c^3*d-2*a^3*b*c*d^3-_ + 7*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (105a d - 75a b c d - 30a b c d - 30a b c d - 75a b c d + 105b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 48b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 16a b c d - 56b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 22a b c d - 22a b c d + 70b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 40a b c d + 34a b c d + 40a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 4 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1092 +--a0:=integrate(t0,x) +--E 970 + +--S 971 of 1092 +--m0:=a0-r0 +--E 971 + +--S 972 of 1092 +--d0:=D(m0,x) +--E 972 + +)clear all + +--S 973 of 1092 +t0:=x^2*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1092 +r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ + (a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*_ + (4*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/32*(4*a*b*c*d-5*(b*c+a*d)^2)*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)-1/64*(b*c-a*d)*_ + (4*a*b*c*d-5*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 8b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b d + 4a b c d - 10b c d)x + 15a d - 7a b c d - 7a b c d +--R + +--R 3 3 +--R 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1092 +--a0:=integrate(t0,x) +--E 975 + +--S 976 of 1092 +--m0:=a0-r0 +--E 976 + +--S 977 of 1092 +--d0:=D(m0,x) +--E 977 + +)clear all + +--S 978 of 1092 +t0:=x*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R +-------+ +-------+ +--R (1) x\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1092 +r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ + 1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*_ + (a^2/b^2-c^2/d^2)*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 3a b c d - 3a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 2b c d)x - 3a d + 2a b c d - 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1092 +--a0:=integrate(t0,x) +--E 980 + +--S 981 of 1092 +--m0:=a0-r0 +--E 981 + +--S 982 of 1092 +--d0:=D(m0,x) +--E 982 + +)clear all + +--S 983 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R +-------+ +-------+ +--R (1) \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1092 +r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d + 2a b c d - b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d + b c)\|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b d\|b \|d +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1092 +--a0:=integrate(t0,x) +--E 985 + +--S 986 of 1092 +--m0:=a0-r0 +--E 986 + +--S 987 of 1092 +--d0:=D(m0,x) +--E 987 + +)clear all + +--S 988 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R x +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1092 +r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ + (b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-+ +-+ \|c \|b x + a +--R (a d + b c)atanh(--------------) - 2\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +-+ +-------+ +--R \|b \|d x + c \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 990 + +--S 991 of 1092 +--m0:=a0-r0 +--E 991 + +--S 992 of 1092 +--d0:=D(m0,x) +--E 992 + +)clear all + +--S 993 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1092 +r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (sqrt(a)*sqrt(c))+2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-+ +-+ \|d \|b x + a +--R 2x\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R / +--R +-+ +-+ +--R x\|a \|c +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1092 +--a0:=integrate(t0,x) +--E 995 + +--S 996 of 1092 +--m0:=a0-r0 +--E 996 + +--S 997 of 1092 +--d0:=D(m0,x) +--E 997 + +)clear all + +--S 998 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1092 +r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-_ + 1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (a d - 2a b c d + b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((- a d - b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a c x \|a \|c +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1092 +--a0:=integrate(t0,x) +--E 1000 + +--S 1001 of 1092 +--m0:=a0-r0 +--E 1001 + +--S 1002 of 1092 +--d0:=D(m0,x) +--E 1002 + +)clear all + +--S 1003 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1092 +r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ + sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/x^3-_ + 1/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+_ + 1/24*(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (- 3a d + 3a b c d + 3a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R ((3a d - 2a b c d + 3b c )x + (- 2a c d - 2a b c )x - 8a c )\|a \|c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 2 3 +-+ +-+ +--R 24a c x \|a \|c +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1092 +--a0:=integrate(t0,x) +--E 1005 + +--S 1006 of 1092 +--m0:=a0-r0 +--E 1006 + +--S 1007 of 1092 +--d0:=D(m0,x) +--E 1007 + +)clear all + +--S 1008 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1092 +r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ + 1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a*c*x^3)+1/96*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^2)-1/192*(b*c+a*d)*_ + (15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (15a d - 12a b c d - 6a b c d - 12a b c d + 15b c )x +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 7a b c d + 7a b c d - 15b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (10a c d - 4a b c d + 10a b c )x + (- 8a c d - 8a b c )x - 48a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 3 4 +-+ +-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1092 +--a0:=integrate(t0,x) +--E 1010 + +--S 1011 of 1092 +--m0:=a0-r0 +--E 1011 + +--S 1012 of 1092 +--d0:=D(m0,x) +--E 1012 + +)clear all + +--S 1013 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1092 +r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ + atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-_ + 1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a*c*x^4)+1/240*(7*b^2*c^2-2*a*b*c*d+7*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^3)-1/960*(b*c+a*d)*_ + (35*b^2*c^2-46*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_ + (a^3*c^3*x^2)+1/1920*(105*b^4*c^4-40*a*b^3*c^3*d-_ + 34*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+105*a^4*d^4)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a^4*c^4*x) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 105a d + 75a b c d + 30a b c d + 30a b c d + 75a b c d +--R + +--R 5 5 +--R - 105b c +--R * +--R +-+ +-------+ +--R 5 \|c \|b x + a +--R x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (105a d - 40a b c d - 34a b c d - 40a b c d + 105b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 70a c d + 22a b c d + 22a b c d - 70a b c )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 4 4 +--R (56a c d - 16a b c d + 56a b c )x + (- 48a c d - 48a b c )x - 384a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 4 4 5 +-+ +-+ +--R 1920a c x \|a \|c +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1092 +--a0:=integrate(t0,x) +--E 1015 + +--S 1016 of 1092 +--m0:=a0-r0 +--E 1016 + +--S 1017 of 1092 +--d0:=D(m0,x) +--E 1017 + +)clear all + +--S 1018 of 1092 +t0:=x^2*(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 3 2 +-------+ +-------+ +--R (1) (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1092 +r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ + (b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+_ + 1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*_ + (3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(7/2))+1/64*(b*c-a*d)*_ + (3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_ + (b^4*d^2)+1/128*(b*c-a*d)^2*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^3) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (105a d - 225a b c d + 90a b c d + 30a b c d + 45a b c d - 45b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 528b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 96a b c d + 24b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 122a b c d + 18a b c d - 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 190a b c d - 36a b c d - 30a b c d + 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 3 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1092 +--a0:=integrate(t0,x) +--E 1020 + +--S 1021 of 1092 +--m0:=a0-r0 +--E 1021 + +--S 1022 of 1092 +--d0:=D(m0,x) +--E 1022 + +)clear all + +--S 1023 of 1092 +t0:=x*(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) (d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1092 +r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ + (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-_ + 1/32*(b*c-a*d)*(3*b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d)-_ + 1/64*(b*c-a*d)^2*(3*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 36a b c d - 18a b c d - 12a b c d + 9b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 72b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b d + 20a b c d + 6b c d)x + 15a d - 31a b c d + 9a b c d +--R + +--R 3 3 +--R - 9b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 2 +-+ +-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1092 +--a0:=integrate(t0,x) +--E 1025 + +--S 1026 of 1092 +--m0:=a0-r0 +--E 1026 + +--S 1027 of 1092 +--d0:=D(m0,x) +--E 1027 + +)clear all + +--S 1028 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R +-------+ +-------+ +--R (1) (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1092 +r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*_ + sqrt(c+d*x)/(b^2*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 9a b c d + 9a b c d - 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 14b c d)x - 3a d + 8a b c d + 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b d\|b \|d +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1092 +--a0:=integrate(t0,x) +--E 1030 + +--S 1031 of 1092 +--m0:=a0-r0 +--E 1031 + +--S 1032 of 1092 +--d0:=D(m0,x) +--E 1032 + +)clear all + +--S 1033 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R x +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1092 +r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ + sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+_ + 1/2*(c+d*x)^(3/2)*sqrt(a+b*x)+1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d + 6a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 8b c\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d + 5b c)\|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b\|b \|d +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1035 + +--S 1036 of 1092 +--m0:=a0-r0 +--E 1036 + +--S 1037 of 1092 +--d0:=D(m0,x) +--E 1037 + +)clear all + +--S 1038 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1092 +r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ + sqrt(c)/sqrt(a)+(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*_ + sqrt(a+b*x)/x+2*d*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ \|d \|b x + a +--R (a d + 3b c)x\|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|b x + a +--R (- 3a d - b c)x\|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (d x - c)\|a \|b \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R x\|a \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1040 + +--S 1041 of 1092 +--m0:=a0-r0 +--E 1041 + +--S 1042 of 1092 +--d0:=D(m0,x) +--E 1042 + +)clear all + +--S 1043 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1092 +r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ + 1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_ + 1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/x^2-1/4*(b*c+3*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ +-+ +-+ +-+ \|d \|b x + a +--R 8a d x \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 3a d - 6a b c d + b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((- 5a d - b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a x \|a \|c +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1045 + +--S 1046 of 1092 +--m0:=a0-r0 +--E 1046 + +--S 1047 of 1092 +--d0:=D(m0,x) +--E 1047 + +)clear all + +--S 1048 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1092 +r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-_ + 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (3a d - 9a b c d + 9a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R ((- 3a d - 8a b c d + 3b c )x + (- 14a c d - 2a b c )x - 8a c )\|a +--R * +--R +-+ +-------+ +-------+ +--R \|c \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 24a c x \|a \|c +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1092 +--a0:=integrate(t0,x) +--E 1050 + +--S 1051 of 1092 +--m0:=a0-r0 +--E 1051 + +--S 1052 of 1092 +--d0:=D(m0,x) +--E 1052 + +)clear all + +--S 1053 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1092 +r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ + sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/4*(c+d*x)^(3/2)*_ + sqrt(a+b*x)/x^4-1/24*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+_ + 1/96*(5*b^2*c/a-10*b*d-3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^2)-_ + 1/192*(15*b^3*c^3-31*a*b^2*c^2*d+9*a^2*b*c*d^2-9*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c )x +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (9a d - 9a b c d + 31a b c d - 15b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 6a c d - 20a b c d + 10a b c )x + (- 72a c d - 8a b c )x - 48a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 2 4 +-+ +-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1092 +--a0:=integrate(t0,x) +--E 1055 + +--S 1056 of 1092 +--m0:=a0-r0 +--E 1056 + +--S 1057 of 1092 +--d0:=D(m0,x) +--E 1057 + +)clear all + +--S 1058 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1092 +r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_ + 1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a*x^4)+1/240*(7*b^2*c/a-_ + 12*b*d-3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)-_ + 1/960*(35*b^3*c^3-61*a*b^2*c^2*d+9*a^2*b*c*d^2-15*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x^2)+1/1920*(105*b^4*c^4-_ + 190*a*b^3*c^3*d+36*a^2*b^2*c^2*d^2+30*a^3*b*c*d^3-45*a^4*d^4)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^3*x) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c ) +--R * +--R +-+ +-------+ +--R 5 \|c \|b x + a +--R x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 45a d + 30a b c d + 36a b c d - 190a b c d + 105b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (30a c d - 18a b c d + 122a b c d - 70a b c )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 +--R (- 24a c d - 96a b c d + 56a b c )x + (- 528a c d - 48a b c )x +--R + +--R 4 4 +--R - 384a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 4 3 5 +-+ +-+ +--R 1920a c x \|a \|c +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1092 +--a0:=integrate(t0,x) +--E 1060 + +--S 1061 of 1092 +--m0:=a0-r0 +--E 1061 + +--S 1062 of 1092 +--d0:=D(m0,x) +--E 1062 + +)clear all + +--S 1063 of 1092 +t0:=x^2*(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 4 3 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1092 +r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ + (c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ + (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*_ + (a+b*x)^(3/2)*(c+d*x)^(7/2)/(b^2*d^2)+1/6*x*(a+b*x)^(3/2)*_ + (c+d*x)^(7/2)/(b*d)-1/512*(b*c-a*d)^4*(5*b^2*c^2+14*a*b*c*d+_ + 21*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(11/2)*d^(7/2))+1/256*(b*c-a*d)^2*(5*b^2*c^2+14*a*b*c*d+_ + 21*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^5*d^2)+_ + 1/512*(b*c-a*d)^3*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^3) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 315a d + 1050a b c d - 1125a b c d + 300a b c d + 75a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 75b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 1280b d x + (128a b d + 3200b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 144a b d + 416a b c d + 2160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (168a b d - 488a b c d + 408a b c d + 40b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 616a b c d - 524a b c d + 40a b c d - 50b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 315a d - 945a b c d + 838a b c d - 90a b c d - 65a b c d + 75b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 5 3 +-+ +-+ +--R 7680b d \|b \|d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1092 +--a0:=integrate(t0,x) +--E 1065 + +--S 1066 of 1092 +--m0:=a0-r0 +--E 1066 + +--S 1067 of 1092 +--d0:=D(m0,x) +--E 1067 + +)clear all + +--S 1068 of 1092 +t0:=x*(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 3 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1092 +r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ + 1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+_ + 1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*_ + (3*b*c+7*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(9/2)*d^(5/2))-1/64*(b*c-a*d)^2*(3*b*c+7*a*d)*(a+b*x)^(3/2)*_ + sqrt(c+d*x)/(b^4*d)-1/128*(b*c-a*d)^3*(3*b*c+7*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^2) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 105a d - 375a b c d + 450a b c d - 150a b c d - 75a b c d +--R + +--R 5 5 +--R 45b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 1008b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 176a b c d + 744b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 222a b c d + 218a b c d + 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 340a b c d - 346a b c d + 60a b c d - 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 2 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1092 +--a0:=integrate(t0,x) +--E 1070 + +--S 1071 of 1092 +--m0:=a0-r0 +--E 1071 + +--S 1072 of 1092 +--d0:=D(m0,x) +--E 1072 + +)clear all + +--S 1073 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1092 +r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ + (c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/b^3+5/64*(b*c-a*d)^3*sqrt(a+b*x)*_ + sqrt(c+d*x)/(b^3*d) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1092 +--a0:=integrate(t0,x) +--E 1075 + +--S 1076 of 1092 +--m0:=a0-r0 +--E 1076 + +--S 1077 of 1092 +--d0:=D(m0,x) +--E 1077 + +)clear all + +--S 1078 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1092 +r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ + 1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+_ + 1/12*(5*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b+1/3*(c+d*x)^(5/2)*_ + sqrt(a+b*x)+1/8*(5*b*c-a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 15a b c d + 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 48b c \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 26b c d)x - 3a d + 14a b c d + 33b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1080 + +--S 1081 of 1092 +--m0:=a0-r0 +--E 1081 + +--S 1082 of 1092 +--d0:=D(m0,x) +--E 1082 + +)clear all + +--S 1083 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1092 +r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*_ + (c+d*x)^(3/2)*sqrt(a+b*x)-(c+d*x)^(5/2)*sqrt(a+b*x)/x+_ + 1/4*d*(11*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ \|d \|b x + a +--R (- a d + 10a b c d + 15b c )x\|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|b x + a +--R (- 20a b c d - 4b c )x\|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 +-+ +-+ +-------+ +-------+ +--R (2b d x + (a d + 9b c d)x - 4b c )\|a \|b \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b x\|a \|b +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1085 + +--S 1086 of 1092 +--m0:=a0-r0 +--E 1086 + +--S 1087 of 1092 +--d0:=D(m0,x) +--E 1087 + +)clear all + +--S 1088 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1092 +r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-_ + 1/4*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x)-_ + 1/2*(c+d*x)^(5/2)*sqrt(a+b*x)/x^2+1/4*d*(b*c+11*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/a +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-+ +-+ \|d \|b x + a +--R (4a d + 20a b c d)x \|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a +--R (- 15a d - 10a b c d + b c )x \|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 +-+ +-+ +-------+ +-------+ +--R (4a d x + (- 9a c d - b c )x - 2a c )\|a \|b \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a x \|a \|b +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1090 + +--S 1091 of 1092 +--m0:=a0-r0 +--E 1091 + +--S 1092 of 1092 +--d0:=D(m0,x) +--E 1092 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3a.input.pdf b/src/axiom-website/CATS/rich3a.input.pdf new file mode 100644 index 0000000..4bb733e Binary files /dev/null and b/src/axiom-website/CATS/rich3a.input.pdf differ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index bb82835..f3acf95 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4246,6 +4246,8 @@ src/axiom-website/CATS/index.html, rich2.input src/axiom-website/CATS/rich1a statistics update 20130723.01.tpd.patch src/axiom-website/CATS/rich1b statistics update +20130725.01.tpd.patch +src/axiom-website/CATS/rich2, rich3a diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index c366df6..3b9d29b 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -432,7 +432,8 @@ CATSTESTS= \ These long-running tests have been split into a different group so we can run them in parallel. <>= -NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress +NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress \ + rich3a.regress RICHTESTS= \ richalgebraic000-099.regress \ @@ -786,7 +787,8 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/poly1.input ${OUT}/psgenfcn.input \ ${OUT}/quat.input ${OUT}/quat1.input ${OUT}/ribbon.input \ ${OUT}/ribbons.input ${OUT}/ribbonsnew.input \ - ${OUT}/rich1a.input ${OUT}/rich1b.input ${OUT}/rich2.input \ + ${OUT}/rich1a.input ${OUT}/rich1b.input \ + ${OUT}/rich2.input ${OUT}/rich3a.input \ ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ @@ -871,7 +873,8 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ ${OUT}/spadprof.input \ ${OUT}/synonym2.input ${OUT}/torus.input -NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input ${OUT}/rich2.input +NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input \ + ${OUT}/rich2.input ${OUT}/rich3a.input RICHINPUT= \ ${OUT}/richalgebraic000-099.input \ @@ -1190,8 +1193,9 @@ DOCFILES= \ ${DOC}/regset.input.dvi ${DOC}/repa6.input.dvi \ ${DOC}/ribbon.input.dvi ${DOC}/ribbons.input.dvi \ ${DOC}/ribbonsnew.input.dvi \ - ${DOC}/rich1a.input.dvi ${DOC}/rich2.input.dvi \ - ${DOC}/rich1b.input.dvi \ + ${DOC}/rich1a.input.dvi ${DOC}/rich1b.input.dvi \ + ${DOC}/rich2.input.dvi \ + ${DOC}/rich3a.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ diff --git a/src/input/rich2.input.pamphlet b/src/input/rich2.input.pamphlet index cc76c42..0494093 100644 --- a/src/input/rich2.input.pamphlet +++ b/src/input/rich2.input.pamphlet @@ -6,7 +6,16 @@ \author{Albert Rich and Timothy Daly} \maketitle \begin{abstract} -\verb|2.1.2 (a+b x)^m (A+B x) (d+e x)^p| +\verb|(a+b x)^m (A+B x) (d+e x)^p| +There are: +\begin{itemize} +\item 249 integrals in this file. +\item 249 supplied "optimal results". +\item 230 matching answers. +\item 24 cases where Axiom supplied 2 results. +\item 34 cases that Axiom failed to integrate. +\item 6 that contain expressions Axiom does not recognize. +\end{itemize} \end{abstract} \eject \tableofcontents @@ -101,15 +110,10 @@ m0:=a0-r0 --E 4 --S 5 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 2 m log(x) m + 2 m + 1 ---R (B b x + (A b + B a)x + A a)%e - B b x + (- A b - B a)x ---R + ---R m ---R - A a x +--R (5) 0 --R Type: Expression(Integer) --E 5 @@ -817,15 +821,10 @@ m0:=a0-r0 --E 64 --S 65 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 2 3 2 2 2 2 m log(x) ---R (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )%e ---R + ---R 2 m + 3 2 m + 2 2 m + 1 2 m ---R - B b x + (- A b - 2B a b)x + (- 2A a b - B a )x - A a x +--R (5) 0 --R Type: Expression(Integer) --E 65 @@ -1714,24 +1713,10 @@ m0:=a0-r0 --E 134 --S 135 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 3 4 3 2 3 2 2 2 2 3 ---R B b x + (A b + 3B a b )x + (3A a b + 3B a b)x + (3A a b + B a )x ---R + ---R 3 ---R A a ---R * ---R m log(x) ---R %e ---R + ---R 3 m + 4 3 2 m + 3 2 2 m + 2 ---R - B b x + (- A b - 3B a b )x + (- 3A a b - 3B a b)x ---R + ---R 2 3 m + 1 3 m ---R (- 3A a b - B a )x - A a x +--R (5) 0 --R Type: Expression(Integer) --E 135 @@ -3126,27 +3111,10 @@ m0:=a0-r0 --E 214 --S 215 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 5 6 5 4 5 4 2 3 4 ---R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x ---R + ---R 2 3 3 2 3 3 2 4 2 4 5 5 ---R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a ---R * ---R m log(x) ---R %e ---R + ---R 5 m + 6 5 4 m + 5 4 2 3 m + 4 ---R - B b x + (- A b - 5B a b )x + (- 5A a b - 10B a b )x ---R + ---R 2 3 3 2 m + 3 3 2 4 m + 2 ---R (- 10A a b - 10B a b )x + (- 10A a b - 5B a b)x ---R + ---R 4 5 m + 1 5 m ---R (- 5A a b - B a )x - A a x +--R (5) 0 --R Type: Expression(Integer) --E 215 @@ -6034,45 +6002,10 @@ m0:=a0-r0 --E 309 --S 310 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 10 11 10 9 10 9 2 8 9 ---R B b x + (A b + 10B a b )x + (10A a b + 45B a b )x ---R + ---R 2 8 3 7 8 3 7 4 6 7 ---R (45A a b + 120B a b )x + (120A a b + 210B a b )x ---R + ---R 4 6 5 5 6 5 5 6 4 5 ---R (210A a b + 252B a b )x + (252A a b + 210B a b )x ---R + ---R 6 4 7 3 4 7 3 8 2 3 ---R (210A a b + 120B a b )x + (120A a b + 45B a b )x ---R + ---R 8 2 9 2 9 10 10 ---R (45A a b + 10B a b)x + (10A a b + B a )x + A a ---R * ---R m log(x) ---R %e ---R + ---R 10 m + 11 10 9 m + 10 ---R - B b x + (- A b - 10B a b )x ---R + ---R 9 2 8 m + 9 2 8 3 7 m + 8 ---R (- 10A a b - 45B a b )x + (- 45A a b - 120B a b )x ---R + ---R 3 7 4 6 m + 7 4 6 5 5 m + 6 ---R (- 120A a b - 210B a b )x + (- 210A a b - 252B a b )x ---R + ---R 5 5 6 4 m + 5 6 4 7 3 m + 4 ---R (- 252A a b - 210B a b )x + (- 210A a b - 120B a b )x ---R + ---R 7 3 8 2 m + 3 8 2 9 m + 2 ---R (- 120A a b - 45B a b )x + (- 45A a b - 10B a b)x ---R + ---R 9 10 m + 1 10 m ---R (- 10A a b - B a )x - A a x +--R (5) 0 --R Type: Expression(Integer) --E 310 @@ -35374,62 +35307,10 @@ m0:=a0-r0 --E 1282 --S 1283 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 2 3 2 2 2 2 3 2 ---R (a d f - 2a b d e f + b d e f)n - 2a d f + 4a b d e f ---R + ---R 2 2 ---R - 2b d e f ---R * ---R x ---R + ---R 2 3 2 2 2 2 3 2 2 2 ---R (a c f - 2a b c e f + b c e f)n - 2a c f + 4a b c e f - 2b c e f ---R * ---R (n - 3)log(f x + e) ---R %e ---R + ---R 2 2 2 - n ---R ((a b d f - b d e)n + (- 2a b d + b c)f + b d e)(b x + a) ---R * ---R n - 1 ---R (f x + e) ---R + ---R 2 2 ---R ((- a d f + b d e f)n + (2a d - b c)f - b d e f) ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 2 2 2 2 2 ---R (a b c f + (- a b d - b c)e f + b d e )n - a b c f ---R + ---R 2 2 2 ---R (a b d + b c)e f - b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 2 ---R (f x + e) ---R + ---R 3 2 2 3 ---R (- a c f + (a d + b c)e f - b d e f)n + 2a c f ---R + ---R 2 2 ---R (- 2a d - 2b c)e f + 2b d e f ---R * ---R - n + 1 n - 3 ---R (b x + a) (f x + e) ---R * ---R n log(b x + a) ---R %e ---R / ---R 2 3 2 2 2 2 3 2 2 2 n log(b x + a) ---R ((a f - 2a b e f + b e f)n - 2a f + 4a b e f - 2b e f)%e +--R (5) 0 --R Type: Expression(Integer) --E 1283 @@ -35722,141 +35603,10 @@ m0:=a0-r0 --E 1287 --S 1288 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 3 4 2 3 2 2 2 3 3 2 ---R (a d f - 3a b d e f + 3a b d e f - b d e f)n ---R + ---R 3 4 2 3 2 2 2 3 3 3 4 ---R (- 5a d f + 15a b d e f - 15a b d e f + 5b d e f)n + 6a d f ---R + ---R 2 3 2 2 2 3 3 ---R - 18a b d e f + 18a b d e f - 6b d e f ---R * ---R x ---R + ---R 3 4 2 3 2 2 2 3 3 2 ---R (a c f - 3a b c e f + 3a b c e f - b c e f)n ---R + ---R 3 4 2 3 2 2 2 3 3 3 4 ---R (- 5a c f + 15a b c e f - 15a b c e f + 5b c e f)n + 6a c f ---R + ---R 2 3 2 2 2 3 3 ---R - 18a b c e f + 18a b c e f - 6b c e f ---R * ---R (n - 4)log(f x + e) ---R %e ---R + ---R 2 3 2 3 3 - n ---R ((a b d f - b d e)n + (- 3a b d + 2b c)f + b d e)(b x + a) ---R * ---R n - 1 ---R (f x + e) ---R + ---R 2 2 2 2 2 ---R ((- a b d f + b d e f)n + (3a b d - 2b c)f - b d e f) ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 2 2 2 3 2 2 ---R (a b d f - 2a b d e f + b d e )n ---R + ---R 2 2 2 2 3 3 2 ---R ((- 4a b d + 2a b c)f + (6a b d - 2b c)e f - 2b d e )n ---R + ---R 2 2 2 2 3 3 2 ---R (3a b d - 2a b c)f + (- 4a b d + 2b c)e f + b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 2 ---R (f x + e) ---R + ---R 2 3 2 2 2 2 ---R (- a d f + 2a b d e f - b d e f)n ---R + ---R 2 3 2 2 2 2 ---R ((5a d - 2a b c)f + (- 8a b d + 2b c)e f + 3b d e f)n ---R + ---R 2 3 2 2 2 2 ---R (- 6a d + 4a b c)f + (8a b d - 4b c)e f - 2b d e f ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 2 3 2 2 2 2 3 2 ---R a b c f + (- a b d - 2a b c)e f + (2a b d + b c)e f ---R + ---R 3 3 ---R - b d e ---R * ---R 2 ---R n ---R + ---R 2 3 2 2 2 ---R - 3a b c f + (3a b d + 6a b c)e f ---R + ---R 2 3 2 3 3 ---R (- 6a b d - 3b c)e f + 3b d e ---R * ---R n ---R + ---R 2 3 2 2 2 2 3 2 ---R 2a b c f + (- 2a b d - 4a b c)e f + (4a b d + 2b c)e f ---R + ---R 3 3 ---R - 2b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 3 ---R (f x + e) ---R + ---R 2 4 2 3 2 2 2 ---R - a c f + (a d + 2a b c)e f + (- 2a b d - b c)e f ---R + ---R 2 3 ---R b d e f ---R * ---R 2 ---R n ---R + ---R 2 4 2 3 2 2 2 ---R 5a c f + (- 5a d - 10a b c)e f + (10a b d + 5b c)e f ---R + ---R 2 3 ---R - 5b d e f ---R * ---R n ---R + ---R 2 4 2 3 2 2 2 ---R - 6a c f + (6a d + 12a b c)e f + (- 12a b d - 6b c)e f ---R + ---R 2 3 ---R 6b d e f ---R * ---R - n + 1 n - 4 ---R (b x + a) (f x + e) ---R * ---R n log(b x + a) ---R %e ---R / ---R 3 4 2 3 2 2 2 3 3 2 ---R (a f - 3a b e f + 3a b e f - b e f)n ---R + ---R 3 4 2 3 2 2 2 3 3 3 4 2 3 ---R (- 5a f + 15a b e f - 15a b e f + 5b e f)n + 6a f - 18a b e f ---R + ---R 2 2 2 3 3 ---R 18a b e f - 6b e f ---R * ---R n log(b x + a) ---R %e +--R (5) 0 --R Type: Expression(Integer) --E 1288 @@ -36397,248 +36147,10 @@ m0:=a0-r0 --E 1292 --S 1293 of 1293 -d0:=D(m0,x) +d0:=normalize m0 --R --R ---R (5) ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 ---R (a d f - 4a b d e f + 6a b d e f - 4a b d e f + b d e f)n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 ---R - 9a d f + 36a b d e f - 54a b d e f + 36a b d e f ---R + ---R 4 4 ---R - 9b d e f ---R * ---R 2 ---R n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 ---R 26a d f - 104a b d e f + 156a b d e f - 104a b d e f ---R + ---R 4 4 ---R 26b d e f ---R * ---R n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 ---R - 24a d f + 96a b d e f - 144a b d e f + 96a b d e f ---R + ---R 4 4 ---R - 24b d e f ---R * ---R x ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 ---R (a c f - 4a b c e f + 6a b c e f - 4a b c e f + b c e f)n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 ---R (- 9a c f + 36a b c e f - 54a b c e f + 36a b c e f - 9b c e f)n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 ---R 26a c f - 104a b c e f + 156a b c e f - 104a b c e f ---R + ---R 4 4 ---R 26b c e f ---R * ---R n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 ---R - 24a c f + 96a b c e f - 144a b c e f + 96a b c e f - 24b c e f ---R * ---R (n - 5)log(f x + e) ---R %e ---R + ---R 3 4 3 4 4 - n ---R ((2a b d f - 2b d e)n + (- 8a b d + 6b c)f + 2b d e)(b x + a) ---R * ---R n - 1 ---R (f x + e) ---R + ---R 2 2 3 2 3 2 3 ---R ((- 2a b d f + 2b d e f)n + (8a b d - 6b c)f - 2b d e f) ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 2 2 2 3 4 2 2 ---R (2a b d f - 4a b d e f + 2b d e )n ---R + ---R 2 2 3 2 3 4 4 2 ---R ((- 10a b d + 6a b c)f + (14a b d - 6b c)e f - 4b d e )n ---R + ---R 2 2 3 2 3 4 4 2 ---R (8a b d - 6a b c)f + (- 10a b d + 6b c)e f + 2b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 2 ---R (f x + e) ---R + ---R 2 3 2 2 3 2 2 ---R (- 2a b d f + 4a b d e f - 2b d e f)n ---R + ---R 2 2 3 2 3 2 3 2 ---R ((12a b d - 6a b c)f + (- 18a b d + 6b c)e f + 6b d e f)n ---R + ---R 2 2 3 2 3 2 3 2 ---R (- 16a b d + 12a b c)f + (20a b d - 12b c)e f - 4b d e f ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 3 3 2 2 2 3 2 4 3 3 ---R (a b d f - 3a b d e f + 3a b d e f - b d e )n ---R + ---R 3 2 2 3 2 2 3 2 ---R (- 7a b d + 3a b c)f + (18a b d - 6a b c)e f ---R + ---R 3 4 2 4 3 ---R (- 15a b d + 3b c)e f + 4b d e ---R * ---R 2 ---R n ---R + ---R 3 2 2 3 2 2 3 2 ---R (14a b d - 9a b c)f + (- 33a b d + 18a b c)e f ---R + ---R 3 4 2 4 3 ---R (24a b d - 9b c)e f - 5b d e ---R * ---R n ---R + ---R 3 2 2 3 2 2 3 2 ---R (- 8a b d + 6a b c)f + (18a b d - 12a b c)e f ---R + ---R 3 4 2 4 3 ---R (- 12a b d + 6b c)e f + 2b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 3 ---R (f x + e) ---R + ---R 3 4 2 3 2 2 2 3 3 3 ---R (- a d f + 3a b d e f - 3a b d e f + b d e f)n ---R + ---R 3 2 4 2 2 3 ---R (9a d - 3a b c)f + (- 24a b d + 6a b c)e f ---R + ---R 2 3 2 2 3 3 ---R (21a b d - 3b c)e f - 6b d e f ---R * ---R 2 ---R n ---R + ---R 3 2 4 2 2 3 ---R (- 26a d + 15a b c)f + (63a b d - 30a b c)e f ---R + ---R 2 3 2 2 3 3 ---R (- 48a b d + 15b c)e f + 11b d e f ---R * ---R n ---R + ---R 3 2 4 2 2 3 ---R (24a d - 18a b c)f + (- 54a b d + 36a b c)e f ---R + ---R 2 3 2 2 3 3 ---R (36a b d - 18b c)e f - 6b d e f ---R * ---R - n + 1 ---R (b x + a) ---R + ---R 3 4 3 2 2 3 2 2 3 2 2 ---R a b c f + (- a b d - 3a b c)e f + (3a b d + 3a b c)e f ---R + ---R 3 4 3 4 4 ---R (- 3a b d - b c)e f + b d e ---R * ---R 3 ---R n ---R + ---R 3 4 3 2 2 3 ---R - 6a b c f + (6a b d + 18a b c)e f ---R + ---R 2 2 3 2 2 3 4 3 4 4 ---R (- 18a b d - 18a b c)e f + (18a b d + 6b c)e f - 6b d e ---R * ---R 2 ---R n ---R + ---R 3 4 3 2 2 3 ---R 11a b c f + (- 11a b d - 33a b c)e f ---R + ---R 2 2 3 2 2 3 4 3 4 4 ---R (33a b d + 33a b c)e f + (- 33a b d - 11b c)e f + 11b d e ---R * ---R n ---R + ---R 3 4 3 2 2 3 ---R - 6a b c f + (6a b d + 18a b c)e f ---R + ---R 2 2 3 2 2 3 4 3 4 4 ---R (- 18a b d - 18a b c)e f + (18a b d + 6b c)e f - 6b d e ---R * ---R - n ---R (b x + a) ---R * ---R n - 4 ---R (f x + e) ---R + ---R 3 5 3 2 4 2 2 2 3 ---R - a c f + (a d + 3a b c)e f + (- 3a b d - 3a b c)e f ---R + ---R 2 3 3 2 3 4 ---R (3a b d + b c)e f - b d e f ---R * ---R 3 ---R n ---R + ---R 3 5 3 2 4 2 2 2 3 ---R 9a c f + (- 9a d - 27a b c)e f + (27a b d + 27a b c)e f ---R + ---R 2 3 3 2 3 4 ---R (- 27a b d - 9b c)e f + 9b d e f ---R * ---R 2 ---R n ---R + ---R 3 5 3 2 4 ---R - 26a c f + (26a d + 78a b c)e f ---R + ---R 2 2 2 3 2 3 3 2 3 4 ---R (- 78a b d - 78a b c)e f + (78a b d + 26b c)e f - 26b d e f ---R * ---R n ---R + ---R 3 5 3 2 4 2 2 2 3 ---R 24a c f + (- 24a d - 72a b c)e f + (72a b d + 72a b c)e f ---R + ---R 2 3 3 2 3 4 ---R (- 72a b d - 24b c)e f + 24b d e f ---R * ---R - n + 1 n - 5 ---R (b x + a) (f x + e) ---R * ---R n log(b x + a) ---R %e ---R / ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 ---R (a f - 4a b e f + 6a b e f - 4a b e f + b e f)n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 ---R (- 9a f + 36a b e f - 54a b e f + 36a b e f - 9b e f)n ---R + ---R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 5 ---R (26a f - 104a b e f + 156a b e f - 104a b e f + 26b e f)n - 24a f ---R + ---R 3 4 2 2 2 3 3 3 2 4 4 ---R 96a b e f - 144a b e f + 96a b e f - 24b e f ---R * ---R n log(b x + a) ---R %e +--R (5) 0 --R Type: Expression(Integer) --E 1293 diff --git a/src/input/rich3a.input.pamphlet b/src/input/rich3a.input.pamphlet new file mode 100644 index 0000000..fc946de --- /dev/null +++ b/src/input/rich3a.input.pamphlet @@ -0,0 +1,24157 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 208 integrals in this file. +\item 210 supplied "optimal results". +\item 170 matching answers. +\item 23 cases where Axiom supplied 2 results. +\item 25 cases that Axiom failed to integrate. +\item 12 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3a.output +)spool rich3a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x) +--R +--R +--R 3 2 n +--R (1) (d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1092 +r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ + a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+_ + (b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 3 2 n + 4 +--R (d n + 6d n + 11d n + 6d)(b x + a) +--R + +--R 3 2 +--R (- 3a d + b c)n + (- 21a d + 7b c)n + (- 42a d + 14b c)n - 24a d +--R + +--R 8b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 2 +--R (3a d - 2a b c)n + (24a d - 16a b c)n + (57a d - 38a b c)n + 36a d +--R + +--R - 24a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- a d + a b c)n + (- 9a d + 9a b c)n + (- 26a d + 26a b c)n +--R + +--R 3 2 +--R - 24a d + 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (b d n + 6b d n + 11b d n + 6b d)x +--R + +--R 3 4 3 3 4 2 3 4 4 3 +--R ((a b d + b c)n + (3a b d + 7b c)n + (2a b d + 14b c)n + 8b c)x +--R + +--R 3 3 2 2 3 2 2 2 3 2 +--R (a b c n + (- 3a b d + 5a b c)n + (- 3a b d + 4a b c)n)x +--R + +--R 2 2 2 3 2 2 3 4 3 +--R (- 2a b c n + (6a b d - 8a b c)n)x + 2a b c n - 6a d + 8a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (b d n + 6b d n + 11b d n + 6b d)x +--R + +--R 3 4 3 3 4 2 3 4 4 3 +--R ((a b d + b c)n + (3a b d + 7b c)n + (2a b d + 14b c)n + 8b c)x +--R + +--R 3 3 2 2 3 2 2 2 3 2 +--R (a b c n + (- 3a b d + 5a b c)n + (- 3a b d + 4a b c)n)x +--R + +--R 2 2 2 3 2 2 3 4 3 +--R (- 2a b c n + (6a b d - 8a b c)n)x + 2a b c n - 6a d + 8a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 2 n + 4 +--R (- d n - 6d n - 11d n - 6d)(b x + a) +--R + +--R 3 2 +--R ((3a d - b c)n + (21a d - 7b c)n + (42a d - 14b c)n + 24a d - 8b c) +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 +--R (- 3a d + 2a b c)n + (- 24a d + 16a b c)n + (- 57a d + 38a b c)n +--R + +--R 2 +--R - 36a d + 24a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 3 3 2 2 3 2 3 +--R (a d - a b c)n + (9a d - 9a b c)n + (26a d - 26a b c)n + 24a d +--R + +--R 2 +--R - 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1092 +t0:=x*(a+b*x)^n*(c+d*x) +--R +--R +--R 2 n +--R (1) (d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1092 +r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ + (b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 n + 3 +--R (d n + 3d n + 2d)(b x + a) +--R + +--R 2 n + 2 +--R ((- 2a d + b c)n + (- 8a d + 4b c)n - 6a d + 3b c)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R ((a d - a b c)n + (5a d - 5a b c)n + 6a d - 6a b c)(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 +--R (b d n + 3b d n + 2b d)x +--R + +--R 2 3 2 2 3 3 2 +--R ((a b d + b c)n + (a b d + 4b c)n + 3b c)x +--R + +--R 2 2 2 2 2 3 2 +--R (a b c n + (- 2a b d + 3a b c)n)x - a b c n + 2a d - 3a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 +--R (b d n + 3b d n + 2b d)x +--R + +--R 2 3 2 2 3 3 2 +--R ((a b d + b c)n + (a b d + 4b c)n + 3b c)x +--R + +--R 2 2 2 2 2 3 2 +--R (a b c n + (- 2a b d + 3a b c)n)x - a b c n + 2a d - 3a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 n + 3 +--R (- d n - 3d n - 2d)(b x + a) +--R + +--R 2 n + 2 +--R ((2a d - b c)n + (8a d - 4b c)n + 6a d - 3b c)(b x + a) +--R + +--R 2 2 2 2 n + 1 +--R ((- a d + a b c)n + (- 5a d + 5a b c)n - 6a d + 6a b c)(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1092 +t0:=(a+b*x)^n*(c+d*x) +--R +--R +--R n +--R (1) (d x + c)(b x + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1092 +r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) +--R +--R +--R n + 2 n + 1 +--R (d n + d)(b x + a) + ((- a d + b c)n - 2a d + 2b c)(b x + a) +--R (2) ---------------------------------------------------------------------- +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R ((b d n + b d)x + ((a b d + b c)n + 2b c)x + a b c n - a d + 2a b c) +--R * +--R n log(b x + a) +--R %e +--R / +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +--R ((b d n + b d)x + ((a b d + b c)n + 2b c)x + a b c n - a d + 2a b c) +--R * +--R n log(b x + a) +--R %e +--R + +--R n + 2 n + 1 +--R (- d n - d)(b x + a) + ((a d - b c)n + 2a d - 2b c)(b x + a) +--R / +--R 2 2 2 2 +--R b n + 3b n + 2b +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1092 +t0:=(a+b*x)^n*(c+d*x)/x +--R +--R +--R n +--R (d x + c)(b x + a) +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1092 +--r0:=d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 17 + +--S 18 of 1092 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1092 +--m0:=a0-r0 +--E 19 + +--S 20 of 1092 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1092 +t0:=x^m*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1092 +r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ + 5*c^3*d*(b*c+2*a*d)*x^(3+m)/(3+m)+10*c^2*d^2*(b*c+a*d)*_ + x^(4+m)/(4+m)+5*c*d^3*(2*b*c+a*d)*x^(5+m)/(5+m)+_ + d^4*(5*b*c+a*d)*x^(6+m)/(6+m)+b*d^5*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m + 1764b d m +--R + +--R 5 +--R 720b d +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 5 4 4 +--R (a d + 5b c d )m + (22a d + 110b c d )m + (190a d + 950b c d )m +--R + +--R 5 4 3 5 4 2 +--R (820a d + 4100b c d )m + (1849a d + 9245b c d )m +--R + +--R 5 4 5 4 +--R (2038a d + 10190b c d )m + 840a d + 4200b c d +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5a c d + b c )m + (130a c d + 26b c )m + (1350a c d + 270b c )m +--R + +--R 4 5 3 4 5 2 +--R (7100a c d + 1420b c )m + (19645a c d + 3929b c )m +--R + +--R 4 5 4 5 +--R (26370a c d + 5274b c )m + 12600a c d + 2520b c +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m + 8028a c m +--R + +--R 5 +--R 5040a c +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 5 5 5 4 5 3 5 2 5 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m + 1764b d m +--R + +--R 5 +--R 720b d +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (a d + 5b c d )m + (22a d + 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (190a d + 950b c d )m + (820a d + 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (1849a d + 9245b c d )m + (2038a d + 10190b c d )m + 840a d +--R + +--R 4 +--R 4200b c d +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 4 5 4 +--R (5a c d + b c )m + (130a c d + 26b c )m + (1350a c d + 270b c )m +--R + +--R 4 5 3 4 5 2 +--R (7100a c d + 1420b c )m + (19645a c d + 3929b c )m +--R + +--R 4 5 4 5 +--R (26370a c d + 5274b c )m + 12600a c d + 2520b c +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m + 8028a c m +--R + +--R 5 +--R 5040a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6 5 5 5 4 5 3 5 2 +--R b d m + 21b d m + 175b d m + 735b d m + 1624b d m +--R + +--R 5 5 +--R 1764b d m + 720b d +--R * +--R 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (a d + 5b c d )m + (22a d + 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (190a d + 950b c d )m + (820a d + 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (1849a d + 9245b c d )m + (2038a d + 10190b c d )m + 840a d +--R + +--R 4 +--R 4200b c d +--R * +--R 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (5a c d + 10b c d )m + (115a c d + 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (1035a c d + 2070b c d )m + (4625a c d + 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (10720a c d + 21440b c d )m + (12060a c d + 24120b c d )m +--R + +--R 4 2 3 +--R 5040a c d + 10080b c d +--R * +--R 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (10a c d + 10b c d )m + (240a c d + 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (2260a c d + 2260b c d )m + (10560a c d + 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (25450a c d + 25450b c d )m + (29520a c d + 29520b c d )m +--R + +--R 2 3 3 2 +--R 12600a c d + 12600b c d +--R * +--R 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (10a c d + 5b c d)m + (250a c d + 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (2470a c d + 1235b c d)m + (12190a c d + 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (31120a c d + 15560b c d)m + (37960a c d + 18980b c d)m +--R + +--R 3 2 4 +--R 16800a c d + 8400b c d +--R * +--R 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (5a c d + b c )m + (130a c d + 26b c )m +--R + +--R 4 5 4 4 5 3 +--R (1350a c d + 270b c )m + (7100a c d + 1420b c )m +--R + +--R 4 5 2 4 5 4 +--R (19645a c d + 3929b c )m + (26370a c d + 5274b c )m + 12600a c d +--R + +--R 5 +--R 2520b c +--R * +--R 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R a c m + 27a c m + 295a c m + 1665a c m + 5104a c m +--R + +--R 5 5 +--R 8028a c m + 5040a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - b d m - 21b d m - 175b d m - 735b d m - 1624b d m - 1764b d m +--R + +--R 5 +--R - 720b d +--R * +--R m + 7 +--R x +--R + +--R 5 4 6 5 4 5 +--R (- a d - 5b c d )m + (- 22a d - 110b c d )m +--R + +--R 5 4 4 5 4 3 +--R (- 190a d - 950b c d )m + (- 820a d - 4100b c d )m +--R + +--R 5 4 2 5 4 5 +--R (- 1849a d - 9245b c d )m + (- 2038a d - 10190b c d )m - 840a d +--R + +--R 4 +--R - 4200b c d +--R * +--R m + 6 +--R x +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 5a c d - 10b c d )m + (- 115a c d - 230b c d )m +--R + +--R 4 2 3 4 4 2 3 3 +--R (- 1035a c d - 2070b c d )m + (- 4625a c d - 9250b c d )m +--R + +--R 4 2 3 2 4 2 3 +--R (- 10720a c d - 21440b c d )m + (- 12060a c d - 24120b c d )m +--R + +--R 4 2 3 +--R - 5040a c d - 10080b c d +--R * +--R m + 5 +--R x +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 10a c d - 10b c d )m + (- 240a c d - 240b c d )m +--R + +--R 2 3 3 2 4 2 3 3 2 3 +--R (- 2260a c d - 2260b c d )m + (- 10560a c d - 10560b c d )m +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 25450a c d - 25450b c d )m + (- 29520a c d - 29520b c d )m +--R + +--R 2 3 3 2 +--R - 12600a c d - 12600b c d +--R * +--R m + 4 +--R x +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 10a c d - 5b c d)m + (- 250a c d - 125b c d)m +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 2470a c d - 1235b c d)m + (- 12190a c d - 6095b c d)m +--R + +--R 3 2 4 2 3 2 4 +--R (- 31120a c d - 15560b c d)m + (- 37960a c d - 18980b c d)m +--R + +--R 3 2 4 +--R - 16800a c d - 8400b c d +--R * +--R m + 3 +--R x +--R + +--R 4 5 6 4 5 5 +--R (- 5a c d - b c )m + (- 130a c d - 26b c )m +--R + +--R 4 5 4 4 5 3 +--R (- 1350a c d - 270b c )m + (- 7100a c d - 1420b c )m +--R + +--R 4 5 2 4 5 4 +--R (- 19645a c d - 3929b c )m + (- 26370a c d - 5274b c )m - 12600a c d +--R + +--R 5 +--R - 2520b c +--R * +--R m + 2 +--R x +--R + +--R 5 6 5 5 5 4 5 3 5 2 5 +--R - a c m - 27a c m - 295a c m - 1665a c m - 5104a c m - 8028a c m +--R + +--R 5 +--R - 5040a c +--R * +--R m + 1 +--R x +--R / +--R 7 6 5 4 3 2 +--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1092 +t0:=x^3*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 9 5 4 8 4 2 3 7 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1092 +r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ + 10/7*c^2*d^2*(b*c+a*d)*x^7+5/8*c*d^3*(2*b*c+a*d)*x^8+_ + 1/9*d^4*(5*b*c+a*d)*x^9+1/10*b*d^5*x^10 +--R +--R +--R (2) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- a c d + -- b c d )x + (- a c d + - b c d)x + (a c d + - b c )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - a c x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 10 1 5 5 4 9 5 4 5 2 3 8 +--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 10 9 9 8 4 +--R + +--R 10 2 3 10 3 2 7 5 3 2 5 4 6 4 1 5 5 +--R (-- a c d + -- b c d )x + (- a c d + - b c d)x + (a c d + - b c )x +--R 7 7 3 6 5 +--R + +--R 1 5 4 +--R - a c x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1092 +t0:=x^2*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 8 5 4 7 4 2 3 6 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1092 +r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ + 1/8*(3*b*c-a*d)*(c+d*x)^8/d^4+1/9*b*(c+d*x)^9/d^4 +--R +--R +--R (2) +--R 1 9 9 1 9 5 8 8 5 8 10 2 7 7 +--R - b d x + (- a d + - b c d )x + (- a c d + -- b c d )x +--R 9 8 8 7 7 +--R + +--R 5 2 7 5 3 6 6 3 6 4 5 5 5 4 5 1 5 4 4 +--R (- a c d + - b c d )x + (2a c d + b c d )x + (- a c d + - b c d )x +--R 3 3 4 4 +--R + +--R 1 5 4 3 1 8 1 9 +--R - a c d x + --- a c d - --- b c +--R 3 168 504 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 32 + +--S 33 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 9 1 5 5 4 8 5 4 10 2 3 7 +--R - b d x + (- a d + - b c d )x + (- a c d + -- b c d )x +--R 9 8 8 7 7 +--R + +--R 5 2 3 5 3 2 6 3 2 4 5 5 4 1 5 4 +--R (- a c d + - b c d )x + (2a c d + b c d)x + (- a c d + - b c )x +--R 3 3 4 4 +--R + +--R 1 5 3 +--R - a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1092 +m0:=a0-r0 +--R +--R +--R 1 8 1 9 +--R - --- a c d + --- b c +--R 168 504 +--R (4) ---------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 34 + +--S 35 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 35 + +)clear all + +--S 36 of 1092 +t0:=x*(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 7 5 4 6 4 2 3 5 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 4 3 2 4 3 4 5 2 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 1092 +r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ + 1/8*b*(c+d*x)^8/d^3 +--R +--R +--R (2) +--R 1 8 8 1 8 5 7 7 5 7 5 2 6 6 +--R - b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 8 7 7 6 3 +--R + +--R 2 6 3 5 5 5 3 5 5 4 4 4 5 4 4 1 5 3 3 +--R (2a c d + 2b c d )x + (- a c d + - b c d )x + (- a c d + - b c d )x +--R 2 4 3 3 +--R + +--R 1 5 3 2 1 7 1 8 +--R - a c d x - -- a c d + --- b c +--R 2 42 168 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 37 + +--S 38 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 8 1 5 5 4 7 5 4 5 2 3 6 +--R - b d x + (- a d + - b c d )x + (- a c d + - b c d )x +--R 8 7 7 6 3 +--R + +--R 2 3 3 2 5 5 3 2 5 4 4 5 4 1 5 3 +--R (2a c d + 2b c d )x + (- a c d + - b c d)x + (- a c d + - b c )x +--R 2 4 3 3 +--R + +--R 1 5 2 +--R - a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 1092 +m0:=a0-r0 +--R +--R +--R 1 7 1 8 +--R -- a c d - --- b c +--R 42 168 +--R (4) ------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 39 + +--S 40 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 40 + +)clear all + +--S 41 of 1092 +t0:=(a+b*x)*(c+d*x)^5 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 1092 +r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 +--R +--R +--R (2) +--R 1 7 7 1 7 5 6 6 6 2 5 5 +--R - b d x + (- a d + - b c d )x + (a c d + 2b c d )x +--R 7 6 6 +--R + +--R 5 2 5 5 3 4 4 10 3 4 5 4 3 3 +--R (- a c d + - b c d )x + (-- a c d + - b c d )x +--R 2 2 3 3 +--R + +--R 5 4 3 1 5 2 2 5 2 1 6 1 7 +--R (- a c d + - b c d )x + a c d x + - a c d - -- b c +--R 2 2 6 42 +--R / +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 42 + +--S 43 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 7 1 5 5 4 6 4 2 3 5 +--R - b d x + (- a d + - b c d )x + (a c d + 2b c d )x +--R 7 6 6 +--R + +--R 5 2 3 5 3 2 4 10 3 2 5 4 3 5 4 1 5 2 +--R (- a c d + - b c d )x + (-- a c d + - b c d)x + (- a c d + - b c )x +--R 2 2 3 3 2 2 +--R + +--R 5 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 1092 +m0:=a0-r0 +--R +--R +--R 1 6 1 7 +--R - - a c d + -- b c +--R 6 42 +--R (4) ------------------- +--R 2 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 44 + +--S 45 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 45 + +)clear all + +--S 46 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1092 +r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ + 5/4*a*c*d^4*x^4+1/5*a*d^5*x^5+1/6*b*(c+d*x)^6/d+a*c^5*log(x) +--R +--R +--R (2) +--R 5 6 6 6 5 5 +--R 60a c d log(x) + 10b d x + (12a d + 60b c d )x +--R + +--R 5 2 4 4 2 4 3 3 3 +--R (75a c d + 150b c d )x + (200a c d + 200b c d )x +--R + +--R 3 3 4 2 2 4 2 5 6 +--R (300a c d + 150b c d )x + (300a c d + 60b c d)x + 10b c +--R / +--R 60d +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 6 5 4 5 +--R 60a c log(x) + 10b d x + (12a d + 60b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (75a c d + 150b c d )x + (200a c d + 200b c d )x +--R + +--R 3 2 4 2 4 5 +--R (300a c d + 150b c d)x + (300a c d + 60b c )x +--R / +--R 60 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1092 +m0:=a0-r0 +--R +--R +--R 6 +--R b c +--R (4) - ---- +--R 6d +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x^2 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1092 +r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ + 5/3*c*d^3*(2*b*c+a*d)*x^3+1/4*d^4*(5*b*c+a*d)*x^4+_ + 1/5*b*d^5*x^5+c^4*(b*c+5*a*d)*log(x) +--R +--R +--R (2) +--R 4 5 5 6 5 4 5 +--R (300a c d + 60b c )x log(x) + 12b d x + (15a d + 75b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100a c d + 200b c d )x + (300a c d + 300b c d )x +--R + +--R 3 2 4 2 5 +--R (600a c d + 300b c d)x - 60a c +--R / +--R 60x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 6 5 4 5 +--R (300a c d + 60b c )x log(x) + 12b d x + (15a d + 75b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (100a c d + 200b c d )x + (300a c d + 300b c d )x +--R + +--R 3 2 4 2 5 +--R (600a c d + 300b c d)x - 60a c +--R / +--R 60x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1092 +t0:=(a+b*x)*(c+d*x)^5/x^3 +--R +--R +--R (1) +--R 5 6 5 4 5 4 2 3 4 +--R b d x + (a d + 5b c d )x + (5a c d + 10b c d )x +--R + +--R 2 3 3 2 3 3 2 4 2 4 5 5 +--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1092 +r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ + 5/2*c*d^3*(2*b*c+a*d)*x^2+1/3*d^4*(5*b*c+a*d)*x^3+_ + 1/4*b*d^5*x^4+5*c^3*d*(b*c+2*a*d)*log(x) +--R +--R +--R (2) +--R 3 2 4 2 5 6 5 4 5 +--R (120a c d + 60b c d)x log(x) + 3b d x + (4a d + 20b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30a c d + 60b c d )x + (120a c d + 120b c d )x +--R + +--R 4 5 5 +--R (- 60a c d - 12b c )x - 6a c +--R / +--R 2 +--R 12x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 5 6 5 4 5 +--R (120a c d + 60b c d)x log(x) + 3b d x + (4a d + 20b c d )x +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (30a c d + 60b c d )x + (120a c d + 120b c d )x +--R + +--R 4 5 5 +--R (- 60a c d - 12b c )x - 6a c +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1092 +t0:=x*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--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 61 + +--S 62 of 1092 +r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ + 1/19*b*(c+d*x)^19/d^3 +--R +--R +--R (2) +--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 62 + +--S 63 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 63 + +--S 64 of 1092 +m0:=a0-r0 +--R +--R +--R 1 18 1 19 +--R --- a c d - ---- b c +--R 306 2907 +--R (4) ----------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 64 + +--S 65 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 65 + +)clear all + +--S 66 of 1092 +t0:=x^2*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--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 66 + +--S 67 of 1092 +r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ + 1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4 +--R +--R +--R (2) +--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 67 + +--S 68 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 68 + +--S 69 of 1092 +m0:=a0-r0 +--R +--R +--R 1 19 1 20 +--R - ---- a c d + ----- b c +--R 2907 19380 +--R (4) --------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 69 + +--S 70 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 70 + +)clear all + +--S 71 of 1092 +t0:=x^3*(a+b*x)*(c+d*x)^16 +--R +--R +--R (1) +--R 16 20 16 15 19 15 2 14 18 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 17 3 13 4 12 16 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 15 5 11 6 10 14 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 13 7 9 8 8 12 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 11 9 7 10 6 10 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 9 11 5 12 4 8 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 7 13 3 14 2 6 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 5 15 16 4 16 3 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1092 +r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ + 3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+_ + 1/21*b*(c+d*x)^21/d^5 +--R +--R +--R (2) +--R 1 21 21 1 21 4 20 20 16 20 120 2 19 19 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 21 20 5 19 19 +--R + +--R 20 2 19 280 3 18 18 560 3 18 1820 4 17 17 +--R (-- a c d + --- b c d )x + (--- a c d + ---- b c d )x +--R 3 9 17 17 +--R + +--R 455 4 17 5 16 16 1456 5 16 8008 6 15 15 +--R (--- a c d + 273b c d )x + (---- a c d + ---- b c d )x +--R 4 5 15 +--R + +--R 6 15 5720 7 14 14 7 14 8 13 13 +--R (572a c d + ---- b c d )x + (880a c d + 990b c d )x +--R 7 +--R + +--R 2145 8 13 2860 9 12 12 9 12 10 11 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 728b c d )x +--R 2 3 +--R + +--R 4004 10 11 2184 11 10 10 1456 11 10 1820 12 9 9 +--R (---- a c d + ---- b c d )x + (---- a c d + ---- b c d )x +--R 5 5 3 9 +--R + +--R 455 12 9 13 8 8 13 8 120 14 7 7 +--R (--- a c d + 70b c d )x + (80a c d + --- b c d )x +--R 2 7 +--R + +--R 14 7 8 15 6 6 16 15 6 1 16 5 5 1 16 5 4 +--R (20a c d + - b c d )x + (-- a c d + - b c d )x + - a c d x +--R 3 5 5 4 +--R + +--R 1 20 1 21 +--R - ----- a c d + ------ b c +--R 19380 101745 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 16 21 1 16 4 15 20 16 15 120 2 14 19 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 21 20 5 19 19 +--R + +--R 20 2 14 280 3 13 18 560 3 13 1820 4 12 17 +--R (-- a c d + --- b c d )x + (--- a c d + ---- b c d )x +--R 3 9 17 17 +--R + +--R 455 4 12 5 11 16 1456 5 11 8008 6 10 15 +--R (--- a c d + 273b c d )x + (---- a c d + ---- b c d )x +--R 4 5 15 +--R + +--R 6 10 5720 7 9 14 7 9 8 8 13 +--R (572a c d + ---- b c d )x + (880a c d + 990b c d )x +--R 7 +--R + +--R 2145 8 8 2860 9 7 12 9 7 10 6 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 728b c d )x +--R 2 3 +--R + +--R 4004 10 6 2184 11 5 10 1456 11 5 1820 12 4 9 +--R (---- a c d + ---- b c d )x + (---- a c d + ---- b c d )x +--R 5 5 3 9 +--R + +--R 455 12 4 13 3 8 13 3 120 14 2 7 +--R (--- a c d + 70b c d )x + (80a c d + --- b c d )x +--R 2 7 +--R + +--R 14 2 8 15 6 16 15 1 16 5 1 16 4 +--R (20a c d + - b c d)x + (-- a c d + - b c )x + - a c x +--R 3 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1092 +m0:=a0-r0 +--R +--R +--R 1 20 1 21 +--R ----- a c d - ------ b c +--R 19380 101745 +--R (4) --------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 74 + +--S 75 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 75 + +)clear all + +--S 76 of 1092 +t0:=x^2*(2+x)^5*(2+3*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R (1) 3x + 32x + 140x + 320x + 400x + 256x + 64x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1092 +r0:=1/3*x^3*(2+x)^6 +--R +--R +--R 1 9 8 7 160 6 5 4 64 3 +--R (2) - x + 4x + 20x + --- x + 80x + 64x + -- x +--R 3 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 1 9 8 7 160 6 5 4 64 3 +--R (3) - x + 4x + 20x + --- x + 80x + 64x + -- x +--R 3 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 4 3 2 2 n +--R (1) (d x + 2c d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1092 +r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ + (a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*_ + (a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ + d^2*(a+b*x)^(5+n)/(b^5*(5+n)) +--R +--R +--R (2) +--R 2 4 2 3 2 2 2 2 n + 5 +--R (d n + 10d n + 35d n + 50d n + 24d )(b x + a) +--R + +--R 2 4 2 3 +--R (- 4a d + 2b c d)n + (- 44a d + 22b c d)n +--R + +--R 2 2 2 2 +--R (- 164a d + 82b c d)n + (- 244a d + 122b c d)n - 120a d + 60b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (6a d - 6a b c d + b c )n + (72a d - 72a b c d + 12b c )n +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (294a d - 294a b c d + 49b c )n + (468a d - 468a b c d + 78b c )n +--R + +--R 2 2 2 2 +--R 240a d - 240a b c d + 40b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 2 2 2 2 4 +--R (- 4a d + 6a b c d - 2a b c )n +--R + +--R 3 2 2 2 2 3 +--R (- 52a d + 78a b c d - 26a b c )n +--R + +--R 3 2 2 2 2 2 +--R (- 236a d + 354a b c d - 118a b c )n +--R + +--R 3 2 2 2 2 3 2 2 +--R (- 428a d + 642a b c d - 214a b c )n - 240a d + 360a b c d +--R + +--R 2 2 +--R - 120a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 2 3 2 2 2 4 4 2 3 2 2 2 3 +--R (a d - 2a b c d + a b c )n + (14a d - 28a b c d + 14a b c )n +--R + +--R 4 2 3 2 2 2 2 +--R (71a d - 142a b c d + 71a b c )n +--R + +--R 4 2 3 2 2 2 4 2 3 2 2 2 +--R (154a d - 308a b c d + 154a b c )n + 120a d - 240a b c d + 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 5 2 3 5 2 2 5 2 5 2 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 2 5 4 4 2 5 3 +--R (a b d + 2b c d)n + (6a b d + 22b c d)n +--R + +--R 4 2 5 2 4 2 5 5 +--R (11a b d + 82b c d)n + (6a b d + 122b c d)n + 60b c d +--R * +--R 4 +--R x +--R + +--R 4 5 2 4 2 3 2 4 5 2 3 +--R (2a b c d + b c )n + (- 4a b d + 16a b c d + 12b c )n +--R + +--R 2 3 2 4 5 2 2 +--R (- 12a b d + 34a b c d + 49b c )n +--R + +--R 2 3 2 4 5 2 5 2 +--R (- 8a b d + 20a b c d + 78b c )n + 40b c +--R * +--R 3 +--R x +--R + +--R 4 2 4 2 3 4 2 3 +--R a b c n + (- 6a b c d + 10a b c )n +--R + +--R 3 2 2 2 3 4 2 2 +--R (12a b d - 36a b c d + 29a b c )n +--R + +--R 3 2 2 2 3 4 2 +--R (12a b d - 30a b c d + 20a b c )n +--R * +--R 2 +--R x +--R + +--R 2 3 2 3 3 2 2 3 2 2 +--R - 2a b c n + (12a b c d - 18a b c )n +--R + +--R 4 2 3 2 2 3 2 +--R (- 24a b d + 60a b c d - 40a b c )n +--R * +--R x +--R + +--R 3 2 2 2 4 3 2 2 5 2 4 3 2 2 +--R 2a b c n + (- 12a b c d + 18a b c )n + 24a d - 60a b c d + 40a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 4 5 2 3 5 2 2 5 2 5 2 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 2 5 4 4 2 5 3 +--R (a b d + 2b c d)n + (6a b d + 22b c d)n +--R + +--R 4 2 5 2 4 2 5 5 +--R (11a b d + 82b c d)n + (6a b d + 122b c d)n + 60b c d +--R * +--R 4 +--R x +--R + +--R 4 5 2 4 2 3 2 4 5 2 3 +--R (2a b c d + b c )n + (- 4a b d + 16a b c d + 12b c )n +--R + +--R 2 3 2 4 5 2 2 +--R (- 12a b d + 34a b c d + 49b c )n +--R + +--R 2 3 2 4 5 2 5 2 +--R (- 8a b d + 20a b c d + 78b c )n + 40b c +--R * +--R 3 +--R x +--R + +--R 4 2 4 2 3 4 2 3 +--R a b c n + (- 6a b c d + 10a b c )n +--R + +--R 3 2 2 2 3 4 2 2 +--R (12a b d - 36a b c d + 29a b c )n +--R + +--R 3 2 2 2 3 4 2 +--R (12a b d - 30a b c d + 20a b c )n +--R * +--R 2 +--R x +--R + +--R 2 3 2 3 3 2 2 3 2 2 +--R - 2a b c n + (12a b c d - 18a b c )n +--R + +--R 4 2 3 2 2 3 2 +--R (- 24a b d + 60a b c d - 40a b c )n +--R * +--R x +--R + +--R 3 2 2 2 4 3 2 2 5 2 4 3 2 2 +--R 2a b c n + (- 12a b c d + 18a b c )n + 24a d - 60a b c d + 40a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 4 2 3 2 2 2 2 n + 5 +--R (- d n - 10d n - 35d n - 50d n - 24d )(b x + a) +--R + +--R 2 4 2 3 2 2 +--R (4a d - 2b c d)n + (44a d - 22b c d)n + (164a d - 82b c d)n +--R + +--R 2 2 +--R (244a d - 122b c d)n + 120a d - 60b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 2 2 2 4 2 2 2 2 3 +--R (- 6a d + 6a b c d - b c )n + (- 72a d + 72a b c d - 12b c )n +--R + +--R 2 2 2 2 2 +--R (- 294a d + 294a b c d - 49b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 468a d + 468a b c d - 78b c )n - 240a d + 240a b c d - 40b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 2 2 2 2 4 3 2 2 2 2 3 +--R (4a d - 6a b c d + 2a b c )n + (52a d - 78a b c d + 26a b c )n +--R + +--R 3 2 2 2 2 2 +--R (236a d - 354a b c d + 118a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (428a d - 642a b c d + 214a b c )n + 240a d - 360a b c d + 120a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 2 3 2 2 2 4 4 2 3 2 2 2 3 +--R (- a d + 2a b c d - a b c )n + (- 14a d + 28a b c d - 14a b c )n +--R + +--R 4 2 3 2 2 2 2 +--R (- 71a d + 142a b c d - 71a b c )n +--R + +--R 4 2 3 2 2 2 4 2 3 +--R (- 154a d + 308a b c d - 154a b c )n - 120a d + 240a b c d +--R + +--R 2 2 2 +--R - 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1092 +t0:=x*(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 3 2 2 n +--R (1) (d x + 2c d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1092 +r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ + (a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/_ + (b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 n + 4 +--R (d n + 6d n + 11d n + 6d )(b x + a) +--R + +--R 2 3 2 2 2 +--R (- 3a d + 2b c d)n + (- 21a d + 14b c d)n + (- 42a d + 28b c d)n +--R + +--R 2 +--R - 24a d + 16b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 2 2 2 3 2 2 2 2 2 +--R (3a d - 4a b c d + b c )n + (24a d - 32a b c d + 8b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (57a d - 76a b c d + 19b c )n + 36a d - 48a b c d + 12b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 2 2 2 3 3 2 2 2 2 2 +--R (- a d + 2a b c d - a b c )n + (- 9a d + 18a b c d - 9a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (- 26a d + 52a b c d - 26a b c )n - 24a d + 48a b c d - 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 4 2 2 4 2 4 2 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 2 4 3 3 2 4 2 3 2 4 +--R (a b d + 2b c d)n + (3a b d + 14b c d)n + (2a b d + 28b c d)n +--R + +--R 4 +--R 16b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 2 2 3 4 2 2 +--R (2a b c d + b c )n + (- 3a b d + 10a b c d + 8b c )n +--R + +--R 2 2 2 3 4 2 4 2 +--R (- 3a b d + 8a b c d + 19b c )n + 12b c +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R a b c n + (- 4a b c d + 7a b c )n +--R + +--R 3 2 2 2 3 2 +--R (6a b d - 16a b c d + 12a b c )n +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R - a b c n + (4a b c d - 7a b c )n - 6a d + 16a b c d - 12a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2 3 4 2 2 4 2 4 2 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 2 4 3 3 2 4 2 +--R (a b d + 2b c d)n + (3a b d + 14b c d)n +--R + +--R 3 2 4 4 +--R (2a b d + 28b c d)n + 16b c d +--R * +--R 3 +--R x +--R + +--R 3 4 2 3 2 2 2 3 4 2 2 +--R (2a b c d + b c )n + (- 3a b d + 10a b c d + 8b c )n +--R + +--R 2 2 2 3 4 2 4 2 +--R (- 3a b d + 8a b c d + 19b c )n + 12b c +--R * +--R 2 +--R x +--R + +--R 3 2 3 2 2 3 2 2 +--R a b c n + (- 4a b c d + 7a b c )n +--R + +--R 3 2 2 2 3 2 +--R (6a b d - 16a b c d + 12a b c )n +--R * +--R x +--R + +--R 2 2 2 2 3 2 2 2 4 2 3 2 2 2 +--R - a b c n + (4a b c d - 7a b c )n - 6a d + 16a b c d - 12a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 3 2 2 2 2 n + 4 +--R (- d n - 6d n - 11d n - 6d )(b x + a) +--R + +--R 2 3 2 2 2 +--R (3a d - 2b c d)n + (21a d - 14b c d)n + (42a d - 28b c d)n +--R + +--R 2 +--R 24a d - 16b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 2 2 2 3 2 2 2 2 2 +--R (- 3a d + 4a b c d - b c )n + (- 24a d + 32a b c d - 8b c )n +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 57a d + 76a b c d - 19b c )n - 36a d + 48a b c d - 12b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 2 2 2 2 3 3 2 2 2 2 2 +--R (a d - 2a b c d + a b c )n + (9a d - 18a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 2 2 2 2 +--R (26a d - 52a b c d + 26a b c )n + 24a d - 48a b c d + 24a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1092 +t0:=(a+b*x)^n*(c+d*x)^2 +--R +--R +--R 2 2 2 n +--R (1) (d x + 2c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1092 +r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ + (b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 2 2 2 n + 3 +--R (d n + 3d n + 2d )(b x + a) +--R + +--R 2 2 2 2 +--R ((- 2a d + 2b c d)n + (- 8a d + 8b c d)n - 6a d + 6b c d) +--R * +--R n + 2 +--R (b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )n + (5a d - 10a b c d + 5b c )n + 6a d +--R + +--R 2 2 +--R - 12a b c d + 6b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 3 2 3 2 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)n + (a b d + 8b c d)n + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )n + (- 2a b d + 6a b c d + 5b c )n + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c n + (- 2a b c d + 5a b c )n + 2a d - 6a b c d + 6a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 2 3 2 3 2 3 +--R (b d n + 3b d n + 2b d )x +--R + +--R 2 2 3 2 2 2 3 3 2 +--R ((a b d + 2b c d)n + (a b d + 8b c d)n + 6b c d)x +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 +--R ((2a b c d + b c )n + (- 2a b d + 6a b c d + 5b c )n + 6b c )x +--R + +--R 2 2 2 2 2 2 3 2 2 2 2 +--R a b c n + (- 2a b c d + 5a b c )n + 2a d - 6a b c d + 6a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 2 2 n + 3 +--R (- d n - 3d n - 2d )(b x + a) +--R + +--R 2 2 2 2 n + 2 +--R ((2a d - 2b c d)n + (8a d - 8b c d)n + 6a d - 6b c d)(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )n + (- 5a d + 10a b c d - 5b c )n - 6a d +--R + +--R 2 2 +--R 12a b c d - 6b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1092 +t0:=(a+b*x)^n*(c+d*x)^2/x +--R +--R +--R 2 2 2 n +--R (d x + 2c d x + c )(b x + a) +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1092 +--r0:=-d*(a*d-b*c*(3+n))*(a+b*x)^(1+n)/(b^2*(1+n)*(2+n))+_ +-- d*(a+b*x)^(1+n)*(c+d*x)/(b*(2+n))-c^2*(a+b*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 97 + +--S 98 of 1092 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 1092 +--m0:=a0-r0 +--E 99 + +--S 100 of 1092 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 1092 +t0:=x^m*(a+b*x)^2*(c+d*x)^5 +--R +--R +--R (1) +--R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 +--R b d x + (2a b d + 5b c d )x + (a d + 10a b c d + 10b c d )x +--R + +--R 2 4 2 3 2 3 2 4 2 2 3 3 2 2 4 3 +--R (5a c d + 20a b c d + 10b c d )x + (10a c d + 20a b c d + 5b c d)x +--R + +--R 2 3 2 4 2 5 2 2 4 5 2 5 +--R (10a c d + 10a b c d + b c )x + (5a c d + 2a b c )x + a c +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1092 +r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ + c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+_ + 5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+_ + 5*c*d^2*(2*b^2*c^2+4*a*b*c*d+a^2*d^2)*x^(5+m)/(5+m)+_ + d^3*(10*b^2*c^2+10*a*b*c*d+a^2*d^2)*x^(6+m)/(6+m)+_ + b*d^4*(5*b*c+2*a*d)*x^(7+m)/(7+m)+b^2*d^5*x^(8+m)/(8+m) +--R +--R +--R (2) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 2 5 2 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m + 13132b d m +--R + +--R 2 5 2 5 +--R 13068b d m + 5040b d +--R * +--R m + 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R m + 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R m + 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R m + 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R m + 4 +--R x +--R + +--R 2 3 2 4 2 5 7 2 3 2 4 2 5 6 +--R (10a c d + 10a b c d + b c )m + (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R m + 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R m + 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R 13132b d m + 13068b d m + 5040b d +--R * +--R 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (10a c d + 10a b c d + b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R b d m + 28b d m + 322b d m + 1960b d m + 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R 13132b d m + 13068b d m + 5040b d +--R * +--R 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (2a b d + 5b c d )m + (58a b d + 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (686a b d + 1715b c d )m + (4270a b d + 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (15008a b d + 37520b c d )m + (29512a b d + 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (29664a b d + 74160b c d )m + 11520a b d + 28800b c d +--R * +--R 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (a d + 10a b c d + 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (30a d + 300a b c d + 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (366a d + 3660a b c d + 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (2340a d + 23400a b c d + 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (8409a d + 84090a b c d + 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (16830a d + 168300a b c d + 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (17144a d + 171440a b c d + 171440b c d )m + 6720a d +--R + +--R 4 2 2 3 +--R 67200a b c d + 67200b c d +--R * +--R 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (5a c d + 20a b c d + 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (155a c d + 620a b c d + 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (1955a c d + 7820a b c d + 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (12905a c d + 51620a b c d + 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (47720a c d + 190880a b c d + 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (97820a c d + 391280a b c d + 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (101520a c d + 406080a b c d + 203040b c d )m + 40320a c d +--R + +--R 2 3 2 3 2 +--R 161280a b c d + 80640b c d +--R * +--R 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (10a c d + 20a b c d + 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (320a c d + 640a b c d + 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (4180a c d + 8360a b c d + 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (28640a c d + 57280a b c d + 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (109930a c d + 219860a b c d + 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (233120a c d + 466240a b c d + 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (248760a c d + 497520a b c d + 124380b c d)m + 100800a c d +--R + +--R 3 2 2 4 +--R 201600a b c d + 50400b c d +--R * +--R 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (10a c d + 10a b c d + b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (330a c d + 330a b c d + 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (4470a c d + 4470a b c d + 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (31950a c d + 31950a b c d + 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (128640a c d + 128640a b c d + 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (286920a c d + 286920a b c d + 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (320480a c d + 320480a b c d + 32048b c )m + 134400a c d +--R + +--R 4 2 5 +--R 134400a b c d + 13440b c +--R * +--R 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (5a c d + 2a b c )m + (170a c d + 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (2390a c d + 956a b c )m + (17900a c d + 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (76445a c d + 30578a b c )m + (183530a c d + 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (223560a c d + 89424a b c )m + 100800a c d + 40320a b c +--R * +--R 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R a c m + 35a c m + 511a c m + 4025a c m + 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R 48860a c m + 69264a c m + 40320a c +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - b d m - 28b d m - 322b d m - 1960b d m - 6769b d m +--R + +--R 2 5 2 2 5 2 5 +--R - 13132b d m - 13068b d m - 5040b d +--R * +--R m + 8 +--R x +--R + +--R 5 2 4 7 5 2 4 6 +--R (- 2a b d - 5b c d )m + (- 58a b d - 145b c d )m +--R + +--R 5 2 4 5 5 2 4 4 +--R (- 686a b d - 1715b c d )m + (- 4270a b d - 10675b c d )m +--R + +--R 5 2 4 3 5 2 4 2 +--R (- 15008a b d - 37520b c d )m + (- 29512a b d - 73780b c d )m +--R + +--R 5 2 4 5 2 4 +--R (- 29664a b d - 74160b c d )m - 11520a b d - 28800b c d +--R * +--R m + 7 +--R x +--R + +--R 2 5 4 2 2 3 7 +--R (- a d - 10a b c d - 10b c d )m +--R + +--R 2 5 4 2 2 3 6 +--R (- 30a d - 300a b c d - 300b c d )m +--R + +--R 2 5 4 2 2 3 5 +--R (- 366a d - 3660a b c d - 3660b c d )m +--R + +--R 2 5 4 2 2 3 4 +--R (- 2340a d - 23400a b c d - 23400b c d )m +--R + +--R 2 5 4 2 2 3 3 +--R (- 8409a d - 84090a b c d - 84090b c d )m +--R + +--R 2 5 4 2 2 3 2 +--R (- 16830a d - 168300a b c d - 168300b c d )m +--R + +--R 2 5 4 2 2 3 2 5 +--R (- 17144a d - 171440a b c d - 171440b c d )m - 6720a d +--R + +--R 4 2 2 3 +--R - 67200a b c d - 67200b c d +--R * +--R m + 6 +--R x +--R + +--R 2 4 2 3 2 3 2 7 +--R (- 5a c d - 20a b c d - 10b c d )m +--R + +--R 2 4 2 3 2 3 2 6 +--R (- 155a c d - 620a b c d - 310b c d )m +--R + +--R 2 4 2 3 2 3 2 5 +--R (- 1955a c d - 7820a b c d - 3910b c d )m +--R + +--R 2 4 2 3 2 3 2 4 +--R (- 12905a c d - 51620a b c d - 25810b c d )m +--R + +--R 2 4 2 3 2 3 2 3 +--R (- 47720a c d - 190880a b c d - 95440b c d )m +--R + +--R 2 4 2 3 2 3 2 2 +--R (- 97820a c d - 391280a b c d - 195640b c d )m +--R + +--R 2 4 2 3 2 3 2 2 4 +--R (- 101520a c d - 406080a b c d - 203040b c d )m - 40320a c d +--R + +--R 2 3 2 3 2 +--R - 161280a b c d - 80640b c d +--R * +--R m + 5 +--R x +--R + +--R 2 2 3 3 2 2 4 7 +--R (- 10a c d - 20a b c d - 5b c d)m +--R + +--R 2 2 3 3 2 2 4 6 +--R (- 320a c d - 640a b c d - 160b c d)m +--R + +--R 2 2 3 3 2 2 4 5 +--R (- 4180a c d - 8360a b c d - 2090b c d)m +--R + +--R 2 2 3 3 2 2 4 4 +--R (- 28640a c d - 57280a b c d - 14320b c d)m +--R + +--R 2 2 3 3 2 2 4 3 +--R (- 109930a c d - 219860a b c d - 54965b c d)m +--R + +--R 2 2 3 3 2 2 4 2 +--R (- 233120a c d - 466240a b c d - 116560b c d)m +--R + +--R 2 2 3 3 2 2 4 2 2 3 +--R (- 248760a c d - 497520a b c d - 124380b c d)m - 100800a c d +--R + +--R 3 2 2 4 +--R - 201600a b c d - 50400b c d +--R * +--R m + 4 +--R x +--R + +--R 2 3 2 4 2 5 7 +--R (- 10a c d - 10a b c d - b c )m +--R + +--R 2 3 2 4 2 5 6 +--R (- 330a c d - 330a b c d - 33b c )m +--R + +--R 2 3 2 4 2 5 5 +--R (- 4470a c d - 4470a b c d - 447b c )m +--R + +--R 2 3 2 4 2 5 4 +--R (- 31950a c d - 31950a b c d - 3195b c )m +--R + +--R 2 3 2 4 2 5 3 +--R (- 128640a c d - 128640a b c d - 12864b c )m +--R + +--R 2 3 2 4 2 5 2 +--R (- 286920a c d - 286920a b c d - 28692b c )m +--R + +--R 2 3 2 4 2 5 2 3 2 +--R (- 320480a c d - 320480a b c d - 32048b c )m - 134400a c d +--R + +--R 4 2 5 +--R - 134400a b c d - 13440b c +--R * +--R m + 3 +--R x +--R + +--R 2 4 5 7 2 4 5 6 +--R (- 5a c d - 2a b c )m + (- 170a c d - 68a b c )m +--R + +--R 2 4 5 5 2 4 5 4 +--R (- 2390a c d - 956a b c )m + (- 17900a c d - 7160a b c )m +--R + +--R 2 4 5 3 2 4 5 2 +--R (- 76445a c d - 30578a b c )m + (- 183530a c d - 73412a b c )m +--R + +--R 2 4 5 2 4 5 +--R (- 223560a c d - 89424a b c )m - 100800a c d - 40320a b c +--R * +--R m + 2 +--R x +--R + +--R 2 5 7 2 5 6 2 5 5 2 5 4 2 5 3 +--R - a c m - 35a c m - 511a c m - 4025a c m - 18424a c m +--R + +--R 2 5 2 2 5 2 5 +--R - 48860a c m - 69264a c m - 40320a c +--R * +--R m + 1 +--R x +--R / +--R 8 7 6 5 4 3 2 +--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1092 +t0:=x^3*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--R 2 16 21 16 2 15 20 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 19 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 18 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 17 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 16 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 15 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 14 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 13 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 12 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 11 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 10 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 9 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 8 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 7 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 6 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 5 2 15 16 4 2 16 3 +--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 106 + +--S 107 of 1092 +r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ + (b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+_ + 3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ + (c+d*x)^20/d^6-1/21*b*(5*b*c-2*a*d)*(c+d*x)^21/d^6+_ + 1/22*b^2*(c+d*x)^22/d^6 +--R +--R +--R (2) +--R 1 2 22 22 2 22 16 2 21 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 1 2 22 8 21 2 2 20 20 +--R (-- a d + - a b c d + 6b c d )x +--R 20 5 +--R + +--R 16 2 21 240 2 20 560 2 3 19 19 +--R (-- a c d + --- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 20 2 2 20 560 3 19 910 2 4 18 18 +--R (-- a c d + --- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 560 2 3 19 3640 4 18 4368 2 5 17 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 455 2 4 18 5 17 1001 2 6 16 16 +--R (--- a c d + 546a b c d + ---- b c d )x +--R 4 2 +--R + +--R 1456 2 5 17 16016 6 16 2288 2 7 15 15 +--R (---- a c d + ----- a b c d + ---- b c d )x +--R 5 15 3 +--R + +--R 2 6 16 11440 7 15 6435 2 8 14 14 +--R (572a c d + ----- a b c d + ---- b c d )x +--R 7 7 +--R + +--R 2 7 15 8 14 2 9 13 13 +--R (880a c d + 1980a b c d + 880b c d )x +--R + +--R 2145 2 8 14 5720 9 13 2002 2 10 12 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 2 3 3 +--R + +--R 2 9 13 10 12 4368 2 11 11 11 +--R (1040a c d + 1456a b c d + ---- b c d )x +--R 11 +--R + +--R 4004 2 10 12 4368 11 11 2 12 10 10 +--R (---- a c d + ---- a b c d + 182b c d )x +--R 5 5 +--R + +--R 1456 2 11 11 3640 12 10 560 2 13 9 9 +--R (---- a c d + ---- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 455 2 12 10 13 9 2 14 8 8 +--R (--- a c d + 140a b c d + 15b c d )x +--R 2 +--R + +--R 2 13 9 240 14 8 16 2 15 7 7 +--R (80a c d + --- a b c d + -- b c d )x +--R 7 7 +--R + +--R 2 14 8 16 15 7 1 2 16 6 6 16 2 15 7 2 16 6 5 +--R (20a c d + -- a b c d + - b c d )x + (-- a c d + - a b c d )x +--R 3 6 5 5 +--R + +--R 1 2 16 6 4 1 2 20 2 2 21 1 2 22 +--R - a c d x - ----- a c d + ------ a b c d - ------ b c +--R 4 19380 101745 447678 +--R / +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 16 22 2 16 16 2 15 21 +--R -- b d x + (-- a b d + -- b c d )x +--R 22 21 21 +--R + +--R 1 2 16 8 15 2 2 14 20 +--R (-- a d + - a b c d + 6b c d )x +--R 20 5 +--R + +--R 16 2 15 240 2 14 560 2 3 13 19 +--R (-- a c d + --- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 20 2 2 14 560 3 13 910 2 4 12 18 +--R (-- a c d + --- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 560 2 3 13 3640 4 12 4368 2 5 11 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 455 2 4 12 5 11 1001 2 6 10 16 +--R (--- a c d + 546a b c d + ---- b c d )x +--R 4 2 +--R + +--R 1456 2 5 11 16016 6 10 2288 2 7 9 15 +--R (---- a c d + ----- a b c d + ---- b c d )x +--R 5 15 3 +--R + +--R 2 6 10 11440 7 9 6435 2 8 8 14 +--R (572a c d + ----- a b c d + ---- b c d )x +--R 7 7 +--R + +--R 2 7 9 8 8 2 9 7 13 +--R (880a c d + 1980a b c d + 880b c d )x +--R + +--R 2145 2 8 8 5720 9 7 2002 2 10 6 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 2 3 3 +--R + +--R 2 9 7 10 6 4368 2 11 5 11 +--R (1040a c d + 1456a b c d + ---- b c d )x +--R 11 +--R + +--R 4004 2 10 6 4368 11 5 2 12 4 10 +--R (---- a c d + ---- a b c d + 182b c d )x +--R 5 5 +--R + +--R 1456 2 11 5 3640 12 4 560 2 13 3 9 +--R (---- a c d + ---- a b c d + --- b c d )x +--R 3 9 9 +--R + +--R 455 2 12 4 13 3 2 14 2 8 +--R (--- a c d + 140a b c d + 15b c d )x +--R 2 +--R + +--R 2 13 3 240 14 2 16 2 15 7 +--R (80a c d + --- a b c d + -- b c d)x +--R 7 7 +--R + +--R 2 14 2 16 15 1 2 16 6 16 2 15 2 16 5 1 2 16 4 +--R (20a c d + -- a b c d + - b c )x + (-- a c d + - a b c )x + - a c x +--R 3 6 5 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 1092 +m0:=a0-r0 +--R +--R +--R 1 2 20 2 2 21 1 2 22 +--R ----- a c d - ------ a b c d + ------ b c +--R 19380 101745 447678 +--R (4) ---------------------------------------------- +--R 6 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 109 + +--S 110 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 110 + +)clear all + +--S 111 of 1092 +t0:=x^2*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--R 2 16 20 16 2 15 19 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 18 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 17 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 16 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 15 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 14 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 13 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 12 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 11 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 10 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 9 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 8 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 7 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 6 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 5 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 4 2 15 16 3 2 16 2 +--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 111 + +--S 112 of 1092 +r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ + (c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-_ + 1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5 +--R +--R +--R (2) +--R 1 2 21 21 1 21 4 2 20 20 +--R -- b d x + (-- a b d + - b c d )x +--R 21 10 5 +--R + +--R 1 2 21 32 20 120 2 2 19 19 +--R (-- a d + -- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 8 2 20 40 2 19 280 2 3 18 18 +--R (- a c d + -- a b c d + --- b c d )x +--R 9 3 9 +--R + +--R 120 2 2 19 1120 3 18 1820 2 4 17 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 2 3 18 455 4 17 2 5 16 16 +--R (35a c d + --- a b c d + 273b c d )x +--R 2 +--R + +--R 364 2 4 17 2912 5 16 8008 2 6 15 15 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 3 5 15 +--R + +--R 2 5 16 6 15 5720 2 7 14 14 +--R (312a c d + 1144a b c d + ---- b c d )x +--R 7 +--R + +--R 2 6 15 7 14 2 8 13 13 +--R (616a c d + 1760a b c d + 990b c d )x +--R + +--R 2860 2 7 14 8 13 2860 2 9 12 12 +--R (---- a c d + 2145a b c d + ---- b c d )x +--R 3 3 +--R + +--R 2 8 13 9 12 2 10 11 11 +--R (1170a c d + 2080a b c d + 728b c d )x +--R + +--R 2 9 12 8008 10 11 2184 2 11 10 10 +--R (1144a c d + ---- a b c d + ---- b c d )x +--R 5 5 +--R + +--R 8008 2 10 11 2912 11 10 1820 2 12 9 9 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 9 3 9 +--R + +--R 2 11 10 12 9 2 13 8 8 +--R (546a c d + 455a b c d + 70b c d )x +--R + +--R 2 12 9 13 8 120 2 14 7 7 +--R (260a c d + 160a b c d + --- b c d )x +--R 7 +--R + +--R 280 2 13 8 14 7 8 2 15 6 6 +--R (--- a c d + 40a b c d + - b c d )x +--R 3 3 +--R + +--R 2 14 7 32 15 6 1 2 16 5 5 2 15 6 1 16 5 4 +--R (24a c d + -- a b c d + - b c d )x + (4a c d + - a b c d )x +--R 5 5 2 +--R + +--R 1 2 16 5 3 1 2 19 2 1 20 1 2 21 +--R - a c d x + ---- a c d - ---- a b c d + ------ b c +--R 3 2907 9690 101745 +--R / +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 16 21 1 16 4 2 15 20 +--R -- b d x + (-- a b d + - b c d )x +--R 21 10 5 +--R + +--R 1 2 16 32 15 120 2 2 14 19 +--R (-- a d + -- a b c d + --- b c d )x +--R 19 19 19 +--R + +--R 8 2 15 40 2 14 280 2 3 13 18 +--R (- a c d + -- a b c d + --- b c d )x +--R 9 3 9 +--R + +--R 120 2 2 14 1120 3 13 1820 2 4 12 17 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 17 17 17 +--R + +--R 2 3 13 455 4 12 2 5 11 16 +--R (35a c d + --- a b c d + 273b c d )x +--R 2 +--R + +--R 364 2 4 12 2912 5 11 8008 2 6 10 15 +--R (--- a c d + ---- a b c d + ---- b c d )x +--R 3 5 15 +--R + +--R 2 5 11 6 10 5720 2 7 9 14 +--R (312a c d + 1144a b c d + ---- b c d )x +--R 7 +--R + +--R 2 6 10 7 9 2 8 8 13 +--R (616a c d + 1760a b c d + 990b c d )x +--R + +--R 2860 2 7 9 8 8 2860 2 9 7 12 +--R (---- a c d + 2145a b c d + ---- b c d )x +--R 3 3 +--R + +--R 2 8 8 9 7 2 10 6 11 +--R (1170a c d + 2080a b c d + 728b c d )x +--R + +--R 2 9 7 8008 10 6 2184 2 11 5 10 +--R (1144a c d + ---- a b c d + ---- b c d )x +--R 5 5 +--R + +--R 8008 2 10 6 2912 11 5 1820 2 12 4 9 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 9 3 9 +--R + +--R 2 11 5 12 4 2 13 3 8 +--R (546a c d + 455a b c d + 70b c d )x +--R + +--R 2 12 4 13 3 120 2 14 2 7 +--R (260a c d + 160a b c d + --- b c d )x +--R 7 +--R + +--R 280 2 13 3 14 2 8 2 15 6 +--R (--- a c d + 40a b c d + - b c d)x +--R 3 3 +--R + +--R 2 14 2 32 15 1 2 16 5 2 15 1 16 4 1 2 16 3 +--R (24a c d + -- a b c d + - b c )x + (4a c d + - a b c )x + - a c x +--R 5 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 1092 +m0:=a0-r0 +--R +--R +--R 1 2 19 2 1 20 1 2 21 +--R - ---- a c d + ---- a b c d - ------ b c +--R 2907 9690 101745 +--R (4) --------------------------------------------- +--R 5 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 114 + +--S 115 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 115 + +)clear all + +--S 116 of 1092 +t0:=x*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (1) +--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 116 + +--S 117 of 1092 +r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ + (c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+_ + 1/20*b^2*(c+d*x)^20/d^4 +--R +--R +--R (2) +--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 117 + +--S 118 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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 118 + +--S 119 of 1092 +m0:=a0-r0 +--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 (4) ----------------------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 119 + +--S 120 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 120 + +)clear all + +--S 121 of 1092 +t0:=x^2*(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 n +--R (1) (d x + 3c d x + 3c d x + c x )(b x + a) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1092 +r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ + (b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*_ + (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+_ + d*(3*b^2*c^2-12*a*b*c*d+10*a^2*d^2)*(a+b*x)^(4+n)/(b^6*(4+n))+_ + d^2*(3*b*c-5*a*d)*(a+b*x)^(5+n)/(b^6*(5+n))+d^3*(a+b*x)^(6+n)/(b^6*(6+n)) +--R +--R +--R (2) +--R 3 5 3 4 3 3 3 2 3 3 n + 6 +--R (d n + 15d n + 85d n + 225d n + 274d n + 120d )(b x + a) +--R + +--R 3 2 5 3 2 4 +--R (- 5a d + 3b c d )n + (- 80a d + 48b c d )n +--R + +--R 3 2 3 3 2 2 +--R (- 475a d + 285b c d )n + (- 1300a d + 780b c d )n +--R + +--R 3 2 3 2 +--R (- 1620a d + 972b c d )n - 720a d + 432b c d +--R * +--R n + 5 +--R (b x + a) +--R + +--R 2 3 2 2 2 5 +--R (10a d - 12a b c d + 3b c d)n +--R + +--R 2 3 2 2 2 4 +--R (170a d - 204a b c d + 51b c d)n +--R + +--R 2 3 2 2 2 3 +--R (1070a d - 1284a b c d + 321b c d)n +--R + +--R 2 3 2 2 2 2 +--R (3070a d - 3684a b c d + 921b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (3960a d - 4752a b c d + 1188b c d)n + 1800a d - 2160a b c d +--R + +--R 2 2 +--R 540b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 10a d + 18a b c d - 9a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 180a d + 324a b c d - 162a b c d + 18b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 1210a d + 2178a b c d - 1089a b c d + 121b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 3720a d + 6696a b c d - 3348a b c d + 372b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 5080a d + 9144a b c d - 4572a b c d + 508b c )n - 2400a d +--R + +--R 2 2 2 2 3 3 +--R 4320a b c d - 2160a b c d + 240b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 5 +--R (5a d - 12a b c d + 9a b c d - 2a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (95a d - 228a b c d + 171a b c d - 38a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (685a d - 1644a b c d + 1233a b c d - 274a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (2305a d - 5532a b c d + 4149a b c d - 922a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (3510a d - 8424a b c d + 6318a b c d - 1404a b c )n + 1800a d +--R + +--R 3 2 2 2 2 3 3 +--R - 4320a b c d + 3240a b c d - 720a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 +--R (- a d + 3a b c d - 3a b c d + a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 4 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 155a d + 465a b c d - 465a b c d + 155a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (- 580a d + 1740a b c d - 1740a b c d + 580a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 3 +--R (- 1044a d + 3132a b c d - 3132a b c d + 1044a b c )n - 720a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 2160a b c d - 2160a b c d + 720a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 6 3 4 6 3 3 6 3 2 6 3 6 3 6 +--R (b d n + 15b d n + 85b d n + 225b d n + 274b d n + 120b d )x +--R + +--R 5 3 6 2 5 5 3 6 2 4 +--R (a b d + 3b c d )n + (10a b d + 48b c d )n +--R + +--R 5 3 6 2 3 5 3 6 2 2 +--R (35a b d + 285b c d )n + (50a b d + 780b c d )n +--R + +--R 5 3 6 2 6 2 +--R (24a b d + 972b c d )n + 432b c d +--R * +--R 5 +--R x +--R + +--R 5 2 6 2 5 2 4 3 5 2 6 2 4 +--R (3a b c d + 3b c d)n + (- 5a b d + 36a b c d + 51b c d)n +--R + +--R 2 4 3 5 2 6 2 3 +--R (- 30a b d + 141a b c d + 321b c d)n +--R + +--R 2 4 3 5 2 6 2 2 +--R (- 55a b d + 216a b c d + 921b c d)n +--R + +--R 2 4 3 5 2 6 2 6 2 +--R (- 30a b d + 108a b c d + 1188b c d)n + 540b c d +--R * +--R 4 +--R x +--R + +--R 5 2 6 3 5 2 4 2 5 2 6 3 4 +--R (3a b c d + b c )n + (- 12a b c d + 42a b c d + 18b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (20a b d - 108a b c d + 195a b c d + 121b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (60a b d - 240a b c d + 336a b c d + 372b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 3 +--R (40a b d - 144a b c d + 180a b c d + 508b c )n + 240b c +--R * +--R 3 +--R x +--R + +--R 5 3 5 2 4 2 5 3 4 +--R a b c n + (- 9a b c d + 16a b c )n +--R + +--R 3 3 2 2 4 2 5 3 3 +--R (36a b c d - 108a b c d + 89a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 60a b d + 252a b c d - 369a b c d + 194a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 +--R (- 60a b d + 216a b c d - 270a b c d + 120a b c )n +--R * +--R 2 +--R x +--R + +--R 2 4 3 4 3 3 2 2 4 3 3 +--R - 2a b c n + (18a b c d - 30a b c )n +--R + +--R 4 2 2 3 3 2 2 4 3 2 +--R (- 72a b c d + 198a b c d - 148a b c )n +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (120a b d - 432a b c d + 540a b c d - 240a b c )n +--R * +--R x +--R + +--R 3 3 3 3 4 2 2 3 3 3 2 +--R 2a b c n + (- 18a b c d + 30a b c )n +--R + +--R 5 2 4 2 2 3 3 3 6 3 5 2 +--R (72a b c d - 198a b c d + 148a b c )n - 120a d + 432a b c d +--R + +--R 4 2 2 3 3 3 +--R - 540a b c d + 240a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 3 5 6 3 4 6 3 3 6 3 2 6 3 6 3 6 +--R (b d n + 15b d n + 85b d n + 225b d n + 274b d n + 120b d )x +--R + +--R 5 3 6 2 5 5 3 6 2 4 +--R (a b d + 3b c d )n + (10a b d + 48b c d )n +--R + +--R 5 3 6 2 3 5 3 6 2 2 +--R (35a b d + 285b c d )n + (50a b d + 780b c d )n +--R + +--R 5 3 6 2 6 2 +--R (24a b d + 972b c d )n + 432b c d +--R * +--R 5 +--R x +--R + +--R 5 2 6 2 5 2 4 3 5 2 6 2 4 +--R (3a b c d + 3b c d)n + (- 5a b d + 36a b c d + 51b c d)n +--R + +--R 2 4 3 5 2 6 2 3 +--R (- 30a b d + 141a b c d + 321b c d)n +--R + +--R 2 4 3 5 2 6 2 2 +--R (- 55a b d + 216a b c d + 921b c d)n +--R + +--R 2 4 3 5 2 6 2 6 2 +--R (- 30a b d + 108a b c d + 1188b c d)n + 540b c d +--R * +--R 4 +--R x +--R + +--R 5 2 6 3 5 2 4 2 5 2 6 3 4 +--R (3a b c d + b c )n + (- 12a b c d + 42a b c d + 18b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (20a b d - 108a b c d + 195a b c d + 121b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 2 +--R (60a b d - 240a b c d + 336a b c d + 372b c )n +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 3 +--R (40a b d - 144a b c d + 180a b c d + 508b c )n + 240b c +--R * +--R 3 +--R x +--R + +--R 5 3 5 2 4 2 5 3 4 +--R a b c n + (- 9a b c d + 16a b c )n +--R + +--R 3 3 2 2 4 2 5 3 3 +--R (36a b c d - 108a b c d + 89a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 60a b d + 252a b c d - 369a b c d + 194a b c )n +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 +--R (- 60a b d + 216a b c d - 270a b c d + 120a b c )n +--R * +--R 2 +--R x +--R + +--R 2 4 3 4 3 3 2 2 4 3 3 +--R - 2a b c n + (18a b c d - 30a b c )n +--R + +--R 4 2 2 3 3 2 2 4 3 2 +--R (- 72a b c d + 198a b c d - 148a b c )n +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (120a b d - 432a b c d + 540a b c d - 240a b c )n +--R * +--R x +--R + +--R 3 3 3 3 4 2 2 3 3 3 2 +--R 2a b c n + (- 18a b c d + 30a b c )n +--R + +--R 5 2 4 2 2 3 3 3 6 3 5 2 +--R (72a b c d - 198a b c d + 148a b c )n - 120a d + 432a b c d +--R + +--R 4 2 2 3 3 3 +--R - 540a b c d + 240a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 5 3 4 3 3 3 2 3 3 n + 6 +--R (- d n - 15d n - 85d n - 225d n - 274d n - 120d )(b x + a) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R (5a d - 3b c d )n + (80a d - 48b c d )n + (475a d - 285b c d )n +--R + +--R 3 2 2 3 2 3 +--R (1300a d - 780b c d )n + (1620a d - 972b c d )n + 720a d +--R + +--R 2 +--R - 432b c d +--R * +--R n + 5 +--R (b x + a) +--R + +--R 2 3 2 2 2 5 +--R (- 10a d + 12a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 4 +--R (- 170a d + 204a b c d - 51b c d)n +--R + +--R 2 3 2 2 2 3 +--R (- 1070a d + 1284a b c d - 321b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 3070a d + 3684a b c d - 921b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 3960a d + 4752a b c d - 1188b c d)n - 1800a d + 2160a b c d +--R + +--R 2 2 +--R - 540b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (10a d - 18a b c d + 9a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (180a d - 324a b c d + 162a b c d - 18b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (1210a d - 2178a b c d + 1089a b c d - 121b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (3720a d - 6696a b c d + 3348a b c d - 372b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (5080a d - 9144a b c d + 4572a b c d - 508b c )n + 