diff --git a/changelog b/changelog index 5584d83..6ff9a33 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20130721 tpd src/axiom-website/patches.html 20130721.01.tpd.patch +20130721 tpd src/input/rich2.input +20130721 tpd src/axiom-website/CATS/index.html 20130720 tpd src/axiom-website/patches.html 20130720.01.tpd.patch 20130720 tpd src/input/rich2.input 20130720 tpd src/input/Makefile diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index c11116e..c39c10a 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -293,6 +293,9 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d x)^n (part 2) source pdf
+ (a+b x)^m (A+B x) (d+e x)^p + source + pdf


Rich



diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 5e3b362..20ff7e5 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4240,6 +4240,8 @@ src/input/rich1a, rich1b src/axiom-website/CATS/index.html, rich1a, rich1b 20130720.01.tpd.patch src/input/rich2.input +20130721.01.tpd.patch +src/axiom-website/CATS/index.html, rich2.input diff --git a/src/input/rich2.input.pamphlet b/src/input/rich2.input.pamphlet index 1aeae06..cc76c42 100644 --- a/src/input/rich2.input.pamphlet +++ b/src/input/rich2.input.pamphlet @@ -6,7 +6,7 @@ \author{Albert Rich and Timothy Daly} \maketitle \begin{abstract} -2.1.2 (a+b x)^m (A+B x) (d+e x)^p +\verb|2.1.2 (a+b x)^m (A+B x) (d+e x)^p| \end{abstract} \eject \tableofcontents @@ -113,12 +113,14 @@ d0:=D(m0,x) --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 (6) B b x + (A b + B a)x + A a x +--R (1) B b x + (A b + B a)x + A a x --R Type: Polynomial(Integer) --E 6 @@ -127,7 +129,7 @@ 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 (7) - B b x + (- A b + - B a)x + - A a x +--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 @@ -137,7 +139,7 @@ a0:=integrate(t0,x) --R --R --R 1 7 1 1 6 1 5 ---R (8) - B b x + (- A b + - B a)x + - A a x +--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 @@ -146,7 +148,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (9) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 9 @@ -154,16 +156,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (10) 0 +--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 (11) B b x + (A b + B a)x + A a x +--R 5 4 3 +--R (1) B b x + (A b + B a)x + A a x --R Type: Polynomial(Integer) --E 11 @@ -171,9 +175,9 @@ t0:=x^3*(a+b*x)*(A+B*x) 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 (12) - B b x + (- A b + - B a)x + - A a x ---R 6 5 5 4 +--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 @@ -181,9 +185,9 @@ r0:=1/4*a*A*x^4+1/5*(A*b+a*B)*x^5+1/6*b*B*x^6 a0:=integrate(t0,x) --R --R ---R 1 6 1 1 5 1 4 ---R (13) - B b x + (- A b + - B a)x + - A a x ---R 6 5 5 4 +--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 @@ -191,7 +195,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (14) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 14 @@ -199,16 +203,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (15) 0 +--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 (16) B b x + (A b + B a)x + A a x +--R 4 3 2 +--R (1) B b x + (A b + B a)x + A a x --R Type: Polynomial(Integer) --E 16 @@ -216,9 +222,9 @@ t0:=x^2*(a+b*x)*(A+B*x) 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 (17) - B b x + (- A b + - B a)x + - A a x ---R 5 4 4 3 +--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 @@ -226,9 +232,9 @@ r0:=1/3*a*A*x^3+1/4*(A*b+a*B)*x^4+1/5*b*B*x^5 a0:=integrate(t0,x) --R --R ---R 1 5 1 1 4 1 3 ---R (18) - B b x + (- A b + - B a)x + - A a x ---R 5 4 4 3 +--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 @@ -236,7 +242,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (19) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 19 @@ -244,16 +250,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (20) 0 +--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 (21) B b x + (A b + B a)x + A a x +--R 3 2 +--R (1) B b x + (A b + B a)x + A a x --R Type: Polynomial(Integer) --E 21 @@ -261,9 +269,9 @@ t0:=x*(a+b*x)*(A+B*x) 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 (22) - B b x + (- A b + - B a)x + - A a x ---R 4 3 3 2 +--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 @@ -271,9 +279,9 @@ r0:=1/2*a*A*x^2+1/3*(A*b+a*B)*x^3+1/4*b*B*x^4 a0:=integrate(t0,x) --R --R ---R 1 4 1 1 3 1 2 ---R (23) - B b x + (- A b + - B a)x + - A a x ---R 4 3 3 2 +--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 @@ -281,7 +289,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (24) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 24 @@ -289,16 +297,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (25) 0 +--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 (26) B b x + (A b + B a)x + A a +--R 2 +--R (1) B b x + (A b + B a)x + A a --R Type: Polynomial(Integer) --E 26 @@ -306,9 +316,9 @@ t0:=(a+b*x)*(A+B*x) 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 (27) - B b x + (- A b + - B a)x + A a x ---R 3 2 2 +--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 @@ -316,9 +326,9 @@ r0:=a*A*x+1/2*(A*b+a*B)*x^2+1/3*b*B*x^3 a0:=integrate(t0,x) --R --R ---R 1 3 1 1 2 ---R (28) - B b x + (- A b + - B a)x + A a x ---R 3 2 2 +--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 @@ -326,7 +336,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (29) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 29 @@ -334,18 +344,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (30) 0 +--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 (31) --------------------------- ---R x +--R 2 +--R B b x + (A b + B a)x + A a +--R (1) --------------------------- +--R x --R Type: Fraction(Polynomial(Integer)) --E 31 @@ -353,10 +365,10 @@ t0:=(a+b*x)*(A+B*x)/x 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 (32) ----------------------------------------------- ---R 2B +--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 @@ -364,10 +376,10 @@ r0:=a*B*x+1/2*b*(A+B*x)^2/B+a*A*log(x) a0:=integrate(t0,x) --R --R ---R 2 ---R 2A a log(x) + B b x + (2A b + 2B a)x ---R (33) ------------------------------------- --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 @@ -375,10 +387,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 ---R A b ---R (34) - --- ---R 2B +--R 2 +--R A b +--R (4) - --- +--R 2B --R Type: Expression(Integer) --E 34 @@ -386,19 +398,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (35) 0 +--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 (36) --------------------------- ---R 2 ---R x +--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 @@ -406,10 +420,10 @@ t0:=(a+b*x)*(A+B*x)/x^2 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 (37) ---------------------------------- ---R x +--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 @@ -417,10 +431,10 @@ r0:=-a*A/x+b*B*x+(A*b+a*B)*log(x) a0:=integrate(t0,x) --R --R ---R 2 ---R (A b + B a)x log(x) + B b x - A a ---R (38) ---------------------------------- ---R x +--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 @@ -428,7 +442,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (39) 0 +--R (4) 0 --R Type: Expression(Integer) --E 39 @@ -436,19 +450,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (40) 0 +--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 (41) --------------------------- ---R 3 ---R x +--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 @@ -456,11 +472,11 @@ t0:=(a+b*x)*(A+B*x)/x^3 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 (42) -------------------------------------- ---R 2 ---R 2x +--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 @@ -468,11 +484,11 @@ r0:=-1/2*a*A/x^2+(-A*b-a*B)/x+b*B*log(x) a0:=integrate(t0,x) --R --R ---R 2 ---R 2B b x log(x) + (- 2A b - 2B a)x - A a ---R (43) -------------------------------------- ---R 2 ---R 2x +--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 @@ -480,7 +496,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (44) 0 +--R (4) 0 --R Type: Expression(Integer) --E 44 @@ -488,19 +504,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (45) 0 +--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 (46) --------------------------- ---R 4 ---R x +--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 @@ -508,12 +526,12 @@ t0:=(a+b*x)*(A+B*x)/x^4 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 (47) ------------------------------------- ---R 3 ---R x +--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 @@ -521,11 +539,11 @@ r0:=-1/3*a*A/x^3+1/2*(-A*b-a*B)/x^2-b*B/x a0:=integrate(t0,x) --R --R ---R 2 ---R - 6B b x + (- 3A b - 3B a)x - 2A a ---R (48) ----------------------------------- ---R 3 ---R 6x +--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 @@ -533,7 +551,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (49) 0 +--R (4) 0 --R Type: Expression(Integer) --E 49 @@ -541,19 +559,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (50) 0 +--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 (51) --------------------------- ---R 5 ---R x +--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 @@ -561,12 +581,12 @@ t0:=(a+b*x)*(A+B*x)/x^5 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 (52) --------------------------------------- ---R 4 ---R x +--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 @@ -574,11 +594,11 @@ r0:=-1/4*a*A/x^4+1/3*(-A*b-a*B)/x^3-1/2*b*B/x^2 a0:=integrate(t0,x) --R --R ---R 2 ---R - 6B b x + (- 4A b - 4B a)x - 3A a ---R (53) ----------------------------------- ---R 4 ---R 12x +--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 @@ -586,7 +606,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (54) 0 +--R (4) 0 --R Type: Expression(Integer) --E 54 @@ -594,19 +614,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (55) 0 +--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 (56) --------------------------- ---R 6 ---R x +--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 @@ -614,12 +636,12 @@ t0:=(a+b*x)*(A+B*x)/x^6 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 (57) --------------------------------------- ---R 5 ---R x +--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 @@ -627,11 +649,11 @@ r0:=-1/5*a*A/x^5+1/4*(-A*b-a*B)/x^4-1/3*b*B/x^3 a0:=integrate(t0,x) --R --R ---R 2 ---R - 20B b x + (- 15A b - 15B a)x - 12A a ---R (58) --------------------------------------- ---R 5 ---R 60x +--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 @@ -639,7 +661,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (59) 0 +--R (4) 0 --R Type: Expression(Integer) --E 59 @@ -647,16 +669,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (60) 0 +--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 (61) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )x +--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 @@ -665,7 +689,7 @@ 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 (62) +--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 + @@ -698,7 +722,7 @@ r0:=a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(2+m)/(2+m)+_ a0:=integrate(t0,x) --R --R ---R (63) +--R (3) --R 2 3 2 2 2 2 4 --R (B b m + 6B b m + 11B b m + 6B b )x --R + @@ -735,7 +759,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (64) +--R (4) --R 2 3 2 2 2 2 4 --R (B b m + 6B b m + 11B b m + 6B b )x --R + @@ -796,7 +820,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (65) +--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 + @@ -805,12 +829,14 @@ d0:=D(m0,x) --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 (66) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--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 @@ -818,9 +844,9 @@ t0:=x^4*(a+b*x)^2*(A+B*x) 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 (67) - 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 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 @@ -828,9 +854,9 @@ 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 a0:=integrate(t0,x) --R --R ---R 1 2 8 1 2 2 7 1 1 2 6 1 2 5 ---R (68) - 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 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 @@ -838,7 +864,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (69) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 69 @@ -846,16 +872,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (70) 0 +--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 (71) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--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 @@ -863,9 +891,9 @@ t0:=x^3*(a+b*x)^2*(A+B*x) 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 (72) - 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 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 @@ -873,9 +901,9 @@ 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 a0:=integrate(t0,x) --R --R ---R 1 2 7 1 2 1 6 2 1 2 5 1 2 4 ---R (73) - 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 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 @@ -883,7 +911,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (74) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 74 @@ -891,16 +919,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (75) 0 +--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 (76) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--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 @@ -908,9 +938,9 @@ t0:=x^2*(a+b*x)^2*(A+B*x) 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 (77) - 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 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 @@ -918,9 +948,9 @@ 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 a0:=integrate(t0,x) --R --R ---R 1 2 6 1 2 2 5 1 1 2 4 1 2 3 ---R (78) - 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 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 @@ -928,7 +958,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (79) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 79 @@ -936,16 +966,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (80) 0 +--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 (81) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x +--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 @@ -953,9 +985,9 @@ t0:=x*(a+b*x)^2*(A+B*x) 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 (82) - 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 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 @@ -963,9 +995,9 @@ 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 a0:=integrate(t0,x) --R --R ---R 1 2 5 1 2 1 4 2 1 2 3 1 2 2 ---R (83) - 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 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 @@ -973,7 +1005,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (84) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 84 @@ -981,16 +1013,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (85) 0 +--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 (86) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a +--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 @@ -998,7 +1032,7 @@ t0:=(a+b*x)^2*(A+B*x) 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 (87) +--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 @@ -1016,9 +1050,9 @@ r0:=1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2 a0:=integrate(t0,x) --R --R ---R 1 2 4 1 2 2 3 1 2 2 2 ---R (88) - B b x + (- A b + - B a b)x + (A a b + - B a )x + A a x ---R 4 3 3 2 +--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 @@ -1026,12 +1060,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 3 1 4 ---R - - A a b + -- B a ---R 3 12 ---R (89) ------------------- ---R 2 ---R b +--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 @@ -1039,18 +1073,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (90) 0 +--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 (91) ---------------------------------------------------- ---R x +--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 @@ -1058,7 +1094,7 @@ t0:=(a+b*x)^2*(A+B*x)/x 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 (92) +--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 ---------------------------------------------------------------------------- @@ -1070,10 +1106,10 @@ 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) 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 (93) --------------------------------------------------------------- ---R 6 +--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 @@ -1081,10 +1117,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 3 ---R B a ---R (94) - ---- ---R 3b +--R 3 +--R B a +--R (4) - ---- +--R 3b --R Type: Expression(Integer) --E 94 @@ -1092,19 +1128,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (95) 0 +--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 (96) ---------------------------------------------------- ---R 2 ---R x +--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 @@ -1112,10 +1150,10 @@ t0:=(a+b*x)^2*(A+B*x)/x^2 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 (97) -------------------------------------------------------------- ---R 2x +--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 @@ -1123,10 +1161,10 @@ 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) 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 (98) -------------------------------------------------------------- ---R 2x +--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 @@ -1134,7 +1172,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (99) 0 +--R (4) 0 --R Type: Expression(Integer) --E 99 @@ -1142,19 +1180,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (100) 0 +--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 (101) ---------------------------------------------------- ---R 3 ---R x +--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 @@ -1162,11 +1202,11 @@ t0:=(a+b*x)^2*(A+B*x)/x^3 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 (102) --------------------------------------------------------------- ---R 2 ---R 2x +--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 @@ -1174,11 +1214,11 @@ 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) 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 (103) --------------------------------------------------------------- ---R 2 ---R 2x +--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 @@ -1186,7 +1226,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (104) 0 +--R (4) 0 --R Type: Expression(Integer) --E 104 @@ -1194,19 +1234,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (105) 0 +--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 (106) ---------------------------------------------------- ---R 4 ---R x +--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 @@ -1214,11 +1256,11 @@ t0:=(a+b*x)^2*(A+B*x)/x^4 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 (107) ------------------------------------------------------------------- ---R 3 ---R 6x +--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 @@ -1226,11 +1268,11 @@ 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) 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 (108) ------------------------------------------------------------------- ---R 3 ---R 6x +--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 @@ -1238,7 +1280,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (109) 0 +--R (4) 0 --R Type: Expression(Integer) --E 109 @@ -1246,19 +1288,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (110) 0 +--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 (111) ---------------------------------------------------- ---R 5 ---R x +--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 @@ -1266,12 +1310,12 @@ t0:=(a+b*x)^2*(A+B*x)/x^5 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 (112) ---------------------------------------------------------------- ---R 4 ---R x +--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 @@ -1279,11 +1323,11 @@ 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 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 (113) ---------------------------------------------------------------- ---R 4 ---R 12x +--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 @@ -1291,7 +1335,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (114) 0 +--R (4) 0 --R Type: Expression(Integer) --E 114 @@ -1299,19 +1343,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (115) 0 +--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 (116) ---------------------------------------------------- ---R 6 ---R x +--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 @@ -1319,12 +1365,12 @@ t0:=(a+b*x)^2*(A+B*x)/x^6 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 (117) -------------------------------------------------------------------- ---R 5 ---R x +--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 @@ -1332,11 +1378,11 @@ 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 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 (118) -------------------------------------------------------------------- ---R 5 ---R 60x +--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 @@ -1344,7 +1390,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (119) 0 +--R (4) 0 --R Type: Expression(Integer) --E 119 @@ -1352,19 +1398,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (120) 0 +--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 (121) ---------------------------------------------------- ---R 7 ---R x +--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 @@ -1372,12 +1420,12 @@ t0:=(a+b*x)^2*(A+B*x)/x^7 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 (122) -------------------------------------------------------------------- ---R 6 ---R x +--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 @@ -1385,11 +1433,11 @@ 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 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 (123) -------------------------------------------------------------------- ---R 6 ---R 60x +--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 @@ -1397,7 +1445,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (124) 0 +--R (4) 0 --R Type: Expression(Integer) --E 124 @@ -1405,19 +1453,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (125) 0 +--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 (126) ---------------------------------------------------- ---R 8 ---R x +--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 @@ -1425,12 +1475,12 @@ t0:=(a+b*x)^2*(A+B*x)/x^8 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 (127) -------------------------------------------------------------------- ---R 7 ---R x +--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 @@ -1438,7 +1488,7 @@ 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 a0:=integrate(t0,x) --R --R ---R (128) +--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 ----------------------------------------------------------------------- @@ -1451,7 +1501,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (129) 0 +--R (4) 0 --R Type: Expression(Integer) --E 129 @@ -1459,15 +1509,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (130) 0 +--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 (131) +--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 + @@ -1485,7 +1537,7 @@ r0:=a^3*A*x^(1+m)/(1+m)+a^2*(3*A*b+a*B)*x^(2+m)/(2+m)+_ b^3*B*x^(5+m)/(5+m) --R --R ---R (132) +--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 + @@ -1531,7 +1583,7 @@ r0:=a^3*A*x^(1+m)/(1+m)+a^2*(3*A*b+a*B)*x^(2+m)/(2+m)+_ a0:=integrate(t0,x) --R --R ---R (133) +--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 + @@ -1580,7 +1632,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (134) +--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 + @@ -1665,7 +1717,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (135) +--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 + @@ -1683,11 +1735,13 @@ d0:=D(m0,x) --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 (136) +--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 + @@ -1701,7 +1755,7 @@ 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 (137) +--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 @@ -1716,7 +1770,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (138) +--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 @@ -1731,7 +1785,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (139) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 139 @@ -1739,15 +1793,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (140) 