2400a d +--R + +--R 2 2 2 2 3 3 +--R - 4320a b c d + 2160a b c d - 240b c +--R * +--R n + 3 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 5 +--R (- 5a d + 12a b c d - 9a b c d + 2a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (- 95a d + 228a b c d - 171a b c d + 38a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 685a d + 1644a b c d - 1233a b c d + 274a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (- 2305a d + 5532a b c d - 4149a b c d + 922a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 3510a d + 8424a b c d - 6318a b c d + 1404a b c )n - 1800a d +--R + +--R 3 2 2 2 2 3 3 +--R 4320a b c d - 3240a b c d + 720a b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 +--R (a d - 3a b c d + 3a b c d - a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 4 +--R (20a d - 60a b c d + 60a b c d - 20a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (155a d - 465a b c d + 465a b c d - 155a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 +--R (580a d - 1740a b c d + 1740a b c d - 580a b c )n +--R + +--R 5 3 4 2 3 2 2 2 3 3 5 3 +--R (1044a d - 3132a b c d + 3132a b c d - 1044a b c )n + 720a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 2160a b c d + 2160a b c d - 720a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 6 6 6 5 6 4 6 3 6 2 6 6 +--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1092 +t0:=x*(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 n +--R (1) (d x + 3c d x + 3c d x + c x)(b x + a) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1092 +r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ + (a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/_ + (b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ + d^3*(a+b*x)^(5+n)/(b^5*(5+n)) +--R +--R +--R (2) +--R 3 4 3 3 3 2 3 3 n + 5 +--R (d n + 10d n + 35d n + 50d n + 24d )(b x + a) +--R + +--R 3 2 4 3 2 3 +--R (- 4a d + 3b c d )n + (- 44a d + 33b c d )n +--R + +--R 3 2 2 3 2 3 +--R (- 164a d + 123b c d )n + (- 244a d + 183b c d )n - 120a d +--R + +--R 2 +--R 90b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 3 2 2 2 4 2 3 2 2 2 3 +--R (6a d - 9a b c d + 3b c d)n + (72a d - 108a b c d + 36b c d)n +--R + +--R 2 3 2 2 2 2 +--R (294a d - 441a b c d + 147b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (468a d - 702a b c d + 234b c d)n + 240a d - 360a b c d + 120b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 4a d + 9a b c d - 6a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 52a d + 117a b c d - 78a b c d + 13b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 236a d + 531a b c d - 354a b c d + 59b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (- 428a d + 963a b c d - 642a b c d + 107b c )n - 240a d +--R + +--R 2 2 2 2 3 3 +--R 540a b c d - 360a b c d + 60b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (a d - 3a b c d + 3a b c d - a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (14a d - 42a b c d + 42a b c d - 14a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (71a d - 213a b c d + 213a b c d - 71a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (154a d - 462a b c d + 462a b c d - 154a b c )n + 120a d +--R + +--R 3 2 2 2 2 3 3 +--R - 360a b c d + 360a b c d - 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 5 3 3 5 3 2 5 3 5 3 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 3 5 2 4 4 3 5 2 3 +--R (a b d + 3b c d )n + (6a b d + 33b c d )n +--R + +--R 4 3 5 2 2 4 3 5 2 5 2 +--R (11a b d + 123b c d )n + (6a b d + 183b c d )n + 90b c d +--R * +--R 4 +--R x +--R + +--R 4 2 5 2 4 2 3 3 4 2 5 2 3 +--R (3a b c d + 3b c d)n + (- 4a b d + 24a b c d + 36b c d)n +--R + +--R 2 3 3 4 2 5 2 2 +--R (- 12a b d + 51a b c d + 147b c d)n +--R + +--R 2 3 3 4 2 5 2 5 2 +--R (- 8a b d + 30a b c d + 234b c d)n + 120b c d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 2 3 2 4 2 5 3 3 +--R (3a b c d + b c )n + (- 9a b c d + 30a b c d + 13b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (12a b d - 54a b c d + 87a b c d + 59b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 3 +--R (12a b d - 45a b c d + 60a b c d + 107b c )n + 60b c +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 3 2 4 3 3 +--R a b c n + (- 6a b c d + 12a b c )n +--R + +--R 3 2 2 2 3 2 4 3 2 +--R (18a b c d - 54a b c d + 47a b c )n +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (- 24a b d + 90a b c d - 120a b c d + 60a b c )n +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R - a b c n + (6a b c d - 12a b c )n +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 +--R (- 18a b c d + 54a b c d - 47a b c )n + 24a d - 90a b c d +--R + +--R 3 2 2 2 3 3 +--R 120a b c d - 60a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 3 4 5 3 3 5 3 2 5 3 5 3 5 +--R (b d n + 10b d n + 35b d n + 50b d n + 24b d )x +--R + +--R 4 3 5 2 4 4 3 5 2 3 +--R (a b d + 3b c d )n + (6a b d + 33b c d )n +--R + +--R 4 3 5 2 2 4 3 5 2 5 2 +--R (11a b d + 123b c d )n + (6a b d + 183b c d )n + 90b c d +--R * +--R 4 +--R x +--R + +--R 4 2 5 2 4 2 3 3 4 2 5 2 3 +--R (3a b c d + 3b c d)n + (- 4a b d + 24a b c d + 36b c d)n +--R + +--R 2 3 3 4 2 5 2 2 +--R (- 12a b d + 51a b c d + 147b c d)n +--R + +--R 2 3 3 4 2 5 2 5 2 +--R (- 8a b d + 30a b c d + 234b c d)n + 120b c d +--R * +--R 3 +--R x +--R + +--R 4 2 5 3 4 2 3 2 4 2 5 3 3 +--R (3a b c d + b c )n + (- 9a b c d + 30a b c d + 13b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (12a b d - 54a b c d + 87a b c d + 59b c )n +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 3 +--R (12a b d - 45a b c d + 60a b c d + 107b c )n + 60b c +--R * +--R 2 +--R x +--R + +--R 4 3 4 2 3 2 4 3 3 +--R a b c n + (- 6a b c d + 12a b c )n +--R + +--R 3 2 2 2 3 2 4 3 2 +--R (18a b c d - 54a b c d + 47a b c )n +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (- 24a b d + 90a b c d - 120a b c d + 60a b c )n +--R * +--R x +--R + +--R 2 3 3 3 3 2 2 2 3 3 2 +--R - a b c n + (6a b c d - 12a b c )n +--R + +--R 4 2 3 2 2 2 3 3 5 3 4 2 +--R (- 18a b c d + 54a b c d - 47a b c )n + 24a d - 90a b c d +--R + +--R 3 2 2 2 3 3 +--R 120a b c d - 60a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 4 3 3 3 2 3 3 n + 5 +--R (- d n - 10d n - 35d n - 50d n - 24d )(b x + a) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (4a d - 3b c d )n + (44a d - 33b c d )n + (164a d - 123b c d )n +--R + +--R 3 2 3 2 +--R (244a d - 183b c d )n + 120a d - 90b c d +--R * +--R n + 4 +--R (b x + a) +--R + +--R 2 3 2 2 2 4 +--R (- 6a d + 9a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 3 +--R (- 72a d + 108a b c d - 36b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 294a d + 441a b c d - 147b c d)n +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 468a d + 702a b c d - 234b c d)n - 240a d + 360a b c d +--R + +--R 2 2 +--R - 120b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (4a d - 9a b c d + 6a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (52a d - 117a b c d + 78a b c d - 13b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (236a d - 531a b c d + 354a b c d - 59b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 +--R (428a d - 963a b c d + 642a b c d - 107b c )n + 240a d +--R + +--R 2 2 2 2 3 3 +--R - 540a b c d + 360a b c d - 60b c +--R * +--R n + 2 +--R (b x + a) +--R + +--R 4 3 3 2 2 2 2 3 3 4 +--R (- a d + 3a b c d - 3a b c d + a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 14a d + 42a b c d - 42a b c d + 14a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 2 +--R (- 71a d + 213a b c d - 213a b c d + 71a b c )n +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 154a d + 462a b c d - 462a b c d + 154a b c )n - 120a d +--R + +--R 3 2 2 2 2 3 3 +--R 360a b c d - 360a b c d + 120a b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 5 5 5 4 5 3 5 2 5 5 +--R b n + 15b n + 85b n + 225b n + 274b n + 120b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1092 +t0:=(a+b*x)^n*(c+d*x)^3 +--R +--R +--R 3 3 2 2 2 3 n +--R (1) (d x + 3c d x + 3c d x + c )(b x + a) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1092 +r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ + (a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/_ + (b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n)) +--R +--R +--R (2) +--R 3 3 3 2 3 3 n + 4 +--R (d n + 6d n + 11d n + 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 +--R (- 3a d + 3b c d )n + (- 21a d + 21b c d )n +--R + +--R 3 2 3 2 +--R (- 42a d + 42b c d )n - 24a d + 24b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 2 3 2 2 2 2 +--R (3a d - 6a b c d + 3b c d)n + (24a d - 48a b c d + 24b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (57a d - 114a b c d + 57b c d)n + 36a d - 72a b c d + 36b c d +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (- 26a d + 78a b c d - 78a b c d + 26b c )n - 24a d + 72a b c d +--R + +--R 2 2 3 3 +--R - 72a b c d + 24b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )n + (3a b d + 21b c d )n +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )n + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)n + (- 3a b d + 15a b c d + 24b c d)n +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)n + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )n + (- 6a b c d + 21a b c d + 9b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )n + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c n + (- 3a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )n - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R n log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1092 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 3 4 3 2 4 3 4 3 4 +--R (b d n + 6b d n + 11b d n + 6b d )x +--R + +--R 3 3 4 2 3 3 3 4 2 2 +--R (a b d + 3b c d )n + (3a b d + 21b c d )n +--R + +--R 3 3 4 2 4 2 +--R (2a b d + 42b c d )n + 24b c d +--R * +--R 3 +--R x +--R + +--R 3 2 4 2 3 2 2 3 3 2 4 2 2 +--R (3a b c d + 3b c d)n + (- 3a b d + 15a b c d + 24b c d)n +--R + +--R 2 2 3 3 2 4 2 4 2 +--R (- 3a b d + 12a b c d + 57b c d)n + 36b c d +--R * +--R 2 +--R x +--R + +--R 3 2 4 3 3 2 2 2 3 2 4 3 2 +--R (3a b c d + b c )n + (- 6a b c d + 21a b c d + 9b c )n +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (6a b d - 24a b c d + 36a b c d + 26b c )n + 24b c +--R * +--R x +--R + +--R 3 3 3 2 2 2 3 3 2 +--R a b c n + (- 3a b c d + 9a b c )n +--R + +--R 3 2 2 2 2 3 3 4 3 3 2 2 2 2 +--R (6a b c d - 21a b c d + 26a b c )n - 6a d + 24a b c d - 36a b c d +--R + +--R 3 3 +--R 24a b c +--R * +--R n log(b x + a) +--R %e +--R + +--R 3 3 3 2 3 3 n + 4 +--R (- d n - 6d n - 11d n - 6d )(b x + a) +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a d - 3b c d )n + (21a d - 21b c d )n + (42a d - 42b c d )n +--R + +--R 3 2 +--R 24a d - 24b c d +--R * +--R n + 3 +--R (b x + a) +--R + +--R 2 3 2 2 2 3 +--R (- 3a d + 6a b c d - 3b c d)n +--R + +--R 2 3 2 2 2 2 +--R (- 24a d + 48a b c d - 24b c d)n +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (- 57a d + 114a b c d - 57b c d)n - 36a d + 72a b c d - 36b c d +--R * +--R n + 2 +--R (b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (a d - 3a b c d + 3a b c d - b c )n +--R + +--R 3 3 2 2 2 2 3 3 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )n +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 +--R (26a d - 78a b c d + 78a b c d - 26b c )n + 24a d - 72a b c d +--R + +--R 2 2 3 3 +--R 72a b c d - 24b c +--R * +--R n + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n + 10b n + 35b n + 50b n + 24b +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1092 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1092 +t0:=(a+b*x)^n*(c+d*x)^3/x +--R +--R +--R 3 3 2 2 2 3 n +--R (d x + 3c d x + 3c d x + c )(b x + a) +--R (1) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1092 +--r0:=3*c^2*d*(a+b*x)^(1+n)/(b*(1+n))-3*a*c*d^2*(a+b*x)^(1+n)/(b^2*(1+n))+_ +-- a^2*d^3*(a+b*x)^(1+n)/(b^3*(1+n))+3*c*d^2*(a+b*x)^(2+n)/(b^2*(2+n))-_ +-- 2*a*d^3*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-_ +-- c^3*(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) +--E 137 + +--S 138 of 1092 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 1092 +--m0:=a0-r0 +--E 139 + +--S 140 of 1092 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 1092 +t0:=x^m*(c+d*x)/(a+b*x) +--R +--R +--R m +--R (d x + c)x +--R (1) ----------- +--R b x + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1092 +--r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b*(1+m)) +--E 142 + +--S 143 of 1092 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 1092 +--m0:=a0-r0 +--E 144 + +--S 145 of 1092 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 1092 +t0:=x^4*(c+d*x)/(a+b*x) +--R +--R +--R 5 4 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1092 +r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ + 1/4*(b*c-a*d)*x^4/b^2+1/5*d*x^5/b+a^4*(b*c-a*d)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 4 5 5 4 5 4 +--R (- 60a d + 60a b c)log(b x + a) + 12b d x + (- 15a b d + 15b c)x +--R + +--R 2 3 4 3 3 2 2 3 2 4 3 2 +--R (20a b d - 20a b c)x + (- 30a b d + 30a b c)x + (60a b d - 60a b c)x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 5 5 4 5 4 +--R (- 60a d + 60a b c)log(b x + a) + 12b d x + (- 15a b d + 15b c)x +--R + +--R 2 3 4 3 3 2 2 3 2 4 3 2 +--R (20a b d - 20a b c)x + (- 30a b d + 30a b c)x + (60a b d - 60a b c)x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1092 +t0:=x^3*(c+d*x)/(a+b*x) +--R +--R +--R 4 3 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1092 +r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ + 1/4*d*x^4/b-a^3*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 4 4 3 4 3 +--R (12a d - 12a b c)log(b x + a) + 3b d x + (- 4a b d + 4b c)x +--R + +--R 2 2 3 2 3 2 2 +--R (6a b d - 6a b c)x + (- 12a b d + 12a b c)x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 4 3 4 3 +--R (12a d - 12a b c)log(b x + a) + 3b d x + (- 4a b d + 4b c)x +--R + +--R 2 2 3 2 3 2 2 +--R (6a b d - 6a b c)x + (- 12a b d + 12a b c)x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1092 +t0:=x^2*(c+d*x)/(a+b*x) +--R +--R +--R 3 2 +--R d x + c x +--R (1) ----------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1092 +r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ + a^2*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 2 3 3 2 3 2 +--R (- 6a d + 6a b c)log(b x + a) + 2b d x + (- 3a b d + 3b c)x +--R + +--R 2 2 +--R (6a b d - 6a b c)x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 3 2 +--R (- 6a d + 6a b c)log(b x + a) + 2b d x + (- 3a b d + 3b c)x +--R + +--R 2 2 +--R (6a b d - 6a b c)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1092 +t0:=x*(c+d*x)/(a+b*x) +--R +--R +--R 2 +--R d x + c x +--R (1) ---------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1092 +r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 +--R +--R +--R 2 2 2 2 +--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x +--R (2) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (2a d - 2a b c)log(b x + a) + b d x + (- 2a b d + 2b c)x +--R (3) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1092 +t0:=(c+d*x)/(a+b*x) +--R +--R +--R d x + c +--R (1) ------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1092 +r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (2) --------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- a d + b c)log(b x + a) + b d x +--R (3) --------------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1092 +t0:=(c+d*x)/(x*(a+b*x)) +--R +--R +--R d x + c +--R (1) ---------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1092 +r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) +--R +--R +--R (a d - b c)log(b x + a) + b c log(x) +--R (2) ------------------------------------ +--R a b +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (a d - b c)log(b x + a) + b c log(x) +--R (3) ------------------------------------ +--R a b +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1092 +t0:=(c+d*x)/(x^2*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1092 +r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 +--R +--R +--R (- a d + b c)x log(b x + a) + (a d - b c)x log(x) - a c +--R (2) ------------------------------------------------------- +--R 2 +--R a x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- a d + b c)x log(b x + a) + (a d - b c)x log(x) - a c +--R (3) ------------------------------------------------------- +--R 2 +--R a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1092 +t0:=(c+d*x)/(x^3*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1092 +r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ + b*(b*c-a*d)*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 +--R (2a b d - 2b c)x log(b x + a) + (- 2a b d + 2b c)x log(x) +--R + +--R 2 2 +--R (- 2a d + 2a b c)x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 +--R (2a b d - 2b c)x log(b x + a) + (- 2a b d + 2b c)x log(x) +--R + +--R 2 2 +--R (- 2a d + 2a b c)x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1092 +t0:=(c+d*x)/(x^4*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1092 +r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ + b^2*(b*c-a*d)*log(x)/a^4+b^2*(b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 3 3 2 3 3 +--R (- 6a b d + 6b c)x log(b x + a) + (6a b d - 6b c)x log(x) +--R + +--R 2 2 2 3 2 3 +--R (6a b d - 6a b c)x + (- 3a d + 3a b c)x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 3 +--R (- 6a b d + 6b c)x log(b x + a) + (6a b d - 6b c)x log(x) +--R + +--R 2 2 2 3 2 3 +--R (6a b d - 6a b c)x + (- 3a d + 3a b c)x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1092 +t0:=(c+d*x)/(x^5*(a+b*x)) +--R +--R +--R d x + c +--R (1) ----------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1092 +r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ + b^2*(b*c-a*d)/(a^4*x)+b^3*(b*c-a*d)*log(x)/a^5-_ + b^3*(b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 4 4 3 4 4 +--R (12a b d - 12b c)x log(b x + a) + (- 12a b d + 12b c)x log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 12a b d + 12a b c)x + (6a b d - 6a b c)x + (- 4a d + 4a b c)x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 4 4 +--R (12a b d - 12b c)x log(b x + a) + (- 12a b d + 12b c)x log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 3 4 +--R (- 12a b d + 12a b c)x + (6a b d - 6a b c)x + (- 4a d + 4a b c)x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1092 +t0:=x^m*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 2 2 m +--R (d x + 2c d x + c )x +--R (1) ---------------------- +--R b x + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1092 +--r0:=-d*(a*d*(2+m)-b*c*(3+m))*x^(1+m)/(b^2*(1+m)*(2+m))+_ +-- d*x^(1+m)*(c+d*x)/(b*(2+m))+(b*c-a*d)^2*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^2*(1+m)) +--E 197 + +--S 198 of 1092 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 1092 +--m0:=a0-r0 +--E 199 + +--S 200 of 1092 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 1092 +t0:=x^4*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 6 5 2 4 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1092 +r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ + 1/3*a*(b*c-a*d)^2*x^3/b^4+1/4*(b*c-a*d)^2*x^4/b^3+_ + 1/5*d*(2*b*c-a*d)*x^5/b^2+1/6*d^2*x^6/b+a^4*(b*c-a*d)^2*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 2 5 4 2 2 6 2 6 +--R (60a d - 120a b c d + 60a b c )log(b x + a) + 10b d x +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (- 12a b d + 24b c d)x + (15a b d - 30a b c d + 15b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 20a b d + 40a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 60a b d + 120a b c d - 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 5 4 2 2 6 2 6 +--R (60a d - 120a b c d + 60a b c )log(b x + a) + 10b d x +--R + +--R 5 2 6 5 2 4 2 5 6 2 4 +--R (- 12a b d + 24b c d)x + (15a b d - 30a b c d + 15b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 20a b d + 40a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 5 2 4 2 3 3 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 60a b d + 120a b c d - 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1092 +t0:=x^3*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 5 4 2 3 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1092 +r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ + 1/3*(b*c-a*d)^2*x^3/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/5*d^2*x^5/b-_ + a^3*(b*c-a*d)^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 2 4 3 2 2 5 2 5 +--R (- 60a d + 120a b c d - 60a b c )log(b x + a) + 12b d x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 15a b d + 30b c d)x + (20a b d - 40a b c d + 20b c )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 30a b d + 60a b c d - 30a b c )x + (60a b d - 120a b c d + 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 3 2 2 5 2 5 +--R (- 60a d + 120a b c d - 60a b c )log(b x + a) + 12b d x +--R + +--R 4 2 5 4 2 3 2 4 5 2 3 +--R (- 15a b d + 30b c d)x + (20a b d - 40a b c d + 20b c )x +--R + +--R 3 2 2 2 3 4 2 2 4 2 3 2 2 3 2 +--R (- 30a b d + 60a b c d - 30a b c )x + (60a b d - 120a b c d + 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1092 +t0:=x^2*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 4 3 2 2 +--R d x + 2c d x + c x +--R (1) --------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1092 +r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ + 1/4*d^2*x^4/b+a^2*(b*c-a*d)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 2 3 2 2 2 4 2 4 +--R (12a d - 24a b c d + 12a b c )log(b x + a) + 3b d x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 4a b d + 8b c d)x + (6a b d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 3 2 +--R (- 12a b d + 24a b c d - 12a b c )x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 2 4 2 4 +--R (12a d - 24a b c d + 12a b c )log(b x + a) + 3b d x +--R + +--R 3 2 4 3 2 2 2 3 4 2 2 +--R (- 4a b d + 8b c d)x + (6a b d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 3 2 +--R (- 12a b d + 24a b c d - 12a b c )x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1092 +t0:=x*(c+d*x)^2/(a+b*x) +--R +--R +--R 2 3 2 2 +--R d x + 2c d x + c x +--R (1) -------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1092 +r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ + a*(b*c-a*d)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 3 2 2 2 2 3 2 3 +--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 2 3 2 3 +--R (- 6a d + 12a b c d - 6a b c )log(b x + a) + 2b d x +--R + +--R 2 2 3 2 2 2 2 3 2 +--R (- 3a b d + 6b c d)x + (6a b d - 12a b c d + 6b c )x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1092 +t0:=(c+d*x)^2/(a+b*x) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1092 +r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x +--R + +--R 2 2 +--R b c +--R / +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(b x + a) + b d x + (- 2a b d + 4b c d)x +--R ----------------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1092 +m0:=a0-r0 +--R +--R +--R 2 +--R c +--R (4) - -- +--R 2b +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1092 +t0:=(c+d*x)^2/(x*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1092 +r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )log(b x + a) + b c log(x) + a b d x +--R (2) ------------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 2 +--R (- a d + 2a b c d - b c )log(b x + a) + b c log(x) + a b d x +--R (3) ------------------------------------------------------------- +--R 2 +--R a b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1092 +t0:=(c+d*x)^2/(x^2*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1092 +r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )x log(b x + a) + (2a b c d - b c )x log(x) - a b c +--R --------------------------------------------------------------------------- +--R 2 +--R a b x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 +--R (a d - 2a b c d + b c )x log(b x + a) + (2a b c d - b c )x log(x) - a b c +--R --------------------------------------------------------------------------- +--R 2 +--R a b x +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1092 +t0:=(c+d*x)^2/(x^3*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1092 +r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ + (b*c-a*d)^2*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )x log(x) + (- 4a c d + 2a b c )x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )x log(x) + (- 4a c d + 2a b c )x - a c +--R / +--R 3 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1092 +t0:=(c+d*x)^2/(x^4*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1092 +r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ + b*(b*c-a*d)^2*log(x)/a^4+b*(b*c-a*d)^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 +--R (6a b d - 12a b c d + 6b c )x log(b x + a) +--R + +--R 2 2 2 3 2 3 +--R (- 6a b d + 12a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- 6a d + 12a b c d - 6a b c )x + (- 6a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 +--R (6a b d - 12a b c d + 6b c )x log(b x + a) +--R + +--R 2 2 2 3 2 3 +--R (- 6a b d + 12a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (- 6a d + 12a b c d - 6a b c )x + (- 6a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1092 +t0:=(c+d*x)^2/(x^5*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1092 +r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ + 1/2*(b*c-a*d)^2/(a^3*x^2)+b*(b*c-a*d)^2/(a^4*x)+_ + b^2*(b*c-a*d)^2*log(x)/a^5-b^2*(b*c-a*d)^2*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 +--R (- 12a b d + 24a b c d - 12b c )x log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (12a b d - 24a b c d + 12b c )x log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (12a b d - 24a b c d + 12a b c )x + (- 6a d + 12a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 8a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 4 +--R (- 12a b d + 24a b c d - 12b c )x log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (12a b d - 24a b c d + 12b c )x log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (12a b d - 24a b c d + 12a b c )x + (- 6a d + 12a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 8a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1092 +t0:=(c+d*x)^2/(x^6*(a+b*x)) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 7 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1092 +r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ + 1/3*(b*c-a*d)^2/(a^3*x^3)+1/2*b*(b*c-a*d)^2/(a^4*x^2)-_ + b^2*(b*c-a*d)^2/(a^5*x)-b^3*(b*c-a*d)^2*log(x)/a^6+_ + b^3*(b*c-a*d)^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 2 5 +--R (60a b d - 120a b c d + 60b c )x log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (- 60a b d + 120a b c d - 60b c )x log(x) +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 60a b d + 120a b c d - 60a b c )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 20a d + 40a b c d - 20a b c )x +--R + +--R 5 4 2 5 2 +--R (- 30a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 5 +--R (60a b d - 120a b c d + 60b c )x log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (- 60a b d + 120a b c d - 60b c )x log(x) +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 60a b d + 120a b c d - 60a b c )x +--R + +--R 4 2 3 2 2 3 2 3 5 2 4 3 2 2 2 +--R (30a b d - 60a b c d + 30a b c )x + (- 20a d + 40a b c d - 20a b c )x +--R + +--R 5 4 2 5 2 +--R (- 30a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1092 +t0:=x^m*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 m +--R (d x + 3c d x + 3c d x + c )x +--R (1) -------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1092 +--r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^(1+m)/(b^3*(1+m))+_ +-- d^2*(3*b*c-a*d)*x^(2+m)/(b^2*(2+m))+d^3*x^(3+m)/(b*(3+m))+_ +-- (b*c-a*d)^3*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^3*(1+m)) +--E 257 + +--S 258 of 1092 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 1092 +--m0:=a0-r0 +--E 259 + +--S 260 of 1092 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 1092 +t0:=x^4*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 7 2 6 2 5 3 4 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1092 +r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ + x^3/b^5+1/4*(b*c-a*d)^3*x^4/b^4+1/5*d*(3*b^2*c^2-_ + 3*a*b*c*d+a^2*d^2)*x^5/b^3+1/6*d^2*(3*b*c-a*d)*x^6/b^2+_ + 1/7*d^3*x^7/b+a^4*(b*c-a*d)^3*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 7 3 6 2 5 2 2 4 3 3 +--R (- 420a d + 1260a b c d - 1260a b c d + 420a b c )log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 60b d x + (- 70a b d + 210b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (84a b d - 252a b c d + 252b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (140a b d - 420a b c d + 420a b c d - 140a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 630a b c d - 630a b c d + 210a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 +--R (420a b d - 1260a b c d + 1260a b c d - 420a b c )x +--R / +--R 8 +--R 420b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 6 2 5 2 2 4 3 3 +--R (- 420a d + 1260a b c d - 1260a b c d + 420a b c )log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 60b d x + (- 70a b d + 210b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (84a b d - 252a b c d + 252b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 105a b d + 315a b c d - 315a b c d + 105b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (140a b d - 420a b c d + 420a b c d - 140a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 630a b c d - 630a b c d + 210a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 +--R (420a b d - 1260a b c d + 1260a b c d - 420a b c )x +--R / +--R 8 +--R 420b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1092 +r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ + 1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_ + 1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/6*d^3*x^6/b-a^3*(b*c-a*d)^3*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 6 3 5 2 4 2 2 3 3 3 6 3 6 +--R (60a d - 180a b c d + 180a b c d - 60a b c )log(b x + a) + 10b d x +--R + +--R 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R (- 12a b d + 36b c d )x + (15a b d - 45a b c d + 45b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 60a b c d - 60a b c d + 20b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 2 4 2 2 3 3 3 6 3 6 +--R (60a d - 180a b c d + 180a b c d - 60a b c )log(b x + a) + 10b d x +--R + +--R 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R (- 12a b d + 36b c d )x + (15a b d - 45a b c d + 45b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 60a b c d - 60a b c d + 20b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R / +--R 7 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1092 +r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ + 1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_ + 1/4*d^2*(3*b*c-a*d)*x^4/b^2+1/5*d^3*x^5/b+a^2*(b*c-a*d)^3*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 5 3 4 2 3 2 2 2 3 3 5 3 5 +--R (- 60a d + 180a b c d - 180a b c d + 60a b c )log(b x + a) + 12b d x +--R + +--R 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R (- 15a b d + 45b c d )x + (20a b d - 60a b c d + 60b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 90a b c d - 90a b c d + 30b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 2 3 2 2 2 3 3 5 3 5 +--R (- 60a d + 180a b c d - 180a b c d + 60a b c )log(b x + a) + 12b d x +--R + +--R 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R (- 15a b d + 45b c d )x + (20a b d - 60a b c d + 60b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 90a b c d - 90a b c d + 30b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R / +--R 6 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1092 +t0:=x*(c+d*x)^3/(a+b*x) +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1092 +r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ + 1/3*d^2*(3*b*c-a*d)*x^3/b^2+1/4*d^3*x^4/b-a*(b*c-a*d)^3*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 4 3 3 2 2 2 2 3 3 4 3 4 +--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x +--R / +--R 5 +--R 12b +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 2 2 2 2 3 3 4 3 4 +--R (12a d - 36a b c d + 36a b c d - 12a b c )log(b x + a) + 3b d x +--R + +--R 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R (- 4a b d + 12b c d )x + (6a b d - 18a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x +--R / +--R 5 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1092 +t0:=(c+d*x)^3/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1092 +r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ + 1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4 +--R +--R +--R (2) +--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(b x + a) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 2 2 +--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x - 3a b c d +--R + +--R 3 3 +--R 5b c +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--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(b x + a) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (- 3a b d + 9b c d )x + (6a b d - 18a b c d + 18b c d)x +--R / +--R 4 +--R 6b +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1092 +m0:=a0-r0 +--R +--R +--R 2 3 +--R 3a c d - 5b c +--R (4) -------------- +--R 2 +--R 6b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1092 +r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ + c^3*log(x)/a-(b*c-a*d)^3*log(a+b*x)/(a*b^3) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 2b c log(x) +--R + +--R 2 3 2 2 3 2 2 +--R a b d x + (- 2a b d + 6a b c d )x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 3 +--R (2a d - 6a b c d + 6a b c d - 2b c )log(b x + a) + 2b c log(x) +--R + +--R 2 3 2 2 3 2 2 +--R a b d x + (- 2a b d + 6a b c d )x +--R / +--R 3 +--R 2a b +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 3 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1092 +r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ + (b*c-a*d)^3*log(a+b*x)/(a^2*b^2) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a) +--R + +--R 2 2 3 3 2 3 2 2 3 +--R (3a b c d - b c )x log(x) + a b d x - a b c +--R / +--R 2 2 +--R a b x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 +--R (- a d + 3a b c d - 3a b c d + b c )x log(b x + a) +--R + +--R 2 2 3 3 2 3 2 2 3 +--R (3a b c d - b c )x log(x) + a b d x - a b c +--R / +--R 2 2 +--R a b x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 4 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1092 +r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(x)/a^3-(b*c-a*d)^3*log(a+b*x)/(a^3*b) +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 3 3 2 2 2 2 3 2 3 +--R (6a b c d - 6a b c d + 2b c )x log(x) + (- 6a b c d + 2a b c )x - a b c +--R / +--R 3 2 +--R 2a b x +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c )x log(b x + a) +--R + +--R 2 2 2 2 3 3 2 2 2 2 3 2 3 +--R (6a b c d - 6a b c d + 2b c )x log(x) + (- 6a b c d + 2a b c )x - a b c +--R / +--R 3 2 +--R 2a b x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 5 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1092 +r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x)-_ + (b*c-a*d)^3*log(x)/a^4+(b*c-a*d)^3*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )x log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 9a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )x log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )x log(x) +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 9a c d + 3a b c )x - 2a c +--R / +--R 4 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1092 +t0:=(c+d*x)^3/(x^5*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 6 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1092 +r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ + 1/2*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^2)+_ + (b*c-a*d)^3/(a^4*x)+b*(b*c-a*d)^3*log(x)/a^5-b*(b*c-a*d)^3*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 36a b c d + 36a b c d - 12b c )x log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 12a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 36a b c d + 36a b c d - 12b c )x log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 36a b c d - 36a b c d + 12b c )x log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 18a b c d - 6a b c )x + (- 12a c d + 4a b c )x - 3a c +--R / +--R 5 4 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1092 +t0:=(c+d*x)^3/(x^6*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 7 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1092 +r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ + 1/3*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^3)+_ + 1/2*(b*c-a*d)^3/(a^4*x^2)-b*(b*c-a*d)^3/(a^5*x)-_ + b^2*(b*c-a*d)^3*log(x)/a^6+b^2*(b*c-a*d)^3*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 30a d + 90a b c d - 90a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 60a c d + 60a b c d - 20a b c )x + (- 45a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (60a b d - 180a b c d + 180a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 30a d + 90a b c d - 90a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 60a c d + 60a b c d - 20a b c )x + (- 45a c d + 15a b c )x - 12a c +--R / +--R 6 5 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1092 +t0:=(c+d*x)^3/(x^7*(a+b*x)) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 8 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1092 +r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ + 1/4*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^4)+_ + 1/3*(b*c-a*d)^3/(a^4*x^3)-1/2*b*(b*c-a*d)^3/(a^5*x^2)+_ + b^2*(b*c-a*d)^3/(a^6*x)+b^3*(b*c-a*d)^3*log(x)/a^7-_ + b^3*(b*c-a*d)^3*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 45a c d + 45a b c d - 15a b c )x + (- 36a c d + 12a b c )x - 10a c +--R / +--R 7 6 +--R 60a x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 180a b c d + 180a b c d - 60b c )x log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 180a b c d - 180a b c d + 60b c )x log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 180a b c d - 180a b c d + 60a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 90a b c d + 90a b c d - 30a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 20a d + 60a b c d - 60a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 45a c d + 45a b c d - 15a b c )x + (- 36a c d + 12a b c )x - 10a c +--R / +--R 7 6 +--R 60a x +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)) +--R +--R +--R m +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1092 +--r0:=b*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)*(1+m))-_ +-- d*x^(1+m)*hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)*(1+m)) +--E 322 + +--S 323 of 1092 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 1092 +--m0:=a0-r0 +--E 324 + +--S 325 of 1092 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)) +--R +--R +--R 5 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1092 +r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ + 1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*x^2/(b^3*d^3)-_ + 1/3*(b*c+a*d)*x^3/(b^2*d^2)+1/4*x^4/(b*d)-_ + a^5*log(a+b*x)/(b^5*(b*c-a*d))+c^5*log(c+d*x)/(d^5*(b*c-a*d)) +--R +--R +--R (2) +--R 5 5 5 5 4 5 5 4 4 +--R - 12b c log(d x + c) + 12a d log(b x + a) + (3a b d - 3b c d )x +--R + +--R 2 3 5 5 2 3 3 3 2 5 5 3 2 2 4 5 5 4 +--R (- 4a b d + 4b c d )x + (6a b d - 6b c d )x + (- 12a b d + 12b c d)x +--R / +--R 5 6 6 5 +--R 12a b d - 12b c d +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 5 5 4 4 +--R - 12b c log(d x + c) + 12a d log(b x + a) + (3a b d - 3b c d )x +--R + +--R 2 3 5 5 2 3 3 3 2 5 5 3 2 2 4 5 5 4 +--R (- 4a b d + 4b c d )x + (6a b d - 6b c d )x + (- 12a b d + 12b c d)x +--R / +--R 5 6 6 5 +--R 12a b d - 12b c d +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)) +--R +--R +--R 4 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1092 +r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ + 1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/3*x^3/(b*d)+_ + a^4*log(a+b*x)/(b^4*(b*c-a*d))-c^4*log(c+d*x)/(d^4*(b*c-a*d)) +--R +--R +--R (2) +--R 4 4 4 4 3 4 4 3 3 +--R 6b c log(d x + c) - 6a d log(b x + a) + (2a b d - 2b c d )x +--R + +--R 2 2 4 4 2 2 2 3 4 4 3 +--R (- 3a b d + 3b c d )x + (6a b d - 6b c d)x +--R / +--R 4 5 5 4 +--R 6a b d - 6b c d +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 4 4 3 3 +--R 6b c log(d x + c) - 6a d log(b x + a) + (2a b d - 2b c d )x +--R + +--R 2 2 4 4 2 2 2 3 4 4 3 +--R (- 3a b d + 3b c d )x + (6a b d - 6b c d)x +--R / +--R 4 5 5 4 +--R 6a b d - 6b c d +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)) +--R +--R +--R 3 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1092 +r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ + c^3*log(c+d*x)/(d^3*(b*c-a*d)) +--R +--R +--R (2) +--R 3 3 3 3 2 3 3 2 2 +--R - 2b c log(d x + c) + 2a d log(b x + a) + (a b d - b c d )x +--R + +--R 2 3 3 2 +--R (- 2a b d + 2b c d)x +--R / +--R 3 4 4 3 +--R 2a b d - 2b c d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 3 2 3 3 2 2 +--R - 2b c log(d x + c) + 2a d log(b x + a) + (a b d - b c d )x +--R + +--R 2 3 3 2 +--R (- 2a b d + 2b c d)x +--R / +--R 3 4 4 3 +--R 2a b d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1092 +r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) +--R +--R +--R 2 2 2 2 2 2 +--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x +--R (2) ------------------------------------------------------- +--R 2 3 3 2 +--R a b d - b c d +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 +--R b c log(d x + c) - a d log(b x + a) + (a b d - b c d)x +--R (3) ------------------------------------------------------- +--R 2 3 3 2 +--R a b d - b c d +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1092 +t0:=x/((a+b*x)*(c+d*x)) +--R +--R +--R x +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1092 +r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) +--R +--R +--R - b c log(d x + c) + a d log(b x + a) +--R (2) ------------------------------------- +--R 2 2 +--R a b d - b c d +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1092 +a0:=integrate(t0,x) +--R +--R +--R - b c log(d x + c) + a d log(b x + a) +--R (3) ------------------------------------- +--R 2 2 +--R a b d - b c d +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1092 +t0:=1/((a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1092 +r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) +--R +--R +--R log(d x + c) - log(b x + a) +--R (2) --------------------------- +--R a d - b c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1092 +a0:=integrate(t0,x) +--R +--R +--R log(d x + c) - log(b x + a) +--R (3) --------------------------- +--R a d - b c +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1092 +r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) +--R +--R +--R - a d log(d x + c) + b c log(b x + a) + (a d - b c)log(x) +--R (2) --------------------------------------------------------- +--R 2 2 +--R a c d - a b c +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1092 +a0:=integrate(t0,x) +--R +--R +--R - a d log(d x + c) + b c log(b x + a) + (a d - b c)log(x) +--R (3) --------------------------------------------------------- +--R 2 2 +--R a c d - a b c +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 4 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 1092 +r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ + b^2*log(a+b*x)/(a^2*(b*c-a*d))-d^2*log(c+d*x)/(c^2*(b*c-a*d)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R a d x log(d x + c) - b c x log(b x + a) + (- a d + b c )x log(x) - a c d +--R + +--R 2 +--R a b c +--R / +--R 3 2 2 3 +--R (a c d - a b c )x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R a d x log(d x + c) - b c x log(b x + a) + (- a d + b c )x log(x) - a c d +--R + +--R 2 +--R a b c +--R / +--R 3 2 2 3 +--R (a c d - a b c )x +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 5 4 3 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1092 +r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ + log(x)/(a^3*c^3)-b^3*log(a+b*x)/(a^3*(b*c-a*d))+_ + d^3*log(c+d*x)/(c^3*(b*c-a*d)) +--R +--R +--R (2) +--R 3 3 2 3 3 2 3 3 3 3 2 +--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (2a d - 2b c )x log(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (2a c d - 2a b c )x - a c d + a b c +--R / +--R 4 3 3 4 2 +--R (2a c d - 2a b c )x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 3 3 2 3 3 3 3 2 +--R - 2a d x log(d x + c) + 2b c x log(b x + a) + (2a d - 2b c )x log(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (2a c d - 2a b c )x - a c d + a b c +--R / +--R 4 3 3 4 2 +--R (2a c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1092 +t0:=1/(x^4*(a+b*x)*(c+d*x)) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 6 5 4 +--R b d x + (a d + b c)x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1092 +r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ + (-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*_ + log(x)/(a^4*c^4)+b^4*log(a+b*x)/(a^4*(b*c-a*d))-_ + d^4*log(c+d*x)/(c^4*(b*c-a*d)) +--R +--R +--R (2) +--R 4 4 3 4 4 3 4 4 4 4 3 +--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 6a d + 6b c )x log(x) +--R + +--R 4 3 3 4 2 4 2 2 2 2 4 4 3 3 4 +--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c +--R / +--R 5 4 4 5 3 +--R (6a c d - 6a b c )x +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 4 4 3 4 4 4 4 3 +--R 6a d x log(d x + c) - 6b c x log(b x + a) + (- 6a d + 6b c )x log(x) +--R + +--R 4 3 3 4 2 4 2 2 2 2 4 4 3 3 4 +--R (- 6a c d + 6a b c )x + (3a c d - 3a b c )x - 2a c d + 2a b c +--R / +--R 5 4 4 5 3 +--R (6a c d - 6a b c )x +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)^2) +--R +--R +--R m +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1092 +--r0:=-d*x^(1+m)/(c*(b*c-a*d)*(c+d*x))+b^2*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^2*(1+m))-b*d*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^2*(1+m))+d*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)*(1+m)) +--E 377 + +--S 378 of 1092 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 1092 +--m0:=a0-r0 +--E 379 + +--S 380 of 1092 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 1092 +t0:=x^m/((1-a*x)^2*(1+a*x)) +--R +--R +--R m +--R x +--R (1) --------------------- +--R 3 3 2 2 +--R a x - a x - a x + 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1092 +--r0:=1/2*x^(1+m)/(1-a*x)+1/4*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-a*x)/(1+m)+1/4*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,a*x)/(1+m)-1/2*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,a*x)/(1+m) +--E 382 + +--S 383 of 1092 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 1092 +--m0:=a0-r0 +--E 384 + +--S 385 of 1092 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)^2) +--R +--R +--R 5 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1092 +r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ + 1/2*(2*b*c+a*d)*x^2/(b^2*d^3)+1/3*x^3/(b*d^2)-_ + c^5/(d^5*(b*c-a*d)*(c+d*x))-a^5*log(a+b*x)/(b^4*(b*c-a*d)^2)-_ + c^4*(4*b*c-5*a*d)*log(c+d*x)/(d^5*(b*c-a*d)^2) +--R +--R +--R (2) +--R 4 4 2 5 5 4 5 5 6 +--R ((30a b c d - 24b c d)x + 30a b c d - 24b c )log(d x + c) +--R + +--R 5 6 5 5 2 3 6 4 5 5 2 4 4 +--R (- 6a d x - 6a c d )log(b x + a) + (2a b d - 4a b c d + 2b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (- 3a b d + 2a b c d + 5a b c d - 4b c d )x +--R + +--R 4 6 3 2 5 4 3 3 5 4 2 2 +--R (6a b d - 3a b c d - 15a b c d + 12b c d )x +--R + +--R 4 5 4 4 2 5 5 4 5 5 6 +--R (6a b c d - 24a b c d + 18b c d)x + 6a b c d - 6b c +--R / +--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 +--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 2 5 5 4 5 5 6 +--R ((30a b c d - 24b c d)x + 30a b c d - 24b c )log(d x + c) +--R + +--R 5 6 5 5 2 3 6 4 5 5 2 4 4 +--R (- 6a d x - 6a c d )log(b x + a) + (2a b d - 4a b c d + 2b c d )x +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 3 +--R (- 3a b d + 2a b c d + 5a b c d - 4b c d )x +--R + +--R 4 6 3 2 5 4 3 3 5 4 2 2 +--R (6a b d - 3a b c d - 15a b c d + 12b c d )x +--R + +--R 4 5 4 4 2 5 5 4 5 5 6 +--R (6a b c d - 24a b c d + 18b c d)x + 6a b c d - 6b c +--R / +--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 +--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)^2) +--R +--R +--R 4 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1092 +r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ + c^4/(d^4*(b*c-a*d)*(c+d*x))+a^4*log(a+b*x)/(b^3*(b*c-a*d)^2)+_ + c^3*(3*b*c-4*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^2) +--R +--R +--R (2) +--R 3 3 2 4 4 3 4 4 5 +--R ((- 8a b c d + 6b c d)x - 8a b c d + 6b c )log(d x + c) +--R + +--R 4 5 4 4 2 2 5 3 4 4 2 3 3 +--R (2a d x + 2a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 2a b d + a b c d + 4a b c d - 3b c d )x +--R + +--R 3 4 3 3 2 4 4 3 4 4 5 +--R (- 2a b c d + 6a b c d - 4b c d)x - 2a b c d + 2b c +--R / +--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 +--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 4 4 3 4 4 5 +--R ((- 8a b c d + 6b c d)x - 8a b c d + 6b c )log(d x + c) +--R + +--R 4 5 4 4 2 2 5 3 4 4 2 3 3 +--R (2a d x + 2a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 2 +--R (- 2a b d + a b c d + 4a b c d - 3b c d )x +--R + +--R 3 4 3 3 2 4 4 3 4 4 5 +--R (- 2a b c d + 6a b c d - 4b c d)x - 2a b c d + 2b c +--R / +--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 +--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)^2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1092 +r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ + a^3*log(a+b*x)/(b^2*(b*c-a*d)^2)-c^2*(2*b*c-3*a*d)*log(c+d*x)/_ + (d^3*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 2 2 3 3 2 3 3 4 +--R ((3a b c d - 2b c d)x + 3a b c d - 2b c )log(d x + c) +--R + +--R 3 4 3 3 2 4 2 3 3 2 2 2 +--R (- a d x - a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 2 3 2 2 2 3 3 2 3 3 4 +--R (a b c d - 2a b c d + b c d)x + a b c d - b c +--R / +--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 3 2 3 3 4 +--R ((3a b c d - 2b c d)x + 3a b c d - 2b c )log(d x + c) +--R + +--R 3 4 3 3 2 4 2 3 3 2 2 2 +--R (- a d x - a c d )log(b x + a) + (a b d - 2a b c d + b c d )x +--R + +--R 2 3 2 2 2 3 3 2 3 3 4 +--R (a b c d - 2a b c d + b c d)x + a b c d - b c +--R / +--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)^2) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1092 +r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ + c*(b*c-2*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 2 2 2 2 3 +--R ((- 2a b c d + b c d)x - 2a b c d + b c )log(d x + c) +--R + +--R 2 3 2 2 2 2 3 +--R (a d x + a c d )log(b x + a) - a b c d + b c +--R / +--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 3 +--R ((- 2a b c d + b c d)x - 2a b c d + b c )log(d x + c) +--R + +--R 2 3 2 2 2 2 3 +--R (a d x + a c d )log(b x + a) - a b c d + b c +--R / +--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 +--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1092 +t0:=x/((a+b*x)*(c+d*x)^2) +--R +--R +--R x +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1092 +r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (2) +--R 2 2 2 +--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d - b c +--R -------------------------------------------------------------------------- +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 +--R (a d x + a c d)log(d x + c) + (- a d x - a c d)log(b x + a) + a c d - b c +--R -------------------------------------------------------------------------- +--R 2 4 3 2 2 2 2 3 2 2 2 3 +--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1092 +t0:=1/((a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1092 +r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (2) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (- b d x - b c)log(d x + c) + (b d x + b c)log(b x + a) - a d + b c +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 2 2 2 2 2 3 +--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------ +--R 2 4 2 3 2 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1092 +r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ + b^2*log(a+b*x)/(a*(b*c-a*d)^2)+d*(2*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^2) +--R +--R +--R (2) +--R 2 3 2 2 2 2 +--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c) +--R + +--R 2 2 2 3 +--R (- b c d x - b c )log(b x + a) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c )log(x) + a c d +--R + +--R 2 +--R - a b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 +--R ((- a d + 2a b c d )x - a c d + 2a b c d)log(d x + c) +--R + +--R 2 2 2 3 +--R (- b c d x - b c )log(b x + a) +--R + +--R 2 3 2 2 2 2 2 2 2 3 2 2 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c )log(x) + a c d +--R + +--R 2 +--R - a b c d +--R / +--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 +--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1092 +r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ + (b*c+2*a*d)*log(x)/(a^2*c^3)+b^3*log(a+b*x)/(a^2*(b*c-a*d)^2)-_ + d^2*(3*b*c-2*a*d)*log(c+d*x)/(c^3*(b*c-a*d)^2) +--R +--R +--R (2) +--R 3 4 2 3 2 3 3 2 2 2 +--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x)log(d x + c) +--R + +--R 3 3 2 3 4 +--R (b c d x + b c x)log(b x + a) +--R + +--R 3 4 2 3 3 3 2 3 3 2 2 2 3 4 +--R ((- 2a d + 3a b c d - b c d)x + (- 2a c d + 3a b c d - b c )x)log(x) +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 2 4 +--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c +--R / +--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 +--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 3 2 3 3 2 2 2 +--R ((2a d - 3a b c d )x + (2a c d - 3a b c d )x)log(d x + c) +--R + +--R 3 3 2 3 4 +--R (b c d x + b c x)log(b x + a) +--R + +--R 3 4 2 3 3 3 2 3 3 2 2 2 3 4 +--R ((- 2a d + 3a b c d - b c d)x + (- 2a c d + 3a b c d - b c )x)log(x) +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 2 4 +--R (- 2a c d + 3a b c d - a b c d)x - a c d + 2a b c d - a b c +--R / +--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 +--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 2 6 2 5 2 4 2 3 +--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1092 +r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ + d^3/(c^3*(b*c-a*d)*(c+d*x))+(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*log(x)/_ + (a^3*c^4)-b^4*log(a+b*x)/(a^3*(b*c-a*d)^2)+d^3*(4*b*c-3*a*d)*_ + log(c+d*x)/(c^4*(b*c-a*d)^2) +--R +--R +--R (2) +--R 4 5 3 4 3 4 4 3 2 3 2 +--R ((- 6a d + 8a b c d )x + (- 6a c d + 8a b c d )x )log(d x + c) +--R + +--R 4 4 3 4 5 2 +--R (- 2b c d x - 2b c x )log(b x + a) +--R + +--R 4 5 3 4 4 4 3 4 4 3 2 3 4 5 2 +--R ((6a d - 8a b c d + 2b c d)x + (6a c d - 8a b c d + 2b c )x )log(x) +--R + +--R 4 4 3 2 3 3 4 2 +--R (6a c d - 8a b c d + 2a b c d)x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 3 2 3 4 2 2 5 +--R (3a c d - 4a b c d - a b c d + 2a b c )x - a c d + 2a b c d - a b c +--R / +--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 +--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 4 3 4 4 3 2 3 2 +--R ((- 6a d + 8a b c d )x + (- 6a c d + 8a b c d )x )log(d x + c) +--R + +--R 4 4 3 4 5 2 +--R (- 2b c d x - 2b c x )log(b x + a) +--R + +--R 4 5 3 4 4 4 3 4 4 3 2 3 4 5 2 +--R ((6a d - 8a b c d + 2b c d)x + (6a c d - 8a b c d + 2b c )x )log(x) +--R + +--R 4 4 3 2 3 3 4 2 +--R (6a c d - 8a b c d + 2a b c d)x +--R + +--R 4 2 3 3 3 2 2 2 4 3 5 4 3 2 3 4 2 2 5 +--R (3a c d - 4a b c d - a b c d + 2a b c )x - a c d + 2a b c d - a b c +--R / +--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 +--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1092 +t0:=x^m/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R m +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1092 +--r0:=-1/2*d*x^(1+m)/(c*(b*c-a*d)*(c+d*x)^2)-_ +-- b*d*x^(1+m)/(c*(b*c-a*d)^2*(c+d*x))-_ +-- 1/2*d*(1-m)*x^(1+m)/(c^2*(b*c-a*d)*(c+d*x))+_ +-- b^3*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^3*(1+m))-b^2*d*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^3*(1+m))+b*d*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)^2*(1+m))+_ +-- 1/2*d*(1-m)*m*x^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^3*(b*c-a*d)*(1+m)) +--E 432 + +--S 433 of 1092 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 1092 +--m0:=a0-r0 +--E 434 + +--S 435 of 1092 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 1092 +t0:=x^6/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 1092 +r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ + 1/2*(3*b*c+a*d)*x^2/(b^2*d^4)+1/3*x^3/(b*d^3)+_ + 1/2*c^6/(d^6*(b*c-a*d)*(c+d*x)^2)-_ + c^5*(5*b*c-6*a*d)/(d^6*(b*c-a*d)^2*(c+d*x))+_ + a^6*log(a+b*x)/(b^4*(b*c-a*d)^3)-_ + c^4*(10*b^2*c^2-24*a*b*c*d+15*a^2*d^2)*log(c+d*x)/(d^6*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 4 4 4 5 5 3 6 6 2 2 +--R (90a b c d - 144a b c d + 60b c d )x +--R + +--R 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (180a b c d - 288a b c d + 120b c d)x + 90a b c d - 144a b c d +--R + +--R 6 8 +--R 60b c +--R * +--R log(d x + c) +--R + +--R 6 8 2 6 7 6 2 6 +--R (- 6a d x - 12a c d x - 6a c d )log(b x + a) +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 4 +--R (- 3a b d + 4a b c d + 6a b c d - 12a b c d + 5b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 3 +--R (6a b d - 6a b c d + 2a b c d - 30a b c d + 48a b c d - 20b c d )x +--R + +--R 5 7 4 2 2 6 2 4 4 4 5 5 3 6 6 2 2 +--R (12a b c d - 3a b c d - 102a b c d + 156a b c d - 63b c d )x +--R + +--R 5 2 6 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (6a b c d - 24a b c d + 24a b c d - 6b c d)x + 33a b c d - 60a b c d +--R + +--R 6 8 +--R 27b c +--R / +--R 3 4 11 2 5 10 6 2 9 7 3 8 2 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 3 4 10 2 5 2 9 6 3 8 7 4 7 3 4 2 9 +--R (12a b c d - 36a b c d + 36a b c d - 12b c d )x + 6a b c d +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R - 18a b c d + 18a b c d - 6b c d +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 4 4 5 5 3 6 6 2 2 +--R (90a b c d - 144a b c d + 60b c d )x +--R + +--R 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (180a b c d - 288a b c d + 120b c d)x + 90a b c d - 144a b c d +--R + +--R 6 8 +--R 60b c +--R * +--R log(d x + c) +--R + +--R 6 8 2 6 7 6 2 6 +--R (- 6a d x - 12a c d x - 6a c d )log(b x + a) +--R + +--R 3 3 8 2 4 7 5 2 6 6 3 5 5 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 4 +--R (- 3a b d + 4a b c d + 6a b c d - 12a b c d + 5b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 3 +--R (6a b d - 6a b c d + 2a b c d - 30a b c d + 48a b c d - 20b c d )x +--R + +--R 5 7 4 2 2 6 2 4 4 4 5 5 3 6 6 2 2 +--R (12a b c d - 3a b c d - 102a b c d + 156a b c d - 63b c d )x +--R + +--R 5 2 6 2 4 5 3 5 6 2 6 7 2 4 6 2 5 7 +--R (6a b c d - 24a b c d + 24a b c d - 6b c d)x + 33a b c d - 60a b c d +--R + +--R 6 8 +--R 27b c +--R / +--R 3 4 11 2 5 10 6 2 9 7 3 8 2 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 3 4 10 2 5 2 9 6 3 8 7 4 7 3 4 2 9 +--R (12a b c d - 36a b c d + 36a b c d - 12b c d )x + 6a b c d +--R + +--R 2 5 3 8 6 4 7 7 5 6 +--R - 18a b c d + 18a b c d - 6b c d +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1092 +t0:=x^5/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 1092 +r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ + 1/2*c^5/(d^5*(b*c-a*d)*(c+d*x)^2)+c^4*(4*b*c-5*a*d)/_ + (d^5*(b*c-a*d)^2*(c+d*x))-a^5*log(a+b*x)/(b^3*(b*c-a*d)^3)+_ + c^3*(6*b^2*c^2-15*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 3 3 4 4 4 3 5 5 2 2 +--R (- 20a b c d + 30a b c d - 12b c d )x +--R + +--R 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 40a b c d + 60a b c d - 24b c d)x - 20a b c d + 30a b c d +--R + +--R 5 7 +--R - 12b c +--R * +--R log(d x + c) +--R + +--R 5 7 2 5 6 5 2 5 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (- 2a b d + 2a b c d + 6a b c d - 10a b c d + 4b c d )x +--R + +--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (- 4a b c d + a b c d + 21a b c d - 29a b c d + 11b c d )x +--R + +--R 4 2 5 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 2a b c d + 2a b c d + 2a b c d - 2b c d)x - 9a b c d + 16a b c d +--R + +--R 5 7 +--R - 7b c +--R / +--R 3 3 10 2 4 9 5 2 8 6 3 7 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 3 9 2 4 2 8 5 3 7 6 4 6 3 3 2 8 2 4 3 7 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 5 4 6 6 5 5 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 4 4 4 3 5 5 2 2 +--R (- 20a b c d + 30a b c d - 12b c d )x +--R + +--R 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 40a b c d + 60a b c d - 24b c d)x - 20a b c d + 30a b c d +--R + +--R 5 7 +--R - 12b c +--R * +--R log(d x + c) +--R + +--R 5 7 2 5 6 5 2 5 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 3 2 7 2 3 6 4 2 5 5 3 4 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (- 2a b d + 2a b c d + 6a b c d - 10a b c d + 4b c d )x +--R + +--R 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (- 4a b c d + a b c d + 21a b c d - 29a b c d + 11b c d )x +--R + +--R 4 2 5 2 3 4 3 4 5 2 5 6 2 3 5 2 4 6 +--R (- 2a b c d + 2a b c d + 2a b c d - 2b c d)x - 9a b c d + 16a b c d +--R + +--R 5 7 +--R - 7b c +--R / +--R 3 3 10 2 4 9 5 2 8 6 3 7 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 3 9 2 4 2 8 5 3 7 6 4 6 3 3 2 8 2 4 3 7 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 5 4 6 6 5 5 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1092 +t0:=x^4/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 1092 +r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ + c^3*(3*b*c-4*a*d)/(d^4*(b*c-a*d)^2*(c+d*x))+_ + a^4*log(a+b*x)/(b^2*(b*c-a*d)^3)-_ + c^2*(3*b^2*c^2-8*a*b*c*d+6*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 2 2 4 3 3 3 4 4 2 2 +--R (12a b c d - 16a b c d + 6b c d )x +--R + +--R 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 4 6 +--R (24a b c d - 32a b c d + 12b c d)x + 12a b c d - 16a b c d + 6b c +--R * +--R log(d x + c) +--R + +--R 4 6 2 4 5 4 2 4 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x +--R + +--R 3 2 4 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 +--R (2a b c d + 2a b c d - 8a b c d + 4b c d)x + 7a b c d - 12a b c d +--R + +--R 4 6 +--R 5b c +--R / +--R 3 2 9 2 3 8 4 2 7 5 3 6 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 2 8 2 3 2 7 4 3 6 5 4 5 3 2 2 7 2 3 3 6 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 4 4 5 5 5 4 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 4 3 3 3 4 4 2 2 +--R (12a b c d - 16a b c d + 6b c d )x +--R + +--R 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 4 6 +--R (24a b c d - 32a b c d + 12b c d)x + 12a b c d - 16a b c d + 6b c +--R * +--R log(d x + c) +--R + +--R 4 6 2 4 5 4 2 4 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 2 4 3 3 3 4 4 2 2 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x +--R + +--R 3 2 4 2 2 3 3 3 4 2 4 5 2 2 4 2 3 5 +--R (2a b c d + 2a b c d - 8a b c d + 4b c d)x + 7a b c d - 12a b c d +--R + +--R 4 6 +--R 5b c +--R / +--R 3 2 9 2 3 8 4 2 7 5 3 6 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 2 8 2 3 2 7 4 3 6 5 4 5 3 2 2 7 2 3 3 6 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 4 4 5 5 5 4 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1092 +t0:=x^3/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 1092 +r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ + (d^3*(b*c-a*d)^2*(c+d*x))-a^3*log(a+b*x)/(b*(b*c-a*d)^3)+_ + c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 2 4 2 2 3 3 3 2 2 +--R (- 6a b c d + 6a b c d - 2b c d )x +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 12a b c d + 12a b c d - 4b c d)x - 6a b c d + 6a b c d - 2b c +--R * +--R log(d x + c) +--R + +--R 3 5 2 3 4 3 2 3 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 6a b c d + 10a b c d - 4b c d)x - 5a b c d + 8a b c d - 3b c +--R / +--R 3 8 2 2 7 3 2 6 4 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 7 2 2 2 6 3 3 5 4 4 4 3 2 6 2 2 3 5 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 3 4 4 4 5 3 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 3 3 2 2 +--R (- 6a b c d + 6a b c d - 2b c d )x +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 12a b c d + 12a b c d - 4b c d)x - 6a b c d + 6a b c d - 2b c +--R * +--R log(d x + c) +--R + +--R 3 5 2 3 4 3 2 3 +--R (2a d x + 4a c d x + 2a c d )log(b x + a) +--R + +--R 2 2 3 2 3 2 3 4 2 3 2 2 4 3 5 +--R (- 6a b c d + 10a b c d - 4b c d)x - 5a b c d + 8a b c d - 3b c +--R / +--R 3 8 2 2 7 3 2 6 4 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 7 2 2 2 6 3 3 5 4 4 4 3 2 6 2 2 3 5 +--R (4a b c d - 12a b c d + 12a b c d - 4b c d )x + 2a b c d - 6a b c d +--R + +--R 3 4 4 4 5 3 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1092 +t0:=x^2/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 1092 +r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ + (d^2*(b*c-a*d)^2*(c+d*x))+a^2*log(a+b*x)/(b*c-a*d)^3-_ + a^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 4 2 2 3 2 2 2 +--R (2a d x + 4a c d x + 2a c d )log(d x + c) +--R + +--R 2 4 2 2 3 2 2 2 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4a c d - 6a b c d + 2b c d)x + 3a c d - 4a b c d + b c +--R / +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 2 5 2 3 4 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 3 3 5 2 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 2 2 +--R (2a d x + 4a c d x + 2a c d )log(d x + c) +--R + +--R 2 4 2 2 3 2 2 2 +--R (- 2a d x - 4a c d x - 2a c d )log(b x + a) +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (4a c d - 6a b c d + 2b c d)x + 3a c d - 4a b c d + b c +--R / +--R 3 7 2 6 2 2 5 3 3 4 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 2 5 2 3 4 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 3 3 5 2 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1092 +t0:=x/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 1092 +r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ + a*b*log(a+b*x)/(b*c-a*d)^3+a*b*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 3 2 2 2 +--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c) +--R + +--R 3 2 2 2 2 3 2 +--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a) + (- 2a d + 2a b c d )x +--R + +--R 2 2 2 3 +--R - a c d + b c +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 2 3 5 +--R 6a b c d - 2b c d +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 +--R (- 2a b d x - 4a b c d x - 2a b c d)log(d x + c) +--R + +--R 3 2 2 2 2 3 2 +--R (2a b d x + 4a b c d x + 2a b c d)log(b x + a) + (- 2a d + 2a b c d )x +--R + +--R 2 2 2 3 +--R - a c d + b c +--R / +--R 3 6 2 5 2 2 4 3 3 3 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 5 2 2 4 2 3 3 3 4 2 3 2 4 2 3 3 +--R (4a c d - 12a b c d + 12a b c d - 4b c d )x + 2a c d - 6a b c d +--R + +--R 2 4 2 3 5 +--R 6a b c d - 2b c d +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1092 +t0:=1/((a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 3 4 3 2 3 2 2 2 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 1092 +r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ + b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (2b d x + 4b c d x + 2b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- 2b d x - 4b c d x - 2b c )log(b x + a) + (2a b d - 2b c d)x - a d +--R + +--R 2 2 +--R 4a b c d - 3b c +--R / +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1092 +t0:=1/(x*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 5 3 2 4 2 2 3 2 3 2 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 1092 +r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ + (c^2*(b*c-a*d)^2*(c+d*x))+log(x)/(a*c^3)-_ + b^3*log(a+b*x)/(a*(b*c-a*d)^3)+d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_ + log(c+d*x)/(c^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 5 2 4 2 2 3 2 +--R (- 2a d + 6a b c d - 6a b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2b c d x + 4b c d x + 2b c )log(b x + a) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x + 2a c d - 6a b c d +--R + +--R 2 2 7 3 8 +--R 6a b c d - 2a b c +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 2 4 2 2 3 2 +--R (- 2a d + 6a b c d - 6a b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (- 4a c d + 12a b c d - 12a b c d )x - 2a c d + 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 3 4 3 5 +--R (2b c d x + 4b c d x + 2b c )log(b x + a) +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (2a d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 2 3 2 +--R (4a c d - 12a b c d + 12a b c d - 4b c d)x + 2a c d - 6a b c d +--R + +--R 2 4 3 5 +--R 6a b c d - 2b c +--R * +--R log(x) +--R + +--R 3 4 2 2 3 2 3 2 3 2 3 2 3 2 2 4 +--R (2a c d - 6a b c d + 4a b c d )x + 3a c d - 8a b c d + 5a b c d +--R / +--R 4 3 5 3 4 4 2 2 5 3 3 6 2 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 4 4 4 3 5 3 2 2 6 2 3 7 4 5 3 3 6 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x + 2a c d - 6a b c d +--R + +--R 2 2 7 3 8 +--R 6a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1092 +t0:=1/(x^2*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 6 3 2 5 2 2 4 2 3 3 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 2 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1092 +r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ + d^2*(3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x))-(b*c+3*a*d)*_ + log(x)/(a^2*c^4)+b^4*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ + d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 6 3 5 2 2 2 4 3 +--R (6a d - 16a b c d + 12a b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 2 +--R (12a c d - 32a b c d + 24a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 +--R (6a c d - 16a b c d + 12a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 4 2 3 4 5 2 4 6 +--R (- 2b c d x - 4b c d x - 2b c x)log(b x + a) +--R + +--R 4 6 3 5 2 2 2 4 4 4 2 3 +--R (- 6a d + 16a b c d - 12a b c d + 2b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 5 2 +--R (- 12a c d + 32a b c d - 24a b c d + 4b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 4 6 +--R (- 6a c d + 16a b c d - 12a b c d + 2b c )x +--R * +--R log(x) +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 2 +--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d +--R + +--R 2 2 5 3 6 +--R - 6a b c d + 2a b c +--R / +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 3 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 5 2 2 2 4 3 +--R (6a d - 16a b c d + 12a b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 2 +--R (12a c d - 32a b c d + 24a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 +--R (6a c d - 16a b c d + 12a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 4 2 3 4 5 2 4 6 +--R (- 2b c d x - 4b c d x - 2b c x)log(b x + a) +--R + +--R 4 6 3 5 2 2 2 4 4 4 2 3 +--R (- 6a d + 16a b c d - 12a b c d + 2b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 4 5 2 +--R (- 12a c d + 32a b c d - 24a b c d + 4b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 4 6 +--R (- 6a c d + 16a b c d - 12a b c d + 2b c )x +--R * +--R log(x) +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 2 +--R (- 6a c d + 16a b c d - 12a b c d + 2a b c d )x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (- 9a c d + 24a b c d - 19a b c d + 4a b c d)x - 2a c d + 6a b c d +--R + +--R 2 2 5 3 6 +--R - 6a b c d + 2a b c +--R / +--R 5 4 5 4 5 4 3 2 6 3 2 3 7 2 3 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 5 5 4 4 6 3 3 2 7 2 2 3 8 2 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 5 6 3 4 7 2 3 2 8 2 3 9 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1092 +t0:=1/(x^3*(a+b*x)*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 7 3 2 6 2 2 5 2 3 4 +--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x +--R + +--R 3 3 +--R a c x +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1092 +r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ + (c+d*x)^2)-d^3*(4*b*c-3*a*d)/(c^4*(b*c-a*d)^2*(c+d*x))+_ + (b^2*c^2+3*a*b*c*d+6*a^2*d^2)*log(x)/(a^3*c^5)-b^5*_ + log(a+b*x)/(a^3*(b*c-a*d)^3)+d^3*(10*b^2*c^2-15*a*b*c*d+6*a^2*d^2)*_ + log(c+d*x)/(c^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 7 4 6 3 2 2 5 4 +--R (- 12a d + 30a b c d - 20a b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 3 +--R (- 24a c d + 60a b c d - 40a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 +--R (- 12a c d + 30a b c d - 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 5 2 4 5 6 3 5 7 2 +--R (2b c d x + 4b c d x + 2b c x )log(b x + a) +--R + +--R 5 7 4 6 3 2 2 5 5 5 2 4 +--R (12a d - 30a b c d + 20a b c d - 2b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 5 6 3 +--R (24a c d - 60a b c d + 40a b c d - 4b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 5 7 2 +--R (12a c d - 30a b c d + 20a b c d - 2b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 3 2 3 4 4 5 2 3 +--R (12a c d - 30a b c d + 20a b c d - 2a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (18a c d - 45a b c d + 30a b c d + a b c d - 4a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (4a c d - 10a b c d + 6a b c d + 2a b c d - 2a b c )x - a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R 3a b c d - 3a b c d + a b c +--R / +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 4 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 3 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 6 7 3 5 8 2 4 2 9 3 3 10 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 4 6 3 2 2 5 4 +--R (- 12a d + 30a b c d - 20a b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 3 +--R (- 24a c d + 60a b c d - 40a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 +--R (- 12a c d + 30a b c d - 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 5 2 4 5 6 3 5 7 2 +--R (2b c d x + 4b c d x + 2b c x )log(b x + a) +--R + +--R 5 7 4 6 3 2 2 5 5 5 2 4 +--R (12a d - 30a b c d + 20a b c d - 2b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 5 6 3 +--R (24a c d - 60a b c d + 40a b c d - 4b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 5 7 2 +--R (12a c d - 30a b c d + 20a b c d - 2b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 5 3 2 3 4 4 5 2 3 +--R (12a c d - 30a b c d + 20a b c d - 2a b c d )x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 2 +--R (18a c d - 45a b c d + 30a b c d + a b c d - 4a b c d)x +--R + +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 4 7 5 4 3 +--R (4a c d - 10a b c d + 6a b c d + 2a b c d - 2a b c )x - a c d +--R + +--R 4 5 2 3 2 6 2 3 7 +--R 3a b c d - 3a b c d + a b c +--R / +--R 6 5 5 5 6 4 4 2 7 3 3 3 8 2 4 +--R (2a c d - 6a b c d + 6a b c d - 2a b c d )x +--R + +--R 6 6 4 5 7 3 4 2 8 2 3 3 9 3 +--R (4a c d - 12a b c d + 12a b c d - 4a b c d)x +--R + +--R 6 7 3 5 8 2 4 2 9 3 3 10 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1092 +t0:=x^4*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 6 5 2 4 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1092 +r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ + 1/3*(b*c-3*a*d)*(b*c-a*d)*x^3/b^4+1/2*d*(b*c-a*d)*x^4/b^3+_ + 1/5*d^2*x^5/b^2-a^4*(b*c-a*d)^2/(b^7*(a+b*x))-_ + 2*a^3*(2*b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 180a b d + 300a b c d - 120a b c )x - 180a d + 300a b c d +--R + +--R 4 2 2 +--R - 120a b c +--R * +--R log(b x + a) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6b d x + (- 9a b d + 15b c d)x + (15a b d - 25a b c d + 10b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 30a b d + 50a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (90a b d - 150a b c d + 60a b c )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (150a b d - 240a b c d + 90a b c )x - 30a d + 60a b c d - 30a b c +--R / +--R 8 7 +--R 30b x + 30a b +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 2 3 3 2 6 2 5 +--R (- 180a b d + 300a b c d - 120a b c )x - 180a d + 300a b c d +--R + +--R 4 2 2 +--R - 120a b c +--R * +--R log(b x + a) +--R + +--R 6 2 6 5 2 6 5 2 4 2 5 6 2 4 +--R 6b d x + (- 9a b d + 15b c d)x + (15a b d - 25a b c d + 10b c )x +--R + +--R 3 3 2 2 4 5 2 3 +--R (- 30a b d + 50a b c d - 20a b c )x +--R + +--R 4 2 2 3 3 2 4 2 2 +--R (90a b d - 150a b c d + 60a b c )x +--R + +--R 5 2 4 2 3 3 2 6 2 5 4 2 2 +--R (150a b d - 240a b c d + 90a b c )x - 30a d + 60a b c d - 30a b c +--R / +--R 8 7 +--R 30b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1092 +t0:=x^3*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1092 +r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ + 2/3*d*(b*c-a*d)*x^3/b^3+1/4*d^2*x^4/b^2+_ + a^3*(b*c-a*d)^2/(b^6*(a+b*x))+a^2*(3*b*c-5*a*d)*(b*c-a*d)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R ((60a b d - 96a b c d + 36a b c )x + 60a d - 96a b c d + 36a b c ) +--R * +--R log(b x + a) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3b d x + (- 5a b d + 8b c d)x + (10a b d - 16a b c d + 6b c )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 30a b d + 48a b c d - 18a b c )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 48a b d + 72a b c d - 24a b c )x + 12a d - 24a b c d + 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R ((60a b d - 96a b c d + 36a b c )x + 60a d - 96a b c d + 36a b c ) +--R * +--R log(b x + a) +--R + +--R 5 2 5 4 2 5 4 2 3 2 4 5 2 3 +--R 3b d x + (- 5a b d + 8b c d)x + (10a b d - 16a b c d + 6b c )x +--R + +--R 3 2 2 2 3 4 2 2 +--R (- 30a b d + 48a b c d - 18a b c )x +--R + +--R 4 2 3 2 2 3 2 5 2 4 3 2 2 +--R (- 48a b d + 72a b c d - 24a b c )x + 12a d - 24a b c d + 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1092 +t0:=x^2*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +--R d x + 2c d x + c x +--R (1) --------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1092 +r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ + a^2*(b*c-a*d)^2/(b^5*(a+b*x))-2*a*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((- 12a b d + 18a b c d - 6a b c )x - 12a d + 18a b c d - 6a b c ) +--R * +--R log(b x + a) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R b d x + (- 2a b d + 3b c d)x + (6a b d - 9a b c d + 3b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (9a b d - 12a b c d + 3a b c )x - 3a d + 6a b c d - 3a b c +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R ((- 12a b d + 18a b c d - 6a b c )x - 12a d + 18a b c d - 6a b c ) +--R * +--R log(b x + a) +--R + +--R 4 2 4 3 2 4 3 2 2 2 3 4 2 2 +--R b d x + (- 2a b d + 3b c d)x + (6a b d - 9a b c d + 3b c )x +--R + +--R 3 2 2 2 3 2 4 2 3 2 2 2 +--R (9a b d - 12a b c d + 3a b c )x - 3a d + 6a b c d - 3a b c +--R / +--R 6 5 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1092 +t0:=x*(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 3 2 2 +--R d x + 2c d x + c x +--R (1) -------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1092 +r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ + (b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d +--R + +--R 2 2 2 +--R - 4a b c d + 2a b c +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((6a b d - 8a b c d + 2b c )x + 6a d - 8a b c d + 2a b c )log(b x + a) +--R + +--R 3 2 3 2 2 3 2 2 2 2 3 2 +--R b d x + (- 3a b d + 4b c d)x + (- 4a b d + 4a b c d)x + 2a d +--R + +--R 2 2 2 +--R - 4a b c d + 2a b c +--R / +--R 5 4 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1092 +t0:=(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1092 +r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 +--R ((- 2a b d + 2b c d)x - 2a d + 2a b c d)log(b x + a) + b d x + a b d x +--R + +--R 2 2 2 2 +--R - a d + 2a b c d - b c +--R / +--R 4 3 +--R b x + a b +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1092 +t0:=(c+d*x)^2/(x*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) -------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1092 +r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) +--R +--R +--R (2) +--R 2 2 3 2 3 2 2 2 3 2 2 2 +--R ((a b d - b c )x + a d - a b c )log(b x + a) + (b c x + a b c )log(x) +--R + +--R 3 2 2 2 2 +--R a d - 2a b c d + a b c +--R / +--R 2 3 3 2 +--R a b x + a b +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 2 3 2 2 2 3 2 2 2 +--R ((a b d - b c )x + a d - a b c )log(b x + a) + (b c x + a b c )log(x) +--R + +--R 3 2 2 2 2 +--R a d - 2a b c d + a b c +--R / +--R 2 3 3 2 +--R a b x + a b +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1092 +t0:=(c+d*x)^2/(x^2*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1092 +r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ + log(x)/a^3+2*c*(b*c-a*d)*log(a+b*x)/a^3 +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x)log(b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((2a b c d - 2b c )x + (2a b c d - 2a b c )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- a d + 2a b c d - 2a b c )x - a b c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 2 2 2 +--R ((- 2a b c d + 2b c )x + (- 2a b c d + 2a b c )x)log(b x + a) +--R + +--R 2 3 2 2 2 2 2 +--R ((2a b c d - 2b c )x + (2a b c d - 2a b c )x)log(x) +--R + +--R 3 2 2 2 2 2 2 +--R (- a d + 2a b c d - 2a b c )x - a b c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1092 +t0:=(c+d*x)^2/(x^3*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1092 +r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ + (b*c-a*d)*(3*b*c-a*d)*log(x)/a^4-(b*c-a*d)*(3*b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((- 2a b d + 8a b c d - 6b c )x + (- 2a d + 8a b c d - 6a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 8a b c d + 6b c )x + (2a d - 8a b c d + 6a b c )x )log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (2a d - 8a b c d + 6a b c )x + (- 4a c d + 3a b c )x - a c +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((- 2a b d + 8a b c d - 6b c )x + (- 2a d + 8a b c d - 6a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 8a b c d + 6b c )x + (2a d - 8a b c d + 6a b c )x )log(x) +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (2a d - 8a b c d + 6a b c )x + (- 4a c d + 3a b c )x - a c +--R / +--R 4 3 5 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1092 +t0:=(c+d*x)^2/(x^4*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1092 +r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ + (a^4*x)-b*(b*c-a*d)^2/(a^4*(a+b*x))-2*b*(b*c-a*d)*(2*b*c-a*d)*_ + log(x)/a^5+2*b*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R ((6a b d - 18a b c d + 12b c )x + (6a b d - 18a b c d + 12a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (- 6a b d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6a b d + 18a b c d - 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 6a b d + 18a b c d - 12a b c )x + (- 3a d + 9a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 3a c d + 2a b c )x - a c +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 2 4 3 2 2 2 3 2 3 +--R ((6a b d - 18a b c d + 12b c )x + (6a b d - 18a b c d + 12a b c )x ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 4 2 4 +--R (- 6a b d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 6a b d + 18a b c d - 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (- 6a b d + 18a b c d - 12a b c )x + (- 3a d + 9a b c d - 6a b c )x +--R + +--R 4 3 2 4 2 +--R (- 3a c d + 2a b c )x - a c +--R / +--R 5 4 6 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1092 +t0:=(c+d*x)^2/(x^5*(a+b*x)^2) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) --------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1092 +r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ + (3*b*c-a*d)/(a^4*x^2)+2*b*(b*c-a*d)*(2*b*c-a*d)/(a^5*x)+_ + b^2*(b*c-a*d)^2/(a^5*(a+b*x))+b^2*(5*b*c-3*a*d)*(b*c-a*d)*_ + log(x)/a^6-b^2*(5*b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 2 5 +--R (- 36a b d + 96a b c d - 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 36a b d + 96a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (36a b d - 96a b c d + 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (36a b d - 96a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (36a b d - 96a b c d + 60a b c )x + (18a b d - 48a b c d + 30a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (- 6a d + 16a b c d - 10a b c )x + (- 8a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 2 5 +--R (- 36a b d + 96a b c d - 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (- 36a b d + 96a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 5 2 5 +--R (36a b d - 96a b c d + 60b c )x +--R + +--R 3 2 2 2 3 4 2 4 +--R (36a b d - 96a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (36a b d - 96a b c d + 60a b c )x + (18a b d - 48a b c d + 30a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (- 6a d + 16a b c d - 10a b c )x + (- 8a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1092 +t0:=x^4*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 7 2 6 2 5 3 4 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1092 +r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ + (b*c-a*d)^2*x^2/b^6+1/3*(b*c-4*a*d)*(b*c-a*d)^2*x^3/b^5+_ + 3/4*d*(b*c-a*d)^2*x^4/b^4+1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+_ + 1/6*d^3*x^6/b^2-a^4*(b*c-a*d)^3/(b^8*(a+b*x))-_ + a^3*(4*b*c-7*a*d)*(b*c-a*d)^2*log(a+b*x)/b^8 +--R +--R +--R (2) +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (420a b d - 1080a b c d + 900a b c d - 240a b c )x + 420a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 1080a b c d + 900a b c d - 240a b c +--R * +--R log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 10b d x + (- 14a b d + 36b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (21a b d - 54a b c d + 45b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 35a b d + 90a b c d - 75a b c d + 20b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (70a b d - 180a b c d + 150a b c d - 40a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 540a b c d - 450a b c d + 120a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 360a b d + 900a b c d - 720a b c d + 180a b c )x + 60a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 180a b c d + 180a b c d - 60a b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (420a b d - 1080a b c d + 900a b c d - 240a b c )x + 420a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 1080a b c d + 900a b c d - 240a b c +--R * +--R log(b x + a) +--R + +--R 7 3 7 6 3 7 2 6 +--R 10b d x + (- 14a b d + 36b c d )x +--R + +--R 2 5 3 6 2 7 2 5 +--R (21a b d - 54a b c d + 45b c d)x +--R + +--R 3 4 3 2 5 2 6 2 7 3 4 +--R (- 35a b d + 90a b c d - 75a b c d + 20b c )x +--R + +--R 4 3 3 3 4 2 2 5 2 6 3 3 +--R (70a b d - 180a b c d + 150a b c d - 40a b c )x +--R + +--R 5 2 3 4 3 2 3 4 2 2 5 3 2 +--R (- 210a b d + 540a b c d - 450a b c d + 120a b c )x +--R + +--R 6 3 5 2 2 4 3 2 3 4 3 7 3 +--R (- 360a b d + 900a b c d - 720a b c d + 180a b c )x + 60a d +--R + +--R 6 2 5 2 2 4 3 3 +--R - 180a b c d + 180a b c d - 60a b c +--R / +--R 9 8 +--R 60b x + 60a b +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1092 +r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ + x^2/b^5+d*(b*c-a*d)^2*x^3/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_ + 1/5*d^3*x^5/b^2+a^3*(b*c-a*d)^3/(b^7*(a+b*x))+_ + 3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 120a b d + 300a b c d - 240a b c d + 60a b c )x - 120a d +--R + +--R 5 2 4 2 2 3 3 3 +--R 300a b c d - 240a b c d + 60a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R 4b d x + (- 6a b d + 15b c d )x + (10a b d - 25a b c d + 20b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 50a b c d - 40a b c d + 10b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 150a b c d + 120a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (100a b d - 240a b c d + 180a b c d - 40a b c )x - 20a d + 60a b c d +--R + +--R 4 2 2 3 3 3 +--R - 60a b c d + 20a b c +--R / +--R 8 7 +--R 20b x + 20a b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (- 120a b d + 300a b c d - 240a b c d + 60a b c )x - 120a d +--R + +--R 5 2 4 2 2 3 3 3 +--R 300a b c d - 240a b c d + 60a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R 4b d x + (- 6a b d + 15b c d )x + (10a b d - 25a b c d + 20b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 50a b c d - 40a b c d + 10b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 150a b c d + 120a b c d - 30a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (100a b d - 240a b c d + 180a b c d - 40a b c )x - 20a d + 60a b c d +--R + +--R 4 2 2 3 3 3 +--R - 60a b c d + 20a b c +--R / +--R 8 7 +--R 20b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1092 +r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ + 1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/4*d^3*x^4/b^2-a^2*_ + (b*c-a*d)^3/(b^6*(a+b*x))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (60a b d - 144a b c d + 108a b c d - 24a b c )x + 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 144a b c d + 108a b c d - 24a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 3b d x + (- 5a b d + 12b c d )x + (10a b d - 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 72a b c d - 54a b c d + 12b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (- 48a b d + 108a b c d - 72a b c d + 12a b c )x + 12a d - 36a b c d +--R + +--R 3 2 2 2 3 3 +--R 36a b c d - 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (60a b d - 144a b c d + 108a b c d - 24a b c )x + 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R - 144a b c d + 108a b c d - 24a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 3b d x + (- 5a b d + 12b c d )x + (10a b d - 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 30a b d + 72a b c d - 54a b c d + 12b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (- 48a b d + 108a b c d - 72a b c d + 12a b c )x + 12a d - 36a b c d +--R + +--R 3 2 2 2 3 3 +--R 36a b c d - 12a b c +--R / +--R 7 6 +--R 12b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1092 +t0:=x*(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1092 +r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ + a*(b*c-a*d)^3/(b^5*(a+b*x))+(b*c-4*a*d)*(b*c-a*d)^2*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d +--R + +--R 2 2 2 3 3 +--R - 36a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d +--R + +--R 3 3 +--R 6a b c +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (- 24a b d + 54a b c d - 36a b c d + 6b c )x - 24a d + 54a b c d +--R + +--R 2 2 2 3 3 +--R - 36a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 4 2 2 +--R 2b d x + (- 4a b d + 9b c d )x + (12a b d - 27a b c d + 18b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (18a b d - 36a b c d + 18a b c d)x - 6a d + 18a b c d - 18a b c d +--R + +--R 3 3 +--R 6a b c +--R / +--R 6 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1092 +t0:=(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1092 +r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ + 3*d*(b*c-a*d)^2*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b 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 2b x + 2a b +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R ((6a b d - 12a b c d + 6b c d)x + 6a d - 12a b c d + 6a b c d) +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 3 +--R b d x + (- 3a b d + 6b c d )x + (- 4a b d + 6a b 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 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 561 + +--S 562 of 1092 +r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ + (b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x)/(a^2*b^3) +--R +--R +--R (2) +--R 3 3 2 2 2 4 3 4 3 3 2 3 3 +--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 2 2 3 2 3 3 4 3 3 2 2 2 2 +--R (b c x + a b c )log(x) + a b d x + a b d x - a d + 3a b c d - 3a b c d +--R + +--R 3 3 +--R a b c +--R / +--R 2 4 3 3 +--R a b x + a b +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 4 3 4 3 3 2 3 3 +--R ((- 2a b d + 3a b c d - b c )x - 2a d + 3a b c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 4 3 3 3 2 2 3 2 3 3 4 3 3 2 2 2 2 +--R (b c x + a b c )log(x) + a b d x + a b d x - a d + 3a b c d - 3a b c d +--R + +--R 3 3 +--R a b c +--R / +--R 2 4 3 3 +--R a b x + a b +--R Type: Union(Expression(Integer),...) +--E 563 + +--S 564 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 565 + +)clear all + +--S 566 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 1092 +r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ + log(x)/a^3+(b*c-a*d)^2*(2*b*c+a*d)*log(a+b*x)/(a^3*b^2) +--R +--R +--R (2) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x) +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3a b c d - 2b c )x + (3a b c d - 2a b c )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c +--R / +--R 3 3 2 4 2 +--R a b x + a b x +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 3 2 4 3 2 2 2 3 3 +--R ((a b d - 3a b c d + 2b c )x + (a d - 3a b c d + 2a b c )x) +--R * +--R log(b x + a) +--R + +--R 3 2 4 3 2 2 2 2 3 3 +--R ((3a b c d - 2b c )x + (3a b c d - 2a b c )x)log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 2 3 +--R (a d - 3a b c d + 3a b c d - 2a b c )x - a b c +--R / +--R 3 3 2 4 2 +--R a b x + a b x +--R Type: Union(Expression(Integer),...) +--E 568 + +--S 569 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 570 + +)clear all + +--S 571 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 571 + +--S 572 of 1092 +r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ + (a^3*b*(a+b*x))+3*c*(b*c-a*d)^2*log(x)/a^4-3*c*(b*c-a*d)^2*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 2 4 3 3 +--R (- 6a b c d + 12a b c d - 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- 6a b c d + 12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 4 3 3 +--R (6a b c d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (6a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- 2a d + 6a b c d - 12a b c d + 6a b c )x + (- 6a b c d + 3a b c )x +--R + +--R 3 3 +--R - a b c +--R / +--R 4 2 3 5 2 +--R 2a b x + 2a b x +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 2 4 3 3 +--R (- 6a b c d + 12a b c d - 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (- 6a b c d + 12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 2 2 2 3 2 4 3 3 +--R (6a b c d - 12a b c d + 6b c )x +--R + +--R 3 2 2 2 2 3 3 2 +--R (6a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 2 3 2 2 2 3 +--R (- 2a d + 6a b c d - 12a b c d + 6a b c )x + (- 6a b c d + 3a b c )x +--R + +--R 3 3 +--R - a b c +--R / +--R 4 2 3 5 2 +--R 2a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 573 + +--S 574 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 575 + +)clear all + +--S 576 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1092 +r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ + (a^4*x)-(b*c-a*d)^3/(a^4*(a+b*x))-(b*c-a*d)^2*(4*b*c-a*d)*log(x)/_ + a^5+(b*c-a*d)^2*(4*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 6a b d + 36a b c d - 54a b c d + 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 36a b c d - 54a b c d + 24a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 36a b c d + 54a b c d - 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 27a b c d - 12a b c )x + (- 9a c d + 4a b c )x - 2a c +--R / +--R 5 4 6 3 +--R 6a b x + 6a x +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 6a b d + 36a b c d - 54a b c d + 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 36a b c d - 54a b c d + 24a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 36a b c d + 54a b c d - 24b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (6a d - 36a b c d + 54a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (- 18a c d + 27a b c d - 12a b c )x + (- 9a c d + 4a b c )x - 2a c +--R / +--R 5 4 6 3 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 578 + +--S 579 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1092 +t0:=(c+d*x)^3/(x^5*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 7 6 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 581 + +--S 582 of 1092 +r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ + 3/2*c*(b*c-a*d)^2/(a^4*x^2)+(b*c-a*d)^2*(4*b*c-a*d)/_ + (a^5*x)+b*(b*c-a*d)^3/(a^5*(a+b*x))+b*(5*b*c-2*a*d)*_ + (b*c-a*d)^2*log(x)/a^6-b*(5*b*c-2*a*d)*(b*c-a*d)^2*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (24a b d - 108a b c d + 144a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (24a b d - 108a b c d + 144a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 24a b d + 108a b c d - 144a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 12a d + 54a b c d - 72a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 24a b c d - 10a b c )x + (- 12a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (24a b d - 108a b c d + 144a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (24a b d - 108a b c d + 144a b c d - 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 24a b d + 108a b c d - 144a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 24a b d + 108a b c d - 144a b c d + 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 12a d + 54a b c d - 72a b c d + 30a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 24a b c d - 10a b c )x + (- 12a c d + 5a b c )x - 3a c +--R / +--R 6 5 7 4 +--R 12a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 583 + +--S 584 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1092 +t0:=(c+d*x)^3/(x^6*(a+b*x)^2) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 2 8 7 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1092 +r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ + (a^4*x^3)+1/2*(b*c-a*d)^2*(4*b*c-a*d)/(a^5*x^2)-_ + b*(5*b*c-2*a*d)*(b*c-a*d)^2/(a^6*x)-b^2*(b*c-a*d)^3/_ + (a^6*(a+b*x))-3*b^2*(b*c-a*d)^2*(2*b*c-a*d)*log(x)/a^7+_ + 3*b^2*(b*c-a*d)^2*(2*b*c-a*d)*log(a+b*x)/a^7 +--R +--R +--R (2) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 240a b c d - 300a b c d + 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 240a b c d - 300a b c d + 120a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 240a b c d + 300a b c d - 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R * +--R log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 120a b c d + 150a b c d - 60a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 10a d + 40a b c d - 50a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 20a c d + 25a b c d - 10a b c )x + (- 15a c d + 6a b c )x - 4a c +--R / +--R 7 6 8 5 +--R 20a b x + 20a x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (- 60a b d + 240a b c d - 300a b c d + 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (- 60a b d + 240a b c d - 300a b c d + 120a b c )x +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 4 2 5 2 6 3 6 +--R (60a b d - 240a b c d + 300a b c d - 120b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R * +--R log(x) +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 5 +--R (60a b d - 240a b c d + 300a b c d - 120a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 4 +--R (30a b d - 120a b c d + 150a b c d - 60a b c )x +--R + +--R 6 3 5 2 4 2 2 3 3 3 3 +--R (- 10a d + 40a b c d - 50a b c d + 20a b c )x +--R + +--R 6 2 5 2 4 2 3 2 6 2 5 3 6 3 +--R (- 20a c d + 25a b c d - 10a b c )x + (- 15a c d + 6a b c )x - 4a c +--R / +--R 7 6 8 5 +--R 20a b x + 20a x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1092 +t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 +--R +--R +--R 3 2 +-+ +--R (- 27x + 54x - 36x + 8)\|x +--R (1) ----------------------------- +--R 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1092 +r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ + 125*sqrt(x)/(1+x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (2) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1092 +r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ + 1/5*(62-513*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (3) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1092 +a0:=integrate(t0,x) +--R +--R +--R +-+ 3 2 +-+ +--R (2875x + 2875)atan(\|x ) + (- 54x + 306x - 1890x - 2875)\|x +--R (4) -------------------------------------------------------------- +--R 5x + 5 +--R Type: Union(Expression(Integer),...) +--E 594 + +--S 595 of 1092 +m0a:=a0-r0a +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1092 +d0:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1092 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1092 +d0:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1092 +t0:=x^6/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 6 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 599 + +--S 600 of 1092 +r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ + 1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-_ + c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/_ + (b^5*(b*c-a*d)^3)-2*c^5*(2*b*c-3*a*d)*log(c+d*x)/(d^5*(b*c-a*d)^3) +--R +--R +--R (2) +--R 6 5 2 7 6 2 2 5 5 2 6 6 7 7 +--R (- 18a b c d + 12b c d)x + (- 18a b c d - 6a b c d + 12b c )x +--R + +--R 2 5 6 6 7 +--R - 18a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 7 5 2 6 2 7 7 6 6 5 2 2 5 +--R (- 12a b d + 18a b c d )x + (- 12a d + 6a b c d + 18a b c d )x +--R + +--R 7 6 6 2 5 +--R - 12a c d + 18a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 3 +--R (6a b d - 11a b c d + 3a b c d - 3a b c d + 11a b c d - 6b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 2 +--R (9a b d - 9a b c d - 9a b c d + 9a b c d + 9a b c d - 9b c d)x +--R + +--R 7 7 6 6 5 2 2 5 2 5 5 2 6 6 7 7 +--R (- 3a d + 12a b c d - 15a b c d + 15a b c d - 12a b c d + 3b c )x +--R + +--R 7 6 6 2 5 2 5 6 6 7 +--R - 3a c d + 3a b c d - 3a b c d + 3a b c +--R / +--R 3 6 9 2 7 8 8 2 7 9 3 6 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 9 3 6 8 8 3 6 9 4 5 4 5 8 3 6 2 7 +--R (3a b d - 6a b c d + 6a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 2 7 3 6 8 4 5 +--R 9a b c d - 3a b c d +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 2 7 6 2 2 5 5 2 6 6 7 7 +--R (- 18a b c d + 12b c d)x + (- 18a b c d - 6a b c d + 12b c )x +--R + +--R 2 5 6 6 7 +--R - 18a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 7 5 2 6 2 7 7 6 6 5 2 2 5 +--R (- 12a b d + 18a b c d )x + (- 12a d + 6a b c d + 18a b c d )x +--R + +--R 7 6 6 2 5 +--R - 12a c d + 18a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 5 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 3 +--R (6a b d - 11a b c d + 3a b c d - 3a b c d + 11a b c d - 6b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 2 +--R (9a b d - 9a b c d - 9a b c d + 9a b c d + 9a b c d - 9b c d)x +--R + +--R 7 7 6 6 5 2 2 5 2 5 5 2 6 6 7 7 +--R (- 3a d + 12a b c d - 15a b c d + 15a b c d - 12a b c d + 3b c )x +--R + +--R 7 6 6 2 5 2 5 6 6 7 +--R - 3a c d + 3a b c d - 3a b c d + 3a b c +--R / +--R 3 6 9 2 7 8 8 2 7 9 3 6 2 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 9 3 6 8 8 3 6 9 4 5 4 5 8 3 6 2 7 +--R (3a b d - 6a b c d + 6a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 2 7 3 6 8 4 5 +--R 9a b c d - 3a b c d +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1092 +t0:=x^5/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 5 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 604 + +--S 605 of 1092 +r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ + (a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*_ + log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/_ + (d^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 4 2 6 5 2 2 4 4 2 5 5 6 6 +--R (10a b c d - 6b c d)x + (10a b c d + 4a b c d - 6b c )x +--R + +--R 2 4 5 5 6 +--R 10a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 6 4 2 5 2 6 6 5 5 4 2 2 4 +--R (6a b d - 10a b c d )x + (6a d - 4a b c d - 10a b c d )x +--R + +--R 6 5 5 2 4 +--R 6a c d - 10a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 3 +--R (- 3a b d + 6a b c d - 6a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 2 +--R (- 4a b d + 5a b c d + 5a b c d - 5a b c d - 5a b c d + 4b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 6 5 +--R (2a d - 6a b c d + 8a b c d - 8a b c d + 6a b c d - 2b c )x + 2a c d +--R + +--R 5 2 4 2 4 5 5 6 +--R - 2a b c d + 2a b c d - 2a b c +--R / +--R 3 5 8 2 6 7 7 2 6 8 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 4 8 3 5 7 7 3 5 8 4 4 4 4 7 3 5 2 6 +--R (2a b d - 4a b c d + 4a b c d - 2b c d )x + 2a b c d - 6a b c d +--R + +--R 2 6 3 5 7 4 4 +--R 6a b c d - 2a b c d +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 2 6 5 2 2 4 4 2 5 5 6 6 +--R (10a b c d - 6b c d)x + (10a b c d + 4a b c d - 6b c )x +--R + +--R 2 4 5 5 6 +--R 10a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 6 4 2 5 2 6 6 5 5 4 2 2 4 +--R (6a b d - 10a b c d )x + (6a d - 4a b c d - 10a b c d )x +--R + +--R 6 5 5 2 4 +--R 6a c d - 10a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 4 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 3 +--R (- 3a b d + 6a b c d - 6a b c d + 3b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 2 +--R (- 4a b d + 5a b c d + 5a b c d - 5a b c d - 5a b c d + 4b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 6 5 +--R (2a d - 6a b c d + 8a b c d - 8a b c d + 6a b c d - 2b c )x + 2a c d +--R + +--R 5 2 4 2 4 5 5 6 +--R - 2a b c d + 2a b c d - 2a b c +--R / +--R 3 5 8 2 6 7 7 2 6 8 3 5 2 +--R (2a b d - 6a b c d + 6a b c d - 2b c d )x +--R + +--R 4 4 8 3 5 7 7 3 5 8 4 4 4 4 7 3 5 2 6 +--R (2a b d - 4a b c d + 4a b c d - 2b c d )x + 2a b c d - 6a b c d +--R + +--R 2 6 3 5 7 4 4 +--R 6a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1092 +t0:=x^4/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 4 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 609 + +--S 610 of 1092 +r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ + 2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-_ + 2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 3 2 5 4 2 2 3 3 2 4 4 5 5 +--R (- 4a b c d + 2b c d)x + (- 4a b c d - 2a b c d + 2b c )x +--R + +--R 2 3 4 4 5 +--R - 4a b c d + 2a b c +--R * +--R log(d x + c) +--R + +--R 4 5 3 2 4 2 5 5 4 4 3 2 2 3 +--R (- 2a b d + 4a b c d )x + (- 2a d + 2a b c d + 4a b c d )x +--R + +--R 5 4 4 2 3 +--R - 2a c d + 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 2 +--R (a b d - 2a b c d + 2a b c d - b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 4 +--R (- a d + 2a b c d - 3a b c d + 3a b c d - 2a b c d + b c )x - a c d +--R + +--R 4 2 3 2 3 4 4 5 +--R a b c d - a b c d + a b c +--R / +--R 3 4 7 2 5 6 6 2 5 7 3 4 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 3 6 3 4 2 5 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 5 3 4 6 4 3 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 5 4 2 2 3 3 2 4 4 5 5 +--R (- 4a b c d + 2b c d)x + (- 4a b c d - 2a b c d + 2b c )x +--R + +--R 2 3 4 4 5 +--R - 4a b c d + 2a b c +--R * +--R log(d x + c) +--R + +--R 4 5 3 2 4 2 5 5 4 4 3 2 2 3 +--R (- 2a b d + 4a b c d )x + (- 2a d + 2a b c d + 4a b c d )x +--R + +--R 5 4 4 2 3 +--R - 2a c d + 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 2 +--R (a b d - 2a b c d + 2a b c d - b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 5 4 +--R (- a d + 2a b c d - 3a b c d + 3a b c d - 2a b c d + b c )x - a c d +--R + +--R 4 2 3 2 3 4 4 5 +--R a b c d - a b c d + a b c +--R / +--R 3 4 7 2 5 6 6 2 5 7 3 4 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 3 7 3 4 6 6 3 4 7 4 3 4 3 6 3 4 2 5 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 5 3 4 6 4 3 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1092 +t0:=x^3/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 3 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 614 + +--S 615 of 1092 +r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ + a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+_ + c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (3a b c d - b c d)x + (3a b c d + 2a b c d - b c )x + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(d x + c) +--R + +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (a b d - 3a b c d )x + (a d - 2a b c d - 3a b c d )x + a c d +--R + +--R 3 2 2 +--R - 3a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 3 4 +--R (a d - a b c d + a b c d - b c )x + a c d - a b c d + a b c d - a b c +--R / +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 4 2 5 3 3 2 4 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 4 3 3 5 4 2 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (3a b c d - b c d)x + (3a b c d + 2a b c d - b c )x + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(d x + c) +--R + +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (a b d - 3a b c d )x + (a d - 2a b c d - 3a b c d )x + a c d +--R + +--R 3 2 2 +--R - 3a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 3 4 +--R (a d - a b c d + a b c d - b c )x + a c d - a b c d + a b c d - a b c +--R / +--R 3 3 6 2 4 5 5 2 4 6 3 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 2 6 3 3 5 5 3 3 6 4 2 4 2 5 3 3 2 4 +--R (a b d - 2a b c d + 2a b c d - b c d )x + a b c d - 3a b c d +--R + +--R 2 4 3 3 5 4 2 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1092 +t0:=x^2/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 2 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 619 + +--S 620 of 1092 +r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ + 2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b c d x + (- 2a b c d - 2a b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b c d x + (2a b c d + 2a b c d)x + 2a b c d)log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 3 +--R (- a d + a b c d - a b c d + b c )x - a c d + a b c +--R / +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 4 4 3 2 2 3 +--R (a b d - 2a b c d + 2a b c d - b c d)x + a b c d - 3a b c d +--R + +--R 2 3 3 2 4 4 +--R 3a b c d - a b c d +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b c d x + (- 2a b c d - 2a b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a b c d x + (2a b c d + 2a b c d)x + 2a b c d)log(b x + a) +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 3 +--R (- a d + a b c d - a b c d + b c )x - a c d + a b c +--R / +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (a b d - 3a b c d + 3a b c d - b c d )x +--R + +--R 4 5 3 2 4 4 3 2 5 4 4 4 3 2 2 3 +--R (a b d - 2a b c d + 2a b c d - b c d)x + a b c d - 3a b c d +--R + +--R 2 3 3 2 4 4 +--R 3a b c d - a b c d +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1092 +t0:=x/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 624 + +--S 625 of 1092 +r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ + (b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 +--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c ) +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (a d - b c )x + 2a c d - 2a b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R ((a b d + b c d)x + (a d + 2a b c d + b c )x + a c d + a b c ) +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- a b d - b c d)x + (- a d - 2a b c d - b c )x - a c d - a b c ) +--R * +--R log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (a d - b c )x + 2a c d - 2a b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1092 +t0:=1/((a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--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: Fraction(Polynomial(Integer)) +--E 629 + +--S 630 of 1092 +r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ + 2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3 +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 +--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2b d x + (- 2a b d - 2b c d)x - 2a b c d)log(d x + c) +--R + +--R 2 2 2 2 2 +--R (2b d x + (2a b d + 2b c d)x + 2a b c d)log(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (- 2a b d + 2b c d)x - a d + b c +--R / +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1092 +t0:=1/(x*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--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 2 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 634 + +--S 635 of 1092 +r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ + log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ + d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3) +--R +--R +--R (2) +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x - a c d +--R + +--R 3 2 2 +--R 3a b c d +--R * +--R log(d x + c) +--R + +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x - 3a b c d +--R + +--R 3 4 +--R a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(x) +--R + +--R 3 3 3 3 4 3 3 2 2 2 2 3 3 4 +--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c +--R / +--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 2 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 4 2 5 +--R (a c d - 2a b c d + 2a b c d - a b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 3 6 +--R - a b c +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 2 2 3 2 4 4 3 3 2 2 2 2 4 3 +--R (- a b d + 3a b c d )x + (- a d + 2a b c d + 3a b c d )x - a c d +--R + +--R 3 2 2 +--R 3a b c d +--R * +--R log(d x + c) +--R + +--R 3 2 2 4 3 2 2 2 2 2 3 3 4 4 2 2 3 +--R (- 3a b c d + b c d)x + (- 3a b c d - 2a b c d + b c )x - 3a b c d +--R + +--R 3 4 +--R a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (a b d - 3a b c d + 3a b c d - b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 2 2 3 +--R (a d - 2a b c d + 2a b c d - b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 4 +--R - a b c +--R * +--R log(x) +--R + +--R 3 3 3 3 4 3 3 2 2 2 2 3 3 4 +--R (a b c d - a b c d)x + a c d - a b c d + a b c d - a b c +--R / +--R 5 2 4 4 2 3 3 3 3 4 2 2 4 5 2 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 4 2 5 +--R (a c d - 2a b c d + 2a b c d - a b c )x + a c d - 3a b c d + 3a b c d +--R + +--R 3 3 6 +--R - a b c +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 639 + +--S 640 of 1092 +r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ + d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_ + 2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+_ + 2*d^3*(2*b*c-a*d)*log(c+d*x)/(c^3*(b*c-a*d)^3) +--R +--R +--R (2) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x +--R + +--R 5 4 4 2 3 +--R (2a c d - 4a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x +--R + +--R 2 3 4 4 5 +--R (4a b c d - 2a b c )x +--R * +--R log(b x + a) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2a d + 2a b c d + 4a b c d - 4a b c d - 2a b c d + 2b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2a c d + 4a b c d - 4a b c d + 2a b c )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d +--R + +--R 3 2 4 2 3 5 +--R - 3a b c d + a b c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (a c d - 2a b c d + 2a b c d - a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (a c d - 3a b c d + 3a b c d - a b c )x +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 3 2 4 3 5 5 4 4 3 2 2 3 2 +--R (2a b d - 4a b c d )x + (2a d - 2a b c d - 4a b c d )x +--R + +--R 5 4 4 2 3 +--R (2a c d - 4a b c d )x +--R * +--R log(d x + c) +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (4a b c d - 2b c d)x + (4a b c d + 2a b c d - 2b c )x +--R + +--R 2 3 4 4 5 +--R (4a b c d - 2a b c )x +--R * +--R log(b x + a) +--R + +--R 4 5 3 2 4 4 3 2 5 4 3 +--R (- 2a b d + 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- 2a d + 2a b c d + 4a b c d - 4a b c d - 2a b c d + 2b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R (- 2a c d + 4a b c d - 4a b c d + 2a b c )x +--R * +--R log(x) +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 2a b c d + 4a b c d - 4a b c d + 2a b c d)x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d + 3a b c d - 3a b c d + 2a b c )x - a c d + 3a b c d +--R + +--R 3 2 4 2 3 5 +--R - 3a b c d + a b c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (a b c d - 3a b c d + 3a b c d - a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (a c d - 2a b c d + 2a b c d - a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (a c d - 3a b c d + 3a b c d - a b c )x +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +)clear all + +--S 644 of 1092 +t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 7 2 2 6 2 2 2 2 5 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 4 2 2 3 +--R (2a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 644 + +--S 645 of 1092 +r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ + b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+_ + (3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*_ + log(a+b*x)/(a^4*(b*c-a*d)^3)-d^4*(5*b*c-3*a*d)*_ + log(c+d*x)/(c^4*(b*c-a*d)^3) +--R +--R +--R (2) +--R 5 6 4 2 5 4 6 6 5 5 4 2 2 4 3 +--R (- 6a b d + 10a b c d )x + (- 6a d + 4a b c d + 10a b c d )x +--R + +--R 6 5 5 2 4 2 +--R (- 6a c d + 10a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 2 6 5 4 2 4 4 2 5 5 6 6 3 +--R (- 10a b c d + 6b c d)x + (- 10a b c d - 4a b c d + 6b c )x +--R + +--R 2 4 5 5 6 2 +--R (- 10a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 5 4 2 6 5 4 +--R (6a b d - 10a b c d + 10a b c d - 6b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3 +--R (6a d - 4a b c d - 10a b c d + 10a b c d + 4a b c d - 6b c )x +--R + +--R 6 5 5 2 4 2 4 5 5 6 2 +--R (6a c d - 10a b c d + 10a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 5 5 4 2 2 4 2 4 4 2 5 5 3 +--R (6a b c d - 10a b c d + 10a b c d - 6a b c d)x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 2 +--R (6a c d - 7a b c d - 5a b c d + 5a b c d + 7a b c d - 6a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x - a c d + 3a b c d +--R + +--R 4 2 5 3 3 6 +--R - 3a b c d + a b c +--R / +--R 7 4 4 6 2 5 3 5 3 6 2 4 4 7 4 +--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x +--R + +--R 8 4 4 7 5 3 5 3 7 4 4 8 3 +--R (2a c d - 4a b c d + 4a b c d - 2a b c )x +--R + +--R 8 5 3 7 6 2 6 2 7 5 3 8 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 4 2 5 4 6 6 5 5 4 2 2 4 3 +--R (- 6a b d + 10a b c d )x + (- 6a d + 4a b c d + 10a b c d )x +--R + +--R 6 5 5 2 4 2 +--R (- 6a c d + 10a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 2 6 5 4 2 4 4 2 5 5 6 6 3 +--R (- 10a b c d + 6b c d)x + (- 10a b c d - 4a b c d + 6b c )x +--R + +--R 2 4 5 5 6 2 +--R (- 10a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 5 4 2 6 5 4 +--R (6a b d - 10a b c d + 10a b c d - 6b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3 +--R (6a d - 4a b c d - 10a b c d + 10a b c d + 4a b c d - 6b c )x +--R + +--R 6 5 5 2 4 2 4 5 5 6 2 +--R (6a c d - 10a b c d + 10a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 5 5 4 2 2 4 2 4 4 2 5 5 3 +--R (6a b c d - 10a b c d + 10a b c d - 6a b c d)x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 2 +--R (6a c d - 7a b c d - 5a b c d + 5a b c d + 7a b c d - 6a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 6 3 3 5 4 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x - a c d + 3a b c d +--R + +--R 4 2 5 3 3 6 +--R - 3a b c d + a b c +--R / +--R 7 4 4 6 2 5 3 5 3 6 2 4 4 7 4 +--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x +--R + +--R 8 4 4 7 5 3 5 3 7 4 4 8 3 +--R (2a c d - 4a b c d + 4a b c d - 2a b c )x +--R + +--R 8 5 3 7 6 2 6 2 7 5 3 8 2 +--R (2a c d - 6a b c d + 6a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 646 + +--S 647 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1092 +t0:=x^7/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 649 + +--S 650 of 1092 +r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ + (b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/_ + (d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*_ + (c+d*x))+a^6*(7*b*c-4*a*d)*log(a+b*x)/(b^5*(b*c-a*d)^4)-_ + c^5*(10*b^2*c^2-28*a*b*c*d+21*a^2*d^2)*log(c+d*x)/(d^6*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 6 5 4 7 6 3 8 7 2 3 +--R (- 126a b c d + 168a b c d - 60b c d )x +--R + +--R 3 5 5 4 2 6 6 3 7 7 2 8 8 2 +--R (- 126a b c d - 84a b c d + 276a b c d - 120b c d)x +--R + +--R 3 5 6 3 2 6 7 2 7 8 8 9 3 5 7 2 +--R (- 252a b c d + 210a b c d + 48a b c d - 60b c )x - 126a b c d +--R + +--R 2 6 8 7 9 +--R 168a b c d - 60a b c +--R * +--R log(d x + c) +--R + +--R 7 9 6 2 8 3 8 9 7 8 6 2 2 7 2 +--R (- 24a b d + 42a b c d )x + (- 24a d - 6a b c d + 84a b c d )x +--R + +--R 8 8 7 2 7 6 2 3 6 8 2 7 7 3 6 +--R (- 48a c d + 60a b c d + 42a b c d )x - 24a c d + 42a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 6 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 7 4 5 +--R - 4a b d + 11a b c d - 4a b c d - 14a b c d + 16a b c d +--R + +--R 8 5 4 +--R - 5b c d +--R * +--R 5 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 12a b d - 29a b c d + 16a b c d - 14a b c d + 56a b c d +--R + +--R 7 5 4 8 6 3 +--R - 61a b c d + 20b c d +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 18a b d - 12a b c d - 46a b c d + 7a b c d + 42a b c d +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 94a b c d - 166a b c d + 63b c d +--R * +--R 3 +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 3 5 5 4 +--R - 6a d + 42a b c d - 60a b c d - 21a b c d + 150a b c d +--R + +--R 2 6 6 3 7 7 2 8 8 +--R - 138a b c d + 27a b c d + 6b c d +--R * +--R 2 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 3 5 6 3 2 6 7 2 +--R - 12a c d + 30a b c d - 36a b c d + 48a b c d - 75a b c d +--R + +--R 7 8 8 9 +--R 72a b c d - 27b c +--R * +--R x +--R + +--R 8 2 7 7 3 6 3 5 7 2 2 6 8 7 9 +--R - 6a c d + 6a b c d - 39a b c d + 66a b c d - 27a b c +--R / +--R 4 6 12 3 7 11 2 8 2 10 9 3 9 10 4 8 3 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 5 12 4 6 11 3 7 2 10 2 8 3 9 9 4 8 +--R 6a b d - 12a b c d - 12a b c d + 48a b c d - 42a b c d +--R + +--R 10 5 7 +--R 12b c d +--R * +--R 2 +--R x +--R + +--R 5 5 11 4 6 2 10 3 7 3 9 2 8 4 8 9 5 7 +--R 12a b c d - 42a b c d + 48a b c d - 12a b c d - 12a b c d +--R + +--R 10 6 6 +--R 6b c d +--R * +--R x +--R + +--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 +--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 4 7 6 3 8 7 2 3 +--R (- 126a b c d + 168a b c d - 60b c d )x +--R + +--R 3 5 5 4 2 6 6 3 7 7 2 8 8 2 +--R (- 126a b c d - 84a b c d + 276a b c d - 120b c d)x +--R + +--R 3 5 6 3 2 6 7 2 7 8 8 9 3 5 7 2 +--R (- 252a b c d + 210a b c d + 48a b c d - 60b c )x - 126a b c d +--R + +--R 2 6 8 7 9 +--R 168a b c d - 60a b c +--R * +--R log(d x + c) +--R + +--R 7 9 6 2 8 3 8 9 7 8 6 2 2 7 2 +--R (- 24a b d + 42a b c d )x + (- 24a d - 6a b c d + 84a b c d )x +--R + +--R 8 8 7 2 7 6 2 3 6 8 2 7 7 3 6 +--R (- 48a c d + 60a b c d + 42a b c d )x - 24a c d + 42a b c d +--R * +--R log(b x + a) +--R + +--R 4 4 9 3 5 8 2 6 2 7 7 3 6 8 4 5 6 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 9 4 4 8 3 5 2 7 2 6 3 6 7 4 5 +--R - 4a b d + 11a b c d - 4a b c d - 14a b c d + 16a b c d +--R + +--R 8 5 4 +--R - 5b c d +--R * +--R 5 +--R x +--R + +--R 6 2 9 5 3 8 4 4 2 7 3 5 3 6 2 6 4 5 +--R 12a b d - 29a b c d + 16a b c d - 14a b c d + 56a b c d +--R + +--R 7 5 4 8 6 3 +--R - 61a b c d + 20b c d +--R * +--R 4 +--R x +--R + +--R 7 9 6 2 8 5 3 2 7 4 4 3 6 3 5 4 5 +--R 18a b d - 12a b c d - 46a b c d + 7a b c d + 42a b c d +--R + +--R 2 6 5 4 7 6 3 8 7 2 +--R 94a b c d - 166a b c d + 63b c d +--R * +--R 3 +--R x +--R + +--R 8 9 7 8 6 2 2 7 5 3 3 6 3 5 5 4 +--R - 6a d + 42a b c d - 60a b c d - 21a b c d + 150a b c d +--R + +--R 2 6 6 3 7 7 2 8 8 +--R - 138a b c d + 27a b c d + 6b c d +--R * +--R 2 +--R x +--R + +--R 8 8 7 2 7 6 2 3 6 3 5 6 3 2 6 7 2 +--R - 12a c d + 30a b c d - 36a b c d + 48a b c d - 75a b c d +--R + +--R 7 8 8 9 +--R 72a b c d - 27b c +--R * +--R x +--R + +--R 8 2 7 7 3 6 3 5 7 2 2 6 8 7 9 +--R - 6a c d + 6a b c d - 39a b c d + 66a b c d - 27a b c +--R / +--R 4 6 12 3 7 11 2 8 2 10 9 3 9 10 4 8 3 +--R (6a b d - 24a b c d + 36a b c d - 24a b c d + 6b c d )x +--R + +--R 5 5 12 4 6 11 3 7 2 10 2 8 3 9 9 4 8 +--R 6a b d - 12a b c d - 12a b c d + 48a b c d - 42a b c d +--R + +--R 10 5 7 +--R 12b c d +--R * +--R 2 +--R x +--R + +--R 5 5 11 4 6 2 10 3 7 3 9 2 8 4 8 9 5 7 +--R 12a b c d - 42a b c d + 48a b c d - 12a b c d - 12a b c d +--R + +--R 10 6 6 +--R 6b c d +--R * +--R x +--R + +--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 +--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d +--R Type: Union(Expression(Integer),...) +--E 651 + +--S 652 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 653 + +)clear all + +--S 654 of 1092 +t0:=x^6/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 654 + +--S 655 of 1092 +r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ + (a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/_ + (d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/_ + (b^4*(b*c-a*d)^4)+3*c^4*(2*b^2*c^2-6*a*b*c*d+5*a^2*d^2)*_ + log(c+d*x)/(d^5*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 5 4 4 6 5 3 7 6 2 3 +--R (30a b c d - 36a b c d + 12b c d )x +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 2 +--R (30a b c d + 24a b c d - 60a b c d + 24b c d)x +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 3 4 6 2 +--R (60a b c d - 42a b c d - 12a b c d + 12b c )x + 30a b c d +--R + +--R 2 5 7 6 8 +--R - 36a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 8 5 2 7 3 7 8 5 2 2 6 2 +--R (6a b d - 12a b c d )x + (6a d - 24a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 7 2 6 6 3 5 +--R (12a c d - 18a b c d - 12a b c d )x + 6a c d - 12a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 5 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c d )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 7 5 3 4 +--R (- 3a b d + 8a b c d - 2a b c d - 12a b c d + 13a b c d - 4b c d )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 4a b d + 4a b c d + 13a b c d - 12a b c d - 22a b c d +--R + +--R 6 5 3 7 6 2 +--R 32a b c d - 11b c d +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 2 5 5 3 +--R 2a d - 10a b c d + 17a b c d + 6a b c d - 34a b c d + 28a b c d +--R + +--R 6 6 2 7 7 +--R - 11a b c d + 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 3 4 5 3 2 5 6 2 6 7 +--R 4a c d - 8a b c d + 10a b c d - 8a b c d + 11a b c d - 16a b c d +--R + +--R 7 8 +--R 7b c +--R * +--R x +--R + +--R 7 2 6 6 3 5 3 4 6 2 2 5 7 6 8 +--R 2a c d - 2a b c d + 11a b c d - 18a b c d + 7a b c +--R / +--R 4 5 11 3 6 10 2 7 2 9 8 3 8 9 4 7 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 4 11 4 5 10 3 6 2 9 2 7 3 8 8 4 7 9 5 6 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 4 10 4 5 2 9 3 6 3 8 2 7 4 7 8 5 6 9 6 5 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 4 6 5 3 7 6 2 3 +--R (30a b c d - 36a b c d + 12b c d )x +--R + +--R 3 4 4 4 2 5 5 3 6 6 2 7 7 2 +--R (30a b c d + 24a b c d - 60a b c d + 24b c d)x +--R + +--R 3 4 5 3 2 5 6 2 6 7 7 8 3 4 6 2 +--R (60a b c d - 42a b c d - 12a b c d + 12b c )x + 30a b c d +--R + +--R 2 5 7 6 8 +--R - 36a b c d + 12a b c +--R * +--R log(d x + c) +--R + +--R 6 8 5 2 7 3 7 8 5 2 2 6 2 +--R (6a b d - 12a b c d )x + (6a d - 24a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 7 2 6 6 3 5 +--R (12a c d - 18a b c d - 12a b c d )x + 6a c d - 12a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 8 3 4 7 2 5 2 6 6 3 5 7 4 4 5 +--R (a b d - 4a b c d + 6a b c d - 4a b c d + b c d )x +--R + +--R 5 2 8 4 3 7 3 4 2 6 2 5 3 5 6 4 4 7 5 3 4 +--R (- 3a b d + 8a b c d - 2a b c d - 12a b c d + 13a b c d - 4b c d )x +--R + +--R 6 8 5 2 7 4 3 2 6 3 4 3 5 2 5 4 4 +--R - 4a b d + 4a b c d + 13a b c d - 12a b c d - 22a b c d +--R + +--R 6 5 3 7 6 2 +--R 32a b c d - 11b c d +--R * +--R 3 +--R x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 3 4 4 4 2 5 5 3 +--R 2a d - 10a b c d + 17a b c d + 6a b c d - 34a b c d + 28a b c d +--R + +--R 6 6 2 7 7 +--R - 11a b c d + 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 3 4 5 3 2 5 6 2 6 7 +--R 4a c d - 8a b c d + 10a b c d - 8a b c d + 11a b c d - 16a b c d +--R + +--R 7 8 +--R 7b c +--R * +--R x +--R + +--R 7 2 6 6 3 5 3 4 6 2 2 5 7 6 8 +--R 2a c d - 2a b c d + 11a b c d - 18a b c d + 7a b c +--R / +--R 4 5 11 3 6 10 2 7 2 9 8 3 8 9 4 7 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 4 11 4 5 10 3 6 2 9 2 7 3 8 8 4 7 9 5 6 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 4 10 4 5 2 9 3 6 3 8 2 7 4 7 8 5 6 9 6 5 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 656 + +--S 657 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 658 + +)clear all + +--S 659 of 1092 +t0:=x^5/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 659 + +--S 660 of 1092 +r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ + (c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+_ + a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*_ + (3*b^2*c^2-10*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 4 3 4 5 4 3 6 5 2 3 +--R (- 20a b c d + 20a b c d - 6b c d )x +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (- 20a b c d - 20a b c d + 34a b c d - 12b c d)x +--R + +--R 3 3 4 3 2 4 5 2 5 6 6 7 3 3 5 2 +--R (- 40a b c d + 20a b c d + 8a b c d - 6b c )x - 20a b c d +--R + +--R 2 4 6 5 7 +--R 20a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 7 4 2 6 3 6 7 5 6 4 2 2 5 2 +--R (- 4a b d + 10a b c d )x + (- 4a d + 2a b c d + 20a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 6 2 5 5 3 4 +--R (- 8a c d + 16a b c d + 10a b c d )x - 4a c d + 10a b c d +--R * +--R log(b x + a) +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 4 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 6 5 2 3 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 2a d + 6a b c d - 14a b c d + 16a b c d - 14a b c d +--R + +--R 5 5 2 6 6 +--R 12a b c d - 4b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 5 6 +--R - 4a c d + 6a b c d - 8a b c d + 2a b c d - a b c d + 10a b c d +--R + +--R 6 7 +--R - 5b c +--R * +--R x +--R + +--R 6 2 5 5 3 4 3 3 5 2 2 4 6 5 7 +--R - 2a c d + 2a b c d - 9a b c d + 14a b c d - 5a b c +--R / +--R 4 4 10 3 5 9 2 6 2 8 7 3 7 8 4 6 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 8 5 5 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 3 9 4 4 2 8 3 5 3 7 2 6 4 6 7 5 5 8 6 4 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 4 5 4 3 6 5 2 3 +--R (- 20a b c d + 20a b c d - 6b c d )x +--R + +--R 3 3 3 4 2 4 4 3 5 5 2 6 6 2 +--R (- 20a b c d - 20a b c d + 34a b c d - 12b c d)x +--R + +--R 3 3 4 3 2 4 5 2 5 6 6 7 3 3 5 2 +--R (- 40a b c d + 20a b c d + 8a b c d - 6b c )x - 20a b c d +--R + +--R 2 4 6 5 7 +--R 20a b c d - 6a b c +--R * +--R log(d x + c) +--R + +--R 5 7 4 2 6 3 6 7 5 6 4 2 2 5 2 +--R (- 4a b d + 10a b c d )x + (- 4a d + 2a b c d + 20a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 6 2 5 5 3 4 +--R (- 8a c d + 16a b c d + 10a b c d )x - 4a c d + 10a b c d +--R * +--R log(b x + a) +--R + +--R 4 2 7 3 3 6 2 4 2 5 5 3 4 6 4 3 4 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 2 6 3 3 2 5 2 4 3 4 5 4 3 6 5 2 3 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 2a d + 6a b c d - 14a b c d + 16a b c d - 14a b c d +--R + +--R 5 5 2 6 6 +--R 12a b c d - 4b c d +--R * +--R 2 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 5 6 +--R - 4a c d + 6a b c d - 8a b c d + 2a b c d - a b c d + 10a b c d +--R + +--R 6 7 +--R - 5b c +--R * +--R x +--R + +--R 6 2 5 5 3 4 3 3 5 2 2 4 6 5 7 +--R - 2a c d + 2a b c d - 9a b c d + 14a b c d - 5a b c +--R / +--R 4 4 10 3 5 9 2 6 2 8 7 3 7 8 4 6 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 3 10 4 4 9 3 5 2 8 2 6 3 7 7 4 6 8 5 5 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 3 9 4 4 2 8 3 5 3 7 2 6 4 6 7 5 5 8 6 4 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1092 +t0:=x^4/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 664 + +--S 665 of 1092 +r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ + 2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*_ + log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*_ + log(c+d*x)/(d^3*(b*c-a*d)^4) +--R +--R +--R (2) +--R 2 3 2 4 4 3 3 5 4 2 3 +--R (12a b c d - 8a b c d + 2b c d )x +--R + +--R 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (12a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 3 2 3 3 2 3 4 2 4 5 5 6 3 2 4 2 2 3 5 +--R (24a b c d - 4a b c d - 4a b c d + 2b c )x + 12a b c d - 8a b c d +--R + +--R 4 6 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 4 6 3 2 5 3 5 6 4 5 3 2 2 4 2 +--R (2a b d - 8a b c d )x + (2a d - 4a b c d - 16a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 5 2 4 4 3 3 +--R (4a c d - 14a b c d - 8a b c d )x + 2a c d - 8a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 5 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 2a b c d + 8a b c d - 12a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 4a b c d + 8a b c d - 5a b c d - 6a b c d + 3b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 2a b c d + 7a b c d - 10a b c d + 3a b c +--R / +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 7 5 4 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 4 3 3 5 4 2 3 +--R (12a b c d - 8a b c d + 2b c d )x +--R + +--R 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (12a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 3 2 3 3 2 3 4 2 4 5 5 6 3 2 4 2 2 3 5 +--R (24a b c d - 4a b c d - 4a b c d + 2b c )x + 12a b c d - 8a b c d +--R + +--R 4 6 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 4 6 3 2 5 3 5 6 4 5 3 2 2 4 2 +--R (2a b d - 8a b c d )x + (2a d - 4a b c d - 16a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 5 2 4 4 3 3 +--R (4a c d - 14a b c d - 8a b c d )x + 2a c d - 8a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 5 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 2a b c d + 8a b c d - 12a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 4a b c d + 8a b c d - 5a b c d - 6a b c d + 3b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 2a b c d + 7a b c d - 10a b c d + 3a b c +--R / +--R 4 3 9 3 4 8 2 5 2 7 6 3 6 7 4 5 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 2 9 4 3 8 3 4 2 7 2 5 3 6 6 4 5 7 5 4 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 2 8 4 3 2 7 3 4 3 6 2 5 4 5 6 5 4 7 6 3 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 668 + +)clear all + +--S 669 of 1092 +t0:=x^3/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 669 + +--S 670 of 1092 +r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ + c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/_ + (b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 2 3 2 +--R - 6a b c d x + (- 6a b c d - 12a b c d )x +--R + +--R 3 2 3 2 2 3 2 3 3 2 +--R (- 12a b c d - 6a b c d )x - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 3 2 3 2 2 3 2 +--R 6a b c d x + (6a b c d + 12a b c d )x + (12a b c d + 6a b c d )x +--R + +--R 3 3 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 2a d + 2a b c d - 6a b c d + 8a b c d - 2b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 4a c d - 2a b c d + 3a b c d + 4a b c d - b c )x - 2a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 3a b c d + 6a b c d - a b c +--R / +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 7 4 2 2 6 3 3 3 5 2 4 4 4 5 5 3 6 6 2 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 2 3 2 +--R - 6a b c d x + (- 6a b c d - 12a b c d )x +--R + +--R 3 2 3 2 2 3 2 3 3 2 +--R (- 12a b c d - 6a b c d )x - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 3 2 3 2 2 3 2 +--R 6a b c d x + (6a b c d + 12a b c d )x + (12a b c d + 6a b c d )x +--R + +--R 3 3 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 2a d + 2a b c d - 6a b c d + 8a b c d - 2b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 4a c d - 2a b c d + 3a b c d + 4a b c d - b c )x - 2a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 3a b c d + 6a b c d - a b c +--R / +--R 4 2 8 3 3 7 2 4 2 6 5 3 5 6 4 4 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 8 4 2 7 3 3 2 6 2 4 3 5 5 4 4 6 5 3 2 +--R (2a b d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 7 4 2 2 6 3 3 3 5 2 4 4 4 5 5 3 6 6 2 +--R (4a b c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d )x +--R + +--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 +--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 673 + +)clear all + +--S 674 of 1092 +t0:=x^2/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 674 + +--S 675 of 1092 +r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ + 2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+_ + a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (2a b d + 4a b c d )x + (2a d + 8a b c d + 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (4a c d + 10a b c d + 4a b c d)x + 2a c d + 4a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (- 2a b d - 4a b c d )x + (- 2a d - 8a b c d - 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (- 4a c d - 10a b c d - 4a b c d)x - 2a c d - 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 2 3 2 2 2 2 +--R (2a d + 2a b c d - 4a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 2 4 +--R (8a c d - 5a b c d - 2a b c d - b c )x + 5a c d - 4a b c d - a b c +--R / +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (2a b d + 4a b c d )x + (2a d + 8a b c d + 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (4a c d + 10a b c d + 4a b c d)x + 2a c d + 4a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 3 3 3 4 2 3 2 2 2 2 +--R (- 2a b d - 4a b c d )x + (- 2a d - 8a b c d - 8a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 2 2 2 3 +--R (- 4a c d - 10a b c d - 4a b c d)x - 2a c d - 4a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 2 3 2 2 2 2 +--R (2a d + 2a b c d - 4a b c d )x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 2 4 +--R (8a c d - 5a b c d - 2a b c d - b c )x + 5a c d - 4a b c d - a b c +--R / +--R 4 7 3 2 6 2 3 2 5 4 3 4 5 4 3 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 7 4 6 3 2 2 5 2 3 3 4 4 4 3 5 5 2 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d )x +--R + +--R 5 6 4 2 5 3 2 3 4 2 3 4 3 4 5 2 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c d)x +--R + +--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d +--R Type: Union(Expression(Integer),...) +--E 676 + +--S 677 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 678 + +)clear all + +--S 679 of 1092 +t0:=x/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 679 + +--S 680 of 1092 +r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ + ((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-_ + b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 3 2 2 +--R (- 4a b d + 2a b c d + 2b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (- 4a b d - 2b c d )x + (- 4a b d - 10a b c d - 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (- 8a b c d - 8a b c d - 2b c )x - 4a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 2 3 3 2 3 2 3 2 2 3 2 2 +--R (4a b d + 2b c d )x + (4a b d + 10a b c d + 4b c d)x +--R + +--R 2 2 2 2 3 3 2 2 2 3 +--R (8a b c d + 8a b c d + 2b c )x + 4a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 2 3 2 2 3 2 2 +--R (- 4a b d + 2a b c d + 2b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 2a d - 5a b c d + 4a b c d + 3b c )x - a c d - 4a b c d + 5a b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 681 + +--S 682 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 683 + +)clear all + +--S 684 of 1092 +t0:=1/((a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 5 3 2 2 4 2 3 2 2 2 3 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 2 2 2 3 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c +--R Type: Fraction(Polynomial(Integer)) +--E 684 + +--S 685 of 1092 +r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ + 2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_ + 3*b^2*d*log(c+d*x)/(b*c-a*d)^4 +--R +--R +--R (2) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 3a b c d - 2b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 2 2 2 3 2 2 2 +--R (6b d x + (6a b d + 12b c d )x + (12a b c d + 6b c d)x + 6a b c d) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 +--R - 6b d x + (- 6a b d - 12b c d )x + (- 12a b c d - 6b c d)x +--R + +--R 2 2 +--R - 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (6a b d - 6b c d )x + (3a b d + 6a b c d - 9b c d)x - a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 3a b c d - 2b c +--R / +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 686 + +--S 687 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1092 +t0:=1/(x*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 6 3 2 2 5 2 3 2 2 2 4 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 3 2 2 3 2 2 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1092 +r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ + d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-_ + b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^4) +--R +--R +--R (2) +--R 4 6 3 2 5 2 3 2 4 3 +--R (- 2a b d + 8a b c d - 12a b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 2 +--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 2 4 +--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d +--R + +--R 4 3 3 3 2 4 2 +--R 8a b c d - 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 3 3 5 4 2 3 2 3 3 3 4 4 2 5 5 2 +--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x +--R + +--R 2 3 4 2 4 5 5 6 2 3 5 4 6 +--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c +--R * +--R log(b x + a) +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R * +--R log(x) +--R + +--R 4 5 3 2 2 4 2 3 3 3 4 4 2 2 +--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 2 4 +--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d +--R + +--R 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 10a b c d + 7a b c d - 2a b c d + 2a b c +--R / +--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 3 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 2 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 3 2 5 2 3 2 4 3 +--R (- 2a b d + 8a b c d - 12a b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 2 +--R (- 2a d + 4a b c d + 4a b c d - 24a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 5 2 4 +--R (- 4a c d + 14a b c d - 16a b c d - 12a b c d )x - 2a c d +--R + +--R 4 3 3 3 2 4 2 +--R 8a b c d - 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 3 3 5 4 2 3 2 3 3 3 4 4 2 5 5 2 +--R (8a b c d - 2b c d )x + (8a b c d + 14a b c d - 4b c d)x +--R + +--R 2 3 4 2 4 5 5 6 2 3 5 4 6 +--R (16a b c d + 4a b c d - 2b c )x + 8a b c d - 2a b c +--R * +--R log(b x + a) +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (2a b d - 8a b c d + 12a b c d - 8a b c d + 2b c d )x +--R + +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (2a d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2b c )x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R * +--R log(x) +--R + +--R 4 5 3 2 2 4 2 3 3 3 4 4 2 2 +--R (2a b c d - 8a b c d + 4a b c d + 2a b c d )x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 2 4 +--R (2a c d - 5a b c d - 4a b c d + 3a b c d + 4a b c d)x + 3a c d +--R + +--R 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 10a b c d + 7a b c d - 2a b c d + 2a b c +--R / +--R 6 3 6 5 2 4 5 4 3 5 4 3 4 6 3 2 5 7 2 3 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 7 3 6 6 4 5 5 2 5 4 4 3 6 3 3 4 7 2 2 5 8 2 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 7 4 5 6 5 4 5 2 6 3 4 3 7 2 3 4 8 2 5 9 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 +--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 7 3 2 2 6 2 3 2 2 2 5 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 4 2 2 3 3 2 3 2 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1092 +r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ + 1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/_ + (c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+_ + b^4*(2*b*c-5*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^4)+_ + d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^4) +--R +--R +--R (2) +--R 5 7 4 2 6 3 3 2 5 4 +--R (6a b d - 20a b c d + 20a b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 3 +--R (6a d - 8a b c d - 20a b c d + 40a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 +--R (12a c d - 34a b c d + 20a b c d + 20a b c d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 +--R (6a c d - 20a b c d + 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 +--R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x +--R * +--R log(b x + a) +--R + +--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 +--R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d +--R + +--R 5 5 2 6 6 +--R 16a b c d - 8b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d +--R + +--R 5 6 6 7 +--R 2a b c d - 4b c +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 +--R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 +--R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d +--R + +--R 5 6 +--R - 8a b c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 7 4 2 6 3 3 2 5 4 +--R (6a b d - 20a b c d + 20a b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 3 +--R (6a d - 8a b c d - 20a b c d + 40a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 +--R (12a c d - 34a b c d + 20a b c d + 20a b c d )x +--R + +--R 6 2 5 5 3 4 4 2 4 3 +--R (6a c d - 20a b c d + 20a b c d )x +--R * +--R log(d x + c) +--R + +--R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 +--R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x +--R + +--R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 +--R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x +--R * +--R log(b x + a) +--R + +--R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 +--R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x +--R + +--R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 +--R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d +--R + +--R 5 5 2 6 6 +--R 16a b c d - 8b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d +--R + +--R 5 6 6 7 +--R 2a b c d - 4b c +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 +--R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x +--R * +--R log(x) +--R + +--R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 +--R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x +--R + +--R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 +--R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d +--R + +--R 5 6 +--R - 8a b c d +--R * +--R 2 +--R x +--R + +--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 +--R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x +--R + +--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 +--R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c +--R / +--R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 696 + +--S 697 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +)clear all + +--S 699 of 1092 +t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 2 3 8 3 2 2 7 2 3 2 2 2 6 +--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x +--R + +--R 2 2 2 2 3 5 2 2 3 4 2 3 3 +--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 699 + +--S 700 of 1092 +r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ + (a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/_ + (c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/_ + (a^4*c^5)-3*b^5*(b*c-2*a*d)*log(a+b*x)/(a^4*(b*c-a*d)^4)-_ + 3*d^4*(5*b^2*c^2-6*a*b*c*d+2*a^2*d^2)*log(c+d*x)/(c^5*(b*c-a*d)^4) +--R +--R +--R (2) +--R 6 8 5 2 7 4 3 2 6 5 +--R (- 12a b d + 36a b c d - 30a b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 4 +--R (- 12a d + 12a b c d + 42a b c d - 60a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 +--R (- 24a c d + 60a b c d - 24a b c d - 30a b c d )x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 +--R (- 12a c d + 36a b c d - 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 6 5 3 7 6 2 5 2 5 5 3 6 6 2 7 7 4 +--R (12a b c d - 6b c d )x + (12a b c d + 18a b c d - 12b c d)x +--R + +--R 2 5 6 2 7 8 3 2 5 7 6 8 2 +--R (24a b c d - 6b c )x + (12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 8 5 2 7 4 3 2 6 6 5 3 7 6 2 5 +--R (12a b d - 36a b c d + 30a b c d - 12a b c d + 6b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 2 5 5 3 +--R 12a d - 12a b c d - 42a b c d + 60a b c d - 12a b c d +--R + +--R 6 6 2 7 7 +--R - 18a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 2 5 6 2 +--R 24a c d - 60a b c d + 24a b c d + 30a b c d - 24a b c d +--R + +--R 7 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 5 7 6 8 2 +--R (12a c d - 36a b c d + 30a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 6 7 5 2 2 6 4 3 3 5 2 5 5 3 6 6 2 4 +--R (12a b c d - 36a b c d + 30a b c d - 12a b c d + 6a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R 12a c d - 18a b c d - 24a b c d + 45a b c d - 6a b c d +--R + +--R 2 5 6 2 6 7 +--R - 21a b c d + 12a b c d +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R 18a c d - 50a b c d + 33a b c d + 12a b c d - 13a b c d +--R + +--R 2 5 7 6 8 +--R - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R (4a c d - 13a b c d + 12a b c d + 2a b c d - 8a b c d + 3a b c )x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +--R - a c d + 4a b c d - 6a b c d + 4a b c d - a b c +--R / +--R 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 4 5 9 2 5 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 4 5 10 4 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 4 5 11 3 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 8 5 2 7 4 3 2 6 5 +--R (- 12a b d + 36a b c d - 30a b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 4 +--R (- 12a d + 12a b c d + 42a b c d - 60a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 +--R (- 24a c d + 60a b c d - 24a b c d - 30a b c d )x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 +--R (- 12a c d + 36a b c d - 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 6 5 3 7 6 2 5 2 5 5 3 6 6 2 7 7 4 +--R (12a b c d - 6b c d )x + (12a b c d + 18a b c d - 12b c d)x +--R + +--R 2 5 6 2 7 8 3 2 5 7 6 8 2 +--R (24a b c d - 6b c )x + (12a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 8 5 2 7 4 3 2 6 6 5 3 7 6 2 5 +--R (12a b d - 36a b c d + 30a b c d - 12a b c d + 6b c d )x +--R + +--R 7 8 6 7 5 2 2 6 4 3 3 5 2 5 5 3 +--R 12a d - 12a b c d - 42a b c d + 60a b c d - 12a b c d +--R + +--R 6 6 2 7 7 +--R - 18a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 2 5 6 2 +--R 24a c d - 60a b c d + 24a b c d + 30a b c d - 24a b c d +--R + +--R 7 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 2 5 7 6 8 2 +--R (12a c d - 36a b c d + 30a b c d - 12a b c d + 6a b c )x +--R * +--R log(x) +--R + +--R 6 7 5 2 2 6 4 3 3 5 2 5 5 3 6 6 2 4 +--R (12a b c d - 36a b c d + 30a b c d - 12a b c d + 6a b c d )x +--R + +--R 7 7 6 2 6 5 2 3 5 4 3 4 4 3 4 5 3 +--R 12a c d - 18a b c d - 24a b c d + 45a b c d - 6a b c d +--R + +--R 2 5 6 2 6 7 +--R - 21a b c d + 12a b c d +--R * +--R 3 +--R x +--R + +--R 7 2 6 6 3 5 5 2 4 4 4 3 5 3 3 4 6 2 +--R 18a c d - 50a b c d + 33a b c d + 12a b c d - 13a b c d +--R + +--R 2 5 7 6 8 +--R - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 7 3 5 6 4 4 5 2 5 3 4 3 6 2 3 4 7 2 5 8 +--R (4a c d - 13a b c d + 12a b c d + 2a b c d - 8a b c d + 3a b c )x +--R + +--R 7 4 4 6 5 3 5 2 6 2 4 3 7 3 4 8 +--R - a c d + 4a b c d - 6a b c d + 4a b c d - a b c +--R / +--R 8 5 6 7 2 6 5 6 3 7 4 5 4 8 3 4 5 9 2 5 +--R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x +--R + +--R 9 5 6 8 6 5 7 2 7 4 6 3 8 3 5 4 9 2 4 5 10 4 +--R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x +--R + +--R 9 6 5 8 7 4 7 2 8 3 6 3 9 2 5 4 10 4 5 11 3 +--R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x +--R + +--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 +--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 701 + +--S 702 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 703 + +)clear all + +--S 704 of 1092 +t0:=x^2/((-1+x)^2*(1+x)^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 704 + +--S 705 of 1092 +r0:=1/2*x/(1-x^2)-1/2*atanh(x) +--R +--R +--R 2 +--R (- x + 1)atanh(x) - x +--R (2) ---------------------- +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1092 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (- x + 1)log(x + 1) + (x - 1)log(x - 1) - 2x +--R (3) ---------------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1092 +m0:=a0-r0 +--R +--R +--R - log(x + 1) + log(x - 1) + 2atanh(x) +--R (4) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1092 +t0:=b^2*x^m/(b+a*x^2)^2 +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1092 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 710 + +--S 711 of 1092 +--a0:=integrate(t0,x) +--E 711 + +--S 712 of 1092 +--m0:=a0-r0 +--E 712 + +--S 713 of 1092 +--d0:=D(m0,x) +--E 713 + +)clear all + +--S 714 of 1092 +t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1092 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 715 + +--S 716 of 1092 +--a0:=integrate(t0,x) +--E 716 + +--S 717 of 1092 +--m0:=a0-r0 +--E 717 + +--S 718 of 1092 +--d0:=D(m0,x) +--E 718 + +)clear all + +--S 719 of 1092 +t0:=x^3*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 719 + +--S 720 of 1092 +r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ + 3/2*d*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+d^2*(b*c-a*d)*x^3/b^4+_ + 1/4*d^3*x^4/b^3+1/2*a^3*(b*c-a*d)^3/(b^7*(a+b*x)^2)-_ + 3*a^2*(b*c-2*a*d)*(b*c-a*d)^2/(b^7*(a+b*x))-_ + 3*a*(b*c-a*d)*(b^2*c^2-5*a*b*c*d+5*a^2*d^2)*log(a+b*x)/b^7 +--R +--R +--R (2) +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 120a b c d + 72a b c d - 12a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (120a b d - 240a b c d + 144a b c d - 24a b c )x + 60a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 120a b c d + 72a b c d - 12a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R b d x + (- 2a b d + 4b c d )x + (5a b d - 10a b c d + 6b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 40a b c d - 24a b c d + 4b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 68a b d + 126a b c d - 66a b c d + 8a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (- 16a b d + 12a b c d + 12a b c d - 8a b c )x + 22a d - 54a b c d +--R + +--R 4 2 2 3 3 3 +--R 42a b c d - 10a b c +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (60a b d - 120a b c d + 72a b c d - 12a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 +--R (120a b d - 240a b c d + 144a b c d - 24a b c )x + 60a d +--R + +--R 5 2 4 2 2 3 3 3 +--R - 120a b c d + 72a b c d - 12a b c +--R * +--R log(b x + a) +--R + +--R 6 3 6 5 3 6 2 5 2 4 3 5 2 6 2 4 +--R b d x + (- 2a b d + 4b c d )x + (5a b d - 10a b c d + 6b c d)x +--R + +--R 3 3 3 2 4 2 5 2 6 3 3 +--R (- 20a b d + 40a b c d - 24a b c d + 4b c )x +--R + +--R 4 2 3 3 3 2 2 4 2 5 3 2 +--R (- 68a b d + 126a b c d - 66a b c d + 8a b c )x +--R + +--R 5 3 4 2 2 3 3 2 2 4 3 6 3 5 2 +--R (- 16a b d + 12a b c d + 12a b c d - 8a b c )x + 22a d - 54a b c d +--R + +--R 4 2 2 3 3 3 +--R 42a b c d - 10a b c +--R / +--R 9 2 8 2 7 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1092 +t0:=x^2*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 724 + +--S 725 of 1092 +r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ + 1/3*d^3*x^3/b^3-1/2*a^2*(b*c-a*d)^3/(b^6*(a+b*x)^2)+_ + a*(2*b*c-5*a*d)*(b*c-a*d)^2/(b^6*(a+b*x))+(b*c-a*d)*_ + (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*log(a+b*x)/b^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 60a b d + 108a b c d - 54a b c d + 6b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 120a b d + 216a b c d - 108a b c d + 12a b c )x - 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 108a b c d - 54a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 2b d x + (- 5a b d + 9b c d )x + (20a b d - 36a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 2 +--R (63a b d - 99a b c d + 36a b c d)x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (6a b d + 18a b c d - 36a b c d + 12a b c )x - 27a d + 63a b c d +--R + +--R 3 2 2 2 3 3 +--R - 45a b c d + 9a b c +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 2 +--R (- 60a b d + 108a b c d - 54a b c d + 6b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 +--R (- 120a b d + 216a b c d - 108a b c d + 12a b c )x - 60a d +--R + +--R 4 2 3 2 2 2 3 3 +--R 108a b c d - 54a b c d + 6a b c +--R * +--R log(b x + a) +--R + +--R 5 3 5 4 3 5 2 4 2 3 3 4 2 5 2 3 +--R 2b d x + (- 5a b d + 9b c d )x + (20a b d - 36a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 4 2 2 +--R (63a b d - 99a b c d + 36a b c d)x +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 3 4 2 +--R (6a b d + 18a b c d - 36a b c d + 12a b c )x - 27a d + 63a b c d +--R + +--R 3 2 2 2 3 3 +--R - 45a b c d + 9a b c +--R / +--R 8 2 7 2 6 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1092 +t0:=x*(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R d x + 3c d x + 3c d x + c x +--R (1) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 729 + +--S 730 of 1092 +r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ + (b^5*(a+b*x)^2)-(b*c-4*a*d)*(b*c-a*d)^2/(b^5*(a+b*x))+_ + 3*d*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 +--R +--R +--R (2) +--R 2 2 3 3 2 4 2 2 +--R (12a b d - 18a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (24a b d - 36a b c d + 12a b c d)x + 12a d - 18a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 2 +--R b d x + (- 4a b d + 6b c d )x + (- 11a b d + 12a b c d )x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (2a b d - 12a b c d + 12a b c d - 2b c )x + 7a d - 15a b c d +--R + +--R 2 2 2 3 3 +--R 9a b c d - a b c +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 3 2 4 2 2 +--R (12a b d - 18a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 3 2 2 2 2 +--R (24a b d - 36a b c d + 12a b c d)x + 12a d - 18a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 4 3 4 3 3 4 2 3 2 2 3 3 2 2 +--R b d x + (- 4a b d + 6b c d )x + (- 11a b d + 12a b c d )x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 3 2 +--R (2a b d - 12a b c d + 12a b c d - 2b c )x + 7a d - 15a b c d +--R + +--R 2 2 2 3 3 +--R 9a b c d - a b c +--R / +--R 7 2 6 2 5 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 731 + +--S 732 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 733 + +)clear all + +--S 734 of 1092 +t0:=(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 734 + +--S 735 of 1092 +r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ + (b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4 +--R +--R +--R (2) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3 2 2 2 3 2 2 3 3 +--R (- 6a b d + 6b c d )x + (- 12a b d + 12a b c d )x - 6a d +--R + +--R 2 2 +--R 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 3 3 2 3 2 2 3 2 2 3 2 3 3 +--R 2b d x + 4a b d x + (- 4a b d + 12a b c d - 6b c d)x - 5a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 3a b c d - b c +--R / +--R 6 2 5 2 4 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 1092 +t0:=(c+d*x)^3/(x*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 739 + +--S 740 of 1092 +r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ + (a^2*b^3*(a+b*x))+c^3*log(x)/a^3-(c^3/a^3-d^3/b^3)*log(a+b*x) +--R +--R +--R (2) +--R 3 2 3 5 3 2 4 3 4 3 5 3 2 3 3 +--R ((2a b d - 2b c )x + (4a b d - 4a b c )x + 2a d - 2a b c ) +--R * +--R log(b x + a) +--R + +--R 5 3 2 4 3 2 3 3 4 3 3 2 2 4 3 +--R (2b c x + 4a b c x + 2a b c )log(x) + (4a b d - 6a b c d + 2a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 +--R 3a d - 3a b c d - 3a b c d + 3a b c +--R / +--R 3 5 2 4 4 5 3 +--R 2a b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 5 3 2 4 3 4 3 5 3 2 3 3 +--R ((2a b d - 2b c )x + (4a b d - 4a b c )x + 2a d - 2a b c ) +--R * +--R log(b x + a) +--R + +--R 5 3 2 4 3 2 3 3 4 3 3 2 2 4 3 +--R (2b c x + 4a b c x + 2a b c )log(x) + (4a b d - 6a b c d + 2a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 +--R 3a d - 3a b c d - 3a b c d + 3a b c +--R / +--R 3 5 2 4 4 5 3 +--R 2a b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 741 + +--S 742 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1092 +t0:=(c+d*x)^3/(x^2*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 744 + +--S 745 of 1092 +r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ + (2*b*c+a*d)/(a^3*b^2*(a+b*x))-3*c^2*(b*c-a*d)*log(x)/a^4+_ + 3*c^2*(b*c-a*d)*log(a+b*x)/a^4 +--R +--R +--R (2) +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (- 6a b c d + 6b c )x + (- 12a b c d + 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (- 6a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (6a b c d - 6b c )x + (12a b c d - 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (6a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R (- 2a b d + 6a b c d - 6a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 2 3 +--R (- a d - 3a b c d + 9a b c d - 9a b c )x - 2a b c +--R / +--R 4 4 3 5 3 2 6 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (- 6a b c d + 6b c )x + (- 12a b c d + 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (- 6a b c d + 6a b c )x +--R * +--R log(b x + a) +--R + +--R 4 2 5 3 3 2 3 2 4 3 2 +--R (6a b c d - 6b c )x + (12a b c d - 12a b c )x +--R + +--R 3 2 2 2 3 3 +--R (6a b c d - 6a b c )x +--R * +--R log(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R (- 2a b d + 6a b c d - 6a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 2 3 +--R (- a d - 3a b c d + 9a b c d - 9a b c )x - 2a b c +--R / +--R 4 4 3 5 3 2 6 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1092 +t0:=(c+d*x)^3/(x^3*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 749 + +--S 750 of 1092 +r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ + (a^3*b*(a+b*x)^2)+3*c*(b*c-a*d)^2/(a^4*(a+b*x))+3*c*(b*c-a*d)*_ + (2*b*c-a*d)*log(x)/a^5-3*c*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 +--R +--R +--R (2) +--R 2 3 2 4 2 5 3 4 +--R (- 6a b c d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12a b c d + 36a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6a b c d + 18a b c d - 12a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6a b c d - 18a b c d + 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12a b c d - 36a b c d + 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6a b c d - 18a b c d + 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6a b c d - 18a b c d + 12a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- a d + 9a b c d - 27a b c d + 18a b c )x + (- 6a b c d + 4a b c )x +--R + +--R 4 3 +--R - a b c +--R / +--R 5 3 4 6 2 3 7 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 2 5 3 4 +--R (- 6a b c d + 18a b c d - 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (- 12a b c d + 36a b c d - 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (- 6a b c d + 18a b c d - 12a b c )x +--R * +--R log(b x + a) +--R + +--R 2 3 2 4 2 5 3 4 +--R (6a b c d - 18a b c d + 12b c )x +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (12a b c d - 36a b c d + 24a b c )x +--R + +--R 4 2 3 2 2 2 3 3 2 +--R (6a b c d - 18a b c d + 12a b c )x +--R * +--R log(x) +--R + +--R 3 2 2 2 3 2 4 3 3 +--R (6a b c d - 18a b c d + 12a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 2 4 2 3 2 3 +--R (- a d + 9a b c d - 27a b c d + 18a b c )x + (- 6a b c d + 4a b c )x +--R + +--R 4 3 +--R - a b c +--R / +--R 5 3 4 6 2 3 7 2 +--R 2a b x + 4a b x + 2a b x +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1092 +t0:=(c+d*x)^3/(x^4*(a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1092 +r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ + (2*b*c-a*d)/(a^5*x)-1/2*(b*c-a*d)^3/(a^4*(a+b*x)^2)-(b*c-a*d)^2*_ + (4*b*c-a*d)/(a^5*(a+b*x))-(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ + log(x)/a^6+(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*log(a+b*x)/a^6 +--R +--R +--R (2) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 6a b d + 54a b c d - 108a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 108a b c d - 216a b c d + 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 6a d + 54a b c d - 108a b c d + 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (6a b d - 54a b c d + 108a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 108a b c d + 216a b c d - 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (6a d - 54a b c d + 108a b c d - 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 54a b c d + 108a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (9a d - 81a b c d + 162a b c d - 90a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 36a b c d - 20a b c )x + (- 9a c d + 5a b c )x - 2a c +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (- 6a b d + 54a b c d - 108a b c d + 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (- 12a b d + 108a b c d - 216a b c d + 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (- 6a d + 54a b c d - 108a b c d + 60a b c )x +--R * +--R log(b x + a) +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (6a b d - 54a b c d + 108a b c d - 60b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (12a b d - 108a b c d + 216a b c d - 120a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (6a d - 54a b c d + 108a b c d - 60a b c )x +--R * +--R log(x) +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (6a b d - 54a b c d + 108a b c d - 60a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (9a d - 81a b c d + 162a b c d - 90a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (- 18a c d + 36a b c d - 20a b c )x + (- 9a c d + 5a b c )x - 2a c +--R / +--R 6 2 5 7 4 8 3 +--R 6a b x + 12a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1092 +t0:=x^7/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 7 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 759 + +--S 760 of 1092 +r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ + (a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/_ + (d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-_ + 3*a^5*(7*b^2*c^2-7*a*b*c*d+2*a^2*d^2)*log(a+b*x)/(b^5*(b*c-a*d)^5)+_ + 3*c^5*(2*b^2*c^2-7*a*b*c*d+7*a^2*d^2)*log(c+d*x)/(d^5*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 7 5 4 8 6 3 9 7 2 4 +--R (- 42a b c d + 42a b c d - 12b c d )x +--R + +--R 3 6 5 4 8 7 2 9 8 3 +--R (- 84a b c d + 60a b c d - 24b c d)x +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 2 +--R (- 42a b c d - 126a b c d + 114a b c d - 6a b c d - 12b c )x +--R + +--R 4 5 6 3 2 7 8 8 9 4 5 7 2 3 6 8 +--R (- 84a b c d + 60a b c d - 24a b c )x - 42a b c d + 42a b c d +--R + +--R 2 7 9 +--R - 12a b c +--R * +--R log(d x + c) +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 +--R (12a b d - 42a b c d + 42a b c d )x +--R + +--R 8 9 7 2 8 5 4 3 6 3 +--R (24a b d - 60a b c d + 84a b c d )x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 2 +--R (12a d + 6a b c d - 114a b c d + 126a b c d + 42a b c d )x +--R + +--R 9 8 8 2 7 6 3 4 5 9 2 7 8 3 6 +--R (24a c d - 60a b c d + 84a b c d )x + 12a c d - 42a b c d +--R + +--R 7 2 4 5 +--R 42a b c d +--R * +--R log(b x + a) +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 6 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 +--R - 4a b d + 16a b c d - 20a b c d + 20a b c d - 16a b c d +--R + +--R 9 6 3 +--R 4b c d +--R * +--R 5 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R - 11a b d + 35a b c d - 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 21a b c d - 35a b c d + 11b c d +--R * +--R 4 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 +--R 2a b d - 20a b c d + 66a b c d - 86a b c d + 86a b c d +--R + +--R 2 7 6 3 8 7 2 9 8 +--R - 66a b c d + 20a b c d - 2b c d +--R * +--R 3 +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 +--R 7a d - 16a b c d + 6a b c d + 11a b c d - 50a b c d + 50a b c d +--R + +--R 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 11a b c d - 6a b c d + 16a b c d - 7b c +--R * +--R 2 +--R x +--R + +--R 9 8 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 +--R 14a c d - 38a b c d + 28a b c d - 16a b c d + 16a b c d +--R + +--R 3 6 7 2 2 7 8 8 9 +--R - 28a b c d + 38a b c d - 14a b c +--R * +--R x +--R + +--R 9 2 7 8 3 6 7 2 4 5 4 5 7 2 3 6 8 2 7 9 +--R 7a c d - 20a b c d + 13a b c d - 13a b c d + 20a b c d - 7a b c +--R / +--R 5 7 12 4 8 11 3 9 2 10 2 10 3 9 11 4 8 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 12 5 7 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 6 12 5 7 11 4 8 2 10 2 10 4 8 11 5 7 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 12 6 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 5 12 6 6 11 5 7 2 10 4 8 3 9 3 9 4 8 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 10 5 7 11 6 6 12 7 5 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 5 11 6 6 2 10 5 7 3 9 3 9 5 7 2 10 6 6 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 7 5 +--R - 4a b c d +--R * +--R x +--R + +--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 5 4 8 6 3 9 7 2 4 +--R (- 42a b c d + 42a b c d - 12b c d )x +--R + +--R 3 6 5 4 8 7 2 9 8 3 +--R (- 84a b c d + 60a b c d - 24b c d)x +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 2 +--R (- 42a b c d - 126a b c d + 114a b c d - 6a b c d - 12b c )x +--R + +--R 4 5 6 3 2 7 8 8 9 4 5 7 2 3 6 8 +--R (- 84a b c d + 60a b c d - 24a b c )x - 42a b c d + 42a b c d +--R + +--R 2 7 9 +--R - 12a b c +--R * +--R log(d x + c) +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 +--R (12a b d - 42a b c d + 42a b c d )x +--R + +--R 8 9 7 2 8 5 4 3 6 3 +--R (24a b d - 60a b c d + 84a b c d )x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 2 +--R (12a d + 6a b c d - 114a b c d + 126a b c d + 42a b c d )x +--R + +--R 9 8 8 2 7 6 3 4 5 9 2 7 8 3 6 +--R (24a c d - 60a b c d + 84a b c d )x + 12a c d - 42a b c d +--R + +--R 7 2 4 5 +--R 42a b c d +--R * +--R log(b x + a) +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 6 +--R (a b d - 5a b c d + 10a b c d - 10a b c d + 5a b c d - b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 +--R - 4a b d + 16a b c d - 20a b c d + 20a b c d - 16a b c d +--R + +--R 9 6 3 +--R 4b c d +--R * +--R 5 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R - 11a b d + 35a b c d - 21a b c d - 35a b c d + 35a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 21a b c d - 35a b c d + 11b c d +--R * +--R 4 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 +--R 2a b d - 20a b c d + 66a b c d - 86a b c d + 86a b c d +--R + +--R 2 7 6 3 8 7 2 9 8 +--R - 66a b c d + 20a b c d - 2b c d +--R * +--R 3 +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 +--R 7a d - 16a b c d + 6a b c d + 11a b c d - 50a b c d + 50a b c d +--R + +--R 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 11a b c d - 6a b c d + 16a b c d - 7b c +--R * +--R 2 +--R x +--R + +--R 9 8 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 +--R 14a c d - 38a b c d + 28a b c d - 16a b c d + 16a b c d +--R + +--R 3 6 7 2 2 7 8 8 9 +--R - 28a b c d + 38a b c d - 14a b c +--R * +--R x +--R + +--R 9 2 7 8 3 6 7 2 4 5 4 5 7 2 3 6 8 2 7 9 +--R 7a c d - 20a b c d + 13a b c d - 13a b c d + 20a b c d - 7a b c +--R / +--R 5 7 12 4 8 11 3 9 2 10 2 10 3 9 11 4 8 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 12 5 7 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 6 12 5 7 11 4 8 2 10 2 10 4 8 11 5 7 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 12 6 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 5 12 6 6 11 5 7 2 10 4 8 3 9 3 9 4 8 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 10 5 7 11 6 6 12 7 5 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 5 11 6 6 2 10 5 7 3 9 3 9 5 7 2 10 6 6 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 7 5 +--R - 4a b c d +--R * +--R x +--R + +--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 761 + +--S 762 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +)clear all + +--S 764 of 1092 +t0:=x^6/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 6 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 764 + +--S 765 of 1092 +r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ + (b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-_ + 3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^4*(b*c-a*d)^5)-3*c^4*_ + (b^2*c^2-4*a*b*c*d+5*a^2*d^2)*log(c+d*x)/(d^4*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 6 4 4 7 5 3 8 6 2 4 +--R (30a b c d - 24a b c d + 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 3 +--R (60a b c d + 12a b c d - 36a b c d + 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 2 +--R (30a b c d + 96a b c d - 60a b c d + 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 4 4 6 2 +--R (60a b c d + 12a b c d - 36a b c d + 12a b c )x + 30a b c d +--R + +--R 3 5 7 2 6 8 +--R - 24a b c d + 6a b c +--R * +--R log(d x + c) +--R + +--R 6 2 8 5 3 7 4 4 2 6 4 +--R (- 6a b d + 24a b c d - 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 +--R (- 12a b d + 36a b c d - 12a b c d - 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 2 +--R (- 6a d + 60a b c d - 96a b c d - 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 8 2 6 +--R (- 12a c d + 36a b c d - 12a b c d - 60a b c d )x - 6a c d +--R + +--R 7 3 5 6 2 4 4 +--R 24a b c d - 30a b c d +--R * +--R log(b x + a) +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 5 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 4 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 4a b d + 16a b c d - 30a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 30a b c d - 16a b c d + 4b c d +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 5a d + 8a b c d + 9a b c d - 4a b c d + 4a b c d - 9a b c d +--R + +--R 7 7 8 8 +--R - 8a b c d + 5b c +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 10a c d + 28a b c d - 14a b c d + 8a b c d - 8a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 14a b c d - 28a b c d + 10a b c +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R - 5a c d + 16a b c d - 11a b c d + 11a b c d - 16a b c d + 5a b c +--R / +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 10 4 7 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 11 5 6 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 2 9 4 7 10 5 6 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 6 5 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 3 8 4 7 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 9 5 6 10 6 5 11 7 4 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 4 10 6 5 2 9 5 6 3 8 3 8 5 6 2 9 6 5 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 7 4 +--R - 4a b c d +--R * +--R x +--R + +--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 4 4 7 5 3 8 6 2 4 +--R (30a b c d - 24a b c d + 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 3 +--R (60a b c d + 12a b c d - 36a b c d + 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 2 +--R (30a b c d + 96a b c d - 60a b c d + 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 4 4 6 2 +--R (60a b c d + 12a b c d - 36a b c d + 12a b c )x + 30a b c d +--R + +--R 3 5 7 2 6 8 +--R - 24a b c d + 6a b c +--R * +--R log(d x + c) +--R + +--R 6 2 8 5 3 7 4 4 2 6 4 +--R (- 6a b d + 24a b c d - 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 +--R (- 12a b d + 36a b c d - 12a b c d - 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 2 +--R (- 6a d + 60a b c d - 96a b c d - 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 8 2 6 +--R (- 12a c d + 36a b c d - 12a b c d - 60a b c d )x - 6a c d +--R + +--R 7 3 5 6 2 4 4 +--R 24a b c d - 30a b c d +--R * +--R log(b x + a) +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 5 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 4 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 4a b d + 16a b c d - 30a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 30a b c d - 16a b c d + 4b c d +--R * +--R 3 +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 5a d + 8a b c d + 9a b c d - 4a b c d + 4a b c d - 9a b c d +--R + +--R 7 7 8 8 +--R - 8a b c d + 5b c +--R * +--R 2 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 10a c d + 28a b c d - 14a b c d + 8a b c d - 8a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 14a b c d - 28a b c d + 10a b c +--R * +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R - 5a c d + 16a b c d - 11a b c d + 11a b c d - 16a b c d + 5a b c +--R / +--R 5 6 11 4 7 10 3 8 2 9 2 9 3 8 10 4 7 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 11 5 6 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 5 11 5 6 10 4 7 2 9 2 9 4 7 10 5 6 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 11 6 5 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 4 11 6 5 10 5 6 2 9 4 7 3 8 3 8 4 7 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 9 5 6 10 6 5 11 7 4 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 4 10 6 5 2 9 5 6 3 8 3 8 5 6 2 9 6 5 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 7 4 +--R - 4a b c d +--R * +--R x +--R + +--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 768 + +)clear all + +--S 769 of 1092 +t0:=x^5/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 5 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 769 + +--S 770 of 1092 +r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ + (b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+_ + c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-_ + 5*a*b*c*d+a^2*d^2)*log(a+b*x)/(b^3*(b*c-a*d)^5)+c^3*(b^2*c^2-_ + 5*a*b*c*d+10*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^5) +--R +--R +--R (2) +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (- 20a b c d + 10a b c d - 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (- 40a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (- 20a b c d - 70a b c d + 18a b c d + 2a b c d - 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (- 40a b c d - 20a b c d + 16a b c d - 4a b c )x - 20a b c d +--R + +--R 3 4 6 2 5 7 +--R 10a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (2a b d - 10a b c d + 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (4a b d - 16a b c d + 20a b c d + 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (2a d - 2a b c d - 18a b c d + 70a b c d + 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (4a c d - 16a b c d + 20a b c d + 40a b c d )x + 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R - 10a b c d + 20a b c d +--R * +--R log(b x + a) +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 14a b c d + 10a b c d - 10a b c d + 14a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 3a d - 4a b c d - 19a b c d + 20a b c d - 20a b c d + 19a b c d +--R + +--R 6 6 7 7 +--R 4a b c d - 3b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (6a c d - 20a b c d + 4a b c d - 4a b c d + 20a b c d - 6a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 10 5 5 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 2 8 4 6 9 5 5 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 6 4 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 3 9 6 4 2 8 5 5 3 7 3 7 5 5 2 8 6 4 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 9 7 3 +--R - 4a b c d +--R * +--R x +--R + +--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (- 20a b c d + 10a b c d - 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (- 40a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (- 20a b c d - 70a b c d + 18a b c d + 2a b c d - 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (- 40a b c d - 20a b c d + 16a b c d - 4a b c )x - 20a b c d +--R + +--R 3 4 6 2 5 7 +--R 10a b c d - 2a b c +--R * +--R log(d x + c) +--R + +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (2a b d - 10a b c d + 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (4a b d - 16a b c d + 20a b c d + 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (2a d - 2a b c d - 18a b c d + 70a b c d + 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (4a c d - 16a b c d + 20a b c d + 40a b c d )x + 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R - 10a b c d + 20a b c d +--R * +--R log(b x + a) +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 14a b c d + 10a b c d - 10a b c d + 14a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 3a d - 4a b c d - 19a b c d + 20a b c d - 20a b c d + 19a b c d +--R + +--R 6 6 7 7 +--R 4a b c d - 3b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (6a c d - 20a b c d + 4a b c d - 4a b c d + 20a b c d - 6a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 5 5 10 4 6 9 3 7 2 8 2 8 3 7 9 4 6 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 10 5 5 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 4 10 5 5 9 4 6 2 8 2 8 4 6 9 5 5 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 10 6 4 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 3 10 6 4 9 5 5 2 8 4 6 3 7 3 7 4 6 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 8 5 5 9 6 4 10 7 3 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 3 9 6 4 2 8 5 5 3 7 3 7 5 5 2 8 6 4 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 9 7 3 +--R - 4a b c d +--R * +--R x +--R + +--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 771 + +--S 772 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 773 + +)clear all + +--S 774 of 1092 +t0:=x^4/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 4 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 774 + +--S 775 of 1092 +r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ + (a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/_ + (d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-_ + 6*a^2*c^2*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R 12a b c d x + (24a b c d + 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 4 2 3 3 3 3 4 2 +--R (12a b c d + 48a b c d + 12a b c d )x + (24a b c d + 24a b c d )x +--R + +--R 4 2 4 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R - 12a b c d x + (- 24a b c d - 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (- 12a b c d - 48a b c d - 12a b c d )x +--R + +--R 4 2 3 3 3 3 4 2 4 2 4 2 +--R (- 24a b c d - 24a b c d )x - 12a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (- 2a b d + 10a b c d - 8a b c d + 8a b c d - 10a b c d + 2b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 2 +--R (- a d + 4a b c d + 13a b c d - 13a b c d - 4a b c d + b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (- 2a c d + 14a b c d + 4a b c d - 4a b c d - 14a b c d + 2a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 +--R - a c d + 8a b c d - 8a b c d + a b c +--R / +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 9 6 3 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 2 7 6 3 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 8 7 2 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R 12a b c d x + (24a b c d + 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 4 2 3 3 3 3 4 2 +--R (12a b c d + 48a b c d + 12a b c d )x + (24a b c d + 24a b c d )x +--R + +--R 4 2 4 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 2 4 2 4 4 3 3 2 4 2 4 3 3 3 +--R - 12a b c d x + (- 24a b c d - 24a b c d )x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 2 +--R (- 12a b c d - 48a b c d - 12a b c d )x +--R + +--R 4 2 3 3 3 3 4 2 4 2 4 2 +--R (- 24a b c d - 24a b c d )x - 12a b c d +--R * +--R log(b x + a) +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 3 +--R (- 2a b d + 10a b c d - 8a b c d + 8a b c d - 10a b c d + 2b c d)x +--R + +--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 2 +--R (- a d + 4a b c d + 13a b c d - 13a b c d - 4a b c d + b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6 +--R (- 2a c d + 14a b c d + 4a b c d - 4a b c d - 14a b c d + 2a b c )x +--R + +--R 6 2 4 5 3 3 3 3 5 2 4 6 +--R - a c d + 8a b c d - 8a b c d + a b c +--R / +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 8 4 5 9 5 4 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 3 9 5 4 8 4 5 2 7 2 7 4 5 8 5 4 9 6 3 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 3 6 4 5 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 7 5 4 8 6 3 9 7 2 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 2 8 6 3 2 7 5 4 3 6 3 6 5 4 2 7 6 3 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 8 7 2 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 776 + +--S 777 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1092 +t0:=x^3/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 3 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 779 + +--S 780 of 1092 +r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ + 1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-_ + 3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/_ + (b*c-a*d)^5 +--R +--R +--R (2) +--R 2 3 4 4 2 3 4 +--R (- 6a b c d - 6a b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 6a b c d - 30a b c d - 30a b c d - 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 3 4 4 2 3 4 3 2 4 2 3 2 3 4 3 2 3 +--R (6a b c d + 6a b c d )x + (12a b c d + 24a b c d + 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (6a b c d + 30a b c d + 30a b c d + 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 4 4 3 2 3 +--R (- 6a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- a d - 4a b c d - 19a b c d + 19a b c d + 4a b c d + b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d - 14a b c d + 14a b c d + 2a b c )x - a c d - 9a b c d +--R + +--R 3 2 4 2 3 5 +--R 9a b c d + a b c +--R / +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 7 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 4 2 3 4 +--R (- 6a b c d - 6a b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 6a b c d - 30a b c d - 30a b c d - 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 2 3 4 4 2 3 4 3 2 4 2 3 2 3 4 3 2 3 +--R (6a b c d + 6a b c d )x + (12a b c d + 24a b c d + 12a b c d )x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (6a b c d + 30a b c d + 30a b c d + 6a b c d)x +--R + +--R 4 2 3 3 2 3 2 2 3 4 4 3 2 3 2 4 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 3 2 4 4 3 2 3 +--R (- 6a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (- a d - 4a b c d - 19a b c d + 19a b c d + 4a b c d + b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 5 2 3 4 3 2 +--R (- 2a c d - 14a b c d + 14a b c d + 2a b c )x - a c d - 9a b c d +--R + +--R 3 2 4 2 3 5 +--R 9a b c d + a b c +--R / +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 7 4 4 8 5 3 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 8 6 2 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R 2a b d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 18a b c d + 2a b c d - 2b c d +--R * +--R 2 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 7 +--R - 4a b c d +--R * +--R x +--R + +--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d +--R Type: Union(Expression(Integer),...) +--E 781 + +--S 782 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +)clear all + +--S 784 of 1092 +t0:=x^2/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 2 +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 784 + +--S 785 of 1092 +r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ + 1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+_ + (b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+_ + a^2*d^2)*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 2 2 4 3 3 4 2 2 4 +--R (2a b d + 8a b c d + 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (4a b d + 20a b c d + 20a b c d + 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (2a d + 16a b c d + 36a b c d + 16a b c d + 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (4a c d + 20a b c d + 20a b c d + 4a b c )x + 2a c d + 8a b c d +--R + +--R 2 2 4 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 4 +--R (- 2a b d - 8a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- 4a b d - 20a b c d - 20a b c d - 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 2a d - 16a b c d - 36a b c d - 16a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (- 4a c d - 20a b c d - 20a b c d - 4a b c )x - 2a c d - 8a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (2a b d + 6a b c d - 6a b c d - 2b c d)x +--R + +--R 4 4 3 3 3 3 4 4 2 +--R (3a d + 12a b c d - 12a b c d - 3b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 2 2 4 +--R (10a c d + 6a b c d - 6a b c d - 10a b c )x + 6a c d - 6a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 3 4 2 2 4 +--R (2a b d + 8a b c d + 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (4a b d + 20a b c d + 20a b c d + 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (2a d + 16a b c d + 36a b c d + 16a b c d + 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (4a c d + 20a b c d + 20a b c d + 4a b c )x + 2a c d + 8a b c d +--R + +--R 2 2 4 +--R 2a b c +--R * +--R log(d x + c) +--R + +--R 2 2 4 3 3 4 2 2 4 +--R (- 2a b d - 8a b c d - 2b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (- 4a b d - 20a b c d - 20a b c d - 4b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (- 2a d - 16a b c d - 36a b c d - 16a b c d - 2b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (- 4a c d - 20a b c d - 20a b c d - 4a b c )x - 2a c d - 8a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R log(b x + a) +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (2a b d + 6a b c d - 6a b c d - 2b c d)x +--R + +--R 4 4 3 3 3 3 4 4 2 +--R (3a d + 12a b c d - 12a b c d - 3b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 2 2 4 +--R (10a c d + 6a b c d - 6a b c d - 10a b c )x + 6a c d - 6a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 786 + +--S 787 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 788 + +)clear all + +--S 789 of 1092 +t0:=x/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R x +--R / +--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: Fraction(Polynomial(Integer)) +--E 789 + +--S 790 of 1092 +r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ + 1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-_ + 3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*_ + log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (- 6a b d - 6b c d )x + (- 12a b d - 24a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d - 30a b c d - 30a b c d - 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (6a b d + 6b c d )x + (12a b d + 24a b c d + 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b d + 30a b c d + 30a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 2 4 4 2 2 3 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d + 6b c d )x + (- 9a b d - 9a b c d + 9a b c d + 9b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (- 2a d - 14a b c d + 14a b c d + 2b c )x - a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d + a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (- 6a b d - 6b c d )x + (- 12a b d - 24a b c d - 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d - 30a b c d - 30a b c d - 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 12a b c d - 24a b c d - 12a b c d)x - 6a b c d - 6a b c d +--R * +--R log(d x + c) +--R + +--R 3 4 4 3 4 2 2 4 3 3 4 2 2 3 +--R (6a b d + 6b c d )x + (12a b d + 24a b c d + 12b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 2 +--R (6a b d + 30a b c d + 30a b c d + 6b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (12a b c d + 24a b c d + 12a b c d)x + 6a b c d + 6a b c d +--R * +--R log(b x + a) +--R + +--R 2 2 4 4 2 2 3 3 4 2 2 3 3 2 2 4 3 2 +--R (- 6a b d + 6b c d )x + (- 9a b d - 9a b c d + 9a b c d + 9b c d)x +--R + +--R 4 4 3 3 3 3 4 4 4 3 3 2 2 +--R (- 2a d - 14a b c d + 14a b c d + 2b c )x - a c d - 9a b c d +--R + +--R 2 2 3 3 4 +--R 9a b c d + a b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 791 + +--S 792 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 793 + +)clear all + +--S 794 of 1092 +t0:=1/((a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--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: Fraction(Polynomial(Integer)) +--E 794 + +--S 795 of 1092 +r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ + 1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_ + 6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5 +--R +--R +--R (2) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 3 4 4 3 3 +--R 12b d x + (24a b d + 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (12a b d + 48a b c d + 12b c d )x + (24a b c d + 24a b c d )x +--R + +--R 2 2 2 2 +--R 12a b c d +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 +--R - 12b d x + (- 24a b d - 24b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 2 2 3 3 2 2 +--R (- 12a b d - 48a b c d - 12b c d )x + (- 24a b c d - 24a b c d )x +--R + +--R 2 2 2 2 +--R - 12a b c d +--R * +--R log(b x + a) +--R + +--R 3 4 4 3 3 2 2 4 4 2 2 2 +--R (12a b d - 12b c d )x + (18a b d - 18b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 24a b c d - 24a b c d - 4b c d)x - a d + 8a b c d +--R + +--R 3 3 4 4 +--R - 8a b c d + b c +--R / +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 4 +--R (2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 7 6 3 +--R (4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4b c d)x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d + 18a b c d +--R + +--R 6 6 7 7 +--R 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 796 + +--S 797 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 798 + +)clear all + +--S 799 of 1092 +t0:=1/(x*(a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 7 2 3 3 2 6 2 3 2 2 3 2 5 +--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 4 3 2 2 2 2 3 3 +--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 2 3 3 +--R (3a c d + 3a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 799 + +--S 800 of 1092 +r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ + (a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/_ + (c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-_ + 5*a*b*c*d+10*a^2*d^2)*log(a+b*x)/(a^3*(b*c-a*d)^5)+_ + d^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^3*(b*c-a*d)^5) +--R +--R +--R (2) +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (- 2a b d + 10a b c d - 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (- 4a b d + 16a b c d - 20a b c d - 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (- 2a d + 2a b c d + 18a b c d - 70a b c d - 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (- 4a c d + 16a b c d - 20a b c d - 40a b c d )x - 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R 10a b c d - 20a b c d +--R * +--R log(d x + c) +--R + +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (20a b c d - 10a b c d + 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (40a b c d + 20a b c d - 16a b c d + 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (20a b c d + 70a b c d - 18a b c d - 2a b c d + 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (40a b c d + 20a b c d - 16a b c d + 4a b c )x + 20a b c d +--R + +--R 3 4 6 2 5 7 +--R - 10a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 7 5 2 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b c d + 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 6 7 +--R - 4a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R * +--R