0 +--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 (141) +--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 + @@ -1761,7 +1817,7 @@ 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 (142) +--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 @@ -1776,7 +1832,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (143) +--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 @@ -1791,7 +1847,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (144) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 144 @@ -1799,15 +1855,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (145) 0 +--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 (146) +--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 + @@ -1821,7 +1879,7 @@ 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 (147) +--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 @@ -1836,7 +1894,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (148) +--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 @@ -1851,7 +1909,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (149) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 149 @@ -1859,15 +1917,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (150) 0 +--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 (151) +--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 + @@ -1881,7 +1941,7 @@ 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 (152) +--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 @@ -1899,7 +1959,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (153) +--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 @@ -1914,12 +1974,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 5 1 6 ---R -- A a b - -- B a ---R 20 60 ---R (154) ------------------ ---R 3 ---R b +--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 @@ -1927,15 +1987,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (155) 0 +--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 (156) +--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) @@ -1945,7 +2007,7 @@ t0:=(a+b*x)^3*(A+B*x) 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 (157) +--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 @@ -1963,7 +2025,7 @@ r0:=1/4*(A*b-a*B)*(a+b*x)^4/b^2+1/5*B*(a+b*x)^5/b^2 a0:=integrate(t0,x) --R --R ---R (158) +--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 @@ -1978,12 +2040,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 4 1 5 ---R - - A a b + -- B a ---R 4 20 ---R (159) ------------------- ---R 2 ---R b +--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 @@ -1991,15 +2053,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (160) 0 +--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 (161) +--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 ---------------------------------------------------------------------------- @@ -2011,7 +2075,7 @@ t0:=(a+b*x)^3*(A+B*x)/x 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 (162) +--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 + @@ -2026,7 +2090,7 @@ 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) a0:=integrate(t0,x) --R --R ---R (163) +--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 + @@ -2041,10 +2105,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 4 ---R B a ---R (164) - ---- ---R 4b +--R 4 +--R B a +--R (4) - ---- +--R 4b --R Type: Expression(Integer) --E 164 @@ -2052,15 +2116,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (165) 0 +--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 (166) +--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 ---------------------------------------------------------------------------- @@ -2074,7 +2140,7 @@ 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 (167) +--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 + @@ -2089,7 +2155,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (168) +--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 + @@ -2104,7 +2170,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (169) 0 +--R (4) 0 --R Type: Expression(Integer) --E 169 @@ -2112,15 +2178,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (170) 0 +--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 (171) +--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 ---------------------------------------------------------------------------- @@ -2134,7 +2202,7 @@ 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 (172) +--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 + @@ -2150,7 +2218,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (173) +--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 + @@ -2166,7 +2234,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (174) 0 +--R (4) 0 --R Type: Expression(Integer) --E 174 @@ -2174,15 +2242,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (175) 0 +--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 (176) +--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 ---------------------------------------------------------------------------- @@ -2196,7 +2266,7 @@ 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 (177) +--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 + @@ -2212,7 +2282,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (178) +--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 + @@ -2228,7 +2298,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (179) 0 +--R (4) 0 --R Type: Expression(Integer) --E 179 @@ -2236,15 +2306,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (180) 0 +--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 (181) +--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 ---------------------------------------------------------------------------- @@ -2258,7 +2330,7 @@ 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 (182) +--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 + @@ -2274,7 +2346,7 @@ 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)+_ a0:=integrate(t0,x) --R --R ---R (183) +--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 + @@ -2290,10 +2362,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 4 ---R A b ---R (184) ---- ---R 4a +--R 4 +--R A b +--R (4) ---- +--R 4a --R Type: Expression(Integer) --E 184 @@ -2301,15 +2373,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (185) 0 +--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 (186) +--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 ---------------------------------------------------------------------------- @@ -2323,7 +2397,7 @@ 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 (187) +--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 @@ -2341,7 +2415,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (188) +--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 + @@ -2357,7 +2431,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (189) 0 +--R (4) 0 --R Type: Expression(Integer) --E 189 @@ -2365,15 +2439,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (190) 0 +--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 (191) +--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 ---------------------------------------------------------------------------- @@ -2387,7 +2463,7 @@ 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 (192) +--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 @@ -2405,7 +2481,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (193) +--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 + @@ -2421,7 +2497,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (194) 0 +--R (4) 0 --R Type: Expression(Integer) --E 194 @@ -2429,15 +2505,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (195) 0 +--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 (196) +--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 ---------------------------------------------------------------------------- @@ -2451,7 +2529,7 @@ 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 (197) +--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 @@ -2469,7 +2547,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (198) +--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 + @@ -2485,7 +2563,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (199) 0 +--R (4) 0 --R Type: Expression(Integer) --E 199 @@ -2493,15 +2571,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (200) 0 +--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 (201) +--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 ---------------------------------------------------------------------------- @@ -2515,7 +2595,7 @@ 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 (202) +--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 @@ -2533,7 +2613,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (203) +--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 + @@ -2549,7 +2629,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (204) 0 +--R (4) 0 --R Type: Expression(Integer) --E 204 @@ -2557,15 +2637,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (205) 0 +--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 (206) +--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 ---------------------------------------------------------------------------- @@ -2579,7 +2661,7 @@ 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 (207) +--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 @@ -2597,7 +2679,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (208) +--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 + @@ -2613,7 +2695,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (209) 0 +--R (4) 0 --R Type: Expression(Integer) --E 209 @@ -2621,15 +2703,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (210) 0 +--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 (211) +--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 + @@ -2648,7 +2732,7 @@ r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(2+m)/(2+m)+_ b^5*B*x^(7+m)/(7+m) --R --R ---R (212) +--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 + @@ -2745,7 +2829,7 @@ r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(2+m)/(2+m)+_ a0:=integrate(t0,x) --R --R ---R (213) +--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 + @@ -2847,7 +2931,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (214) +--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 + @@ -3045,7 +3129,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (215) +--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 + @@ -3066,11 +3150,13 @@ d0:=D(m0,x) --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 (216) +--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 + @@ -3085,7 +3171,7 @@ 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+_ 1/11*b^4*(A*b+5*a*B)*x^11+1/12*b^5*B*x^12 --R --R ---R (217) +--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 @@ -3104,7 +3190,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (218) +--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 @@ -3123,7 +3209,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (219) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 219 @@ -3131,15 +3217,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (220) 0 +--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 (221) +--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 + @@ -3154,7 +3242,7 @@ 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+_ 1/10*b^4*(A*b+5*a*B)*x^10+1/11*b^5*B*x^11 --R --R ---R (222) +--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 @@ -3173,7 +3261,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (223) +--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 @@ -3192,7 +3280,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (224) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 224 @@ -3200,15 +3288,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (225) 0 +--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 (226) +--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 + @@ -3223,7 +3313,7 @@ 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+_ 1/9*b^4*(A*b+5*a*B)*x^9+1/10*b^5*B*x^10 --R --R ---R (227) +--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 @@ -3242,7 +3332,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (228) +--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 @@ -3261,7 +3351,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (229) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 229 @@ -3269,15 +3359,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (230) 0 +--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 (231) +--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 + @@ -3291,7 +3383,7 @@ 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 (232) +--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 @@ -3313,7 +3405,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (233) +--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 @@ -3332,12 +3424,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 8 1 9 ---R - --- A a b + --- B a ---R 168 504 ---R (234) ---------------------- ---R 4 ---R b +--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 @@ -3345,15 +3437,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (235) 0 +--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 (236) +--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 + @@ -3367,7 +3461,7 @@ 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 (237) +--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 @@ -3389,7 +3483,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (238) +--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 @@ -3408,12 +3502,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 7 1 8 ---R -- A a b - --- B a ---R 42 168 ---R (239) ------------------- ---R 3 ---R b +--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 @@ -3421,15 +3515,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (240) 0 +--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 (241) +--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 + @@ -3442,7 +3538,7 @@ t0:=(a+b*x)^5*(A+B*x) 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 (242) +--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 @@ -3464,7 +3560,7 @@ r0:=1/6*(A*b-a*B)*(a+b*x)^6/b^2+1/7*B*(a+b*x)^7/b^2 a0:=integrate(t0,x) --R --R ---R (243) +--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 @@ -3482,12 +3578,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 6 1 7 ---R - - A a b + -- B a ---R 6 42 ---R (244) ------------------- ---R 2 ---R b +--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 @@ -3495,15 +3591,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (245) 0 +--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 (246) +--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 + @@ -3519,7 +3617,7 @@ 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 (247) +--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 + @@ -3537,7 +3635,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (248) +--R (3) --R 5 5 6 5 4 5 --R 60A a log(x) + 10B b x + (12A b + 60B a b )x --R + @@ -3555,10 +3653,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 6 ---R B a ---R (249) - ---- ---R 6b +--R 6 +--R B a +--R (4) - ---- +--R 6b --R Type: Expression(Integer) --E 249 @@ -3566,15 +3664,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (250) 0 +--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 (251) +--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 + @@ -3592,7 +3692,7 @@ 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+_ 1/5*b^5*B*x^5+a^4*(5*A*b+a*B)*log(x) --R --R ---R (252) +--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 + @@ -3610,7 +3710,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (253) +--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 + @@ -3628,7 +3728,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (254) 0 +--R (4) 0 --R Type: Expression(Integer) --E 254 @@ -3636,15 +3736,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (255) 0 +--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 (256) +--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 + @@ -3662,7 +3764,7 @@ 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+_ 1/4*b^5*B*x^4+5*a^3*b*(2*A*b+a*B)*log(x) --R --R ---R (257) +--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 + @@ -3681,7 +3783,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (258) +--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 + @@ -3700,7 +3802,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (259) 0 +--R (4) 0 --R Type: Expression(Integer) --E 259 @@ -3708,15 +3810,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (260) 0 +--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 (261) +--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 + @@ -3734,7 +3838,7 @@ 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+_ 10*a^2*b^2*(A*b+a*B)*log(x) --R --R ---R (262) +--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 + @@ -3753,7 +3857,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (263) +--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 + @@ -3772,7 +3876,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (264) 0 +--R (4) 0 --R Type: Expression(Integer) --E 264 @@ -3780,15 +3884,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (265) 0 +--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 (266) +--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 + @@ -3806,7 +3912,7 @@ 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-_ 5*a*b^3*(A*b+2*a*B)*log(x) --R --R ---R (267) +--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 + @@ -3825,7 +3931,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (268) +--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 + @@ -3844,7 +3950,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (269) 0 +--R (4) 0 --R Type: Expression(Integer) --E 269 @@ -3852,15 +3958,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (270) 0 +--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 (271) +--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 + @@ -3878,7 +3986,7 @@ 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-_ b^4*(A*b+5*a*B)*log(x) --R --R ---R (272) +--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 + @@ -3897,7 +4005,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (273) +--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 + @@ -3916,7 +4024,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (274) 0 +--R (4) 0 --R Type: Expression(Integer) --E 274 @@ -3924,15 +4032,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (275) 0 +--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 (276) +--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 + @@ -3949,7 +4059,7 @@ 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 (277) +--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 + @@ -3968,7 +4078,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (278) +--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 + @@ -3987,10 +4097,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 6 ---R A b ---R (279) ---- ---R 6a +--R 6 +--R A b +--R (4) ---- +--R 6a --R Type: Expression(Integer) --E 279 @@ -3998,15 +4108,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (280) 0 +--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 (281) +--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 + @@ -4022,7 +4134,7 @@ t0:=(a+b*x)^5*(A+B*x)/x^8 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 (282) +--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 @@ -4044,7 +4156,7 @@ 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) a0:=integrate(t0,x) --R --R ---R (283) +--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 + @@ -4063,11 +4175,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 7 6 ---R - A b + 7B a b ---R (284) ---------------- ---R 2 ---R 42a +--R 7 6 +--R - A b + 7B a b +--R (4) ---------------- +--R 2 +--R 42a --R Type: Expression(Integer) --E 284 @@ -4075,15 +4187,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (285) 0 +--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 (286) +--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 + @@ -4100,7 +4214,7 @@ 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 (287) +--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 @@ -4122,7 +4236,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (288) +--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 + @@ -4141,11 +4255,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 8 7 ---R A b - 4B a b ---R (289) -------------- ---R 3 ---R 168a +--R 8 7 +--R A b - 4B a b +--R (4) -------------- +--R 3 +--R 168a --R Type: Expression(Integer) --E 289 @@ -4153,15 +4267,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (290) 0 +--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 (291) +--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 + @@ -4179,7 +4295,7 @@ 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-_ 1/4*b^4*(A*b+5*a*B)/x^4-1/3*b^5*B/x^3 --R --R ---R (292) +--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 @@ -4201,7 +4317,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (293) +--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 + @@ -4220,7 +4336,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (294) 0 +--R (4) 0 --R Type: Expression(Integer) --E 294 @@ -4228,15 +4344,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (295) 0 +--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 (296) +--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 + @@ -4254,7 +4372,7 @@ 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-_ 1/5*b^4*(A*b+5*a*B)/x^5-1/4*b^5*B/x^4 --R --R ---R (297) +--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 @@ -4276,7 +4394,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (298) +--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 + @@ -4295,7 +4413,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (299) 0 +--R (4) 0 --R Type: Expression(Integer) --E 299 @@ -4303,15 +4421,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (300) 0 +--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 (301) +--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 + @@ -4329,7 +4449,7 @@ 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-_ 1/6*b^4*(A*b+5*a*B)/x^6-1/5*b^5*B/x^5 --R --R ---R (302) +--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 @@ -4351,7 +4471,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (303) +--R (3) --R 5 6 5 4 5 --R - 2772B b x + (- 2310A b - 11550B a b )x --R + @@ -4370,7 +4490,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (304) 0 +--R (4) 0 --R Type: Expression(Integer) --E 304 @@ -4378,15 +4498,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (305) 0 +--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 (306) +--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 + @@ -4420,7 +4542,7 @@ r0:=a^10*A*x^(1+m)/(1+m)+a^9*(10*A*b+a*B)*x^(2+m)/(2+m)+_ b^9*(A*b+10*a*B)*x^(11+m)/(11+m)+b^10*B*x^(12+m)/(12+m) --R --R ---R (307) +--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 + @@ -4777,7 +4899,7 @@ r0:=a^10*A*x^(1+m)/(1+m)+a^9*(10*A*b+a*B)*x^(2+m)/(2+m)+_ a0:=integrate(t0,x) --R --R ---R (308) +--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 + @@ -5151,7 +5273,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (309) +--R (4) --R 10 11 10 10 10 9 10 8 --R B b m + 66B b m + 1925B b m + 32670B b m --R + @@ -5915,7 +6037,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (310) +--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 + @@ -5954,11 +6076,13 @@ d0:=D(m0,x) --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 (311) +--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 + @@ -5985,7 +6109,7 @@ r0:=1/11*a^10*A*x^11+1/12*a^9*(10*A*b+a*B)*x^12+_ 1/21*b^9*(A*b+10*a*B)*x^21+1/22*b^10*B*x^22 --R --R ---R (312) +--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 @@ -6012,7 +6136,7 @@ r0:=1/11*a^10*A*x^11+1/12*a^9*(10*A*b+a*B)*x^12+_ a0:=integrate(t0,x) --R --R ---R (313) +--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 @@ -6039,7 +6163,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (314) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 314 @@ -6047,15 +6171,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (315) 0 +--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 (316) +--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 + @@ -6082,7 +6208,7 @@ r0:=1/10*a^10*A*x^10+1/11*a^9*(10*A*b+a*B)*x^11+_ 1/20*b^9*(A*b+10*a*B)*x^20+1/21*b^10*B*x^21 --R --R ---R (317) +--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 @@ -6109,7 +6235,7 @@ r0:=1/10*a^10*A*x^10+1/11*a^9*(10*A*b+a*B)*x^11+_ a0:=integrate(t0,x) --R --R ---R (318) +--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 @@ -6136,7 +6262,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (319) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 319 @@ -6144,15 +6270,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (320) 0 +--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 (321) +--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 + @@ -6179,7 +6307,7 @@ r0:=1/9*a^10*A*x^9+1/10*a^9*(10*A*b+a*B)*x^10+_ 1/19*b^9*(A*b+10*a*B)*x^19+1/20*b^10*B*x^20 --R --R ---R (322) +--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 @@ -6206,7 +6334,7 @@ r0:=1/9*a^10*A*x^9+1/10*a^9*(10*A*b+a*B)*x^10+_ a0:=integrate(t0,x) --R --R ---R (323) +--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 @@ -6233,7 +6361,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (324) 0 +--R (4) 0 --R Type: Polynomial(Fraction(Integer)) --E 324 @@ -6241,15 +6369,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (325) 0 +--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 (326) +--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 + @@ -6278,7 +6408,7 @@ r0:=-1/11*a^7*(A*b-a*B)*(a+b*x)^11/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 (327) +--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 @@ -6312,7 +6442,7 @@ r0:=-1/11*a^7*(A*b-a*B)*(a+b*x)^11/b^9+_ a0:=integrate(t0,x) --R --R ---R (328) +--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 @@ -6339,12 +6469,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 18 1 19 ---R ------ A a b - ------ B a ---R 350064 831402 ---R (329) ---------------------------- ---R 9 ---R b +--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 @@ -6352,15 +6482,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (330) 0 +--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 (331) +--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 + @@ -6387,7 +6519,7 @@ 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+_ 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 (332) +--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 @@ -6421,7 +6553,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (333) +--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 @@ -6448,12 +6580,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 17 1 18 ---R - ------ A a b + ------ B a ---R 136136 350064 ---R (334) ------------------------------ ---R 8 ---R b +--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 @@ -6461,15 +6593,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (335) 0 +--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 (336) +--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 + @@ -6496,7 +6630,7 @@ r0:=-1/11*a^5*(A*b-a*B)*(a+b*x)^11/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 (337) +--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 @@ -6530,7 +6664,7 @@ r0:=-1/11*a^5*(A*b-a*B)*(a+b*x)^11/b^7+_ a0:=integrate(t0,x) --R --R ---R (338) +--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 @@ -6557,12 +6691,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 16 1 17 ---R ----- A a b - ------ B a ---R 48048 136136 ---R (339) --------------------------- ---R 7 ---R b +--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 @@ -6570,15 +6704,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (340) 0 +--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 (341) +--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 + @@ -6604,7 +6740,7 @@ r0:=1/11*a^4*(A*b-a*B)*(a+b*x)^11/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 (342) +--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 @@ -6638,7 +6774,7 @@ r0:=1/11*a^4*(A*b-a*B)*(a+b*x)^11/b^6-_ a0:=integrate(t0,x) --R --R ---R (343) +--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 @@ -6665,12 +6801,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 15 1 16 ---R - ----- A a b + ----- B a ---R 15015 48048 ---R (344) ---------------------------- ---R 6 ---R b +--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 @@ -6678,15 +6814,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (345) 0 +--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 (346) +--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 + @@ -6711,7 +6849,7 @@ r0:=-1/11*a^3*(A*b-a*B)*(a+b*x)^11/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 (347) +--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 @@ -6745,7 +6883,7 @@ r0:=-1/11*a^3*(A*b-a*B)*(a+b*x)^11/b^5+_ a0:=integrate(t0,x) --R --R ---R (348) +--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 @@ -6772,12 +6910,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 14 1 15 ---R ---- A a b - ----- B a ---R 4004 15015 ---R (349) ------------------------- ---R 5 ---R b +--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 @@ -6785,15 +6923,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (350) 0 +--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 (351) +--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 + @@ -6817,7 +6957,7 @@ r0:=1/11*a^2*(A*b-a*B)*(a+b*x)^11/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 (352) +--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 @@ -6851,7 +6991,7 @@ r0:=1/11*a^2*(A*b-a*B)*(a+b*x)^11/b^4-_ a0:=integrate(t0,x) --R --R ---R (353) +--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 @@ -6878,12 +7018,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 13 1 14 ---R - --- A a b + ---- B a ---R 858 4004 ---R (354) ------------------------- ---R 4 ---R b +--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 @@ -6891,15 +7031,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (355) 0 +--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 (356) +--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 + @@ -6922,7 +7064,7 @@ 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 (357) +--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 @@ -6955,7 +7097,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (358) +--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 @@ -6982,12 +7124,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 12 1 13 ---R --- A a b - --- B a ---R 132 858 ---R (359) ---------------------- ---R 3 ---R b +--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 @@ -6995,15 +7137,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (360) 0 +--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 (361) +--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 + @@ -7025,7 +7169,7 @@ t0:=(a+b*x)^10*(A+B*x) 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 (362) +--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 @@ -7058,7 +7202,7 @@ r0:=1/11*(A*b-a*B)*(a+b*x)^11/b^2+1/12*B*(a+b*x)^12/b^2 a0:=integrate(t0,x) --R --R ---R (363) +--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 @@ -7083,12 +7227,12 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 1 11 1 12 ---R - -- A a b + --- B a ---R 11 132 ---R (364) ----------------------- ---R 2 ---R b +--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 @@ -7096,15 +7240,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (365) 0 +--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 (366) +--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 + @@ -7131,7 +7277,7 @@ r0:=10*a^9*A*b*x+45/2*a^8*A*b^2*x^2+40*a^7*A*b^3*x^3+_ 1/10*A*b^10*x^10+1/11*B*(a+b*x)^11/b+a^10*A*log(x) --R --R ---R (367) +--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 + @@ -7158,7 +7304,7 @@ r0:=10*a^9*A*b*x+45/2*a^8*A*b^2*x^2+40*a^7*A*b^3*x^3+_ a0:=integrate(t0,x) --R --R ---R (368) +--R (3) --R 10 10 11 10 9 10 --R 27720A a log(x) + 2520B b x + (2772A b + 27720B a b )x --R + @@ -7185,10 +7331,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 11 ---R B a ---R (369) - ----- ---R 11b +--R 11 +--R B a +--R (4) - ----- +--R 11b --R Type: Expression(Integer) --E 369 @@ -7196,15 +7342,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (370) 0 +--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 (371) +--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 + @@ -7233,7 +7381,7 @@ 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+_ 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 (372) +--R (2) --R 9 10 10 11 --R (25200A a b + 2520B a )x log(x) + 252B b x --R + @@ -7260,7 +7408,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (373) +--R (3) --R 9 10 10 11 --R (25200A a b + 2520B a )x log(x) + 252B b x --R + @@ -7287,7 +7435,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (374) 0 +--R (4) 0 --R Type: Expression(Integer) --E 374 @@ -7295,15 +7443,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (375) 0 +--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 (376) +--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 + @@ -7332,7 +7482,7 @@ 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+_ 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 (377) +--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 + @@ -7357,7 +7507,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (378) +--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 + @@ -7382,7 +7532,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (379) 0 +--R (4) 0 --R Type: Expression(Integer) --E 379 @@ -7390,15 +7540,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (380) 0 +--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 (381) +--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 + @@ -7427,7 +7579,7 @@ 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+_ 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 (382) +--R (2) --R 7 3 8 2 3 10 11 --R (20160A a b + 7560B a b )x log(x) + 21B b x --R + @@ -7455,7 +7607,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (383) +--R (3) --R 7 3 8 2 3 10 11 --R (20160A a b + 7560B a b )x log(x) + 21B b x --R + @@ -7483,7 +7635,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (384) 0 +--R (4) 0 --R Type: Expression(Integer) --E 384 @@ -7491,15 +7643,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (385) 0 +--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 (386) +--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 + @@ -7528,7 +7682,7 @@ 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-_ 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 (387) +--R (2) --R 6 4 7 3 4 10 11 --R (17640A a b + 10080B a b )x log(x) + 12B b x --R + @@ -7556,7 +7710,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (388) +--R (3) --R 6 4 7 3 4 10 11 --R (17640A a b + 10080B a b )x log(x) + 12B b x --R + @@ -7584,7 +7738,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (389) 0 +--R (4) 0 --R Type: Expression(Integer) --E 389 @@ -7592,15 +7746,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (390) 0 +--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 (391) +--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 + @@ -7629,7 +7785,7 @@ 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-_ 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 (392) +--R (2) --R 5 5 6 4 5 10 11 --R (15120A a b + 12600B a b )x log(x) + 10B b x --R + @@ -7657,7 +7813,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (393) +--R (3) --R 5 5 6 4 5 10 11 --R (15120A a b + 12600B a b )x log(x) + 10B b x --R + @@ -7685,7 +7841,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (394) 0 +--R (4) 0 --R Type: Expression(Integer) --E 394 @@ -7693,15 +7849,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (395) 0 +--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 (396) +--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 + @@ -7730,7 +7888,7 @@ 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-_ 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 (397) +--R (2) --R 4 6 5 5 6 10 11 --R (12600A a b + 15120B a b )x log(x) + 12B b x --R + @@ -7758,7 +7916,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (398) +--R (3) --R 4 6 5 5 6 10 11 --R (12600A a b + 15120B a b )x log(x) + 12B b x --R + @@ -7786,7 +7944,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (399) 0 +--R (4) 0 --R Type: Expression(Integer) --E 399 @@ -7794,15 +7952,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (400) 0 +--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 (401) +--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 + @@ -7831,7 +7991,7 @@ 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-_ 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 (402) +--R (2) --R 3 7 4 6 7 10 11 --R (10080A a b + 17640B a b )x log(x) + 21B b x --R + @@ -7859,7 +8019,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (403) +--R (3) --R 3 7 4 6 7 10 11 --R (10080A a b + 17640B a b )x log(x) + 21B b x --R + @@ -7887,7 +8047,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (404) 0 +--R (4) 0 --R Type: Expression(Integer) --E 404 @@ -7895,15 +8055,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (405) 0 +--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 (406) +--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 + @@ -7932,7 +8094,7 @@ 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-_ 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 (407) +--R (2) --R 2 8 3 7 8 10 11 --R (7560A a b + 20160B a b )x log(x) + 56B b x --R + @@ -7960,7 +8122,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (408) +--R (3) --R 2 8 3 7 8 10 11 --R (7560A a b + 20160B a b )x log(x) + 56B b x --R + @@ -7988,7 +8150,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (409) 0 +--R (4) 0 --R Type: Expression(Integer) --E 409 @@ -7996,15 +8158,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (410) 0 +--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 (411) +--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 + @@ -8033,7 +8197,7 @@ 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-_ 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 (412) +--R (2) --R 9 2 8 9 10 11 --R (5040A a b + 22680B a b )x log(x) + 252B b x --R + @@ -8061,7 +8225,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (413) +--R (3) --R 9 2 8 9 10 11 --R (5040A a b + 22680B a b )x log(x) + 252B b x --R + @@ -8089,7 +8253,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (414) 0 +--R (4) 0 --R Type: Expression(Integer) --E 414 @@ -8097,15 +8261,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (415) 0 +--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 (416) +--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 + @@ -8134,7 +8300,7 @@ 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-_ 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 (417) +--R (2) --R 10 9 10 10 11 --R (2520A b + 25200B a b )x log(x) + 2520B b x --R + @@ -8162,7 +8328,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (418) +--R (3) --R 10 9 10 10 11 --R (2520A b + 25200B a b )x log(x) + 2520B b x --R + @@ -8190,7 +8356,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (419) 0 +--R (4) 0 --R Type: Expression(Integer) --E 419 @@ -8198,15 +8364,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (420) 0 +--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 (421) +--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 + @@ -8234,7 +8402,7 @@ 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-_ 10*a*b^9*B/x-1/11*A*(a+b*x)^11/(a*x^11)+b^10*B*log(x) --R --R ---R (422) +--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 + @@ -8262,7 +8430,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (423) +--R (3) --R 10 11 10 9 10 --R 27720B b x log(x) + (- 27720A b - 277200B a b )x --R + @@ -8290,10 +8458,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 11 ---R A b ---R (424) ----- ---R 11a +--R 11 +--R A b +--R (4) ----- +--R 11a --R Type: Expression(Integer) --E 424 @@ -8301,15 +8469,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (425) 0 +--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 (426) +--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 + @@ -8334,7 +8504,7 @@ t0:=(a+b*x)^10*(A+B*x)/x^13 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 (427) +--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 @@ -8367,7 +8537,7 @@ 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) a0:=integrate(t0,x) --R --R ---R (428) +--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 + @@ -8392,11 +8562,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 12 11 ---R - A b + 12B a b ---R (429) ------------------- ---R 2 ---R 132a +--R 12 11 +--R - A b + 12B a b +--R (4) ------------------- +--R 2 +--R 132a --R Type: Expression(Integer) --E 429 @@ -8404,15 +8574,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (430) 0 +--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 (431) +--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 + @@ -8438,7 +8610,7 @@ 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 (432) +--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 @@ -8471,7 +8643,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (433) +--R (3) --R 10 11 10 9 10 --R - 858B b x + (- 572A b - 5720B a b )x --R + @@ -8499,11 +8671,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 13 12 ---R 2A b - 13B a b ---R (434) ------------------ ---R 3 ---R 1716a +--R 13 12 +--R 2A b - 13B a b +--R (4) ------------------ +--R 3 +--R 1716a --R Type: Expression(Integer) --E 434 @@ -8511,15 +8683,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (435) 0 +--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 (436) +--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 + @@ -8546,7 +8720,7 @@ 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)-_ 1/12012*b^2*(3*A*b-14*a*B)*(a+b*x)^11/(a^4*x^11) --R --R ---R (437) +--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 @@ -8580,7 +8754,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (438) +--R (3) --R 10 11 10 9 10 --R - 4004B b x + (- 3003A b - 30030B a b )x --R + @@ -8608,11 +8782,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 14 13 ---R - 3A b + 14B a b ---R (439) -------------------- ---R 4 ---R 12012a +--R 14 13 +--R - 3A b + 14B a b +--R (4) -------------------- +--R 4 +--R 12012a --R Type: Expression(Integer) --E 439 @@ -8620,15 +8794,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (440) 0 +--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 (441) +--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 + @@ -8656,7 +8832,7 @@ 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)-_ 1/60060*b^3*(4*A*b-15*a*B)*(a+b*x)^11/(a^5*x^11) --R --R ---R (442) +--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 @@ -8690,7 +8866,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (443) +--R (3) --R 10 11 10 9 10 --R - 15015B b x + (- 12012A b - 120120B a b )x --R + @@ -8718,11 +8894,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 15 14 ---R 4A b - 15B a b ---R (444) ------------------ ---R 5 ---R 60060a +--R 15 14 +--R 4A b - 15B a b +--R (4) ------------------ +--R 5 +--R 60060a --R Type: Expression(Integer) --E 444 @@ -8730,15 +8906,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (445) 0 +--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 (446) +--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 + @@ -8767,7 +8945,7 @@ 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)-_ 1/240240*b^4*(5*A*b-16*a*B)*(a+b*x)^11/(a^6*x^11) --R --R ---R (447) +--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 @@ -8801,7 +8979,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (448) +--R (3) --R 10 11 10 9 10 --R - 48048B b x + (- 40040A b - 400400B a b )x --R + @@ -8829,11 +9007,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 16 15 ---R - 5A b + 16B a b ---R (449) -------------------- ---R 6 ---R 240240a +--R 16 15 +--R - 5A b + 16B a b +--R (4) -------------------- +--R 6 +--R 240240a --R Type: Expression(Integer) --E 449 @@ -8841,15 +9019,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (450) 0 +--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 (451) +--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 + @@ -8879,7 +9059,7 @@ 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)-_ 1/816816*b^5*(6*A*b-17*a*B)*(a+b*x)^11/(a^7*x^11) --R --R ---R (452) +--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 @@ -8913,7 +9093,7 @@ 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)-_ a0:=integrate(t0,x) --R --R ---R (453) +--R (3) --R 10 11 10 9 10 --R - 136136B b x + (- 116688A b - 1166880B a b )x --R + @@ -8950,11 +9130,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 17 16 ---R 6A b - 17B a b ---R (454) ------------------ ---R 7 ---R 816816a +--R 17 16 +--R 6A b - 17B a b +--R (4) ------------------ +--R 7 +--R 816816a --R Type: Expression(Integer) --E 454 @@ -8962,15 +9142,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (455) 0 +--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 (456) +--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 + @@ -9000,7 +9182,7 @@ r0:=-1/18*a^10*A/x^18-1/17*a^9*(10*A*b+a*B)/x^17-_ 1/8*b^9*(A*b+10*a*B)/x^8-1/7*b^10*B/x^7 --R --R ---R (457) +--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 @@ -9030,7 +9212,7 @@ r0:=-1/18*a^10*A/x^18-1/17*a^9*(10*A*b+a*B)/x^17-_ a0:=integrate(t0,x) --R --R ---R (458) +--R (3) --R 10 11 10 9 10 --R - 350064B b x + (- 306306A b - 3063060B a b )x --R + @@ -9067,7 +9249,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (459) 0 +--R (4) 0 --R Type: Expression(Integer) --E 459 @@ -9075,15 +9257,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (460) 0 +--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 (461) +--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 + @@ -9113,7 +9297,7 @@ r0:=-1/19*a^10*A/x^19-1/18*a^9*(10*A*b+a*B)/x^18-_ 1/9*b^9*(A*b+10*a*B)/x^9-1/8*b^10*B/x^8 --R --R ---R (462) +--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 @@ -9143,7 +9327,7 @@ r0:=-1/19*a^10*A/x^19-1/18*a^9*(10*A*b+a*B)/x^18-_ a0:=integrate(t0,x) --R --R ---R (463) +--R (3) --R 10 11 10 9 10 --R - 831402B b x + (- 739024A b - 7390240B a b )x --R + @@ -9183,7 +9367,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (464) 0 +--R (4) 0 --R Type: Expression(Integer) --E 464 @@ -9191,15 +9375,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (465) 0 +--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 (466) +--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 + @@ -9229,7 +9415,7 @@ r0:=-1/20*a^10*A/x^20-1/19*a^9*(10*A*b+a*B)/x^19-_ 1/10*b^9*(A*b+10*a*B)/x^10-1/9*b^10*B/x^9 --R --R ---R (467) +--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 @@ -9259,7 +9445,7 @@ r0:=-1/20*a^10*A/x^20-1/19*a^9*(10*A*b+a*B)/x^19-_ a0:=integrate(t0,x) --R --R ---R (468) +--R (3) --R 10 11 10 9 10 --R - 1847560B b x + (- 1662804A b - 16628040B a b )x --R + @@ -9299,7 +9485,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (469) 0 +--R (4) 0 --R Type: Expression(Integer) --E 469 @@ -9307,15 +9493,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (470) 0 +--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 (471) +--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 + @@ -9363,7 +9551,7 @@ r0:=1/21*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^21)-_ 1/10*b^10*B/(e^12*(d+e*x)^10) --R --R ---R (472) +--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 @@ -9583,7 +9771,7 @@ r0:=1/21*(b*d-a*e)^10*(B*d-A*e)/(e^12*(d+e*x)^21)-_ a0:=integrate(t0,x) --R --R ---R (473) +--R (3) --R 10 11 11 --R - 3879876B b e x --R + @@ -9823,7 +10011,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (474) 0 +--R (4) 0 --R Type: Expression(Integer) --E 474 @@ -9831,15 +10019,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (475) 0 +--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 (476) +--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 + @@ -9857,7 +10047,7 @@ 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+_ 1/6*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 (477) +--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 + @@ -9919,7 +10109,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (478) +--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 + @@ -9975,7 +10165,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (479) +--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 + @@ -9991,15 +10181,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (480) 0 +--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 (481) +--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 + @@ -10016,7 +10208,7 @@ 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+_ 1/5*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 (482) +--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 + @@ -10066,7 +10258,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (483) +--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 + @@ -10110,7 +10302,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (484) +--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 + @@ -10126,15 +10318,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (485) 0 +--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 (486) +--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 ---------------------------------------------------------------------------- @@ -10148,7 +10342,7 @@ 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+_ (A*b-a*B)*(b*d-a*e)^3*log(a+b*x)/b^5 --R --R ---R (487) +--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 + @@ -10183,7 +10377,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (488) +--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 + @@ -10215,11 +10409,11 @@ a0:=integrate(t0,x) 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 (489) -------------------------------------------------------- ---R 3 ---R 12b e +--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 @@ -10227,18 +10421,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (490) 0 +--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 (491) ---------------------------------------------------- ---R b x + a +--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 @@ -10247,7 +10443,7 @@ 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 (492) +--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 + @@ -10274,7 +10470,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (493) +--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 * @@ -10295,11 +10491,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 3 ---R (- 3A b + 3B a)d e - 2B b d ---R (494) ---------------------------- ---R 2 ---R 6b e +--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 @@ -10307,18 +10503,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (495) 0 +--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 (496) --------------------------- ---R b x + a +--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 @@ -10326,7 +10524,7 @@ t0:=(A+B*x)*(d+e*x)/(a+b*x) 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 (497) +--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 + @@ -10342,7 +10540,7 @@ 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 a0:=integrate(t0,x) --R --R ---R (498) +--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 + @@ -10358,10 +10556,10 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 ---R A e ---R (499) - ---- ---R 2B b +--R 2 +--R A e +--R (4) - ---- +--R 2B b --R Type: Expression(Integer) --E 499 @@ -10369,17 +10567,19 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (500) 0 +--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 (501) ------- ---R b x + a +--R B x + A +--R (1) ------- +--R b x + a --R Type: Fraction(Polynomial(Integer)) --E 501 @@ -10387,10 +10587,10 @@ t0:=(A+B*x)/(a+b*x) 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 (502) ------------------------------- ---R 2 ---R b +--R (A b - B a)log(b x + a) + B b x +--R (2) ------------------------------- +--R 2 +--R b --R Type: Expression(Integer) --E 502 @@ -10398,10 +10598,10 @@ r0:=B*x/b+(A*b-a*B)*log(a+b*x)/b^2 a0:=integrate(t0,x) --R --R ---R (A b - B a)log(b x + a) + B b x ---R (503) ------------------------------- ---R 2 ---R b +--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 @@ -10409,7 +10609,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (504) 0 +--R (4) 0 --R Type: Expression(Integer) --E 504 @@ -10417,18 +10617,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (505) 0 +--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 (506) --------------------------- ---R 2 ---R b e x + (a e + b d)x + a d +--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 @@ -10436,10 +10638,10 @@ t0:=(A+B*x)/((a+b*x)*(d+e*x)) 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 (507) --------------------------------------------------------- ---R 2 2 ---R a b e - b d e +--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 @@ -10447,10 +10649,10 @@ 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)) 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 (508) --------------------------------------------------------- ---R 2 2 ---R a b e - b d e +--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 @@ -10458,7 +10660,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (509) 0 +--R (4) 0 --R Type: Expression(Integer) --E 509 @@ -10466,18 +10668,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (510) 0 +--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 (511) ---------------------------------------------------- ---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 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 @@ -10486,7 +10690,7 @@ 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 (512) +--R (2) --R 2 --R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) --R + @@ -10505,7 +10709,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (513) +--R (3) --R 2 --R ((- A b + B a)e x + (- A b + B a)d e)log(e x + d) --R + @@ -10524,7 +10728,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (514) 0 +--R (4) 0 --R Type: Expression(Integer) --E 514 @@ -10532,15 +10736,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (515) 0 +--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 (516) +--R (1) --R B x + A --R ---------------------------------------------------------------------------- --R 3 4 3 2 3 2 2 2 2 3 3 @@ -10553,7 +10759,7 @@ 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 (517) +--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 * @@ -10588,7 +10794,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (518) +--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 * @@ -10623,7 +10829,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (519) 0 +--R (4) 0 --R Type: Expression(Integer) --E 519 @@ -10631,15 +10837,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (520) 0 +--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 (521) +--R (1) --R B x + A --R / --R 4 5 4 3 4 3 2 2 3 @@ -10657,7 +10865,7 @@ r0:=1/3*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^3)+_ 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 (522) +--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 + @@ -10709,7 +10917,7 @@ r0:=1/3*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^3)+_ a0:=integrate(t0,x) --R --R ---R (523) +--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 + @@ -10761,7 +10969,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (524) 0 +--R (4) 0 --R Type: Expression(Integer) --E 524 @@ -10769,15 +10977,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (525) 0 +--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 (526) +--R (1) --R B x + A --R / --R 5 6 5 4 5 4 2 3 4 @@ -10796,7 +11006,7 @@ r0:=1/4*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^4)+_ 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 (527) +--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 + @@ -10889,7 +11099,7 @@ r0:=1/4*(-B*d+A*e)/(e*(b*d-a*e)*(d+e*x)^4)+_ a0:=integrate(t0,x) --R --R ---R (528) +--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 + @@ -10982,7 +11192,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (529) 0 +--R (4) 0 --R Type: Expression(Integer) --E 529 @@ -10990,15 +11200,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (530) 0 +--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 (531) +--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 + @@ -11019,7 +11231,7 @@ r0:=5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*x/b^6-_ 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 (532) +--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 + @@ -11095,7 +11307,7 @@ r0:=5*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*x/b^6-_ a0:=integrate(t0,x) --R --R ---R (533) +--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 + @@ -11171,7 +11383,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (534) +--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 + @@ -11187,15 +11399,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (535) 0 +--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 (536) +--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 + @@ -11215,7 +11429,7 @@ r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-_ 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 (537) +--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 + @@ -11273,7 +11487,7 @@ r0:=2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-_ a0:=integrate(t0,x) --R --R ---R (538) +--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 + @@ -11331,11 +11545,11 @@ a0:=integrate(t0,x) 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 (539) ---------------------------------------------------------------- ---R 6 ---R 12b +--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 @@ -11343,15 +11557,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (540) 0 +--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 (541) +--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 ---------------------------------------------------------------------------- @@ -11367,7 +11583,7 @@ r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-_ 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 (542) +--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 + @@ -11408,7 +11624,7 @@ r0:=3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-_ a0:=integrate(t0,x) --R --R ---R (543) +--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 + @@ -11449,11 +11665,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 3 3 2 2 ---R (- 3A a b + 10B a )e - 9B a b d e ---R (544) ----------------------------------- ---R 5 ---R 6b +--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 @@ -11461,19 +11677,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (545) 0 +--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 (546) ---------------------------------------------------- ---R 2 2 2 ---R b x + 2a b x + a +--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 @@ -11483,7 +11701,7 @@ 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-_ (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4 --R --R ---R (547) +--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 + @@ -11510,7 +11728,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (548) +--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 + @@ -11537,7 +11755,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (549) 0 +--R (4) 0 --R Type: Expression(Integer) --E 549 @@ -11545,19 +11763,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (550) 0 +--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 (551) --------------------------- ---R 2 2 2 ---R b x + 2a b x + a +--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 @@ -11566,7 +11786,7 @@ 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 (552) +--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 + @@ -11582,7 +11802,7 @@ r0:=B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+_ a0:=integrate(t0,x) --R --R ---R (553) +--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 + @@ -11598,7 +11818,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (554) 0 +--R (4) 0 --R Type: Expression(Integer) --E 554 @@ -11606,18 +11826,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (555) 0 +--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 (556) ------------------ ---R 2 2 2 ---R b x + 2a b x + a +--R B x + A +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) --E 556 @@ -11625,10 +11847,10 @@ t0:=(A+B*x)/(a+b*x)^2 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 (557) ------------------------------------- ---R 3 2 ---R b x + a b +--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 @@ -11636,10 +11858,10 @@ r0:=(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2 a0:=integrate(t0,x) --R --R ---R (B b x + B a)log(b x + a) - A b + B a ---R (558) ------------------------------------- ---R 3 2 ---R b x + a b +--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 @@ -11647,7 +11869,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (559) 0 +--R (4) 0 --R Type: Expression(Integer) --E 559 @@ -11655,18 +11877,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (560) 0 +--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 (561) ------------------------------------------------- ---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 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 @@ -11675,7 +11899,7 @@ 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 (562) +--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 + @@ -11694,7 +11918,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (563) +--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 + @@ -11713,7 +11937,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (564) 0 +--R (4) 0 --R Type: Expression(Integer) --E 564 @@ -11721,15 +11945,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (565) 0 +--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 (566) +--R (1) --R B x + A --R / --R 2 2 4 2 2 3 2 2 2 2 2 @@ -11746,7 +11972,7 @@ 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(d+e*x)/(b*d-a*e)^3 --R --R ---R (567) +--R (2) --R 2 2 2 2 --R ((- 2A b + B a b)e + B b d e)x --R + @@ -11790,7 +12016,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (568) +--R (3) --R 2 2 2 2 --R ((- 2A b + B a b)e + B b d e)x --R + @@ -11834,7 +12060,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (569) 0 +--R (4) 0 --R Type: Expression(Integer) --E 569 @@ -11842,15 +12068,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (570) 0 +--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 (571) +--R (1) --R B x + A --R / --R 2 3 5 3 2 2 4 2 3 2 2 2 3 @@ -11868,7 +12096,7 @@ r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*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 (572) +--R (2) --R 3 2 3 3 2 3 --R ((6A b - 4B a b )e - 2B b d e )x --R + @@ -11932,7 +12160,7 @@ r0:=-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/_ a0:=integrate(t0,x) --R --R ---R (573) +--R (3) --R 3 2 3 3 2 3 --R ((6A b - 4B a b )e - 2B b d e )x --R + @@ -11996,7 +12224,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (574) 0 +--R (4) 0 --R Type: Expression(Integer) --E 574 @@ -12004,15 +12232,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (575) 0 +--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 (576) +--R (1) --R B x + A --R / --R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 @@ -12035,7 +12265,7 @@ r0:=-b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x))+_ 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 (577) +--R (2) --R 4 3 4 4 3 4 --R ((- 24A b + 18B a b )e + 6B b d e )x --R + @@ -12146,7 +12376,7 @@ r0:=-b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x))+_ a0:=integrate(t0,x) --R --R ---R (578) +--R (3) --R 4 3 4 4 3 4 --R ((- 24A b + 18B a b )e + 6B b d e )x --R + @@ -12257,7 +12487,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (579) 0 +--R (4) 0 --R Type: Expression(Integer) --E 579 @@ -12265,15 +12495,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (580) 0 +--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 (581) +--R (1) --R B x + A --R / --R 2 5 7 5 2 4 6 2 5 4 2 2 3 5 @@ -12297,7 +12529,7 @@ r0:=-b^3*(A*b-a*B)/((b*d-a*e)^5*(a+b*x))+_ 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 (582) +--R (2) --R 5 4 5 5 4 5 --R ((60A b - 48B a b )e - 12B b d e )x --R + @@ -12470,7 +12702,7 @@ r0:=-b^3*(A*b-a*B)/((b*d-a*e)^5*(a+b*x))+_ a0:=integrate(t0,x) --R --R ---R (583) +--R (3) --R 5 4 5 5 4 5 --R ((60A b - 48B a b )e - 12B b d e )x --R + @@ -12643,7 +12875,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (584) 0 +--R (4) 0 --R Type: Expression(Integer) --E 584 @@ -12651,15 +12883,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (585) 0 +--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 (586) +--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 + @@ -12681,7 +12915,7 @@ r0:=10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*x/b^6-_ (b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^7 --R --R ---R (587) +--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 + @@ -12769,7 +13003,7 @@ r0:=10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*x/b^6-_ a0:=integrate(t0,x) --R --R ---R (588) +--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 + @@ -12857,11 +13091,11 @@ a0:=integrate(t0,x) 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 (589) ----------------------------------------------------------------- ---R 7 ---R 12b +--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 @@ -12869,15 +13103,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (590) 0 +--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 (591) +--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 + @@ -12898,7 +13134,7 @@ r0:=2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*x/b^5-_ (2*b*B*d+3*A*b*e-5*a*B*e)*log(a+b*x)/b^6 --R --R ---R (592) +--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 + @@ -12959,7 +13195,7 @@ r0:=2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*x/b^5-_ a0:=integrate(t0,x) --R --R ---R (593) +--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 + @@ -13020,11 +13256,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 3 4 2 3 ---R (- 3A a b + 13B a )e - 12B a b d e ---R (594) ------------------------------------ ---R 6 ---R 6b +--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 @@ -13032,15 +13268,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (595) 0 +--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 (596) +--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 ---------------------------------------------------------------------------- @@ -13056,7 +13294,7 @@ 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-_ 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 (597) +--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 + @@ -13097,7 +13335,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (598) +--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 + @@ -13138,7 +13376,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (599) 0 +--R (4) 0 --R Type: Expression(Integer) --E 599 @@ -13146,19 +13384,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (600) 0 +--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 (601) ---------------------------------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -13168,7 +13408,7 @@ r0:=B*e^2*x/b^3-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)^2)-_ e*(2*b*B*d+A*b*e-3*a*B*e)*log(a+b*x)/b^4 --R --R ---R (602) +--R (2) --R 3 2 2 3 2 --R ((2A b - 6B a b )e + 4B b d e)x --R + @@ -13195,7 +13435,7 @@ r0:=B*e^2*x/b^3-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)^2)-_ a0:=integrate(t0,x) --R --R ---R (603) +--R (3) --R 3 2 2 3 2 --R ((2A b - 6B a b )e + 4B b d e)x --R + @@ -13222,7 +13462,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (604) 0 +--R (4) 0 --R Type: Expression(Integer) --E 604 @@ -13230,19 +13470,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (605) 0 +--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 (606) ---------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -13251,7 +13493,7 @@ 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 (607) +--R (2) --R 2 2 2 --R (2B b e x + 4B a b e x + 2B a e)log(b x + a) --R + @@ -13267,7 +13509,7 @@ r0:=-1/2*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^2)+_ a0:=integrate(t0,x) --R --R ---R (608) +--R (3) --R 2 2 2 --R (2B b e x + 4B a b e x + 2B a e)log(b x + a) --R + @@ -13283,7 +13525,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (609) 0 +--R (4) 0 --R Type: Expression(Integer) --E 609 @@ -13291,18 +13533,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (610) 0 +--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 (611) ---------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -13310,12 +13554,12 @@ t0:=(A+B*x)/(a+b*x)^3 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 (612) ------------------------------------------------------ ---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 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 @@ -13323,10 +13567,10 @@ r0:=-1/2*(A+B*x)^2/((A*b-a*B)*(a+b*x)^2) a0:=integrate(t0,x) --R --R ---R - 2B b x - A b - B a ---R (613) ---------------------- ---R 4 2 3 2 2 ---R 2b x + 4a b x + 2a b +--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 @@ -13334,11 +13578,11 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R 2 ---R B ---R (614) --------------- ---R 3 2 ---R 2A b - 2B a b +--R 2 +--R B +--R (4) --------------- +--R 3 2 +--R 2A b - 2B a b --R Type: Expression(Integer) --E 614 @@ -13346,15 +13590,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (615) 0 +--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 (616) +--R (1) --R B x + A --R ----------------------------------------------------------------------- --R 3 4 2 3 3 2 2 2 3 2 3 @@ -13367,7 +13613,7 @@ 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 (617) +--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 + @@ -13405,7 +13651,7 @@ 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))-_ a0:=integrate(t0,x) --R --R ---R (618) +--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 + @@ -13443,7 +13689,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (619) 0 +--R (4) 0 --R Type: Expression(Integer) --E 619 @@ -13451,15 +13697,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (620) 0 +--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 (621) +--R (1) --R B x + A --R / --R 3 2 5 2 2 3 4 2 2 2 3 2 3 @@ -13478,7 +13726,7 @@ r0:=1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^2)+_ e*(2*b*B*d-3*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^4 --R --R ---R (622) +--R (2) --R 3 2 3 3 2 3 --R ((- 6A b + 2B a b )e + 4B b d e )x --R + @@ -13542,7 +13790,7 @@ r0:=1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^2)+_ a0:=integrate(t0,x) --R --R ---R (623) +--R (3) --R 3 2 3 3 2 3 --R ((- 6A b + 2B a b )e + 4B b d e )x --R + @@ -13606,7 +13854,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (624) 0 +--R (4) 0 --R Type: Expression(Integer) --E 624 @@ -13614,15 +13862,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (625) 0 +--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 (626) +--R (1) --R B x + A --R / --R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 @@ -13645,7 +13895,7 @@ r0:=-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^2)-_ 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 (627) +--R (2) --R 4 3 4 4 3 4 --R ((12A b - 6B a b )e - 6B b d e )x --R + @@ -13756,7 +14006,7 @@ r0:=-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^2)-_ a0:=integrate(t0,x) --R --R ---R (628) +--R (3) --R 4 3 4 4 3 4 --R ((12A b - 6B a b )e - 6B b d e )x --R + @@ -13867,7 +14117,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (629) 0 +--R (4) 0 --R Type: Expression(Integer) --E 629 @@ -13875,15 +14125,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (630) 0 +--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 (631) +--R (1) --R B x + A --R / --R 3 4 7 2 4 3 3 6 2 4 2 3 3 2 2 5 @@ -13910,7 +14162,7 @@ r0:=-1/2*b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x)^2)-_ 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 (632) +--R (2) --R 5 4 5 5 4 5 --R ((- 60A b + 36B a b )e + 24B b d e )x --R + @@ -14088,7 +14340,7 @@ r0:=-1/2*b^2*(A*b-a*B)/((b*d-a*e)^4*(a+b*x)^2)-_ a0:=integrate(t0,x) --R --R ---R (633) +--R (3) --R 5 4 5 5 4 5 --R ((- 60A b + 36B a b )e + 24B b d e )x --R + @@ -14266,7 +14518,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (634) 0 +--R (4) 0 --R Type: Expression(Integer) --E 634 @@ -14274,15 +14526,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (635) 0 +--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 (636) +--R (1) --R 3 5 3 2 4 --R B b e x + ((A b + B a)e + 3B b d e )x --R + @@ -14305,7 +14559,7 @@ 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 (637) +--R (2) --R 6 6 6 5 5 --R 198B b e x + ((234A b + 234B a)e + 720B b d e )x --R + @@ -14336,7 +14590,7 @@ r0:=2/9*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(9/2)/e^3-_ a0:=integrate(t0,x) --R --R ---R (638) +--R (3) --R 6 6 6 5 5 --R 198B b e x + ((234A b + 234B a)e + 720B b d e )x --R + @@ -14367,7 +14621,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (639) 0 +--R (4) 0 --R Type: Expression(Integer) --E 639 @@ -14375,15 +14629,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (640) 0 +--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 (641) +--R (1) --R 2 4 2 3 --R B b e x + ((A b + B a)e + 2B b d e)x --R + @@ -14403,7 +14659,7 @@ 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 (642) +--R (2) --R 5 5 5 4 4 --R 126B b e x + ((154A b + 154B a)e + 322B b d e )x --R + @@ -14431,7 +14687,7 @@ r0:=2/7*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(7/2)/e^3-_ a0:=integrate(t0,x) --R --R ---R (643) +--R (3) --R 5 5 5 4 4 --R 126B b e x + ((154A b + 154B a)e + 322B b d e )x --R + @@ -14459,7 +14715,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (644) 0 +--R (4) 0 --R Type: Expression(Integer) --E 644 @@ -14467,15 +14723,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (645) 0 +--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 (646) +--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 * @@ -14489,7 +14747,7 @@ 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 (647) +--R (2) --R 4 4 4 3 3 --R 70B b e x + ((90A b + 90B a)e + 100B b d e )x --R + @@ -14514,7 +14772,7 @@ r0:=2/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(5/2)/e^3-_ a0:=integrate(t0,x) --R --R ---R (648) +--R (3) --R 4 4 4 3 3 --R 70B b e x + ((90A b + 90B a)e + 100B b d e )x --R + @@ -14539,7 +14797,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (649) 0 +--R (4) 0 --R Type: Expression(Integer) --E 649 @@ -14547,16 +14805,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (650) 0 +--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 (651) (B b x + (A b + B a)x + A a)\|e x + d +--R 2 +-------+ +--R (1) (B b x + (A b + B a)x + A a)\|e x + d --R Type: Expression(Integer) --E 651 @@ -14565,7 +14825,7 @@ 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 (652) +--R (2) --R 3 3 3 2 2 --R 30B b e x + ((42A b + 42B a)e + 6B b d e )x --R + @@ -14587,7 +14847,7 @@ r0:=2/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(3/2)/e^3-_ a0:=integrate(t0,x) --R --R ---R (653) +--R (3) --R 3 3 3 2 2 --R 30B b e x + ((42A b + 42B a)e + 6B b d e )x --R + @@ -14609,7 +14869,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (654) 0 +--R (4) 0 --R Type: Expression(Integer) --E 654 @@ -14617,19 +14877,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (655) 0 +--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 (656) --------------------------- ---R +-------+ ---R \|e x + d +--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 @@ -14638,7 +14900,7 @@ 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 (657) +--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 + @@ -14657,7 +14919,7 @@ r0:=-2/3*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^3+_ a0:=integrate(t0,x) --R --R ---R (658) +--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 + @@ -14676,7 +14938,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (659) 0 +--R (4) 0 --R Type: Expression(Integer) --E 659 @@ -14684,19 +14946,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (660) 0 +--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 (661) --------------------------- ---R +-------+ ---R (e x + d)\|e x + d +--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 @@ -14705,7 +14969,7 @@ 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 (662) +--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 + @@ -14721,7 +14985,7 @@ 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))-_ a0:=integrate(t0,x) --R --R ---R (663) +--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 + @@ -14737,7 +15001,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (664) 0 +--R (4) 0 --R Type: Expression(Integer) --E 664 @@ -14745,19 +15009,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (665) 0 +--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 (666) ------------------------------ ---R 2 2 2 +-------+ ---R (e x + 2d e x + d )\|e x + d +--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 @@ -14766,7 +15032,7 @@ 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 (667) +--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 + @@ -14782,7 +15048,7 @@ r0:=-2/3*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(3/2))+_ a0:=integrate(t0,x) --R --R ---R (668) +--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 + @@ -14798,7 +15064,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (669) 0 +--R (4) 0 --R Type: Expression(Integer) --E 669 @@ -14806,19 +15072,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (670) 0 +--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 (671) ---------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (e x + 3d e x + 3d e x + d )\|e x + d +--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 @@ -14827,7 +15095,7 @@ 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 (672) +--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 + @@ -14843,7 +15111,7 @@ r0:=-2/5*(b*d-a*e)*(B*d-A*e)/(e^3*(d+e*x)^(5/2))+_ a0:=integrate(t0,x) --R --R ---R (673) +--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 + @@ -14859,7 +15127,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (674) 0 +--R (4) 0 --R Type: Expression(Integer) --E 674 @@ -14867,15 +15135,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (675) 0 +--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 (676) +--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 + @@ -14903,7 +15173,7 @@ r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+_ 2/15*b^2*B*(d+e*x)^(15/2)/e^4 --R --R ---R (677) +--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 + @@ -14969,7 +15239,7 @@ r0:=-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+_ a0:=integrate(t0,x) --R --R ---R (678) +--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 + @@ -15035,7 +15305,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (679) 0 +--R (4) 0 --R Type: Expression(Integer) --E 679 @@ -15043,15 +15313,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (680) 0 +--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 (681) +--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 + @@ -15076,7 +15348,7 @@ r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+_ 2/13*b^2*B*(d+e*x)^(13/2)/e^4 --R --R ---R (682) +--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 + @@ -15133,7 +15405,7 @@ r0:=-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+_ a0:=integrate(t0,x) --R --R ---R (683) +--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 + @@ -15190,7 +15462,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (684) 0 +--R (4) 0 --R Type: Expression(Integer) --E 684 @@ -15198,15 +15470,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (685) 0 +--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 (686) +--R (1) --R 2 4 2 2 3 --R B b e x + ((A b + 2B a b)e + B b d)x --R + @@ -15228,7 +15502,7 @@ r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+_ 2/11*b^2*B*(d+e*x)^(11/2)/e^4 --R --R ---R (687) +--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 + @@ -15270,7 +15544,7 @@ r0:=-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+_ a0:=integrate(t0,x) --R --R ---R (688) +--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 + @@ -15312,7 +15586,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (689) 0 +--R (4) 0 --R Type: Expression(Integer) --E 689 @@ -15320,16 +15594,18 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (690) 0 +--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 (691) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )\|e x + d +--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 @@ -15340,7 +15616,7 @@ r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+_ 2/9*b^2*B*(d+e*x)^(9/2)/e^4 --R --R ---R (692) +--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 + @@ -15373,7 +15649,7 @@ r0:=-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+_ a0:=integrate(t0,x) --R --R ---R (693) +--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 + @@ -15406,7 +15682,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (694) 0 +--R (4) 0 --R Type: Expression(Integer) --E 694 @@ -15414,19 +15690,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (695) 0 +--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 (696) ---------------------------------------------------- ---R +-------+ ---R \|e x + d +--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 @@ -15436,7 +15714,7 @@ 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-_ 2/7*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 (697) +--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 + @@ -15461,7 +15739,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (698) +--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 + @@ -15486,7 +15764,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (699) 0 +--R (4) 0 --R Type: Expression(Integer) --E 699 @@ -15494,19 +15772,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (700) 0 +--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 (701) ---------------------------------------------------- ---R +-------+ ---R (e x + d)\|e x + d +--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 @@ -15516,7 +15796,7 @@ r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+_ 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 (702) +--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 + @@ -15535,7 +15815,7 @@ r0:=-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+_ a0:=integrate(t0,x) --R --R ---R (703) +--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 + @@ -15554,7 +15834,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (704) 0 +--R (4) 0 --R Type: Expression(Integer) --E 704 @@ -15562,19 +15842,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (705) 0 +--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 (706) ---------------------------------------------------- ---R 2 2 2 +-------+ ---R (e x + 2d e x + d )\|e x + d +--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 @@ -15585,7 +15867,7 @@ r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+_ 2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4 --R --R ---R (707) +--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 + @@ -15604,7 +15886,7 @@ r0:=2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+_ a0:=integrate(t0,x) --R --R ---R (708) +--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 + @@ -15623,7 +15905,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (709) 0 +--R (4) 0 --R Type: Expression(Integer) --E 709 @@ -15631,19 +15913,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (710) 0 +--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 (711) ---------------------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (e x + 3d e x + 3d e x + d )\|e x + d +--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 @@ -15653,7 +15937,7 @@ r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-_ 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 (712) +--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 + @@ -15672,7 +15956,7 @@ r0:=2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-_ a0:=integrate(t0,x) --R --R ---R (713) +--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 + @@ -15691,7 +15975,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (714) 0 +--R (4) 0 --R Type: Expression(Integer) --E 714 @@ -15699,15 +15983,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (715) 0 +--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 (716) +--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 + @@ -15751,7 +16037,7 @@ r0:=2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)/e^5-_ 2/17*b^3*B*(d+e*x)^(17/2)/e^5 --R --R ---R (717) +--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 + @@ -15838,7 +16124,7 @@ r0:=2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)/e^5-_ a0:=integrate(t0,x) --R --R ---R (718) +--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 + @@ -15925,7 +16211,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (719) 0 +--R (4) 0 --R Type: Expression(Integer) --E 719 @@ -15933,15 +16219,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (720) 0 +--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 (721) +--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 + @@ -15970,7 +16258,7 @@ r0:=2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)/e^5-_ 2/15*b^3*B*(d+e*x)^(15/2)/e^5 --R --R ---R (722) +--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 + @@ -16045,7 +16333,7 @@ r0:=2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)/e^5-_ a0:=integrate(t0,x) --R --R ---R (723) +--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 + @@ -16120,7 +16408,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (724) 0 +--R (4) 0 --R Type: Expression(Integer) --E 724 @@ -16128,15 +16416,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (725) 0 +--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 (726) +--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 + @@ -16162,7 +16452,7 @@ 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-_ 2/13*b^3*B*(d+e*x)^(13/2)/e^5 --R --R ---R (727) +--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 + @@ -16222,7 +16512,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (728) +--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 + @@ -16282,7 +16572,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (729) 0 +--R (4) 0 --R Type: Expression(Integer) --E 729 @@ -16290,15 +16580,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (730) 0 +--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 (731) +--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 + @@ -16318,7 +16610,7 @@ 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-_ 2/11*b^3*B*(d+e*x)^(11/2)/e^5 --R --R ---R (732) +--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 + @@ -16360,7 +16652,7 @@ 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-_ a0:=integrate(t0,x) --R --R ---R (733) +--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 + @@ -16402,7 +16694,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (734) 0 +--R (4) 0 --R Type: Expression(Integer) --E 734 @@ -16410,15 +16702,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (735) 0 +--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 (736) +--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 ---------------------------------------------------------------------------- @@ -16434,7 +16728,7 @@ 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+_ 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 (737) +--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 + @@ -16467,7 +16761,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (738) +--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 + @@ -16500,7 +16794,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (739) 0 +--R (4) 0 --R Type: Expression(Integer) --E 739 @@ -16508,15 +16802,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (740) 0 +--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 (741) +--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 ---------------------------------------------------------------------------- @@ -16532,7 +16828,7 @@ 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*(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 (742) +--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 + @@ -16562,7 +16858,7 @@ r0:=2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/e^5-_ a0:=integrate(t0,x) --R --R ---R (743) +--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 + @@ -16592,7 +16888,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (744) 0 +--R (4) 0 --R Type: Expression(Integer) --E 744 @@ -16600,15 +16896,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (745) 0 +--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 (746) +--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 ---------------------------------------------------------------------------- @@ -16625,7 +16923,7 @@ r0:=-2/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(3/2))-_ (2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/e^5 --R --R ---R (747) +--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 + @@ -16655,7 +16953,7 @@ r0:=-2/3*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(3/2))-_ a0:=integrate(t0,x) --R --R ---R (748) +--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 + @@ -16685,7 +16983,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (749) 0 +--R (4) 0 --R Type: Expression(Integer) --E 749 @@ -16693,15 +16991,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (750) 0 +--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 (751) +--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 ---------------------------------------------------------------------------- @@ -16718,7 +17018,7 @@ r0:=-2/5*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(5/2))+_ 2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/e^5 --R --R ---R (752) +--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 + @@ -16748,7 +17048,7 @@ r0:=-2/5*(b*d-a*e)^3*(B*d-A*e)/(e^5*(d+e*x)^(5/2))+_ a0:=integrate(t0,x) --R --R ---R (753) +--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 + @@ -16778,7 +17078,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (754) 0 +--R (4) 0 --R Type: Expression(Integer) --E 754 @@ -16786,15 +17086,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (755) 0 +--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 (756) +--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 + @@ -16817,7 +17119,7 @@ r0:=2/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^(3/2)/b^4+_ (b*d-a*e)^3*sqrt(d+e*x)/b^5 --R --R ---R (757) +--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 + @@ -16868,7 +17170,7 @@ r0:=2/3*(A*b-a*B)*(b*d-a*e)^2*(d+e*x)^(3/2)/b^4+_ a0:=integrate(t0,x) --R --R ---R (758) +--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 @@ -16975,7 +17277,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (759) +--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 + @@ -17010,7 +17312,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (760) 0 +--R (5) 0 --R Type: Expression(Integer) --E 760 @@ -17018,7 +17320,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (761) +--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 + @@ -17054,18 +17356,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (762) 0 +--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 (763) ---------------------------------------------------------------- ---R b x + a +--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 @@ -17077,7 +17381,7 @@ r0:=2/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(3/2)/b^3+_ (b*d-a*e)^2*sqrt(d+e*x)/b^4 --R --R ---R (764) +--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 + @@ -17114,7 +17418,7 @@ r0:=2/3*(A*b-a*B)*(b*d-a*e)*(d+e*x)^(3/2)/b^3+_ a0:=integrate(t0,x) --R --R ---R (765) +--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 @@ -17187,7 +17491,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (766) +--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 * @@ -17216,7 +17520,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (767) 0 +--R (5) 0 --R Type: Expression(Integer) --E 767 @@ -17224,7 +17528,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (768) +--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 * @@ -17254,18 +17558,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (769) 0 +--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 (770) --------------------------------------- ---R b x + a +--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 @@ -17275,7 +17581,7 @@ r0:=2/3*(A*b-a*B)*(d+e*x)^(3/2)/b^2+2/5*B*(d+e*x)^(5/2)/(b*e)-_ 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 (771) +--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 * @@ -17303,7 +17609,7 @@ r0:=2/3*(A*b-a*B)*(d+e*x)^(3/2)/b^2+2/5*B*(d+e*x)^(5/2)/(b*e)-_ a0:=integrate(t0,x) --R --R ---R (772) +--R (3) --R [ --R +-----------+ --R 2 2 2 |- a e + b d @@ -17362,7 +17668,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (773) +--R (4) --R +-----------+ --R 2 2 |- a e + b d +-+ --R ((- A a b + B a )e + (A b - B a b)d) |----------- \|b @@ -17393,7 +17699,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (774) 0 +--R (5) 0 --R Type: Expression(Integer) --E 774 @@ -17401,7 +17707,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (775) +--R (6) --R 2 2 +-----------+ --R ((- 2A a b + 2B a )e + (2A b - 2B a b)d)\|- a e + b d --R * @@ -17428,18 +17734,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (776) 0 +--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 (777) ------------------- ---R b x + a +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R b x + a --R Type: Expression(Integer) --E 777 @@ -17448,7 +17756,7 @@ 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 (778) +--R (2) --R +-+ +-------+ --R +-----------+ \|b \|e x + d --R (- 6A b + 6B a)e\|- a e + b d atanh(--------------) @@ -17467,7 +17775,7 @@ r0:=2/3*B*(d+e*x)^(3/2)/(b*e)-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/_ a0:=integrate(t0,x) --R --R ---R (779) +--R (3) --R [ --R +-----------+ --R |- a e + b d @@ -17509,7 +17817,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (780) +--R (4) --R +-----------+ --R |- a e + b d +-+ --R (A b - B a) |----------- \|b @@ -17537,7 +17845,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (781) 0 +--R (5) 0 --R Type: Expression(Integer) --E 781 @@ -17545,7 +17853,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (782) +--R (6) --R +-+ +-------+ --R +-----------+ \|b \|e x + d --R (2A b - 2B a)\|- a e + b d atanh(--------------) @@ -17569,18 +17877,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (783) 0 +--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 (784) ------------------- ---R +-------+ ---R (b x + a)\|e x + d +--R B x + A +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|e x + d --R Type: Expression(Integer) --E 784 @@ -17589,7 +17899,7 @@ 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 (785) +--R (2) --R +-+ +-------+ --R \|b \|e x + d +-----------+ +-+ +-------+ --R (- 2A b + 2B a)e atanh(--------------) + 2B\|- a e + b d \|b \|e x + d @@ -17605,7 +17915,7 @@ r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*_ a0:=integrate(t0,x) --R --R ---R (786) +--R (3) --R [ --R (A b - B a)e --R * @@ -17639,7 +17949,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (787) +--R (4) --R +-----------+ +-+ --R (A b - B a)\|- a e + b d \|b --R * @@ -17665,7 +17975,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (788) 0 +--R (5) 0 --R Type: Expression(Integer) --E 788 @@ -17673,7 +17983,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (789) +--R (6) --R +-----------+ +-+ +-------+ --R | 2 \|b \|e x + d --R (2A b - 2B a)\|a b e - b d atanh(--------------) @@ -17696,18 +18006,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (790) 0 +--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 (791) --------------------------------------- ---R 2 +-------+ ---R (b e x + (a e + b d)x + a d)\|e x + d +--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 @@ -17716,7 +18028,7 @@ 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 (792) +--R (2) --R +-+ +-------+ --R +-------+ \|b \|e x + d --R (2A b - 2B a)e\|e x + d atanh(--------------) @@ -17735,7 +18047,7 @@ r0:=-2*(A*b-a*B)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ a0:=integrate(t0,x) --R --R ---R (793) +--R (3) --R [ --R +-------+ --R (A b - B a)e\|e x + d @@ -17776,7 +18088,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (794) +--R (4) --R +-----------+ +-+ --R (A b - B a)\|- a e + b d \|b --R * @@ -17802,7 +18114,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (795) 0 +--R (5) 