log(x) +--R + +--R 5 2 6 4 3 2 5 2 5 4 3 6 5 2 3 +--R (2a b c d - 10a b c d + 10a b c d - 2a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 4a b c d - 17a b c d - 5a b c d + 5a b c d + 17a b c d +--R + +--R 6 6 +--R - 4a b c d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (2a c d - 4a b c d - 16a b c d + 16a b c d + 4a b c d - 2a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 8 2 3 7 7 3 4 6 6 4 5 5 5 5 6 4 4 6 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 3 7 8 2 +--R - 2a b c d +--R * +--R 4 +--R x +--R + +--R 9 3 7 8 2 4 6 7 3 5 5 5 5 7 3 4 6 8 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 3 7 9 +--R - 4a b c d +--R * +--R 3 +--R x +--R + +--R 10 3 7 9 4 6 8 2 5 5 7 3 6 4 6 4 7 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 5 5 8 2 4 6 9 3 7 10 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 2 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 6 4 8 2 5 5 9 4 6 10 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 7 4 3 6 3 4 2 5 4 +--R (- 2a b d + 10a b c d - 20a b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 3 +--R (- 4a b d + 16a b c d - 20a b c d - 40a b c d )x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 +--R (- 2a d + 2a b c d + 18a b c d - 70a b c d - 20a b c d )x +--R + +--R 7 6 6 2 5 5 2 3 4 4 3 4 3 7 2 5 +--R (- 4a c d + 16a b c d - 20a b c d - 40a b c d )x - 2a c d +--R + +--R 6 3 4 5 2 4 3 +--R 10a b c d - 20a b c d +--R * +--R log(d x + c) +--R + +--R 2 5 3 4 6 4 3 7 5 2 4 +--R (20a b c d - 10a b c d + 2b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 3 +--R (40a b c d + 20a b c d - 16a b c d + 4b c d)x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 2 +--R (20a b c d + 70a b c d - 18a b c d - 2a b c d + 2b c )x +--R + +--R 4 3 4 3 3 4 5 2 2 5 6 6 7 4 3 5 2 +--R (40a b c d + 20a b c d - 16a b c d + 4a b c )x + 20a b c d +--R + +--R 3 4 6 2 5 7 +--R - 10a b c d + 2a b c +--R * +--R log(b x + a) +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 2a b d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 7 5 2 +--R - 2b c d +--R * +--R 4 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 2 5 4 3 6 5 2 +--R 4a b d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 7 6 +--R - 4b c d +--R * +--R 3 +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 2a d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 18a b c d + 2a b c d - 2b c +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 6 7 +--R - 4a b c +--R * +--R x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R * +--R log(x) +--R + +--R 5 2 6 4 3 2 5 2 5 4 3 6 5 2 3 +--R (2a b c d - 10a b c d + 10a b c d - 2a b c d )x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 4a b c d - 17a b c d - 5a b c d + 5a b c d + 17a b c d +--R + +--R 6 6 +--R - 4a b c d +--R * +--R 2 +--R x +--R + +--R 7 6 6 2 5 5 2 3 4 3 4 5 2 2 5 6 6 7 +--R (2a c d - 4a b c d - 16a b c d + 16a b c d + 4a b c d - 2a b c )x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R 3a c d - 12a b c d + 9a b c d - 9a b c d + 12a b c d - 3a b c +--R / +--R 8 2 3 7 7 3 4 6 6 4 5 5 5 5 6 4 4 6 7 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 3 7 8 2 +--R - 2a b c d +--R * +--R 4 +--R x +--R + +--R 9 3 7 8 2 4 6 7 3 5 5 5 5 7 3 4 6 8 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 3 7 9 +--R - 4a b c d +--R * +--R 3 +--R x +--R + +--R 10 3 7 9 4 6 8 2 5 5 7 3 6 4 6 4 7 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 5 5 8 2 4 6 9 3 7 10 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 2 +--R x +--R + +--R 10 4 6 9 5 5 8 2 6 4 6 4 8 2 5 5 9 4 6 10 +--R (4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d - 4a b c )x +--R + +--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 +--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c +--R Type: Union(Expression(Integer),...) +--E 801 + +--S 802 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 803 + +)clear all + +--S 804 of 1092 +t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 3 8 2 3 3 2 7 2 3 2 2 3 2 6 +--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 5 3 2 2 2 2 3 4 +--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 3 2 +--R (3a c d + 3a b c )x + a c x +--R Type: Fraction(Polynomial(Integer)) +--E 804 + +--S 805 of 1092 +r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ + (a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*_ + (c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-_ + 3*(b*c+a*d)*log(x)/(a^4*c^4)+3*b^4*(b^2*c^2-4*a*b*c*d+_ + 5*a^2*d^2)*log(a+b*x)/(a^4*(b*c-a*d)^5)-3*d^4*(5*b^2*c^2-_ + 4*a*b*c*d+a^2*d^2)*log(c+d*x)/(c^4*(b*c-a*d)^5) +--R +--R +--R (2) +--R 6 2 8 5 3 7 4 4 2 6 5 +--R (6a b d - 24a b c d + 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 4 +--R (12a b d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 3 +--R (6a d - 60a b c d + 96a b c d + 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 2 +--R (12a c d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 2 6 7 3 5 6 2 4 4 +--R (6a c d - 24a b c d + 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 2 6 4 4 7 5 3 8 6 2 5 +--R (- 30a b c d + 24a b c d - 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 4 +--R (- 60a b c d - 12a b c d + 36a b c d - 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 3 +--R (- 30a b c d - 96a b c d + 60a b c d - 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 2 +--R (- 60a b c d - 12a b c d + 36a b c d - 12a b c )x +--R + +--R 4 4 6 2 3 5 7 2 6 8 +--R (- 30a b c d + 24a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 +--R - 6a b d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 8 6 2 +--R 6b c d +--R * +--R 5 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 12a b d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 12a b c d - 36a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 8 8 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 6a d + 60a b c d - 96a b c d + 96a b c d - 60a b c d +--R + +--R 8 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 12a c d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 12a b c d - 36a b c d + 12a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 +--R - 6a c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 2 6 8 +--R 6a b c +--R * +--R x +--R * +--R log(x) +--R + +--R 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 2 6 5 3 +--R - 6a b c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 7 6 2 +--R 6a b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 12a b c d + 39a b c d - 24a b c d + 24a b c d - 39a b c d +--R + +--R 7 7 +--R 12a b c d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 6a c d + 6a b c d + 40a b c d - 72a b c d + 72a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R - 40a b c d - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R (- 9a c d + 32a b c d - 31a b c d + 31a b c d - 32a b c d + 9a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R - 2a c d + 10a b c d - 20a b c d + 20a b c d - 10a b c d + 2a b c +--R / +--R 9 2 4 7 8 3 5 6 7 4 6 5 6 5 7 4 5 6 8 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 4 7 9 2 +--R - 2a b c d +--R * +--R 5 +--R x +--R + +--R 10 4 7 9 2 5 6 8 3 6 5 6 5 8 3 5 6 9 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 4 7 10 +--R - 4a b c d +--R * +--R 4 +--R x +--R + +--R 11 4 7 10 5 6 9 2 6 5 8 3 7 4 7 4 8 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 6 5 9 2 5 6 10 4 7 11 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 3 +--R x +--R + +--R 11 5 6 10 6 5 9 2 7 4 7 4 9 2 6 5 10 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 5 6 11 +--R - 4a b c +--R * +--R 2 +--R x +--R + +--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 +--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 8 5 3 7 4 4 2 6 5 +--R (6a b d - 24a b c d + 30a b c d )x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 4 +--R (12a b d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 8 6 2 2 6 5 3 3 5 4 4 4 4 3 +--R (6a d - 60a b c d + 96a b c d + 30a b c d )x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 2 +--R (12a c d - 36a b c d + 12a b c d + 60a b c d )x +--R + +--R 8 2 6 7 3 5 6 2 4 4 +--R (6a c d - 24a b c d + 30a b c d )x +--R * +--R log(d x + c) +--R + +--R 2 6 4 4 7 5 3 8 6 2 5 +--R (- 30a b c d + 24a b c d - 6b c d )x +--R + +--R 3 5 4 4 2 6 5 3 7 6 2 8 7 4 +--R (- 60a b c d - 12a b c d + 36a b c d - 12b c d)x +--R + +--R 4 4 4 4 3 5 5 3 2 6 6 2 8 8 3 +--R (- 30a b c d - 96a b c d + 60a b c d - 6b c )x +--R + +--R 4 4 5 3 3 5 6 2 2 6 7 7 8 2 +--R (- 60a b c d - 12a b c d + 36a b c d - 12a b c )x +--R + +--R 4 4 6 2 3 5 7 2 6 8 +--R (- 30a b c d + 24a b c d - 6a b c )x +--R * +--R log(b x + a) +--R + +--R 6 2 8 5 3 7 4 4 2 6 2 6 4 4 7 5 3 +--R - 6a b d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 8 6 2 +--R 6b c d +--R * +--R 5 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 12a b d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R 12a b c d - 36a b c d + 12b c d +--R * +--R 4 +--R x +--R + +--R 8 8 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 6a d + 60a b c d - 96a b c d + 96a b c d - 60a b c d +--R + +--R 8 8 +--R 6b c +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 12a c d + 36a b c d - 12a b c d - 60a b c d + 60a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R 12a b c d - 36a b c d + 12a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 +--R - 6a c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 2 6 8 +--R 6a b c +--R * +--R x +--R * +--R log(x) +--R + +--R 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 2 6 5 3 +--R - 6a b c d + 24a b c d - 30a b c d + 30a b c d - 24a b c d +--R + +--R 7 6 2 +--R 6a b c d +--R * +--R 4 +--R x +--R + +--R 7 7 6 2 2 6 5 3 3 5 3 5 5 3 2 6 6 2 +--R - 12a b c d + 39a b c d - 24a b c d + 24a b c d - 39a b c d +--R + +--R 7 7 +--R 12a b c d +--R * +--R 3 +--R x +--R + +--R 8 7 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 +--R - 6a c d + 6a b c d + 40a b c d - 72a b c d + 72a b c d +--R + +--R 3 5 6 2 2 6 7 7 8 +--R - 40a b c d - 6a b c d + 6a b c +--R * +--R 2 +--R x +--R + +--R 8 2 6 7 3 5 6 2 4 4 4 4 6 2 3 5 7 2 6 8 +--R (- 9a c d + 32a b c d - 31a b c d + 31a b c d - 32a b c d + 9a b c )x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 +--R - 2a c d + 10a b c d - 20a b c d + 20a b c d - 10a b c d + 2a b c +--R / +--R 9 2 4 7 8 3 5 6 7 4 6 5 6 5 7 4 5 6 8 3 +--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d +--R + +--R 4 7 9 2 +--R - 2a b c d +--R * +--R 5 +--R x +--R + +--R 10 4 7 9 2 5 6 8 3 6 5 6 5 8 3 5 6 9 2 +--R 4a b c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 4 7 10 +--R - 4a b c d +--R * +--R 4 +--R x +--R + +--R 11 4 7 10 5 6 9 2 6 5 8 3 7 4 7 4 8 3 +--R 2a c d - 2a b c d - 18a b c d + 50a b c d - 50a b c d +--R + +--R 6 5 9 2 5 6 10 4 7 11 +--R 18a b c d + 2a b c d - 2a b c +--R * +--R 3 +--R x +--R + +--R 11 5 6 10 6 5 9 2 7 4 7 4 9 2 6 5 10 +--R 4a c d - 16a b c d + 20a b c d - 20a b c d + 16a b c d +--R + +--R 5 6 11 +--R - 4a b c +--R * +--R 2 +--R x +--R + +--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 +--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x +--R Type: Union(Expression(Integer),...) +--E 806 + +--S 807 of 1092 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1092 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 808 + +)clear all + +--S 809 of 1092 +t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R 2 +-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1092 +r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ + a^2*sqrt(c+d*x)/(c*x) +--R +--R +--R +-------+ +--R 2 2 \|d x + c 2 2 +-+ +-------+ +--R (a d - 4a b c d)x atanh(----------) + (2b c x - a d)\|c \|d x + c +--R +-+ +--R \|c +--R (2) ------------------------------------------------------------------- +--R +-+ +--R c d x\|c +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-+ +--R 2 2 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4a b c d)x log(-----------------------------) +--R x +--R + +--R 2 2 +-+ +-------+ +--R (4b c x - 2a d)\|c \|d x + c +--R / +--R +-+ +--R 2c d x\|c +--R , +--R +---+ +-------+ +--R 2 2 \|- c \|d x + c 2 2 +---+ +-------+ +--R (a d - 4a b c d)x atan(----------------) + (2b c x - a d)\|- c \|d x + c +--R c +--R --------------------------------------------------------------------------] +--R +---+ +--R c d x\|- c +--R Type: Union(List(Expression(Integer)),...) +--E 811 + +--S 812 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R 2 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4a b c)log(-----------------------------) +--R x +--R + +--R +-------+ +--R 2 \|d x + c +--R (- 2a d + 8a b c)atanh(----------) +--R +-+ +--R \|c +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +--R 2 +---+ \|d x + c +--R (- a d + 4a b c)\|- c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---+ +-------+ +--R 2 +-+ \|- c \|d x + c +--R (a d - 4a b c)\|c atan(----------------) +--R c +--R / +--R +---+ +-+ +--R c\|- c \|c +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 815 + +)clear all + +--S 816 of 1092 +t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) +--R +--R +--R +-------+ +--R (d x + c)\|d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1092 +r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ + sqrt(c)/a^3-(4*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b*c-a*d)/(a^3*sqrt(b))-2*(b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-----------+ \|b \|d x + c +--R ((a b d - 4b c)x + (a d - 4a b c)x)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 +-+ +-+ \|d x + c +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 +-+ +-------+ +--R ((a d - 2a b c)x - a c)\|b \|d x + c +--R / +--R 3 2 4 +-+ +--R (a b x + a x)\|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 |- a d + b c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R 2 2 2 +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 |a d - b c \|d x + c +--R ((2a b d - 8b c)x + (2a d - 8a b c)x) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R +-----------+ +--R 2 2 2 |- a d + b c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 2 +---+ \|d x + c +--R ((- 6a b d + 8b c)x + (- 6a d + 8a b c)x)\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 +-------+ +--R ((2a d - 4a b c)x - 2a c)\|d x + c +--R / +--R 3 2 4 +--R 2a b x + 2a x +--R , +--R +--R +-------+ +--R 2 2 2 +---+ \|d x + c +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 |a d - b c \|d x + c +--R ((a b d - 4b c)x + (a d - 4a b c)x) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 +-------+ +--R ((a d - 2a b c)x - a c)\|d x + c +--R / +--R 3 2 4 +--R a b x + a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 818 + +--S 819 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R |- a d + b c +-+ +--R (a d - 4b c) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (3a d - 4b c)\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 8b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-+ +-+ \|d x + c +--R (6a d - 8b c)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a \|b +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (3a d - 4b c)\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R (- 2a d + 8b c)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-+ +-+ \|d x + c +--R (6a d - 8b c)\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R +-+ |a d - b c \|d x + c +--R (2a d - 8b c)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a \|b +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1092 +t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (1) --------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1092 +r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-_ + 2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-+ +-+ \|b \|d x + c +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 +-----------+ \|d x + c +--R ((- a b d + 4b c)x + (- a d + 4a b c)x)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 +-----------+ +-+ +-------+ +--R (- 2a b x - a )\|- a d + b c \|c \|d x + c +--R / +--R 3 2 4 +-----------+ +-+ +--R (a b x + a x)\|- a d + b c \|c +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R ((a b d - 4b c)x + (a d - 4a b c)x) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 | b +-+ +--R ((3a b d - 4b c)x + (3a d - 4a b c)x) |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 2 +-+ +-------+ +--R (- 4a b x - 2a )\|c \|d x + c +--R / +--R 3 2 4 +-+ +--R (2a b x + 2a x)\|c +--R , +--R +--R 2 2 2 +--R ((a b d - 4b c)x + (a d - 4a b c)x) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 2 2 | b +-+ +--R ((- 6a b d + 8b c)x + (- 6a d + 8a b c)x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 +-+ +-------+ +--R (- 4a b x - 2a )\|c \|d x + c +--R / +--R 3 2 4 +-+ +--R (2a b x + 2a x)\|c +--R , +--R +--R +-----------+ +--R 2 2 2 +---+ | b +--R ((3a b d - 4b c)x + (3a d - 4a b c)x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +---+ +-------+ +--R 2 2 2 \|- c \|d x + c +--R ((- 2a b d + 8b c)x + (- 2a d + 8a b c)x)atan(----------------) +--R c +--R + +--R 2 +---+ +-------+ +--R (- 4a b x - 2a )\|- c \|d x + c +--R / +--R 3 2 4 +---+ +--R (2a b x + 2a x)\|- c +--R , +--R +--R +---+ +-------+ +--R 2 2 2 \|- c \|d x + c +--R ((- a b d + 4b c)x + (- a d + 4a b c)x)atan(----------------) +--R c +--R + +--R +---------+ +--R 2 2 2 +---+ | b +--R ((- 3a b d + 4b c)x + (- 3a d + 4a b c)x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 +---+ +-------+ +--R (- 2a b x - a )\|- c \|d x + c +--R / +--R 3 2 4 +---+ +--R (a b x + a x)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 825 + +--S 826 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-------+ +-+ +--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4b c)\|- a d + b c log(-------------------------------) +--R x +--R + +--R +-----------+ +--R +-----------+ | b +-+ +--R (3a d - 4b c)\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R +-+ +-+ \|b \|d x + c +--R (- 6a d + 8b c)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-----------+ \|d x + c +--R (2a d - 8b c)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-----------+ +-+ +--R 2a \|- a d + b c \|c +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R +-----------+ - 2c\|d x + c + (d x + 2c)\|c +--R (a d - 4b c)\|- a d + b c log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R +-+ +-+ \|b \|d x + c +--R (- 6a d + 8b c)\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R +-----------+ \|d x + c +--R (2a d - 8b c)\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R +-----------+ | b +-+ b\|d x + c +--R (- 6a d + 8b c)\|- a d + b c |--------- \|c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 3 +-----------+ +-+ +--R 2a \|- a d + b c \|c +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 829 + +)clear all + +--S 830 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 4 3 2 2 +-------+ +--R (b x + 2a b x + a x )\|d x + c +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1092 +r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ + (4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*_ + (b*c-a*d)^(3/2))-b*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*c*(b*c-a*d)*(a+b*x))-_ + sqrt(c+d*x)/(a*c*x*(a+b*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +--R +-----------+ \|d x + c +--R \|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 3 2 +-----------+ +-+ +-------+ +--R ((- a b d + 2a b c)x - a d + a b c)\|- a d + b c \|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-----------+ +-+ +--R ((a b c d - a b c )x + (a c d - a b c )x)\|- a d + b c \|c +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 3 2 2 2 2 2 | b +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x) |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|c +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 | b +-+ +--R ((10a b c d - 8b c )x + (10a b c d - 8a b c )x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 3 2 +-+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +-+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|c +--R , +--R +--R +-----------+ +--R 2 3 2 2 2 2 2 +---+ | b +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2a b d + 6a b c d - 8b c )x + (2a d + 6a b c d - 8a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- 2a b d + 4a b c)x - 2a d + 2a b c)\|- c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((2a b c d - 2a b c )x + (2a c d - 2a b c )x)\|- c +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R +---------+ +--R 2 3 2 2 2 2 2 +---+ | b +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 2 2 3 2 +---+ +-------+ +--R ((- a b d + 2a b c)x - a d + a b c)\|- c \|d x + c +--R / +--R 4 3 2 2 2 5 4 2 +---+ +--R ((a b c d - a b c )x + (a c d - a b c )x)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 832 + +--S 833 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 +-----------+ | b +-+ +--R (5a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2c\|d x + c + (d x + 2c)\|c +--R (a d + 3a b c d - 4b c )\|- a d + b c log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|b \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 3 2 +-----------+ +-+ +--R (2a c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-------+ +-+ +--R 2 2 2 2 +-----------+ 2c\|d x + c + (d x + 2c)\|c +--R (a d + 3a b c d - 4b c )\|- a d + b c log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|b \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-----------+ \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 2 2 +-----------+ | b +-+ +--R (10a b c d - 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 4 3 2 +-----------+ +-+ +--R (2a c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 836 + +)clear all + +--S 837 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1092 +r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ + (4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a^3*(b*c-a*d)^(5/2))-d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/_ + (a^2*c^2*(b*c-a*d)^2*sqrt(c+d*x))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*_ + (a+b*x)*sqrt(c+d*x))+(-1)/(a*c*x*(a+b*x)*sqrt(c+d*x)) +--R +--R +--R (2) +--R 3 2 4 3 2 2 2 2 3 3 +-+ +-+ +-------+ +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x)\|b \|c \|d x + c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|d x + c +--R \|- a d + b c \|d x + c atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 2a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 2 2 3 +--R (- 3a d + a b c d + a b c d - 2a b c )x - a c d + 2a b c d - a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((a b c d - 2a b c d + a b c )x + (a c d - 2a b c d + a b c )x) +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|c \|d x + c +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 | b +-+ +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x) |- --------- \|c +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +-+ +--R \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 | b +-+ +--R ((- 14a b c d + 8b c )x + (- 14a b c d + 8a b c )x) |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R +-------+ b\|d x + c +--R \|d x + c atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +-+ +--R \|c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R +-----------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | b +--R ((7a b c d - 4b c )x + (7a b c d - 4a b c )x)\|- c |- --------- +--R \| a d - b c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 4 3 2 +--R (6a b d - 4a b c d - 10a b c d + 8b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (6a d - 4a b c d - 10a b c d + 8a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 6a b d + 4a b c d - 4a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 6a d + 2a b c d + 2a b c d - 4a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 3 +--R - 2a b c +--R * +--R +---+ +--R \|- c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((2a b c d - 4a b c d + 2a b c )x + (2a c d - 4a b c d + 2a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 2 +--R (3a b d - 2a b c d - 5a b c d + 4b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 +--R (3a d - 2a b c d - 5a b c d + 4a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R +---------+ +--R 3 2 4 3 2 2 2 2 3 3 +---+ | b +--R ((- 7a b c d + 4b c )x + (- 7a b c d + 4a b c )x)\|- c |--------- +--R \|a d - b c +--R * +--R +-------+ +--R +-------+ b\|d x + c +--R \|d x + c atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 2a b c d)x +--R + +--R 4 3 3 2 2 2 2 3 3 4 2 3 2 +--R (- 3a d + a b c d + a b c d - 2a b c )x - a c d + 2a b c d +--R + +--R 2 2 3 +--R - a b c +--R * +--R +---+ +--R \|- c +--R / +--R 5 2 2 4 2 3 3 3 4 2 6 2 2 5 3 4 2 4 +--R ((a b c d - 2a b c d + a b c )x + (a c d - 2a b c d + a b c )x) +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 839 + +--S 840 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3a d - 2a b c d - 5a b c d + 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 3 3 +-----------+ | b +-+ +--R (7a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (- 2a d + 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(------------------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|b \|d x + c +--R (- 14a b c d + 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|d x + c +--R (- 6a d + 4a b c d + 10a b c d - 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +-----------+ +--R (3a d - 2a b c d - 5a b c d + 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 3 3 +-+ +-+ \|b \|d x + c +--R (- 14a b c d + 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 +-----------+ \|d x + c +--R (- 6a d + 4a b c d + 10a b c d - 8b c )\|- a d + b c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 2 2 3 3 +-----------+ | b +-+ +--R (- 14a b c d + 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 5 2 2 4 3 3 2 4 +-----------+ +-+ +--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 843 + +)clear all + +--S 844 of 1092 +t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1092 +r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ + (c+d*x)^(3/2))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+_ + (-1)/(a*c*x*(a+b*x)*(c+d*x)^(3/2))+(4*b*c+5*a*d)*atanh(sqrt(c+d*x)/_ + sqrt(c))/(a^3*c^(7/2))-b^(7/2)*(4*b*c-9*a*d)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*(b*c-a*d)^(7/2))-d*(2*b*c-a*d)*_ + (b^2*c^2-a*b*c*d+5*a^2*d^2)/(a^2*c^3*(b*c-a*d)^3*sqrt(c+d*x)) +--R +--R +--R (2) +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (- 27a b c d + 12b c d)x + (- 27a b c d - 15a b c d + 12b c )x +--R + +--R 2 3 4 4 5 +--R (- 27a b c d + 12a b c )x +--R * +--R +-+ +-------+ +--R +-+ +-+ +-------+ \|b \|d x + c +--R \|b \|c \|d x + c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 2 +--R (15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d - 12b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +--R +-----------+ +-------+ \|d x + c +--R \|- a d + b c \|d x + c atanh(----------) +--R +-+ +--R \|c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15a b d + 33a b c d - 9a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15a d + 13a b c d + 35a b c d - 15a b c d + 12a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 5 2 3 +--R (- 20a c d + 41a b c d - 9a b c d - 3a b c d + 6a b c )x - 3a c d +--R + +--R 4 3 2 3 2 4 2 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-----------+ +-+ +--R \|- a d + b c \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3a b c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-----------+ +-+ +-------+ +--R \|- a d + b c \|c \|d x + c +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +-----------+ +--R | b +-+ +-------+ +--R |- --------- \|c \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +--R \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +-------+ +-+ +--R +-------+ 2c\|d x + c + (d x + 2c)\|c +--R \|d x + c log(-----------------------------) +--R x +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (54a b c d - 24b c d)x + (54a b c d + 30a b c d - 24b c )x +--R + +--R 2 3 4 4 5 +--R (54a b c d - 24a b c )x +--R * +--R +---------+ +-------+ +--R | b +-+ +-------+ b\|d x + c +--R |--------- \|c \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +-+ +--R \|c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R , +--R +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +-----------+ +--R +---+ | b +-------+ +--R \|- c |- --------- \|d x + c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (30a b d - 66a b c d + 18a b c d + 42a b c d - 24b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 30a d - 36a b c d - 48a b c d + 60a b c d + 18a b c d +--R + +--R 5 5 +--R - 24b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (30a c d - 66a b c d + 18a b c d + 42a b c d - 24a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 30a b d + 66a b c d - 18a b c d + 12a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 30a d + 26a b c d + 70a b c d - 30a b c d + 24a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 40a c d + 82a b c d - 18a b c d - 6a b c d + 12a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 6a c d + 18a b c d - 18a b c d + 6a b c +--R * +--R +---+ +--R \|- c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (6a b c d - 18a b c d + 18a b c d - 6a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (6a c d - 12a b c d + 12a b c d - 6a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (6a c d - 18a b c d + 18a b c d - 6a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R , +--R +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 3 +--R (15a b d - 33a b c d + 9a b c d + 21a b c d - 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 15a d - 18a b c d - 24a b c d + 30a b c d + 9a b c d +--R + +--R 5 5 +--R - 12b c +--R * +--R 2 +--R x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (15a c d - 33a b c d + 9a b c d + 21a b c d - 12a b c )x +--R * +--R +---+ +-------+ +--R +-------+ \|- c \|d x + c +--R \|d x + c atan(----------------) +--R c +--R + +--R 4 3 2 5 4 3 2 3 3 2 4 4 5 5 2 +--R (27a b c d - 12b c d)x + (27a b c d + 15a b c d - 12b c )x +--R + +--R 2 3 4 4 5 +--R (27a b c d - 12a b c )x +--R * +--R +---------+ +-------+ +--R +---+ | b +-------+ b\|d x + c +--R \|- c |--------- \|d x + c atan(-----------------------) +--R \|a d - b c +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 3 +--R (- 15a b d + 33a b c d - 9a b c d + 6a b c d )x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 2 +--R (- 15a d + 13a b c d + 35a b c d - 15a b c d + 12a b c d)x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R (- 20a c d + 41a b c d - 9a b c d - 3a b c d + 6a b c )x +--R + +--R 5 2 3 4 3 2 3 2 4 2 3 5 +--R - 3a c d + 9a b c d - 9a b c d + 3a b c +--R * +--R +---+ +--R \|- c +--R / +--R 6 3 4 5 2 4 3 4 3 5 2 3 4 6 3 +--R (3a b c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 7 3 4 6 4 3 4 3 6 3 4 7 2 +--R (3a c d - 6a b c d + 6a b c d - 3a b c )x +--R + +--R 7 4 3 6 5 2 5 2 6 4 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 846 + +--S 847 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 3 4 4 +-----------+ | b +-+ +--R (9a b c d - 4b c )\|- a d + b c |- --------- \|c +--R \| a d - b c +--R * +--R +-----------+ +--R | b +-------+ +--R (2a d - 2b c) |- --------- \|d x + c + b d x - a d + 2b c +--R \| a d - b c +--R log(----------------------------------------------------------) +--R b x + a +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5a d - 11a b c d + 3a b c d + 7a b c d - 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|b \|d x + c +--R (18a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10a d + 22a b c d - 6a b c d - 14a b c d + 8b c )\|- a d + b c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (5a d - 11a b c d + 3a b c d + 7a b c d - 4b c )\|- a d + b c +--R * +--R +-------+ +-+ +--R 2c\|d x + c + (d x + 2c)\|c +--R log(-----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 3 3 4 4 +-+ +-+ \|b \|d x + c +--R (18a b c d - 8b c )\|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----------+ +--R (- 10a d + 22a b c d - 6a b c d - 14a b c d + 8b c )\|- a d + b c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +--R 3 3 4 4 +-----------+ | b +-+ +--R (18a b c d - 8b c )\|- a d + b c |--------- \|c +--R \|a d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(-----------------------) +--R +---------+ +--R | b +--R (a d - b c) |--------- +--R \|a d - b c +--R / +--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ +--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1092 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1092 +r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ + 495*a^2*b*c*d^2-693*a^3*d^3)*(c+d*x)^(5/2)/(b^4*d^3)-2/693*_ + (20*b^2*c^2+55*a*b*c*d-99*a^2*d^2)*x*(c+d*x)^(5/2)/(b^3*d^2)+_ + 2/99*(5*b*c-11*a*d)*x^2*(c+d*x)^(5/2)/(b^2*d)+2/11*x^3*(c+d*x)^(5/2)/b+_ + 2*a^3*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)-_ + 2*a^3*(b*c-a*d)^2*sqrt(c+d*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 +-----------+ +--R (6930a d - 13860a b c d + 6930a b c d )\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d + 220a b c d +--R + +--R 5 5 +--R 80b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 6 3 +-+ +--R 3465b d \|b +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 5 5 4 4 3 2 2 3 |- a d + b c +--R (3465a d - 6930a b c d + 3465a b c d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d +--R + +--R 4 4 5 5 +--R 220a b c d + 80b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 3 +--R 3465b d +--R , +--R +--R +---------+ +-------+ +--R 5 5 4 4 3 2 2 3 |a d - b c \|d x + c +--R (6930a d - 13860a b c d + 6930a b c d ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 5 5 5 4 5 5 4 4 +--R 630b d x + (- 770a b d + 1610b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (990a b d - 2090a b c d + 1130b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 1386a b d + 2970a b c d - 1650a b c d + 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (2310a b d - 5082a b c d + 2970a b c d - 110a b c d - 40b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 +--R - 6930a d + 16170a b c d - 10626a b c d + 990a b c d +--R + +--R 4 4 5 5 +--R 220a b c d + 80b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 3 +--R 3465b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 853 + +--S 854 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 5 2 4 3 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 5 2 4 3 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 5 2 4 3 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 5 2 4 3 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1092 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1092 +r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ + 2/63*(2*b*c+9*a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*x*(c+d*x)^(7/2)/(b*d)-_ + 2*a^2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/b^(11/2)+2*a^2*(b*c-a*d)^2*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 +-----------+ +--R (- 630a d + 1260a b c d - 630a b c d )\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 2 +-+ +--R 315b d \|b +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 4 4 3 3 2 2 2 2 |- a d + b c +--R (315a d - 630a b c d + 315a b c d ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 2 +--R 315b d +--R , +--R +--R +---------+ +-------+ +--R 4 4 3 3 2 2 2 2 |a d - b c \|d x + c +--R (- 630a d + 1260a b c d - 630a b c d ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 4 4 4 3 4 4 3 3 +--R 70b d x + (- 90a b d + 190b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (126a b d - 270a b c d + 150b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (- 210a b d + 462a b c d - 270a b c d + 10b c d)x + 630a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 1470a b c d + 966a b c d - 90a b c d - 20b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 2 +--R 315b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 860 + +--S 861 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 2 3 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 4 2 3 2 2 2 +-+ |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1092 +t0:=x*(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R b x + a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1092 +r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ + 2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (210a d - 420a b c d + 210a b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 4 +-+ +--R 105b d\|b +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 3 3 2 2 2 2 |- a d + b c +--R (105a d - 210a b c d + 105a b c d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 105b d +--R , +--R +--R +---------+ +-------+ +--R 3 3 2 2 2 2 |a d - b c \|d x + c +--R (210a d - 420a b c d + 210a b c d) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 3 3 2 3 3 2 2 +--R 30b d x + (- 42a b d + 90b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (70a b d - 154a b c d + 90b c d)x - 210a d + 490a b c d +--R + +--R 2 2 3 3 +--R - 322a b c d + 30b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 +--R 105b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 867 + +--S 868 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1092 +t0:=(c+d*x)^(5/2)/(a+b*x) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1092 +r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*_ + sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 30a d + 60a b c d - 30b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (15a d - 30a b c d + 15b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R , +--R +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 30a d + 60a b c d - 30b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (6b d x + (- 10a b d + 22b c d)x + 30a d - 70a b c d + 46b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 3 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 874 + +--S 875 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (2a d - 4a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 878 + +)clear all + +--S 879 of 1092 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 +--R b x + a x +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1092 +r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (6a d - 12a b c d + 6b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R - 6b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 +-+ +-------+ +--R (2a b d x - 6a d + 14a b c d)\|b \|d x + c +--R / +--R 2 +-+ +--R 3a b \|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (3a d - 6a b c d + 3b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R 3b c \|c log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R 3b c \|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (6a d - 12a b c d + 6b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (3a d - 6a b c d + 3b c ) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 +---+ \|d x + c 2 2 2 +-------+ +--R - 6b c \|- c atan(----------) + (2a b d x - 6a d + 14a b c d)\|d x + c +--R +---+ +--R \|- c +--R / +--R 2 +--R 3a b +--R , +--R +--R +-------+ +--R 2 2 +---+ \|d x + c +--R - 6b c \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (6a d - 12a b c d + 6b c ) |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a b d x - 6a d + 14a b c d)\|d x + c +--R / +--R 2 +--R 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 881 + +--S 882 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d - 2a b c d + b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d - 4a b c d + 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1092 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 3 2 +--R b x + a x +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1092 +r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ + atanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+_ + d*(b*c+2*a*d)*sqrt(c+d*x)/(a*b) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d + 4a b c d - 2b c )x\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (- 5a b c d + 2b c )x\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 +-+ +-------+ +--R (2a d x - a b c )\|b \|d x + c +--R / +--R 2 +-+ +--R a b x\|b +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (2a d - 4a b c d + 2b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )x\|c log(----------------------------) +--R x +--R + +--R 2 2 2 +-------+ +--R (4a d x - 2a b c )\|d x + c +--R / +--R 2 +--R 2a b x +--R , +--R +--R +-+ +-------+ +--R 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )x\|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 4a d + 8a b c d - 4b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (4a d x - 2a b c )\|d x + c +--R / +--R 2 +--R 2a b x +--R , +--R +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R (a d - 2a b c d + b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 +---+ \|d x + c 2 2 2 +-------+ +--R (- 5a b c d + 2b c )x\|- c atan(----------) + (2a d x - a b c )\|d x + c +--R +---+ +--R \|- c +--R / +--R 2 +--R a b x +--R , +--R +--R +-------+ +--R 2 2 +---+ \|d x + c +--R (- 5a b c d + 2b c )x\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 |a d - b c \|d x + c +--R (- 2a d + 4a b c d - 2b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 +-------+ +--R (2a d x - a b c )\|d x + c +--R / +--R 2 +--R a b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 888 + +--S 889 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (2a d - 4a b c d + 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (4a d - 8a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 4b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 2b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (4a d - 8a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 4b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 4a d + 8a b c d - 4b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1092 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 4 3 +--R b x + a x +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1092 +r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ + (a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*_ + atanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^3-1/4*d*(4*b*c-7*a*d)*_ + sqrt(c+d*x)/a^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 +-----------+ \|b \|d x + c +--R (8a d - 16a b c d + 8b c )x \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 2 +-+ +-+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 2 +-+ +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|b \|d x + c +--R / +--R 3 2 +-+ +--R 4a x \|b +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 2 |- a d + b c +--R (8a d - 16a b c d + 8b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )x \|c log(----------------------------) +--R x +--R + +--R 2 2 2 2 +-------+ +--R ((- 18a c d + 8a b c )x - 4a c )\|d x + c +--R / +--R 3 2 +--R 8a x +--R , +--R +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )x \|c log(----------------------------) +--R x +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 |a d - b c \|d x + c +--R (16a d - 32a b c d + 16b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 +-------+ +--R ((- 18a c d + 8a b c )x - 4a c )\|d x + c +--R / +--R 3 2 +--R 8a x +--R , +--R +--R +-----------+ +--R 2 2 2 2 2 |- a d + b c +--R (4a d - 8a b c d + 4b c )x |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-------+ +--R 2 2 2 2 2 +---+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 2 +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|d x + c +--R / +--R 3 2 +--R 4a x +--R , +--R +--R +-------+ +--R 2 2 2 2 2 +---+ \|d x + c +--R (- 15a d + 20a b c d - 8b c )x \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 |a d - b c \|d x + c +--R (8a d - 16a b c d + 8b c )x |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 +-------+ +--R ((- 9a c d + 4a b c )x - 2a c )\|d x + c +--R / +--R 3 2 +--R 4a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 895 + +--S 896 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (8a d - 16a b c d + 8b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 16a d + 32a b c d - 16b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 40a b c d + 16b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 20a b c d + 8b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 16a d + 32a b c d - 16b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 40a b c d + 16b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (16a d - 32a b c d + 16b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1092 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 5 4 +--R b x + a x +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1092 +r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ + 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ + sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*_ + atanh(sqrt(c+d*x)/sqrt(c))/(a^4*sqrt(c))-1/8*(4*b*c-5*a*d)*_ + (2*b*c-a*d)*sqrt(c+d*x)/(a^3*x) +--R +--R +--R (2) +--R 2 2 2 2 3 +-----------+ +-+ +-+ +--R (- 48a d + 96a b c d - 48b c )x \|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 3 \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x - 8a c ) +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 24a x \|c +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 2 3 3 3 +--R (15a d - 90a b c d + 120a b c d - 48b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 3 | 2 +-+ +--R (48a d - 96a b c d + 48b c )x \|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 66a d + 108a b c d - 48a b c )x + (- 52a c d + 24a b c )x +--R + +--R 3 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 48a x \|c +--R , +--R +--R 3 3 2 2 2 2 3 3 3 +--R (15a d - 90a b c d + 120a b c d - 48b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-----------+ +--R 2 2 2 2 3 +-+ | 2 +--R (- 96a d + 192a b c d - 96b c )x \|c \|a b d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 66a d + 108a b c d - 48a b c )x + (- 52a c d + 24a b c )x +--R + +--R 3 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 4 3 +-+ +--R 48a x \|c +--R , +--R +--R +-------------+ +--R 2 2 2 2 3 | 2 +---+ +--R (24a d - 48a b c d + 24b c )x \|- a b d + b c \|- c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R +---+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|- c \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atan(----------------) +--R c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x +--R + +--R 3 2 +--R - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 4 3 +---+ +--R 24a x \|- c +--R , +--R +--R +---+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|- c \|d x + c +--R (- 15a d + 90a b c d - 120a b c d + 48b c )x atan(----------------) +--R c +--R + +--R +-----------+ +--R 2 2 2 2 3 +---+ | 2 +--R (- 48a d + 96a b c d - 48b c )x \|- c \|a b d - b c +--R * +--R +-------+ +--R b\|d x + c +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 2 2 3 2 2 +--R (- 33a d + 54a b c d - 24a b c )x + (- 26a c d + 12a b c )x +--R + +--R 3 2 +--R - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 4 3 +---+ +--R 24a x \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 902 + +--S 903 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 30a b c d + 40a b c d - 16b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +-+ +--R (16a d - 32a b c d + 16b c )\|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ +-+ +-+ \|b \|d x + c +--R (32a d - 64a b c d + 32b c )\|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 60a b c d + 80a b c d - 32b c )atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 30a b c d + 40a b c d - 16b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ +-+ +-+ \|b \|d x + c +--R (32a d - 64a b c d + 32b c )\|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 60a b c d + 80a b c d - 32b c )atanh(----------) +--R +-+ +--R \|c +--R + +--R +-----------+ +-------+ +--R 2 2 2 2 +-+ | 2 b\|d x + c +--R (- 32a d + 64a b c d - 32b c )\|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R / +--R 4 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1092 +t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 5 4 2 3 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1092 +r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ + 180*a*b*c*d-693*a^2*d^2)*(c+d*x)^(5/2)/(b^4*d^2)+_ + 1/63*(10*b*c-99*a*d)*x*(c+d*x)^(5/2)/(b^3*d)+11/9*x^2*(c+d*x)^(5/2)/_ + b^2-x^3*(c+d*x)^(5/2)/(b*(a+b*x))-a^2*(6*b*c-11*a*d)*(b*c-a*d)^(3/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(13/2)+a^2*(6*b*c-11*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/b^6 +--R +--R +--R (2) +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (- 3465a b d + 5355a b c d - 1890a b c d )x - 3465a d +--R + +--R 4 3 3 2 2 2 +--R 5355a b c d - 1890a b c d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b d x + (- 110a b d + 190b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (198a b d - 350a b c d + 150b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 462a b d + 846a b c d - 390a b c d + 10b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (2310a b d - 4494a b c d + 2358a b c d - 170a b c d - 20b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6510a b c d + 3213a b c d - 180a b c d - 20a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 7 2 6 2 +-+ +--R (315b d x + 315a b d )\|b +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (3465a b d - 5355a b c d + 1890a b c d )x + 3465a d +--R + +--R 4 3 3 2 2 2 +--R - 5355a b c d + 1890a b c d +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 5 4 5 4 4 5 3 4 +--R 140b d x + (- 220a b d + 380b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (396a b d - 700a b c d + 300b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 924a b d + 1692a b c d - 780a b c d + 20b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (4620a b d - 8988a b c d + 4716a b c d - 340a b c d - 40b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 6930a d - 13020a b c d + 6426a b c d - 360a b c d - 40a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 7 2 6 2 +--R 630b d x + 630a b d +--R , +--R +--R 4 4 3 2 3 2 3 2 2 5 4 +--R (- 3465a b d + 5355a b c d - 1890a b c d )x - 3465a d +--R + +--R 4 3 3 2 2 2 +--R 5355a b c d - 1890a b c d +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 5 4 5 4 4 5 3 4 +--R 70b d x + (- 110a b d + 190b c d )x +--R + +--R 2 3 4 4 3 5 2 2 3 +--R (198a b d - 350a b c d + 150b c d )x +--R + +--R 3 2 4 2 3 3 4 2 2 5 3 2 +--R (- 462a b d + 846a b c d - 390a b c d + 10b c d)x +--R + +--R 4 4 3 2 3 2 3 2 2 4 3 5 4 +--R (2310a b d - 4494a b c d + 2358a b c d - 170a b c d - 20b c )x +--R + +--R 5 4 4 3 3 2 2 2 2 3 3 4 4 +--R 3465a d - 6510a b c d + 3213a b c d - 180a b c d - 20a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 7 2 6 2 +--R 315b d x + 315a b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 909 + +--S 910 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 4 2 3 2 2 2 |- a d + b c +-+ +--R (11a d - 17a b c d + 6a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (22a d - 34a b c d + 12a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 6 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 4 2 3 2 2 2 +-----------+ \|b \|d x + c +--R (11a d - 17a b c d + 6a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 4 2 3 2 2 2 +-+ |a d - b c \|d x + c +--R (- 11a d + 17a b c d - 6a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 6 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 913 + +)clear all + +--S 914 of 1092 +t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 4 3 2 2 +-------+ +--R (d x + 2c d x + c x )\|d x + c +--R (1) --------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1092 +r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ + (c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-_ + a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*_ + (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(11/2)-_ + a*(4*b*c-9*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^5 +--R +--R +--R (2) +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 4 3 4 3 3 4 2 3 +--R 30b d x + (- 54a b d + 90b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (126a b d - 218a b c d + 90b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 630a b d + 1162a b c d - 554a b c d + 30b c )x - 945a d +--R + +--R 3 2 2 2 2 3 3 +--R 1680a b c d - 749a b c d + 30a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 6 5 +-+ +--R (105b d x + 105a b d)\|b +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 4 3 4 3 3 4 2 3 +--R 60b d x + (- 108a b d + 180b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (252a b d - 436a b c d + 180b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 1260a b d + 2324a b c d - 1108a b c d + 60b c )x - 1890a d +--R + +--R 3 2 2 2 2 3 3 +--R 3360a b c d - 1498a b c d + 60a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 5 +--R 210b d x + 210a b d +--R , +--R +--R 3 3 2 2 2 3 2 4 3 3 2 +--R (945a b d - 1365a b c d + 420a b c d)x + 945a d - 1365a b c d +--R + +--R 2 2 2 +--R 420a b c d +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 4 3 4 3 3 4 2 3 +--R 30b d x + (- 54a b d + 90b c d )x +--R + +--R 2 2 3 3 2 4 2 2 +--R (126a b d - 218a b c d + 90b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 3 +--R (- 630a b d + 1162a b c d - 554a b c d + 30b c )x - 945a d +--R + +--R 3 2 2 2 2 3 3 +--R 1680a b c d - 749a b c d + 30a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 6 5 +--R 105b d x + 105a b d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 916 + +--S 917 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 3 2 2 2 2 |- a d + b c +-+ +--R (9a d - 13a b c d + 4a b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 18a d + 26a b c d - 8a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 3 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 9a d + 13a b c d - 4a b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 3 2 2 2 2 +-+ |a d - b c \|d x + c +--R (9a d - 13a b c d + 4a b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 1092 +t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 3 2 2 +-------+ +--R (d x + 2c d x + c x)\|d x + c +--R (1) -------------------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1092 +r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ + (b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*_ + (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+_ + (2*b*c-7*a*d)*(b*c-a*d)*sqrt(c+d*x)/b^4 +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 +--R (- 105a b d + 135a b c d - 30b c )x - 105a d + 135a b c d +--R + +--R 2 2 +--R - 30a b c +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 14a b d + 22b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (70a b d - 118a b c d + 46b c )x + 105a d - 170a b c d + 61a b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R / +--R 5 4 +-+ +--R (15b x + 15a b )\|b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 2 +--R (105a b d - 135a b c d + 30b c )x + 105a d - 135a b c d +--R + +--R 2 2 +--R 30a b c +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R 3 2 3 2 2 3 2 +--R 12b d x + (- 28a b d + 44b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (140a b d - 236a b c d + 92b c )x + 210a d - 340a b c d + 122a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 4 +--R 30b x + 30a b +--R , +--R +--R 2 2 2 3 2 3 2 2 +--R (- 105a b d + 135a b c d - 30b c )x - 105a d + 135a b c d +--R + +--R 2 2 +--R - 30a b c +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 3 2 2 3 2 +--R 6b d x + (- 14a b d + 22b c d)x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R (70a b d - 118a b c d + 46b c )x + 105a d - 170a b c d + 61a b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 5 4 +--R 15b x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 923 + +--S 924 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (7a d - 9a b c d + 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (14a d - 18a b c d + 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (7a d - 9a b c d + 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 7a d + 9a b c d - 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1092 +t0:=(c+d*x)^(5/2)/(a+b*x)^2 +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1092 +r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*_ + sqrt(c+d*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 +-----------+ +--R ((15a b d - 15b c d)x + 15a d - 15a b c d)\|- a d + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (2b d x + (- 10a b d + 14b c d)x - 15a d + 20a b c d - 3b c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +-+ +--R (3b x + 3a b )\|b +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-----------+ +--R 2 2 2 2 |- a d + b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |----------- +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4b d x + (- 20a b d + 28b c d)x - 30a d + 40a b c d - 6b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 6b x + 6a b +--R , +--R +--R +---------+ +--R 2 2 2 2 |a d - b c +--R ((15a b d - 15b c d)x + 15a d - 15a b c d) |--------- +--R \| b +--R * +--R +-------+ +--R \|d x + c +--R atan(------------) +--R +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2b d x + (- 10a b d + 14b c d)x - 15a d + 20a b c d - 3b c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 +--R 3b x + 3a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 930 + +--S 931 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 |- a d + b c +-+ +--R (5a d - 5b c d) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 10a d + 10b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 +-----------+ \|b \|d x + c +--R (- 5a d + 5b c d)\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +---------+ +-------+ +--R 2 +-+ |a d - b c \|d x + c +--R (5a d - 5b c d)\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1092 +t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1092 +r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ + atanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_ + atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_ + d*(b*c-3*a*d)*sqrt(c+d*x)/(a*b^2) +--R +--R +--R (2) +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 2 2 2 +-+ +-+ \|d x + c +--R (- 2b c x - 2a b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 3 2 2 2 2 +-+ +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|b \|d x + c +--R / +--R 2 3 3 2 +-+ +--R (a b x + a b )\|b +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3a b d - a b c d - 2b c )x + 3a d - a b c d - 2a b c ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-+ +-------+ +--R 3 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (2b c x + 2a b c )\|c log(----------------------------) +--R x +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (4a b d x + 6a d - 4a b c d + 2a b c )\|d x + c +--R / +--R 2 3 3 2 +--R 2a b x + 2a b +--R , +--R +--R +-+ +-------+ +--R 3 2 2 2 +-+ - 2\|c \|d x + c + d x + 2c +--R (b c x + a b c )\|c log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|d x + c +--R / +--R 2 3 3 2 +--R a b x + a b +--R , +--R +--R 2 2 2 3 2 3 2 2 2 2 +--R ((3a b d - a b c d - 2b c )x + 3a d - a b c d - 2a b c ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ - 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-------------------------------------------------) +--R \| b b x + a +--R + +--R +-------+ +--R 3 2 2 2 +---+ \|d x + c +--R (- 4b c x - 4a b c )\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (4a b d x + 6a d - 4a b c d + 2a b c )\|d x + c +--R / +--R 2 3 3 2 +--R 2a b x + 2a b +--R , +--R +--R +-------+ +--R 3 2 2 2 +---+ \|d x + c +--R (- 2b c x - 2a b c )\|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 3 2 2 2 2 +--R ((- 3a b d + a b c d + 2b c )x - 3a d + a b c d + 2a b c ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 2 2 3 2 2 2 2 +-------+ +--R (2a b d x + 3a d - 2a b c d + a b c )\|d x + c +--R / +--R 2 3 3 2 +--R a b x + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 937 + +--S 938 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (3a d - a b c d - 2b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R - 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-------------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R 2b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (6a d - 2a b c d - 4b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 4b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 2 2 +-+ +--R 2a b \|b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R b c \|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (3a d - a b c d - 2b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R 2b c \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (- 3a d + a b c d + 2b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 2 2 +-+ +--R a b \|b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 941 + +)clear all + +--S 942 of 1092 +t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 4 3 2 2 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1092 +r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ + (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-_ + c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 2 +-+ +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c +--R / +--R 3 2 2 4 +-+ +--R (a b x + a b x)\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1092 +r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ + c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ + (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))+_ + d*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*b) +--R +--R +--R (3) +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 3 2 2 2 2 2 +-+ +-+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|b \|c +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 2 +-+ +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|b \|d x + c +--R / +--R 3 2 2 4 +-+ +--R (a b x + a b x)\|b +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R [ +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 2 +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 3 2 2 2 2 2 +-+ +--R ((5a b c d - 4b c )x + (5a b c d - 4a b c )x)\|c +--R * +--R +-+ +-------+ +--R - 2\|c \|d x + c + d x + 2c +--R log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((2a b d + 6a b c d - 8b c )x + (2a d + 6a b c d - 8a b c )x) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 3 2 2 2 2 2 +---+ +--R ((- 10a b c d + 8b c )x + (- 10a b c d + 8a b c )x)\|- c +--R * +--R +-------+ +--R \|d x + c +--R atan(----------) +--R +---+ +--R \|- c +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- 2a d + 4a b c d - 4a b c )x - 2a b c )\|d x + c +--R / +--R 3 2 2 4 +--R 2a b x + 2a b x +--R , +--R +--R 2 3 2 2 2 2 2 +---+ +--R ((- 5a b c d + 4b c )x + (- 5a b c d + 4a b c )x)\|- c +--R * +--R +-------+ +--R \|d x + c +--R atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 2 3 2 2 2 2 +--R ((a b d + 3a b c d - 4b c )x + (a d + 3a b c d - 4a b c )x) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 2 +-------+ +--R ((- a d + 2a b c d - 2a b c )x - a b c )\|d x + c +--R / +--R 3 2 2 4 +--R a b x + a b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 945 + +--S 946 of 1092 +m0a:=a0.1-r0a +--R +--R +--R (5) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d + 3a b c d - 4b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1092 +m0b:=a0.1-r0b +--R +--R +--R (7) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (a d + 3a b c d - 4b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1092 +m0c:=a0.2-r0a +--R +--R +--R (9) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d + 6a b c d - 8b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1092 +d0c:=D(m0c,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1092 +m0d:=a0.2-r0b +--R +--R +--R (11) +--R +-+ +-------+ +--R 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (5a b c d - 4b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 2a d - 6a b c d + 8b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 +-+ +-+ \|d x + c +--R (10a b c d - 8b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (2a d + 6a b c d - 8b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 3 +-+ +--R 2a b\|b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1092 +d0d:=D(m0d,x) +--R +--R +--R (12) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1092 +t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 5 4 2 3 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1092 +r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ + (a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/_ + sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*_ + atanh(sqrt(c+d*x)/sqrt(c))*sqrt(c)/a^4+1/4*(12*b*c-11*a*d)*_ + (b*c-a*d)*sqrt(c+d*x)/(a^3*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +-+ +-------+ +--R +-----------+ \|b \|d x + c +--R \|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +-+ +-+ \|d x + c +--R \|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +-+ +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c )\|b +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +-+ +--R (4a b x + 4a x )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 3 2 3 +--R (15a b d - 40a b c d + 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (15a d - 40a b c d + 24a b c )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|c \|d x + c + d x + 2c +--R \|c log(----------------------------) +--R x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((8a d - 34a b c d + 24a b c )x + (- 18a c d + 12a b c )x - 4a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 8a b x + 8a x +--R , +--R +--R 2 2 2 3 2 3 +--R (15a b d - 40a b c d + 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (15a d - 40a b c d + 24a b c )x +--R * +--R +-+ +-------+ +--R +-+ - 2\|c \|d x + c + d x + 2c +--R \|c log(----------------------------) +--R x +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((8a b d - 56a b c d + 48b c )x + (8a d - 56a b c d + 48a b c )x ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((8a d - 34a b c d + 24a b c )x + (- 18a c d + 12a b c )x - 4a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 8a b x + 8a x +--R , +--R +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((2a b d - 14a b c d + 12b c )x + (2a d - 14a b c d + 12a b c )x ) +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R +-----------+ 2b |----------- \|d x + c + b d x - a d + 2b c +--R |- a d + b c \| b +--R |----------- log(-----------------------------------------------) +--R \| b b x + a +--R + +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +---+ \|d x + c +--R \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 4a b x + 4a x +--R , +--R +--R 2 2 2 3 2 3 +--R (- 15a b d + 40a b c d - 24b c )x +--R + +--R 3 2 2 2 2 2 +--R (- 15a d + 40a b c d - 24a b c )x +--R * +--R +-------+ +--R +---+ \|d x + c +--R \|- c atan(----------) +--R +---+ +--R \|- c +--R + +--R 2 2 2 3 2 3 3 2 2 2 2 2 +--R ((4a b d - 28a b c d + 24b c )x + (4a d - 28a b c d + 24a b c )x ) +--R * +--R +---------+ +-------+ +--R |a d - b c \|d x + c +--R |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R ((4a d - 17a b c d + 12a b c )x + (- 9a c d + 6a b c )x - 2a c ) +--R * +--R +-------+ +--R \|d x + c +--R / +--R 4 3 5 2 +--R 4a b x + 4a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 2 2 |- a d + b c +-+ +--R (4a d - 28a b c d + 24b c ) |----------- \|b +--R \| b +--R * +--R +-----------+ +--R |- a d + b c +-------+ +--R 2b |----------- \|d x + c + b d x - a d + 2b c +--R \| b +--R log(-----------------------------------------------) +--R b x + a +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 40a b c d + 24b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 8a d + 56a b c d - 48b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 80a b c d + 48b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R / +--R 4 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ - 2\|c \|d x + c + d x + 2c +--R (15a d - 40a b c d + 24b c )\|b \|c log(----------------------------) +--R x +--R + +--R +-+ +-------+ +--R 2 2 2 2 +-----------+ \|b \|d x + c +--R (- 8a d + 56a b c d - 48b c )\|- a d + b c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 2 2 2 2 +-+ +-+ \|d x + c +--R (30a d - 80a b c d + 48b c )\|b \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R +---------+ +-------+ +--R 2 2 2 2 +-+ |a d - b c \|d x + c +--R (8a d - 56a b c d + 48b c )\|b |--------- atan(------------) +--R \| b +---------+ +--R |a d - b c +--R |--------- +--R \| b +--R / +--R 4 +-+ +--R 8a \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1092 +t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) +--R +--R +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|d x + c +--R (1) ------------------------------ +--R 2 6 5 2 4 +--R b x + 2a b x + a x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1092 +r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ + (a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_ + sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-_ + 120*a*b^2*c^2*d+60*a^2*b*c*d^2-5*a^3*d^3)*atanh(sqrt(c+d*x)/_ + sqrt(c))/(a^5*sqrt(c))-1/8*b*(32*b^2*c^2-52*a*b*c*d+19*a^2*d^2)*_ + sqrt(c+d*x)/(a^4*(a+b*x))-1/8*(16*b^2*c^2-22*a*b*c*d+5*a^2*d^2)*_ + sqrt(c+d*x)/(a^3*x*(a+b*x)) +--R +--R +--R (2) +--R 2 2 2 3 2 4 +--R (- 72a b d + 264a b c d - 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 72a d + 264a b c d - 192a b c )x +--R * +--R +-+ +-------+ +--R +-----------+ +-+ +-+ \|b \|d x + c +--R \|- a d + b c \|b \|c atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +-------+ +--R \|d x + c +--R atanh(----------) +--R +-+ +--R \|c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (24a b x + 24a x )\|c +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1092 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 3 2 2 2 3 2 4 3 4 +--R (15a b d - 180a b c d + 360a b c d - 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (15a d - 180a b c d + 360a b c d - 192a b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 2 4 +--R (72a b d - 264a b c d + 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (72a d - 264a b c d + 192a b c )x +--R * +--R +-------------+ +--R | 2 +-+ +--R \|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 2 2 2 3 2 3 +--R (- 114a b d + 312a b c d - 192a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 +--R (- 66a d + 164a b c d - 96a b c )x + (- 52a c d + 32a b c )x +--R + +--R 4 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (48a b x + 48a x )\|c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 4 +--R (15a b d - 180a b c d + 360a b c d - 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (15a d - 180a b c d + 360a b c d - 192a b c )x +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 3 2 4 +--R (- 144a b d + 528a b c d - 384b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 144a d + 528a b c d - 384a b c )x +--R * +--R +-----------+ +-------+ +--R +-+ | 2 b\|d x + c +--R \|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 3 2 3 +--R (- 114a b d + 312a b c d - 192a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 +--R (- 66a d + 164a b c d - 96a b c )x + (- 52a c d + 32a b c )x +--R + +--R 4 2 +--R - 16a c +--R * +--R +-+ +-------+ +--R \|c \|d x + c +--R / +--R 5 4 6 3 +-+ +--R (48a b x + 48a x )\|c +--R , +--R +--R 2 2 2 3 2 4 +--R (36a b d - 132a b c d + 96b c )x +--R + +--R 3 2 2 2 2 3 +--R (36a d - 132a b c d + 96a b c )x +--R * +--R +-------------+ +--R | 2 +---+ +--R \|- a b d + b c \|- c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 5 4 6 3 +---+ +--R (24a b x + 24a x )\|- c +--R , +--R +--R 3 3 2 2 2 3 2 4 3 4 +--R (- 15a b d + 180a b c d - 360a b c d + 192b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 180a b c d - 360a b c d + 192a b c )x +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R atan(----------------) +--R c +--R + +--R 2 2 2 3 2 4 +--R (- 72a b d + 264a b c d - 192b c )x +--R + +--R 3 2 2 2 2 3 +--R (- 72a d + 264a b c d - 192a b c )x +--R * +--R +-----------+ +-------+ +--R +---+ | 2 b\|d x + c +--R \|- c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R + +--R 3 2 2 2 3 2 3 +--R (- 57a b d + 156a b c d - 96a b c )x +--R + +--R 4 2 3 2 2 2 2 4 3 2 4 2 +--R (- 33a d + 82a b c d - 48a b c )x + (- 26a c d + 16a b c )x - 8a c +--R * +--R +---+ +-------+ +--R \|- c \|d x + c +--R / +--R 5 4 6 3 +---+ +--R (24a b x + 24a x )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1092 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 60a b c d + 120a b c d - 64b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R +-------------+ +--R 2 2 2 2 | 2 +-+ +--R (24a d - 88a b c d + 64b c )\|- a b d + b c \|c +--R * +--R +-------------+ +--R | 2 +-------+ +--R - 2\|- a b d + b c \|d x + c + b d x - a d + 2b c +--R log(--------------------------------------------------) +--R b x + a +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (48a d - 176a b c d + 128b c )\|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 120a b c d + 240a b c d - 128b c )atanh(----------) +--R +-+ +--R \|c +--R / +--R 5 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1092 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1092 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 3 3 2 2 2 2 3 3 +--R (5a d - 60a b c d + 120a b c d - 64b c ) +--R * +--R +-------+ +-+ +--R - 2c\|d x + c + (d x + 2c)\|c +--R log(-------------------------------) +--R x +--R + +--R 2 2 2 2 +-----------+ +-+ +-+ +--R (48a d - 176a b c d + 128b c )\|- a d + b c \|b \|c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------) +--R +-----------+ +--R \|- a d + b c +--R + +--R +-------+ +--R 3 3 2 2 2 2 3 3 \|d x + c +--R (10a d - 120a b c d + 240a b c d - 128b c )atanh(----------) +--R +-+ +--R \|c +--R + +--R +-----------+ +-------+ +--R 2 2 2 2 +-+ | 2 b\|d x + c +--R (- 48a d + 176a b c d - 128b c )\|c \|a b d - b c atan(--------------) +--R +-----------+ +--R | 2 +--R \|a b d - b c +--R / +--R 5 +-+ +--R 16a \|c +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1092 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1092 +t0:=x^3*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R 3 +-------+ +-------+ +--R (1) x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1092 +r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-_ + 1/960*(105*b^3*c^3-5*a*b^2*c^2*d-17*a^2*b*c*d^2-35*a^3*d^3)*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b^3*d^4)-1/240*(4*a*c-35*b*c^2/d+_ + 7*a^2*d/b)*x*(c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)-1/40*(7*b*c-a*d)*x^2*_ + (c+d*x)^(3/2)*sqrt(a+b*x)/(b*d^2)+1/5*x^3*(c+d*x)^(3/2)*_ + sqrt(a+b*x)/d+1/128*(7*b^4*c^4+2*a*b^3*c^3*d-2*a^3*b*c*d^3-_ + 7*a^4*d^4)*sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^4) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (105a d - 75a b c d - 30a b c d - 30a b c d - 75a b c d + 105b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 48b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 16a b c d - 56b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 22a b c d - 22a b c d + 70b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 40a b c d + 34a b c d + 40a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 4 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1092 +--a0:=integrate(t0,x) +--E 970 + +--S 971 of 1092 +--m0:=a0-r0 +--E 971 + +--S 972 of 1092 +--d0:=D(m0,x) +--E 972 + +)clear all + +--S 973 of 1092 +t0:=x^2*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1092 +r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ + (a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*_ + (4*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ + sqrt(c+d*x)))/(b^(7/2)*d^(7/2))-1/32*(4*a*b*c*d-5*(b*c+a*d)^2)*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d^2)-1/64*(b*c-a*d)*_ + (4*a*b*c*d-5*(b*c+a*d)^2)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^3) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 8b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b d + 4a b c d - 10b c d)x + 15a d - 7a b c d - 7a b c d +--R + +--R 3 3 +--R 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1092 +--a0:=integrate(t0,x) +--E 975 + +--S 976 of 1092 +--m0:=a0-r0 +--E 976 + +--S 977 of 1092 +--d0:=D(m0,x) +--E 977 + +)clear all + +--S 978 of 1092 +t0:=x*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R +-------+ +-------+ +--R (1) x\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1092 +r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ + 1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*_ + (a^2/b^2-c^2/d^2)*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 3a b c d - 3a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 2b c d)x - 3a d + 2a b c d - 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1092 +--a0:=integrate(t0,x) +--E 980 + +--S 981 of 1092 +--m0:=a0-r0 +--E 981 + +--S 982 of 1092 +--d0:=D(m0,x) +--E 982 + +)clear all + +--S 983 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R +-------+ +-------+ +--R (1) \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1092 +r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d + 2a b c d - b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d + b c)\|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b d\|b \|d +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1092 +--a0:=integrate(t0,x) +--E 985 + +--S 986 of 1092 +--m0:=a0-r0 +--E 986 + +--S 987 of 1092 +--d0:=D(m0,x) +--E 987 + +)clear all + +--S 988 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R x +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1092 +r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ + (b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-+ +-+ \|c \|b x + a +--R (a d + b c)atanh(--------------) - 2\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +-+ +-------+ +--R \|b \|d x + c \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 990 + +--S 991 of 1092 +--m0:=a0-r0 +--E 991 + +--S 992 of 1092 +--d0:=D(m0,x) +--E 992 + +)clear all + +--S 993 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1092 +r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (sqrt(a)*sqrt(c))+2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ + sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ +-+ +-+ \|d \|b x + a +--R 2x\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R / +--R +-+ +-+ +--R x\|a \|c +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1092 +--a0:=integrate(t0,x) +--E 995 + +--S 996 of 1092 +--m0:=a0-r0 +--E 996 + +--S 997 of 1092 +--d0:=D(m0,x) +--E 997 + +)clear all + +--S 998 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1092 +r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-_ + 1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (a d - 2a b c d + b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((- a d - b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a c x \|a \|c +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1092 +--a0:=integrate(t0,x) +--E 1000 + +--S 1001 of 1092 +--m0:=a0-r0 +--E 1001 + +--S 1002 of 1092 +--d0:=D(m0,x) +--E 1002 + +)clear all + +--S 1003 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1092 +r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ + sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/x^3-_ + 1/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+_ + 1/24*(3*b^2*c^2-2*a*b*c*d+3*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (- 3a d + 3a b c d + 3a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R ((3a d - 2a b c d + 3b c )x + (- 2a c d - 2a b c )x - 8a c )\|a \|c +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 2 3 +-+ +-+ +--R 24a c x \|a \|c +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1092 +--a0:=integrate(t0,x) +--E 1005 + +--S 1006 of 1092 +--m0:=a0-r0 +--E 1006 + +--S 1007 of 1092 +--d0:=D(m0,x) +--E 1007 + +)clear all + +--S 1008 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1092 +r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ + 1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a*c*x^3)+1/96*(5*b^2*c^2-2*a*b*c*d+5*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^2)-1/192*(b*c+a*d)*_ + (15*b^2*c^2-22*a*b*c*d+15*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^3*x) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (15a d - 12a b c d - 6a b c d - 12a b c d + 15b c )x +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 15a d + 7a b c d + 7a b c d - 15b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (10a c d - 4a b c d + 10a b c )x + (- 8a c d - 8a b c )x - 48a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 3 4 +-+ +-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1092 +--a0:=integrate(t0,x) +--E 1010 + +--S 1011 of 1092 +--m0:=a0-r0 +--E 1011 + +--S 1012 of 1092 +--d0:=D(m0,x) +--E 1012 + +)clear all + +--S 1013 of 1092 +t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 +--R +--R +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R (1) -------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1092 +r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ + atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-_ + 1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a*c*x^4)+1/240*(7*b^2*c^2-2*a*b*c*d+7*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c^2*x^3)-1/960*(b*c+a*d)*_ + (35*b^2*c^2-46*a*b*c*d+35*a^2*d^2)*sqrt(a+b*x)*sqrt(c+d*x)/_ + (a^3*c^3*x^2)+1/1920*(105*b^4*c^4-40*a*b^3*c^3*d-_ + 34*a^2*b^2*c^2*d^2-40*a^3*b*c*d^3+105*a^4*d^4)*sqrt(a+b*x)*_ + sqrt(c+d*x)/(a^4*c^4*x) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R - 105a d + 75a b c d + 30a b c d + 30a b c d + 75a b c d +--R + +--R 5 5 +--R - 105b c +--R * +--R +-+ +-------+ +--R 5 \|c \|b x + a +--R x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (105a d - 40a b c d - 34a b c d - 40a b c d + 105b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (- 70a c d + 22a b c d + 22a b c d - 70a b c )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 4 4 +--R (56a c d - 16a b c d + 56a b c )x + (- 48a c d - 48a b c )x - 384a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 4 4 5 +-+ +-+ +--R 1920a c x \|a \|c +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1092 +--a0:=integrate(t0,x) +--E 1015 + +--S 1016 of 1092 +--m0:=a0-r0 +--E 1016 + +--S 1017 of 1092 +--d0:=D(m0,x) +--E 1017 + +)clear all + +--S 1018 of 1092 +t0:=x^2*(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 3 2 +-------+ +-------+ +--R (1) (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1092 +r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ + (b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+_ + 1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*_ + (3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(7/2))+1/64*(b*c-a*d)*_ + (3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/_ + (b^4*d^2)+1/128*(b*c-a*d)^2*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^3) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (105a d - 225a b c d + 90a b c d + 30a b c d + 45a b c d - 45b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 528b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 96a b c d + 24b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 122a b c d + 18a b c d - 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 190a b c d - 36a b c d - 30a b c d + 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 3 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1092 +--a0:=integrate(t0,x) +--E 1020 + +--S 1021 of 1092 +--m0:=a0-r0 +--E 1021 + +--S 1022 of 1092 +--d0:=D(m0,x) +--E 1022 + +)clear all + +--S 1023 of 1092 +t0:=x*(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R 2 +-------+ +-------+ +--R (1) (d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1092 +r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ + (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-_ + 1/32*(b*c-a*d)*(3*b*c+5*a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^3*d)-_ + 1/64*(b*c-a*d)^2*(3*b*c+5*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(b^3*d^2) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 36a b c d - 18a b c d - 12a b c d + 9b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 72b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 2 2 +--R (- 10a b d + 20a b c d + 6b c d)x + 15a d - 31a b c d + 9a b c d +--R + +--R 3 3 +--R - 9b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 2 +-+ +-+ +--R 192b d \|b \|d +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1092 +--a0:=integrate(t0,x) +--E 1025 + +--S 1026 of 1092 +--m0:=a0-r0 +--E 1026 + +--S 1027 of 1092 +--d0:=D(m0,x) +--E 1027 + +)clear all + +--S 1028 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x) +--R +--R +--R +-------+ +-------+ +--R (1) (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1092 +r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*_ + sqrt(c+d*x)/(b^2*d) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 9a b c d + 9a b c d - 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 14b c d)x - 3a d + 8a b c d + 3b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b d\|b \|d +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1092 +--a0:=integrate(t0,x) +--E 1030 + +--S 1031 of 1092 +--m0:=a0-r0 +--E 1031 + +--S 1032 of 1092 +--d0:=D(m0,x) +--E 1032 + +)clear all + +--S 1033 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R x +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1092 +r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ + sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+_ + 1/2*(c+d*x)^(3/2)*sqrt(a+b*x)+1/4*(3*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d + 6a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 8b c\|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d + 5b c)\|b \|d \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b\|b \|d +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1035 + +--S 1036 of 1092 +--m0:=a0-r0 +--E 1036 + +--S 1037 of 1092 +--d0:=D(m0,x) +--E 1037 + +)clear all + +--S 1038 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1092 +r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ + sqrt(c)/sqrt(a)+(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*_ + sqrt(a+b*x)/x+2*d*sqrt(a+b*x)*sqrt(c+d*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ \|d \|b x + a +--R (a d + 3b c)x\|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R +-+ +-+ \|c \|b x + a +--R (- 3a d - b c)x\|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (d x - c)\|a \|b \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R x\|a \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1040 + +--S 1041 of 1092 +--m0:=a0-r0 +--E 1041 + +--S 1042 of 1092 +--d0:=D(m0,x) +--E 1042 + +)clear all + +--S 1043 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1092 +r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ + 1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_ + 1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/x^2-1/4*(b*c+3*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ +-+ +-+ +-+ \|d \|b x + a +--R 8a d x \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 3a d - 6a b c d + b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((- 5a d - b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a x \|a \|c +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1045 + +--S 1046 of 1092 +--m0:=a0-r0 +--E 1046 + +--S 1047 of 1092 +--d0:=D(m0,x) +--E 1047 + +)clear all + +--S 1048 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1092 +r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + (a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-_ + 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^2*c*x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 3 \|c \|b x + a +--R (3a d - 9a b c d + 9a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R ((- 3a d - 8a b c d + 3b c )x + (- 14a c d - 2a b c )x - 8a c )\|a +--R * +--R +-+ +-------+ +-------+ +--R \|c \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 24a c x \|a \|c +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1092 +--a0:=integrate(t0,x) +--E 1050 + +--S 1051 of 1092 +--m0:=a0-r0 +--E 1051 + +--S 1052 of 1092 +--d0:=D(m0,x) +--E 1052 + +)clear all + +--S 1053 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1092 +r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ + sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/4*(c+d*x)^(3/2)*_ + sqrt(a+b*x)/x^4-1/24*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+_ + 1/96*(5*b^2*c/a-10*b*d-3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^2)-_ + 1/192*(15*b^3*c^3-31*a*b^2*c^2*d+9*a^2*b*c*d^2-9*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c )x +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (9a d - 9a b c d + 31a b c d - 15b c )x +--R + +--R 3 2 2 2 2 3 2 3 2 2 3 3 3 +--R (- 6a c d - 20a b c d + 10a b c )x + (- 72a c d - 8a b c )x - 48a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 3 2 4 +-+ +-+ +--R 192a c x \|a \|c +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1092 +--a0:=integrate(t0,x) +--E 1055 + +--S 1056 of 1092 +--m0:=a0-r0 +--E 1056 + +--S 1057 of 1092 +--d0:=D(m0,x) +--E 1057 + +)clear all + +--S 1058 of 1092 +t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 +--R +--R +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1092 +r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_ + 1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a*x^4)+1/240*(7*b^2*c/a-_ + 12*b*d-3*a*d^2/c)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)-_ + 1/960*(35*b^3*c^3-61*a*b^2*c^2*d+9*a^2*b*c*d^2-15*a^3*d^3)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^3*c^2*x^2)+1/1920*(105*b^4*c^4-_ + 190*a*b^3*c^3*d+36*a^2*b^2*c^2*d^2+30*a^3*b*c*d^3-45*a^4*d^4)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(a^4*c^3*x) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c ) +--R * +--R +-+ +-------+ +--R 5 \|c \|b x + a +--R x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 4 +--R (- 45a d + 30a b c d + 36a b c d - 190a b c d + 105b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 3 +--R (30a c d - 18a b c d + 122a b c d - 70a b c )x +--R + +--R 4 2 2 3 3 2 2 4 2 4 3 3 4 +--R (- 24a c d - 96a b c d + 56a b c )x + (- 528a c d - 48a b c )x +--R + +--R 4 4 +--R - 384a c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R / +--R 4 3 5 +-+ +-+ +--R 1920a c x \|a \|c +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1092 +--a0:=integrate(t0,x) +--E 1060 + +--S 1061 of 1092 +--m0:=a0-r0 +--E 1061 + +--S 1062 of 1092 +--d0:=D(m0,x) +--E 1062 + +)clear all + +--S 1063 of 1092 +t0:=x^2*(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 4 3 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1092 +r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ + (c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ + (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*_ + (a+b*x)^(3/2)*(c+d*x)^(7/2)/(b^2*d^2)+1/6*x*(a+b*x)^(3/2)*_ + (c+d*x)^(7/2)/(b*d)-1/512*(b*c-a*d)^4*(5*b^2*c^2+14*a*b*c*d+_ + 21*a^2*d^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(11/2)*d^(7/2))+1/256*(b*c-a*d)^2*(5*b^2*c^2+14*a*b*c*d+_ + 21*a^2*d^2)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^5*d^2)+_ + 1/512*(b*c-a*d)^3*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^5*d^3) +--R +--R +--R (2) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 315a d + 1050a b c d - 1125a b c d + 300a b c d + 75a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 75b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 1280b d x + (128a b d + 3200b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 144a b d + 416a b c d + 2160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (168a b d - 488a b c d + 408a b c d + 40b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 616a b c d - 524a b c d + 40a b c d - 50b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 315a d - 945a b c d + 838a b c d - 90a b c d - 65a b c d + 75b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 5 3 +-+ +-+ +--R 7680b d \|b \|d +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1092 +--a0:=integrate(t0,x) +--E 1065 + +--S 1066 of 1092 +--m0:=a0-r0 +--E 1066 + +--S 1067 of 1092 +--d0:=D(m0,x) +--E 1067 + +)clear all + +--S 1068 of 1092 +t0:=x*(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 3 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1092 +r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ + 1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+_ + 1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*_ + (3*b*c+7*a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + (b^(9/2)*d^(5/2))-1/64*(b*c-a*d)^2*(3*b*c+7*a*d)*(a+b*x)^(3/2)*_ + sqrt(c+d*x)/(b^4*d)-1/128*(b*c-a*d)^3*(3*b*c+7*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/(b^4*d^2) +--R +--R +--R (2) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 105a d - 375a b c d + 450a b c d - 150a b c d - 75a b c d +--R + +--R 5 5 +--R 45b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 1008b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 176a b c d + 744b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 222a b c d + 218a b c d + 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 340a b c d - 346a b c d + 60a b c d - 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 2 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1092 +--a0:=integrate(t0,x) +--E 1070 + +--S 1071 of 1092 +--m0:=a0-r0 +--E 1071 + +--S 1072 of 1092 +--d0:=D(m0,x) +--E 1072 + +)clear all + +--S 1073 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (1) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1092 +r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ + (c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_ + (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*_ + (a+b*x)^(3/2)*sqrt(c+d*x)/b^3+5/64*(b*c-a*d)^3*sqrt(a+b*x)*_ + sqrt(c+d*x)/(b^3*d) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1092 +--a0:=integrate(t0,x) +--E 1075 + +--S 1076 of 1092 +--m0:=a0-r0 +--E 1076 + +--S 1077 of 1092 +--d0:=D(m0,x) +--E 1077 + +)clear all + +--S 1078 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1092 +r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ + 1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*_ + atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+_ + 1/12*(5*b*c+a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/b+1/3*(c+d*x)^(5/2)*_ + sqrt(a+b*x)+1/8*(5*b*c-a*d)*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b^2 +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 15a b c d + 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 48b c \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 26b c d)x - 3a d + 14a b c d + 33b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1080 + +--S 1081 of 1092 +--m0:=a0-r0 +--E 1081 + +--S 1082 of 1092 +--d0:=D(m0,x) +--E 1082 + +)clear all + +--S 1083 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1092 +r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ + sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ + sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*_ + (c+d*x)^(3/2)*sqrt(a+b*x)-(c+d*x)^(5/2)*sqrt(a+b*x)/x+_ + 1/4*d*(11*b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/b +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 2 +-+ +-+ \|d \|b x + a +--R (- a d + 10a b c d + 15b c )x\|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ \|c \|b x + a +--R (- 20a b c d - 4b c )x\|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 +-+ +-+ +-------+ +-------+ +--R (2b d x + (a d + 9b c d)x - 4b c )\|a \|b \|b x + a \|d x + c +--R / +--R +-+ +-+ +--R 4b x\|a \|b +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1085 + +--S 1086 of 1092 +--m0:=a0-r0 +--E 1086 + +--S 1087 of 1092 +--d0:=D(m0,x) +--E 1087 + +)clear all + +--S 1088 of 1092 +t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (1) ---------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1092 +r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ + sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*_ + sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-_ + 1/4*(b*c+5*a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*x)-_ + 1/2*(c+d*x)^(5/2)*sqrt(a+b*x)/x^2+1/4*d*(b*c+11*a*d)*_ + sqrt(a+b*x)*sqrt(c+d*x)/a +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 2 2 +-+ +-+ \|d \|b x + a +--R (4a d + 20a b c d)x \|a \|d atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 2 2 2 +-+ +-+ \|c \|b x + a +--R (- 15a d - 10a b c d + b c )x \|b \|c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 +-+ +-+ +-------+ +-------+ +--R (4a d x + (- 9a c d - b c )x - 2a c )\|a \|b \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4a x \|a \|b +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1092 (non-algebraic residues) +--a0:=integrate(t0,x) +--E 1090 + +--S 1091 of 1092 +--m0:=a0-r0 +--E 1091 + +--S 1092 of 1092 +--d0:=D(m0,x) +--E 1092 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document}