0 --R Type: Expression(Integer) --E 795 @@ -17810,7 +18122,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (796) +--R (6) --R +-----------+ +-+ +-------+ --R | 2 \|b \|e x + d --R (- 2A b + 2B a)\|a b e - b d atanh(--------------) @@ -17833,18 +18145,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (797) 0 +--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 (798) ---------------------------------------------------------------- ---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 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 @@ -17854,7 +18168,7 @@ r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(3/2))-2*(A*b-a*B)*_ (b*d-a*e)^(5/2)+2*(A*b-a*B)/((b*d-a*e)^2*sqrt(d+e*x)) --R --R ---R (799) +--R (2) --R 2 +-+ +-------+ --R ((- 6A b + 6B a)e x + (- 6A b + 6B a)d e)\|b \|e x + d --R * @@ -17879,7 +18193,7 @@ r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(3/2))-2*(A*b-a*B)*_ a0:=integrate(t0,x) --R --R ---R (800) +--R (3) --R [ --R +-----------+ --R 2 | b +-------+ @@ -17926,7 +18240,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (801) +--R (4) --R +-----------+ --R +-----------+ | b --R (A b - B a)\|- a e + b d |- --------- @@ -17954,7 +18268,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (802) 0 +--R (5) 0 --R Type: Expression(Integer) --E 802 @@ -17962,7 +18276,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (803) +--R (6) --R +-+ +-------+ --R +-+ \|b \|e x + d --R (2A b - 2B a)\|b atanh(--------------) @@ -17986,15 +18300,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (804) 0 +--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 (805) +--R (1) --R B x + A --R / --R 3 4 3 2 3 2 2 2 2 3 @@ -18015,7 +18331,7 @@ r0:=-2/5*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/3*(A*b-a*B)/_ 2*b*(A*b-a*B)/((b*d-a*e)^3*sqrt(d+e*x)) --R --R ---R (806) +--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 + @@ -18058,7 +18374,7 @@ r0:=-2/5*(B*d-A*e)/(e*(b*d-a*e)*(d+e*x)^(5/2))+2/3*(A*b-a*B)/_ a0:=integrate(t0,x) --R --R ---R (807) +--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 @@ -18142,7 +18458,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (808) +--R (4) --R +-----------+ --R 2 +-----------+ | b --R (A b - B a b)\|- a e + b d |- --------- @@ -18170,7 +18486,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (809) 0 +--R (5) 0 --R Type: Expression(Integer) --E 809 @@ -18178,7 +18494,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (810) +--R (6) --R +-+ +-------+ --R 2 +-+ \|b \|e x + d --R (- 2A b + 2B a b)\|b atanh(--------------) @@ -18202,15 +18518,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (811) 0 +--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 (812) +--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 + @@ -18235,7 +18553,7 @@ 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+_ (2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5 --R --R ---R (813) +--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 + @@ -18294,7 +18612,7 @@ 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+_ a0:=integrate(t0,x) --R --R ---R (814) +--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 @@ -18411,7 +18729,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (815) +--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 + @@ -18446,7 +18764,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (816) 0 +--R (5) 0 --R Type: Expression(Integer) --E 816 @@ -18454,7 +18772,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (817) +--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 + @@ -18490,19 +18808,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (818) 0 +--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 (819) ---------------------------------------------------------------- ---R 2 2 2 ---R b x + 2a b x + a +--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 @@ -18515,7 +18835,7 @@ r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+_ (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 (820) +--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 + @@ -18552,7 +18872,7 @@ r0:=1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+_ a0:=integrate(t0,x) --R --R ---R (821) +--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 @@ -18625,7 +18945,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (822) +--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 ) |----------- @@ -18656,7 +18976,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (823) 0 +--R (5) 0 --R Type: Expression(Integer) --E 823 @@ -18664,7 +18984,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (824) +--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 * @@ -18696,19 +19016,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (825) 0 +--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 (826) --------------------------------------- ---R 2 2 2 ---R b x + 2a b x + a +--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 @@ -18720,7 +19042,7 @@ 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))-_ (2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3 --R --R ---R (827) +--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 * @@ -18748,7 +19070,7 @@ 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))-_ a0:=integrate(t0,x) --R --R ---R (828) +--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) @@ -18803,7 +19125,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (829) +--R (4) --R +-----------+ --R |- a e + b d +-+ --R ((3A b - 5B a)e + 2B b d) |----------- \|b @@ -18831,7 +19153,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (830) 0 +--R (5) 0 --R Type: Expression(Integer) --E 830 @@ -18839,7 +19161,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (831) +--R (6) --R +-+ +-------+ --R +-----------+ \|b \|e x + d --R ((3A b - 5B a)e + 2B b d)\|- a e + b d atanh(--------------) @@ -18863,19 +19185,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (832) 0 +--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 (833) ------------------- ---R 2 2 2 ---R b x + 2a b x + a +--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 @@ -18886,7 +19210,7 @@ r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-_ sqrt(d+e*x)/(b^2*(b*d-a*e)) --R --R ---R (834) +--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 * @@ -18908,7 +19232,7 @@ r0:=-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-_ a0:=integrate(t0,x) --R --R ---R (835) +--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) @@ -18952,7 +19276,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (836) +--R (4) --R +-----------+ +-+ --R ((A b - 3B a)e + 2B b d)\|- a e + b d \|b --R * @@ -18978,7 +19302,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (837) 0 +--R (5) 0 --R Type: Expression(Integer) --E 837 @@ -18986,7 +19310,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (838) +--R (6) --R +-----------+ +-+ +-------+ --R | 2 \|b \|e x + d --R ((A b - 3B a)e + 2B b d)\|a b e - b d atanh(--------------) @@ -19009,18 +19333,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (839) 0 +--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 (840) ------------------------------ ---R 2 2 2 +-------+ ---R (b x + 2a b x + a )\|e x + d +--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 @@ -19029,7 +19355,7 @@ 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 (841) +--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 * @@ -19051,7 +19377,7 @@ r0:=-(2*b*B*d-A*b*e-a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ a0:=integrate(t0,x) --R --R ---R (842) +--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) @@ -19095,7 +19421,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (843) +--R (4) --R +-----------+ +-+ --R ((A b + B a)e - 2B b d)\|- a e + b d \|b --R * @@ -19121,7 +19447,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (844) 0 +--R (5) 0 --R Type: Expression(Integer) --E 844 @@ -19129,7 +19455,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (845) +--R (6) --R +-----------+ +-+ +-------+ --R | 2 \|b \|e x + d --R ((A b + B a)e - 2B b d)\|a b e - b d atanh(--------------) @@ -19152,18 +19478,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (846) 0 +--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 (847) ------------------------------------------------------------- ---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 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 @@ -19173,7 +19501,7 @@ 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*(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 (848) +--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 * @@ -19198,7 +19526,7 @@ r0:=-(2*b*B*d-3*A*b*e+a*B*e)*atanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/_ a0:=integrate(t0,x) --R --R ---R (849) +--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) @@ -19253,7 +19581,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (850) +--R (4) --R +-----------+ +-+ --R ((3A b - B a)e - 2B b d)\|- a e + b d \|b --R * @@ -19279,7 +19607,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (851) 0 +--R (5) 0 --R Type: Expression(Integer) --E 851 @@ -19287,7 +19615,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (852) +--R (6) --R +-----------+ +-+ +-------+ --R | 2 \|b \|e x + d --R ((- 3A b + B a)e + 2B b d)\|a b e - b d atanh(--------------) @@ -19310,15 +19638,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (853) 0 +--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 (854) +--R (1) --R B x + A --R / --R 2 2 4 2 2 3 2 2 2 2 2 @@ -19340,7 +19670,7 @@ 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))+_ ((b*d-a*e)^3*sqrt(d+e*x)) --R --R ---R (855) +--R (2) --R 2 2 2 2 --R ((- 15A b + 9B a b)e + 6B b d e)x --R + @@ -19386,7 +19716,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (856) +--R (3) --R [ --R 2 2 2 2 --R ((15A b - 9B a b)e - 6B b d e)x @@ -19476,7 +19806,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (857) +--R (4) --R +-----------+ --R +-----------+ | b --R ((5A b - 3B a)e - 2B b d)\|- a e + b d |- --------- @@ -19504,7 +19834,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (858) 0 +--R (5) 0 --R Type: Expression(Integer) --E 858 @@ -19512,7 +19842,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (859) +--R (6) --R +-+ +-------+ --R +-+ \|b \|e x + d --R ((5A b - 3B a)e - 2B b d)\|b atanh(--------------) @@ -19541,15 +19871,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (860) 0 +--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 (861) +--R (1) --R B x + A --R / --R 2 3 5 3 2 2 4 2 3 2 2 2 3 @@ -19572,7 +19904,7 @@ 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))+_ 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 (862) +--R (2) --R 3 2 3 3 2 3 --R ((105A b - 75B a b )e - 30B b d e )x --R + @@ -19652,7 +19984,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (863) +--R (3) --R [ --R 3 2 3 3 2 3 --R ((105A b - 75B a b )e - 30B b d e )x @@ -19815,7 +20147,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (864) +--R (4) --R +-----------+ --R 2 2 +-----------+ | b --R ((7A b - 5B a b)e - 2B b d)\|- a e + b d |- --------- @@ -19843,7 +20175,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (865) 0 +--R (5) 0 --R Type: Expression(Integer) --E 865 @@ -19851,7 +20183,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (866) +--R (6) --R +-+ +-------+ --R 2 2 +-+ \|b \|e x + d --R ((- 7A b + 5B a b)e + 2B b d)\|b atanh(--------------) @@ -19880,15 +20212,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (867) 0 +--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 (868) +--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 + @@ -19913,7 +20247,7 @@ r0:=7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ 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 (869) +--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 + @@ -19978,7 +20312,7 @@ r0:=7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+_ a0:=integrate(t0,x) --R --R ---R (870) +--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 @@ -20107,7 +20441,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (871) +--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 * @@ -20136,7 +20470,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (872) 0 +--R (5) 0 --R Type: Expression(Integer) --E 872 @@ -20144,7 +20478,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (873) +--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 * @@ -20174,19 +20508,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (874) 0 +--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 (875) ---------------------------------------------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -20199,7 +20535,7 @@ 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))-_ sqrt(d+e*x)/b^4 --R --R ---R (876) +--R (2) --R 3 2 2 3 2 --R ((- 45A b + 105B a b )e - 60B b d e)x --R + @@ -20239,7 +20575,7 @@ 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))-_ a0:=integrate(t0,x) --R --R ---R (877) +--R (3) --R [ --R 3 2 2 3 2 --R ((- 45A b + 105B a b )e - 60B b d e)x @@ -20318,7 +20654,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (878) +--R (4) --R +-----------+ --R 2 |- a e + b d +-+ --R ((- 15A b + 35B a)e - 20B b d e) |----------- \|b @@ -20346,7 +20682,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (879) 0 +--R (5) 0 --R Type: Expression(Integer) --E 879 @@ -20354,7 +20690,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (880) +--R (6) --R +-+ +-------+ --R 2 +-----------+ \|b \|e x + d --R ((15A b - 35B a)e + 20B b d e)\|- a e + b d atanh(--------------) @@ -20378,19 +20714,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (881) 0 +--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 (882) --------------------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -20402,7 +20740,7 @@ 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))-_ sqrt(d+e*x)/(b^3*(b*d-a*e)) --R --R ---R (883) +--R (2) --R 3 2 2 3 2 --R ((- 3A b + 15B a b )e - 12B b d e)x --R + @@ -20436,7 +20774,7 @@ 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))-_ a0:=integrate(t0,x) --R --R ---R (884) +--R (3) --R [ --R 3 2 2 3 2 --R ((3A b - 15B a b )e + 12B b d e)x @@ -20504,7 +20842,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (885) +--R (4) --R 2 +-----------+ +-+ --R ((3A b - 15B a)e + 12B b d e)\|- a e + b d \|b --R * @@ -20530,7 +20868,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (886) 0 +--R (5) 0 --R Type: Expression(Integer) --E 886 @@ -20538,7 +20876,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (887) +--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(--------------) @@ -20564,19 +20902,21 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (888) 0 +--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 (889) ---------------------------- ---R 3 3 2 2 2 3 ---R b x + 3a b x + 3a b x + a +--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 @@ -20587,7 +20927,7 @@ r0:=-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^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 (890) +--R (2) --R 3 2 2 3 2 --R ((- A b - 3B a b )e + 4B b d e)x --R + @@ -20621,7 +20961,7 @@ r0:=-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^2)-_ a0:=integrate(t0,x) --R --R ---R (891) +--R (3) --R [ --R 3 2 2 3 2 --R ((A b + 3B a b )e - 4B b d e)x @@ -20686,7 +21026,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (892) +--R (4) --R 2 +-----------+ +-+ --R ((A b + 3B a)e - 4B b d e)\|- a e + b d \|b --R * @@ -20712,7 +21052,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (893) 0 +--R (5) 0 --R Type: Expression(Integer) --E 893 @@ -20720,7 +21060,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (894) +--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(--------------) @@ -20743,18 +21083,20 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (895) 0 +--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 (896) ---------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (b x + 3a b x + 3a b x + a )\|e x + d +--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 @@ -20765,7 +21107,7 @@ r0:=1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*atanh(sqrt(b)*_ 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 (897) +--R (2) --R 3 2 2 3 2 --R ((- 3A b - B a b )e + 4B b d e)x --R + @@ -20802,7 +21144,7 @@ r0:=1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*atanh(sqrt(b)*_ a0:=integrate(t0,x) --R --R ---R (898) +--R (3) --R [ --R 3 2 2 3 2 --R ((3A b + B a b )e - 4B b d e)x @@ -20876,7 +21218,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (899) +--R (4) --R 2 +-----------+ +-+ --R ((3A b + B a)e - 4B b d e)\|- a e + b d \|b --R * @@ -20902,7 +21244,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (900) 0 +--R (5) 0 --R Type: Expression(Integer) --E 900 @@ -20910,7 +21252,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (901) +--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(--------------) @@ -20933,15 +21275,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (902) 0 +--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 (903) +--R (1) --R B x + A --R / --R 3 4 2 3 3 2 2 2 3 2 3 @@ -20960,7 +21304,7 @@ r0:=3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*atanh(sqrt(b)*_ 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 (904) +--R (2) --R 3 2 2 3 2 --R ((15A b - 3B a b )e - 12B b d e)x --R + @@ -21006,7 +21350,7 @@ r0:=3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*atanh(sqrt(b)*_ a0:=integrate(t0,x) --R --R ---R (905) +--R (3) --R [ --R 3 2 2 3 2 --R ((15A b - 3B a b )e - 12B b d e)x @@ -21101,7 +21445,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (906) +--R (4) --R 2 +-----------+ +-+ --R ((15A b - 3B a)e - 12B b d e)\|- a e + b d \|b --R * @@ -21127,7 +21471,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (907) 0 +--R (5) 0 --R Type: Expression(Integer) --E 907 @@ -21135,7 +21479,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (908) +--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(--------------) @@ -21161,15 +21505,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (909) 0 +--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 (910) +--R (1) --R B x + A --R / --R 3 2 5 2 2 3 4 2 2 2 3 2 3 @@ -21192,7 +21538,7 @@ 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))+_ 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 (911) +--R (2) --R 3 2 3 3 2 3 --R ((- 105A b + 45B a b )e + 60B b d e )x --R + @@ -21272,7 +21618,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (912) +--R (3) --R [ --R 3 2 3 3 2 3 --R ((105A b - 45B a b )e - 60B b d e )x @@ -21428,7 +21774,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (913) +--R (4) --R +-----------+ --R 2 +-----------+ | b --R ((35A b - 15B a)e - 20B b d e)\|- a e + b d |- --------- @@ -21456,7 +21802,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (914) 0 +--R (5) 0 --R Type: Expression(Integer) --E 914 @@ -21464,7 +21810,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (915) +--R (6) --R +-+ +-------+ --R 2 +-+ \|b \|e x + d --R ((35A b - 15B a)e - 20B b d e)\|b atanh(--------------) @@ -21493,15 +21839,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (916) 0 +--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 (917) +--R (1) --R B x + A --R / --R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 @@ -21528,7 +21876,7 @@ 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))+_ 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 (918) +--R (2) --R 4 3 4 4 3 4 --R ((945A b - 525B a b )e - 420B b d e )x --R + @@ -21658,7 +22006,7 @@ 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))+_ a0:=integrate(t0,x) --R --R ---R (919) +--R (3) --R [ --R 4 3 4 4 3 4 --R ((945A b - 525B a b )e - 420B b d e )x @@ -21916,7 +22264,7 @@ a0:=integrate(t0,x) m0:=a0.1-r0 --R --R ---R (920) +--R (4) --R +-----------+ --R 2 2 2 +-----------+ | b --R ((63A b - 35B a b)e - 28B b d e)\|- a e + b d |- --------- @@ -21947,7 +22295,7 @@ m0:=a0.1-r0 d0:=D(m0,x) --R --R ---R (921) 0 +--R (5) 0 --R Type: Expression(Integer) --E 921 @@ -21955,7 +22303,7 @@ d0:=D(m0,x) m0:=a0.2-r0 --R --R ---R (922) +--R (6) --R +-+ +-------+ --R 2 2 2 +-+ \|b \|e x + d --R ((- 63A b + 35B a b)e + 28B b d e)\|b atanh(--------------) @@ -21987,15 +22335,17 @@ m0:=a0.2-r0 d0:=D(m0,x) --R --R ---R (923) 0 +--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 (924) +--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) @@ -22012,7 +22362,7 @@ r0:=-1/48*(b*d-a*e)*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^2) --R --R ---R (925) +--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 + @@ -22074,12 +22424,14 @@ r0:=-1/48*(b*d-a*e)*(3*b*B*d-10*A*b*e+7*a*B*e)*(a+b*x)^(3/2)*_ --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 (926) (B e x + (A e + B d)x + A d)\|b x + a \|e x + d +--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 @@ -22093,7 +22445,7 @@ 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)+_ sqrt(d+e*x)/(b^3*e^2) --R --R ---R (927) +--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 + @@ -22138,12 +22490,14 @@ 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)+_ --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 (928) (B x + A)\|b x + a \|e x + d +--R +-------+ +-------+ +--R (1) (B x + A)\|b x + a \|e x + d --R Type: Expression(Integer) --E 934 @@ -22155,7 +22509,7 @@ 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))*sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^2) --R --R ---R (929) +--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 + @@ -22194,15 +22548,17 @@ r0:=1/3*B*(a+b*x)^(3/2)*(d+e*x)^(3/2)/(b*e)-1/8*(b*d-a*e)^2*_ --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 (930) ------------------- ---R +-------+ ---R \|e x + d +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ------------------- +--R +-------+ +--R \|e x + d --R Type: Expression(Integer) --E 939 @@ -22213,7 +22569,7 @@ 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(a+b*x)*sqrt(d+e*x)/(b*e^2) --R --R ---R (931) +--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 * @@ -22243,15 +22599,17 @@ 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)/_ --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 (932) ------------------- ---R +-------+ ---R (e x + d)\|e x + d +--R +-------+ +--R (B x + A)\|b x + a +--R (1) ------------------- +--R +-------+ +--R (e x + d)\|e x + d --R Type: Expression(Integer) --E 944 @@ -22262,7 +22620,7 @@ r0:=-(3*b*B*d-2*A*b*e-a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ sqrt(a+b*x)*sqrt(d+e*x)/(e^2*(b*d-a*e)) --R --R ---R (933) +--R (2) --R +-+ +-------+ --R +-------+ \|e \|b x + a --R ((2A b + B a)e - 3B b d)\|e x + d atanh(--------------) @@ -22289,15 +22647,17 @@ r0:=-(3*b*B*d-2*A*b*e-a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ --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 (934) ------------------------------ ---R 2 2 2 +-------+ ---R (e x + 2d e x + d )\|e x + d +--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 @@ -22307,7 +22667,7 @@ r0:=-2/3*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ 2*B*sqrt(a+b*x)/(e^2*sqrt(d+e*x)) --R --R ---R (935) +--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 * @@ -22340,15 +22700,17 @@ r0:=-2/3*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ --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 (936) ---------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (e x + 3d e x + 3d e x + d )\|e x + d +--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 @@ -22357,7 +22719,7 @@ 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 (937) +--R (2) --R 2 2 2 --R ((4A b - 10B a b)e + 6B b d)x --R + @@ -22381,66 +22743,61 @@ r0:=-2/5*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ --R Type: Expression(Integer) --E 955 ---S 956 of 1293 +--S 956 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (938) ---R 2 3 2 4 2 ---R ((8A b - 20B a b)d e + 12B b d )x +--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 ((- 4A a b - 20B a )d e + (20A b + 4B a b)d )x - 12A a d e +--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 (20A a b - 8B a )d +--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 + 12A a )e + ((- 5A a b + 2B a )d + (- 20A a b + 8B a )d)e )x +--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 + 36A a d)e ---R + ---R 2 3 2 3 2 2 ---R ((- 15A a b + 6B a )d + (- 60A a b + 24B a )d )e +--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 ---R (9A a d + 36A a d )e ---R + ---R 2 4 2 3 3 ---R ((- 15A a b + 6B a )d + (- 60A a b + 24B a )d )e ---R * ---R x +--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 + 12A a d )e + (- 5A a b + 2B a )d + (- 20A a b + 8B a )d +--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 (30a d e - 60a b d e + 30b d e )x +--R (15a d e - 30a b d e + 15b d e )x --R + ---R 2 4 4 5 3 2 6 2 2 ---R (90a d e - 180a b d e + 90b d e )x +--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 5 3 6 2 2 7 2 6 2 7 2 8 ---R (90a d e - 180a b d e + 90b d e)x + 30a d e - 60a b d e + 30b d +--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 +--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 + 12A a )e + (- 5A a b + 2B a )d + (- 20A a b + 8B a )d ---R (939) ---------------------------------------------------------------- ---R 2 3 2 4 2 5 ---R 30a d e - 60a b d e + 30b d +--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 @@ -22448,19 +22805,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (940) 0 +--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 (941) -------------------------------------------------- ---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 +-------+ +--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 @@ -22471,7 +22830,7 @@ r0:=-2/7*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ (a+b*x)^(3/2)/(e*(b*d-a*e)^3*(d+e*x)^(3/2)) --R --R ---R (942) +--R (2) --R 3 2 2 3 3 --R ((- 16A b + 28B a b )e - 12B b d e)x --R + @@ -22509,117 +22868,117 @@ r0:=-2/7*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ --R Type: Expression(Integer) --E 960 ---S 961 of 1293 +--S 961 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (943) ---R 3 2 4 2 3 5 3 ---R ((- 64A b + 112B a b )d e - 48B b d e)x +--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 ((32A a b - 56B a b)d e + (- 224A b + 416B a b )d e - 168B b d )x +--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 (- 24A a b - 168B a )d e + (112A a b + 416B a b)d e +--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 (- 280A b - 56B a b )d +--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 - 120A a d e + (336A a b - 48B a )d e + (- 280A a b + 112B a b)d +--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 + 240A a )e +--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 + (- 672A a b + 96B a )d)e +--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 + (560A a b - 224B a b)d )e +--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 + 960A a d)e +--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 + (- 2688A a b + 384B a )d )e +--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 + (2240A a b - 896B a b)d )e +--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 + 1440A a d )e +--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 + (- 4032A a b + 576B a )d )e +--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 + (3360A a b - 1344B a b)d )e +--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 + 960A a d )e +--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 + (- 2688A a b + 384B a )d )e +--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 + (2240A a b - 896B a b)d )e +--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 + 240A a d )e +--R 3 5 4 4 2 +--R (15A a d + 15A a d )e --R + ---R 2 3 6 3 4 5 ---R ((- 42A a b + 6B a )d + (- 672A a b + 96B a )d )e +--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 7 2 2 3 6 ---R (35A a b - 14B a b)d + (560A a b - 224B a b)d +--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 (420a d e - 1260a b d e + 1260a b d e - 420b d e )x +--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 (1680a d e - 5040a b d e + 5040a b d e - 1680b d e )x +--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 (2520a d e - 7560a b d e + 7560a b d e - 2520b d e )x +--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 (1680a d e - 5040a b d e + 5040a b d e - 1680b d e)x + 420a d e +--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 - 1260a b d e + 1260a b d e - 420b d +--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 +--S 962 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (944) ---R 3 4 2 2 3 2 3 4 ---R (15A a d + 240A a )e + ((- 42A a b + 6B a )d + (- 672A a b + 96B a )d)e +--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 + (560A a b - 224B a b)d +--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 420a d e - 1260a b d e + 1260a b d e - 420b d +--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 @@ -22627,19 +22986,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (945) 0 +--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 (946) -------------------------------------------------------------- ---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 +-------+ +--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 @@ -22651,7 +23012,7 @@ r0:=-2/9*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ (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 (947) +--R (2) --R 4 3 3 4 2 4 --R ((32A b - 48B a b )e + 16B b d e )x --R + @@ -22716,197 +23077,197 @@ r0:=-2/9*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ --R Type: Expression(Integer) --E 965 ---S 966 of 1293 +--S 966 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (948) ---R 4 3 5 3 4 6 2 4 ---R ((160A b - 240B a b )d e + 80B b d e )x +--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 (- 80A a b + 120B a b )d e + (720A b - 1120B a b )d e +--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 360B b d e +--R 216B b d e --R * --R 3 --R x --R + --R 2 2 3 5 3 3 2 2 6 2 ---R (60A a b - 90B a b)d e + (- 360A a b + 570B a b )d e +--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 (1260A b - 2070B a b )d e + 630B b d +--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 (- 50A a b - 450B a )d e + (270A a b + 1670B a b)d e +--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 (- 630A a b - 2070B a b )d e + (1050A b + 210B a b )d +--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 - 350A a d e + (1350A a b - 100B a )d e +--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 (- 1890A a b + 360B a b)d e + (1050A a b - 420B a b )d +--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 - 875A a )e +--R (- 35A a d - 315A a )e --R + ---R 3 4 2 4 5 7 ---R ((135A a b - 10B a )d + (3375A a b - 250B a )d)e +--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 + (- 4725A a b + 900B a b)d )e +--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 + (2625A a b - 1050B a b )d )e +--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 - 4375A a d)e +--R (- 175A a d - 1575A a d)e --R + ---R 3 4 3 4 5 2 6 ---R ((675A a b - 50B a )d + (16875A a b - 1250B a )d )e +--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 + (- 23625A a b + 4500B a b)d )e +--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 + (13125A a b - 5250B a b )d )e +--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 - 8750A a d )e +--R (- 350A a d - 3150A a d )e --R + ---R 3 4 4 4 5 3 5 ---R ((1350A a b - 100B a )d + (33750A a b - 2500B a )d )e +--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 + (- 47250A a b + 9000B a b)d )e +--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 + (26250A a b - 10500B a b )d )e +--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 - 8750A a d )e +--R (- 350A a d - 3150A a d )e --R + ---R 3 4 5 4 5 4 4 ---R ((1350A a b - 100B a )d + (33750A a b - 2500B a )d )e +--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 + (- 47250A a b + 9000B a b)d )e +--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 + (26250A a b - 10500B a b )d )e +--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 - 4375A a d )e +--R (- 175A a d - 1575A a d )e --R + ---R 3 4 6 4 5 5 3 ---R ((675A a b - 50B a )d + (16875A a b - 1250B a )d )e +--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 + (- 23625A a b + 4500B a b)d )e +--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 + (13125A a b - 5250B a b )d )e +--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 - 875A a d )e +--R (- 35A a d - 315A a d )e --R + ---R 3 4 7 4 5 6 2 ---R ((135A a b - 10B a )d + (3375A a b - 250B a )d )e +--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 + (- 4725A a b + 900B a b)d )e +--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 + (2625A a b - 1050B a b )d +--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 (1575a d e - 6300a b d e + 9450a b d e - 6300a b d e + 1575b d e )x +--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 7875a d e - 31500a b d e + 47250a b d e - 31500a b d e +--R 4725a d e - 18900a b d e + 28350a b d e - 18900a b d e --R + --R 4 10 4 ---R 7875b d e +--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 15750a d e - 63000a b d e + 94500a b d e - 63000a b d e +--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 15750b d e +--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 15750a d e - 63000a b d e + 94500a b d e - 63000a b d e +--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 15750b d e +--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 7875a d e - 31500a b d e + 47250a b d e - 31500a b d e +--R 4725a d e - 18900a b d e + 28350a b d e - 18900a b d e --R + --R 4 13 ---R 7875b d e +--R 4725b d e --R * --R x --R + ---R 4 10 4 3 11 3 2 2 12 2 3 13 4 14 ---R 1575a d e - 6300a b d e + 9450a b d e - 6300a b d e + 1575b d +--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 +--S 967 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (949) +--R (4) --R 4 5 3 ---R (- 35A a d - 875A a )e +--R (- 35A a d - 315A a )e --R + ---R 3 4 2 4 5 2 ---R ((135A a b - 10B a )d + (3375A a b - 250B a )d)e +--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 + (- 4725A a b + 900B a b)d )e +--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 + (2625A a b - 1050B a b )d +--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 1575a d e - 6300a b d e + 9450a b d e - 6300a b d e + 1575b d +--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 @@ -22914,15 +23275,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (950) 0 +--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 (951) +--R (1) --R +-------+ --R (B x + A)\|b x + a --R ------------------------------------------------------------------------- @@ -22941,7 +23304,7 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ (a+b*x)^(3/2)/(e*(b*d-a*e)^5*(d+e*x)^(3/2)) --R --R ---R (952) +--R (2) --R 5 4 4 5 3 5 --R ((- 256A b + 352B a b )e - 96B b d e )x --R + @@ -23050,11 +23413,11 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ --R Type: Expression(Integer) --E 970 ---S 971 of 1293 +--S 971 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (953) +--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 + @@ -23111,127 +23474,127 @@ a0:=integrate(t0,x) --R +-------+ +-------+ --R \|b x + a \|e x + d --R + ---R 5 6 10 ---R (- 315A a d - 315A a )e +--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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 @@ -23294,25 +23657,25 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 971 ---S 972 of 1293 -m0:=a0-r0 +--S 972 of 1293 ok to fail, differs by a constant +m0:=a0-r0 --R --R ---R (954) ---R 5 6 4 ---R (- 315A a d - 315A a )e +--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 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 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 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 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 @@ -23326,15 +23689,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (955) 0 +--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 (956) +--R (1) --R +-------+ --R (B x + A)\|b x + a --R / @@ -23361,7 +23726,7 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ (e*(b*d-a*e)^6*(d+e*x)^(3/2)) --R --R ---R (957) +--R (2) --R 6 5 5 6 4 6 --R ((2560A b - 3328B a b )e + 768B b d e )x --R + @@ -23506,156 +23871,156 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(3/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ --R Type: Expression(Integer) --E 975 ---S 976 of 1293 +--S 976 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (958) ---R 6 5 7 5 6 8 4 6 ---R ((7680A b - 9984B a b )d e + 2304B b d e )x +--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 (- 3840A a b + 4992B a b )d e + (49920A b - 66048B a b )d e +--R (- 5120A a b + 6656B a b )d e + (66560A b - 88064B a b )d e --R + --R 6 9 3 ---R 14976B b d e +--R 19968B b d e --R * --R 5 --R x --R + --R 2 4 3 3 7 5 5 2 4 8 4 ---R (2880A a b - 3744B a b )d e + (- 24960A a b + 33312B a b )d e +--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 (137280A b - 185952B a b )d e + 41184B b d e +--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 (- 2400A a b + 3120B a b )d e + (18720A a b - 25056B a b )d e +--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 (- 68640A a b + 94848B a b )d e +--R 5 2 4 9 3 +--R (- 91520A a b + 126464B a b )d e --R + --R 6 5 10 2 6 11 ---R (205920A b - 288288B a b )d e + 61776B b d e +--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 (2100A a b - 2730B a b)d e + (- 15600A a b + 20910B a b )d e +--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 (51480A a b - 71604B a b )d e +--R (68640A a b - 95472B a b )d e --R + --R 5 2 4 10 2 ---R (- 102960A a b + 149292B a b )d e +--R (- 137280A a b + 199056B a b )d e --R + --R 6 5 11 6 12 ---R (180180A b - 265122B a b )d e + 54054B b d +--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 (- 1890A a b - 24570B a )d e + (13650A a b + 143850B a b)d e +--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 (- 42900A a b - 345540B a b )d e +--R (- 57200A a b - 460720B a b )d e --R + ---R 2 4 3 3 10 2 ---R (77220A a b + 427284B a b )d e +--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 (- 90090A a b - 265122B a b )d e + (90090A b + 18018B a b )d +--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 - 20790A a d e + (122850A a b - 3780B a )d e +--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 (- 300300A a b + 21840B a b)d e + (386100A a b - 51480B a b )d e +--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 (- 270270A a b + 61776B a b )d e + (90090A a b - 36036B a b )d +--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 - 31185A a )e +--R (- 3465A a d - 55440A a )e --R + ---R 5 6 2 6 7 11 ---R ((20475A a b - 630B a )d + (184275A a b - 5670B a )d)e +--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 + (- 450450A a b + 32760B a b)d )e +--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 + (579150A a b - 77220B a b )d )e +--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 (- 405405A a b + 92664B a b )d +--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 + (135135A a b - 54054B a b )d )e +--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 - 218295A a d)e +--R (- 24255A a d - 388080A a d)e --R + --R 5 6 3 6 7 2 10 ---R ((143325A a b - 4410B a )d + (1289925A a b - 39690B a )d )e +--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 (- 3153150A a b + 229320B a b)d +--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 + (4054050A a b - 540540B a b )d )e +--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 (- 2837835A a b + 648648B a b )d +--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 + (945945A a b - 378378B a b )d )e +--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 - 654885A a d )e +--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 + (3869775A a b - 119070B a )d )e +--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 (- 9459450A a b + 687960B a b)d +--R 5 2 6 4 +--R (- 16816800A a b + 1223040B a b)d --R * --R 8 --R e @@ -23664,7 +24029,7 @@ a0:=integrate(t0,x) --R (1351350A a b - 180180B a b )d --R + --R 4 3 5 2 5 ---R (12162150A a b - 1621620B a b )d +--R (21621600A a b - 2882880B a b )d --R * --R 7 --R e @@ -23672,29 +24037,29 @@ a0:=integrate(t0,x) --R 2 4 3 3 7 --R (- 945945A a b + 216216B a b )d --R + ---R 3 4 4 3 6 ---R (- 8513505A a b + 1945944B a b )d +--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 + (2837835A a b - 1135134B a b )d )e +--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 - 1091475A a d )e +--R (- 121275A a d - 1940400A a d )e --R + ---R 5 6 5 6 7 4 8 ---R ((716625A a b - 22050B a )d + (6449625A a b - 198450B a )d )e +--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 (- 15765750A a b + 1146600B a b)d +--R (- 28028000A a b + 2038400B a b)d --R * --R 7 --R e @@ -23703,7 +24068,7 @@ a0:=integrate(t0,x) --R (2252250A a b - 300300B a b )d --R + --R 4 3 5 2 6 ---R (20270250A a b - 2702700B a b )d +--R (36036000A a b - 4804800B a b )d --R * --R 6 --R e @@ -23712,28 +24077,28 @@ a0:=integrate(t0,x) --R (- 1576575A a b + 360360B a b )d --R + --R 3 4 4 3 7 ---R (- 14189175A a b + 3243240B a b )d +--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 + (4729725A a b - 1891890B a b )d )e +--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 - 1091475A a d )e +--R (- 121275A a d - 1940400A a d )e --R + ---R 5 6 6 6 7 5 7 ---R ((716625A a b - 22050B a )d + (6449625A a b - 198450B a )d )e +--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 (- 15765750A a b + 1146600B a b)d +--R (- 28028000A a b + 2038400B a b)d --R * --R 6 --R e @@ -23742,7 +24107,7 @@ a0:=integrate(t0,x) --R (2252250A a b - 300300B a b )d --R + --R 4 3 5 2 7 ---R (20270250A a b - 2702700B a b )d +--R (36036000A a b - 4804800B a b )d --R * --R 5 --R e @@ -23751,7 +24116,7 @@ a0:=integrate(t0,x) --R (- 1576575A a b + 360360B a b )d --R + --R 3 4 4 3 8 ---R (- 14189175A a b + 3243240B a b )d +--R (- 25225200A a b + 5765760B a b )d --R * --R 4 --R e @@ -23760,7 +24125,7 @@ a0:=integrate(t0,x) --R (525525A a b - 210210B a b )d --R + --R 2 5 3 4 9 ---R (4729725A a b - 1891890B a b )d +--R (8408400A a b - 3363360B a b )d --R * --R 3 --R e @@ -23768,17 +24133,17 @@ a0:=integrate(t0,x) --R 3 --R x --R + ---R 6 6 7 5 7 ---R (- 72765A a d - 654885A a d )e +--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 + (3869775A a b - 119070B a )d )e +--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 (- 9459450A a b + 687960B a b)d +--R 5 2 6 7 +--R (- 16816800A a b + 1223040B a b)d --R * --R 5 --R e @@ -23787,7 +24152,7 @@ a0:=integrate(t0,x) --R (1351350A a b - 180180B a b )d --R + --R 4 3 5 2 8 ---R (12162150A a b - 1621620B a b )d +--R (21621600A a b - 2882880B a b )d --R * --R 4 --R e @@ -23795,8 +24160,8 @@ a0:=integrate(t0,x) --R 2 4 3 3 10 --R (- 945945A a b + 216216B a b )d --R + ---R 3 4 4 3 9 ---R (- 8513505A a b + 1945944B a b )d +--R 3 4 4 3 9 +--R (- 15135120A a b + 3459456B a b )d --R * --R 3 --R e @@ -23805,7 +24170,7 @@ a0:=integrate(t0,x) --R (315315A a b - 126126B a b )d --R + --R 2 5 3 4 10 ---R (2837835A a b - 1135134B a b )d +--R (5045040A a b - 2018016B a b )d --R * --R 2 --R e @@ -23814,16 +24179,16 @@ a0:=integrate(t0,x) --R x --R + --R 6 7 7 6 6 ---R (- 24255A a d - 218295A a d )e +--R (- 24255A a d - 388080A a d )e --R + --R 5 6 8 6 7 7 5 ---R ((143325A a b - 4410B a )d + (1289925A a b - 39690B a )d )e +--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 (- 3153150A a b + 229320B a b)d +--R (- 5605600A a b + 407680B a b)d --R * --R 4 --R e @@ -23832,7 +24197,7 @@ a0:=integrate(t0,x) --R (450450A a b - 60060B a b )d --R + --R 4 3 5 2 9 ---R (4054050A a b - 540540B a b )d +--R (7207200A a b - 960960B a b )d --R * --R 3 --R e @@ -23840,154 +24205,154 @@ a0:=integrate(t0,x) --R 2 4 3 3 11 --R (- 315315A a b + 72072B a b )d --R + ---R 3 4 4 3 10 ---R (- 2837835A a b + 648648B a b )d +--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 + (945945A a b - 378378B a b )d )e +--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 - 31185A a d )e +--R (- 3465A a d - 55440A a d )e --R + ---R 5 6 9 6 7 8 4 ---R ((20475A a b - 630B a )d + (184275A a b - 5670B a )d )e +--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 + (- 450450A a b + 32760B a b)d )e +--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 + (579150A a b - 77220B a b )d )e +--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 + (- 405405A a b + 92664B a b )d )e +--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 + (135135A a b - 54054B a b )d +--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 135135a d e - 810810a b d e + 2027025a b d e +--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 - 2702700a b d e + 2027025a b d e - 810810a b d e +--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 135135b d e +--R 180180b d e --R * --R 7 --R x --R + ---R 6 8 12 5 9 11 4 2 10 10 ---R 945945a d e - 5675670a b d e + 14189175a b d e +--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 - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R - 25225200a b d e + 18918900a b d e - 7567560a b d e --R + ---R 6 14 6 ---R 945945b d e +--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 2837835a d e - 17027010a b d e + 42567525a b d e +--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 - 56756700a b d e + 42567525a b d e - 17027010a b d e +--R - 75675600a b d e + 56756700a b d e - 22702680a b d e --R + --R 6 15 5 ---R 2837835b d e +--R 3783780b d e --R * --R 5 --R x --R + --R 6 10 10 5 11 9 4 2 12 8 ---R 4729725a d e - 28378350a b d e + 70945875a b d e +--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 - 94594500a b d e + 70945875a b d e - 28378350a b d e +--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 4729725b d e +--R 6306300b d e --R * --R 4 --R x --R + --R 6 11 9 5 12 8 4 2 13 7 ---R 4729725a d e - 28378350a b d e + 70945875a b d e +--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 - 94594500a b d e + 70945875a b d e - 28378350a b d e +--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 4729725b d e +--R 6306300b d e --R * --R 3 --R x --R + --R 6 12 8 5 13 7 4 2 14 6 ---R 2837835a d e - 17027010a b d e + 42567525a b d e +--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 - 56756700a b d e + 42567525a b d e - 17027010a b d e +--R - 75675600a b d e + 56756700a b d e - 22702680a b d e --R + --R 6 18 2 ---R 2837835b d e +--R 3783780b d e --R * --R 2 --R x --R + ---R 6 13 7 5 14 6 4 2 15 5 ---R 945945a d e - 5675670a b d e + 14189175a b d e +--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 - 18918900a b d e + 14189175a b d e - 5675670a b d e +--R - 25225200a b d e + 18918900a b d e - 7567560a b d e --R + ---R 6 19 ---R 945945b d e +--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 135135a d e - 810810a b d e + 2027025a b d e - 2702700a b d e +--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 2027025a b d e - 810810a b d e + 135135b d +--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 +--S 977 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (959) +--R (4) --R 6 7 5 ---R (- 3465A a d - 31185A a )e +--R (- 3465A a d - 55440A a )e --R + ---R 5 6 2 6 7 4 ---R ((20475A a b - 630B a )d + (184275A a b - 5670B a )d)e +--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 + (- 450450A a b + 32760B a b)d )e +--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 + (579150A a b - 77220B a b )d )e +--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 + (- 405405A a b + 92664B a b )d )e +--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 + (135135A a b - 54054B a b )d +--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 135135a d e - 810810a b d e + 2027025a b d e - 2702700a b d e +--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 2027025a b d e - 810810a b d e + 135135b d +--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 @@ -23995,15 +24360,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (960) 0 +--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 (961) +--R (1) --R 2 4 2 3 --R B b e x + ((A b + B a)e + 2B b d e)x --R + @@ -24031,7 +24398,7 @@ r0:=-1/96*(b*d-a*e)*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ sqrt(d+e*x)/(b^4*e^3) --R --R ---R (962) +--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 + @@ -24108,11 +24475,13 @@ r0:=-1/96*(b*d-a*e)*(5*b*B*d-12*A*b*e+7*a*B*e)*(a+b*x)^(5/2)*_ --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 (963) +--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 * @@ -24131,7 +24500,7 @@ 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)+_ 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 (964) +--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 + @@ -24187,12 +24556,14 @@ 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)+_ --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 (965) (B b x + (A b + B a)x + A a)\|b x + a \|e x + d +--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 @@ -24206,7 +24577,7 @@ r0:=1/4*B*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b*e)-1/64*(b*d-a*e)^3*_ sqrt(d+e*x)/(b^2*e^3) --R --R ---R (966) +--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 + @@ -24251,15 +24622,17 @@ r0:=1/4*B*(a+b*x)^(5/2)*(d+e*x)^(3/2)/(b*e)-1/64*(b*d-a*e)^3*_ --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 (967) --------------------------------------- ---R +-------+ ---R \|e x + d +--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 @@ -24271,7 +24644,7 @@ 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(a+b*x)*sqrt(d+e*x)/(b*e^3) --R --R ---R (968) +--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 + @@ -24310,15 +24683,17 @@ 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)/_ --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 (969) --------------------------------------- ---R +-------+ ---R (e x + d)\|e x + d +--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 @@ -24330,7 +24705,7 @@ r0:=3/4*(b*d-a*e)*(5*b*B*d-4*A*b*e-a*B*e)*atanh(sqrt(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 (970) +--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 * @@ -24366,15 +24741,17 @@ r0:=3/4*(b*d-a*e)*(5*b*B*d-4*A*b*e-a*B*e)*atanh(sqrt(e)*_ --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 (971) --------------------------------------- ---R 2 2 2 +-------+ ---R (e x + 2d e x + d )\|e x + d +--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 @@ -24386,7 +24763,7 @@ r0:=-2/3*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))-_ sqrt(a+b*x)*sqrt(d+e*x)/(e^3*(b*d-a*e)) --R --R ---R (972) +--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 * @@ -24422,15 +24799,17 @@ r0:=-2/3*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))-_ --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 (973) ---------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (e x + 3d e x + 3d e x + d )\|e x + d +--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 @@ -24441,7 +24820,7 @@ r0:=-2/5*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ 2*b*B*sqrt(a+b*x)/(e^3*sqrt(d+e*x)) --R --R ---R (974) +--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 + @@ -24486,15 +24865,17 @@ r0:=-2/5*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ --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 (975) -------------------------------------------------- ---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 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 @@ -24503,7 +24884,7 @@ 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 (976) +--R (2) --R 3 2 3 3 --R ((4A b - 14B a b )e + 10B b d)x --R + @@ -24533,87 +24914,81 @@ r0:=-2/7*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ --R Type: Expression(Integer) --E 1015 ---S 1016 of 1293 +--S 1016 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (977) ---R 3 2 4 3 5 3 ---R ((20A b - 70B a b )d e + 50B b d )x +--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 ((- 10A a b - 140B a b)d e + (70A b + 80B a b )d )x +--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 ((- 80A a b - 70B a )d e + (140A a b + 10B a b)d )x - 50A a d e +--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 (70A a b - 20B a )d +--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 ---R (- 5A a d - 125A a )e ---R + ---R 2 3 2 3 4 4 ---R ((7A a b - 2B a )d + (175A a b - 50B a )d)e ---R * ---R 4 ---R x +--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 - 500A a d)e +--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 + (700A a b - 200B a )d )e +--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 - 750A a d )e +--R (- 30A a d - 120A a d )e --R + ---R 2 3 4 3 4 3 2 ---R ((42A a b - 12B a )d + (1050A a b - 300B a )d )e +--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 - 500A a d )e +--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 + (700A a b - 200B a )d )e +--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 - 125A a d )e + (7A a b - 2B a )d + (175A a b - 50B a )d +--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 (175a d e - 350a b d e + 175b d e )x +--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 (700a d e - 1400a b d e + 700b d e )x +--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 (1050a d e - 2100a b d e + 1050b d e )x +--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 (700a d e - 1400a b d e + 700b d e)x + 175a d e - 350a b d e + 175b d +--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 +--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 - 125A a )e + (7A a b - 2B a )d + (175A a b - 50B a )d ---R (978) ----------------------------------------------------------------- ---R 2 4 2 5 2 6 ---R 175a d e - 350a b d e + 175b d +--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 @@ -24621,19 +24996,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (979) 0 +--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 (980) -------------------------------------------------------------- ---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 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 @@ -24644,7 +25021,7 @@ r0:=-2/9*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ (e*(b*d-a*e)^3*(d+e*x)^(5/2)) --R --R ---R (981) +--R (2) --R 4 3 2 4 4 --R ((- 16A b + 36B a b )e - 20B b d e)x --R + @@ -24694,147 +25071,147 @@ r0:=-2/9*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ --R Type: Expression(Integer) --E 1020 ---S 1021 of 1293 +--S 1021 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (982) ---R 4 3 5 2 4 6 4 ---R ((- 48A b + 108B a b )d e - 60B b d e)x +--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 (24A a b - 54B a b )d e + (- 216A b + 516B a b )d e +--R (16A a b - 36B a b )d e + (- 144A b + 344B a b )d e --R + --R 4 7 ---R - 270B b d +--R - 180B b d --R * --R 3 --R x --R + ---R 2 2 3 5 2 3 2 2 6 ---R (- 18A a b - 432B a b)d e + (108A a b + 1152B a b )d e +--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 (- 378A b - 432B a b )d +--R (- 252A b - 288B a b )d --R * --R 2 --R x --R + --R 3 4 5 2 2 2 3 6 ---R (- 300A a b - 270B a )d e + (864A a b + 516B a b)d e +--R (- 200A a b - 180B a )d e + (576A a b + 344B a b)d e --R + --R 3 2 2 7 ---R (- 756A a b - 54B a b )d +--R (- 504A a b - 36B a b )d --R * --R x --R + ---R 4 5 2 3 4 6 2 2 3 7 ---R - 210A a d e + (540A a b - 60B a )d e + (- 378A a b + 108B a b)d +--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 - 315A a )e +--R (- 35A a d - 140A a )e --R + --R 3 4 2 4 5 6 ---R ((90A a b - 10B a )d + (810A a b - 90B a )d)e +--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 + (- 567A a b + 162B a b)d )e +--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 - 1575A a d)e +--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 + (4050A a b - 450B a )d )e +--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 + (- 2835A a b + 810B a b)d )e +--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 - 3150A a d )e +--R (- 350A a d - 1400A a d )e --R + --R 3 4 4 4 5 3 4 ---R ((900A a b - 100B a )d + (8100A a b - 900B a )d )e +--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 + (- 5670A a b + 1620B a b)d )e +--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 - 3150A a d )e +--R (- 350A a d - 1400A a d )e --R + --R 3 4 5 4 5 4 3 ---R ((900A a b - 100B a )d + (8100A a b - 900B a )d )e +--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 + (- 5670A a b + 1620B a b)d )e +--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 - 1575A a d )e +--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 + (4050A a b - 450B a )d )e +--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 + (- 2835A a b + 810B a b)d )e +--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 - 315A a d )e +--R (- 35A a d - 140A a d )e --R + --R 3 4 7 4 5 6 ---R ((90A a b - 10B a )d + (810A a b - 90B a )d )e +--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 + (- 567A a b + 162B a b)d +--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 (945a d e - 2835a b d e + 2835a b d e - 945b d e )x +--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 (4725a d e - 14175a b d e + 14175a b d e - 4725b d e )x +--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 (9450a d e - 28350a b d e + 28350a b d e - 9450b d e )x +--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 (9450a d e - 28350a b d e + 28350a b d e - 9450b d e )x +--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 (4725a d e - 14175a b d e + 14175a b d e - 4725b d e)x + 945a d e +--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 - 2835a b d e + 2835a b d e - 945b d +--R - 1890a b d e + 1890a b d e - 630b d --R Type: Union(Expression(Integer),...) --E 1021 ---S 1022 of 1293 +--S 1022 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (983) +--R (4) --R 4 5 2 3 4 2 4 5 ---R (- 35A a d - 315A a )e + ((90A a b - 10B a )d + (810A a b - 90B a )d)e +--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 + (- 567A a b + 162B a b)d +--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 945a d e - 2835a b d e + 2835a b d e - 945b d +--R 630a d e - 1890a b d e + 1890a b d e - 630b d --R Type: Expression(Integer) --E 1022 @@ -24842,15 +25219,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (984) 0 +--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 (985) +--R (1) --R 2 +-------+ --R (B b x + (A b + B a)x + A a)\|b x + a --R ------------------------------------------------------------------------- @@ -24867,7 +25246,7 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ (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 (986) +--R (2) --R 5 4 3 5 2 5 --R ((96A b - 176B a b )e + 80B b d e )x --R + @@ -24961,236 +25340,236 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ --R Type: Expression(Integer) --E 1025 ---S 1026 of 1293 +--S 1026 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (987) +--R (3) --R 5 4 6 3 5 7 2 5 ---R ((288A b - 528B a b )d e + 240B b d e )x +--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 (- 144A a b + 264B a b )d e + (1584A b - 3024B a b )d e +--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 1320B b d e +--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 (108A a b - 198B a b )d e + (- 792A a b + 1542B a b )d e +--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 (3564A b - 7194B a b )d e + 2970B b d +--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 (- 90A a b - 3300B a b)d e + (594A a b + 12696B a b )d e +--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 (- 1782A a b - 17028B a b )d e + (4158A b + 4752B a b )d +--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 (- 2520A a b - 2310B a )d e + (9900A a b + 7470B a b)d e +--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 (- 14256A a b - 7194B a b )d e + (8316A a b + 594B a b )d +--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 - 1890A a d e + (6930A a b - 420B a )d e +--R - 1260A a d e + (4620A a b - 280B a )d e --R + ---R 3 2 4 8 2 3 3 2 9 ---R (- 8910A a b + 1320B a b)d e + (4158A a b - 1188B a b )d +--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 + 2835A a )e +--R (315A a d + 1260A a )e --R + ---R 4 5 2 5 6 8 ---R ((- 1155A a b + 70B a )d + (- 10395A a b + 630B a )d)e +--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 + (13365A a b - 1980B a b)d )e +--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 + (- 6237A a b + 1782B a b )d )e +--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 + 17010A a d)e +--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 + (- 62370A a b + 3780B a )d )e +--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 + (80190A a b - 11880B a b)d )e +--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 + (- 37422A a b + 10692B a b )d )e +--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 + 42525A a d )e +--R (4725A a d + 18900A a d )e --R + ---R 4 5 4 5 6 3 6 ---R ((- 17325A a b + 1050B a )d + (- 155925A a b + 9450B a )d )e +--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 + (200475A a b - 29700B a b)d )e +--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 + (- 93555A a b + 26730B a b )d )e +--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 + 56700A a d )e +--R (6300A a d + 25200A a d )e --R + ---R 4 5 5 5 6 4 5 ---R ((- 23100A a b + 1400B a )d + (- 207900A a b + 12600B a )d )e +--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 + (267300A a b - 39600B a b)d )e +--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 + (- 124740A a b + 35640B a b )d )e +--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 + 42525A a d )e +--R (4725A a d + 18900A a d )e --R + ---R 4 5 6 5 6 5 4 ---R ((- 17325A a b + 1050B a )d + (- 155925A a b + 9450B a )d )e +--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 + (200475A a b - 29700B a b)d )e +--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 + (- 93555A a b + 26730B a b )d )e +--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 + 17010A a d )e +--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 + (- 62370A a b + 3780B a )d )e +--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 + (80190A a b - 11880B a b)d )e +--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 + (- 37422A a b + 10692B a b )d )e +--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 + 2835A a d )e +--R (315A a d + 1260A a d )e --R + ---R 4 5 8 5 6 7 2 ---R ((- 1155A a b + 70B a )d + (- 10395A a b + 630B a )d )e +--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 + (13365A a b - 1980B a b)d )e +--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 + (- 6237A a b + 1782B a b )d +--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 10395a d e - 41580a b d e + 62370a b d e - 41580a b d e +--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 10395b d e +--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 62370a d e - 249480a b d e + 374220a b d e - 249480a b d e +--R 41580a d e - 166320a b d e + 249480a b d e - 166320a b d e --R + --R 4 11 5 ---R 62370b d e +--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 155925a d e - 623700a b d e + 935550a b d e - 623700a b d e +--R 103950a d e - 415800a b d e + 623700a b d e - 415800a b d e --R + --R 4 12 4 ---R 155925b d e +--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 207900a d e - 831600a b d e + 1247400a b d e - 831600a b d e +--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 207900b d e +--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 155925a d e - 623700a b d e + 935550a b d e - 623700a b d e +--R 103950a d e - 415800a b d e + 623700a b d e - 415800a b d e --R + --R 4 14 2 ---R 155925b d e +--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 62370a d e - 249480a b d e + 374220a b d e - 249480a b d e +--R 41580a d e - 166320a b d e + 249480a b d e - 166320a b d e --R + --R 4 15 ---R 62370b d e +--R 41580b d e --R * --R x --R + ---R 4 12 4 3 13 3 2 2 14 2 3 15 4 16 ---R 10395a d e - 41580a b d e + 62370a b d e - 41580a b d e + 10395b d +--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 +--S 1027 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (988) +--R (4) --R 5 6 3 ---R (315A a d + 2835A a )e +--R (315A a d + 1260A a )e --R + ---R 4 5 2 5 6 2 ---R ((- 1155A a b + 70B a )d + (- 10395A a b + 630B a )d)e +--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 + (13365A a b - 1980B a b)d )e +--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 + (- 6237A a b + 1782B a b )d +--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 10395a d e - 41580a b d e + 62370a b d e - 41580a b d e + 10395b d +--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 @@ -25198,15 +25577,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (989) 0 +--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 (990) +--R (1) --R 2 +-------+ --R (B b x + (A b + B a)x + A a)\|b x + a --R / @@ -25231,7 +25612,7 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ (a+b*x)^(5/2)/(e*(b*d-a*e)^5*(d+e*x)^(5/2)) --R --R ---R (991) +--R (2) --R 6 5 4 6 3 6 --R ((- 256A b + 416B a b )e - 160B b d e )x --R + @@ -25364,11 +25745,11 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ --R Type: Expression(Integer) --E 1030 ---S 1031 of 1293 +--S 1031 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (992) +--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 + @@ -25683,11 +26064,11 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 1031 ---S 1032 of 1293 +--S 1032 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (993) +--R (4) --R 6 7 4 --R (1155A a d + 18480A a )e --R + @@ -25715,15 +26096,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (994) 0 +--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 (995) +--R (1) --R 2 +-------+ --R (B b x + (A b + B a)x + A a)\|b x + a --R / @@ -25749,7 +26132,7 @@ r0:=-2/15*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ (a+b*x)^(5/2)/(e*(b*d-a*e)^6*(d+e*x)^(5/2)) --R --R ---R (996) +--R (2) --R 7 6 5 7 4 7 --R ((512A b - 768B a b )e + 256B b d e )x --R + @@ -25918,249 +26301,246 @@ r0:=-2/15*(B*d-A*e)*(a+b*x)^(5/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ --R Type: Expression(Integer) --E 1035 ---S 1036 of 1293 +--S 1036 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (997) +--R (3) --R 7 6 8 5 7 9 4 7 ---R ((2560A b - 3840B a b )d e + 1280B b d e )x +--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 (- 1280A a b + 1920B a b )d e + (19200A b - 29440B a b )d e +--R (- 1024A a b + 1536B a b )d e + (15360A b - 23552B a b )d e --R + --R 7 10 3 ---R 9600B b d e +--R 7680B b d e --R * --R 6 --R x --R + --R 2 5 3 4 8 5 6 2 5 9 4 ---R (960A a b - 1440B a b )d e + (- 9600A a b + 14880B a b )d e +--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 (62400A b - 98400B a b )d e + 31200B b d e +--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 (- 800A a b + 1200B a b )d e + (7200A a b - 11200B a b )d e +--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 (- 31200A a b + 50400B a b )d e +--R (- 24960A a b + 40320B a b )d e --R + ---R 7 6 11 2 7 12 ---R (114400A b - 187200B a b )d e + 57200B b d e +--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 (700A a b - 1050B a b )d e + (- 6000A a b + 9350B a b )d e +--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 (23400A a b - 38100B a b )d e +--R (18720A a b - 30480B a b )d e --R + --R 6 2 5 11 2 ---R (- 57200A a b + 97500B a b )d e +--R (- 45760A a b + 78000B a b )d e --R + --R 7 6 12 7 13 ---R (128700A b - 221650B a b )d e + 64350B b d +--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 (- 630A a b - 44100B a b)d e + (5250A a b + 262080B a b )d e +--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 (- 19500A a b - 643800B a b )d e +--R (- 15600A a b - 515040B a b )d e --R + --R 2 5 3 4 11 2 ---R (42900A a b + 826800B a b )d e +--R (34320A a b + 661440B a b )d e --R + ---R 6 2 5 12 7 6 13 ---R (- 64350A a b - 557700B a b )d e + (90090A b + 102960B a b )d +--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 (- 36960A a b - 34650B a )d e + (220500A a b + 191310B a b)d e +--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 (- 546000A a b - 422100B a b )d e +--R (- 436800A a b - 337680B a b )d e --R + --R 3 4 4 3 11 2 ---R (715000A a b + 456300B a b )d e +--R (572000A a b + 365040B a b )d e --R + --R 2 5 3 4 12 ---R (- 514800A a b - 221650B a b )d e +--R (- 411840A a b - 177320B a b )d e --R + --R 6 2 5 13 ---R (180180A a b + 12870B a b )d +--R (144144A a b + 10296B a b )d --R * --R x --R + --R 7 8 5 6 7 9 4 ---R - 30030A a d e + (173250A a b - 4620B a )d e +--R - 24024A a d e + (138600A a b - 3696B a )d e --R + --R 5 2 6 10 3 ---R (- 409500A a b + 25200B a b)d e +--R (- 327600A a b + 20160B a b)d e --R + --R 4 3 5 2 11 2 ---R (500500A a b - 54600B a b )d e +--R (400400A a b - 43680B a b )d e --R + --R 3 4 4 3 12 2 5 3 4 13 ---R (- 321750A a b + 57200B a b )d e + (90090A a b - 25740B a b )d +--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 - 75075A a )e ---R + ---R 6 7 2 7 8 12 ---R ((17325A a b - 462B a )d + (433125A a b - 11550B a )d)e +--R 7 8 13 +--R (3003A a d + 48048A a )e --R + ---R 5 2 6 3 6 2 7 2 11 ---R ((- 40950A a b + 2520B a b)d + (- 1023750A a b + 63000B a b)d )e +--R 6 7 2 7 8 12 +--R ((- 17325A a b + 462B a )d + (- 277200A a b + 7392B a )d)e --R + ---R 4 3 5 2 4 5 3 6 2 3 10 ---R ((50050A a b - 5460B a b )d + (1251250A a b - 136500B a b )d )e +--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 3 4 4 3 5 ---R (- 32175A a b + 5720B a b )d ---R + ---R 4 4 5 3 4 ---R (- 804375A a b + 143000B a b )d +--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 9 +--R 10 --R e --R + ---R 2 5 3 4 6 3 5 4 4 5 8 ---R ((9009A a b - 2574B a b )d + (225225A a b - 64350B a b )d )e +--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 - 600600A a d)e +--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 + (3465000A a b - 92400B a )d )e +--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 ---R (- 327600A a b + 20160B a b)d ---R + ---R 6 2 7 3 ---R (- 8190000A a b + 504000B a b)d ---R * ---R 10 ---R e +--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 (10010000A a b - 1092000B a b )d +--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 ---R (- 257400A a b + 45760B a b )d +--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 4 4 5 3 5 ---R (- 6435000A a b + 1144000B a b )d +--R 3 5 4 4 6 +--R (- 1153152A a b + 329472B a b )d --R * ---R 8 +--R 7 --R e ---R + ---R 2 5 3 4 7 3 5 4 4 6 7 ---R ((72072A a b - 20592B a b )d + (1801800A a b - 514800B a b )d )e --R * --R 7 --R x --R + ---R 7 3 8 2 11 ---R (- 84084A a d - 2102100A a d )e +--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 + (12127500A a b - 323400B a )d )e +--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 (1146600A a b - 70560B a b)d +--R + --R 6 2 7 4 ---R (- 28665000A a b + 1764000B a b)d +--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 4 3 5 2 6 +--R (- 1401400A a b + 152880B a b )d --R + ---R 5 3 6 2 5 ---R (35035000A a b - 3822000B a b )d +--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 3 4 4 3 7 +--R (900900A a b - 160160B a b )d --R + ---R 4 4 5 3 6 ---R (- 22522500A a b + 4004000B a b )d +--R 4 4 5 3 6 +--R (14414400A a b - 2562560B a b )d --R * --R 7 --R e --R + ---R 2 5 3 4 8 3 5 4 4 7 6 ---R ((252252A a b - 72072B a b )d + (6306300A a b - 1801800B a b )d )e +--R 2 5 3 4 8 +--R (- 252252A a b + 72072B a b )d +--R + +--R 3 5 4 4 7 +--R (- 4036032A a b + 1153152B a b )d +--R * +--R 6 +--R e --R * --R 6 --R x --R + ---R 7 4 8 3 10 ---R (- 168168A a d - 4204200A a d )e +--R 7 4 8 3 10 +--R (168168A a d + 2690688A a d )e --R + ---R 6 7 5 7 8 4 9 ---R ((970200A a b - 25872B a )d + (24255000A a b - 646800B a )d )e +--R 6 7 5 7 8 4 9 +--R ((- 970200A a b + 25872B a )d + (- 15523200A a b + 413952B a )d )e --R + --R 5 2 6 6 ---R (- 2293200A a b + 141120B a b)d ---R + +--R (2293200A a b - 141120B a b)d +--R + --R 6 2 7 5 ---R (- 57330000A a b + 3528000B a b)d +--R (36691200A a b - 2257920B a b)d --R * --R 8 --R e --R + ---R 4 3 5 2 7 ---R (2802800A a b - 305760B a b )d +--R 4 3 5 2 7 +--R (- 2802800A a b + 305760B a b )d --R + ---R 5 3 6 2 6 ---R (70070000A a b - 7644000B a b )d +--R 5 3 6 2 6 +--R (- 44844800A a b + 4892160B a b )d --R * --R 7 --R e --R + ---R 3 4 4 3 8 ---R (- 1801800A a b + 320320B a b )d +--R 3 4 4 3 8 +--R (1801800A a b - 320320B a b )d --R + ---R 4 4 5 3 7 ---R (- 45045000A a b + 8008000B a b )d +--R 4 4 5 3 7 +--R (28828800A a b - 5125120B a b )d --R * --R 6 --R e --R + ---R 2 5 3 4 9 ---R (504504A a b - 144144B a b )d +--R 2 5 3 4 9 +--R (- 504504A a b + 144144B a b )d --R + ---R 3 5 4 4 8 ---R (12612600A a b - 3603600B a b )d +--R 3 5 4 4 8 +--R (- 8072064A a b + 2306304B a b )d --R * --R 5 --R e @@ -26168,44 +26548,44 @@ a0:=integrate(t0,x) --R 5 --R x --R + ---R 7 5 8 4 9 ---R (- 210210A a d - 5255250A a d )e +--R 7 5 8 4 9 +--R (210210A a d + 3363360A a d )e --R + ---R 6 7 6 7 8 5 8 ---R ((1212750A a b - 32340B a )d + (30318750A a b - 808500B a )d )e +--R 6 7 6 7 8 5 8 +--R ((- 1212750A a b + 32340B a )d + (- 19404000A a b + 517440B a )d )e --R + --R 5 2 6 7 ---R (- 2866500A a b + 176400B a b)d ---R + +--R (2866500A a b - 176400B a b)d +--R + --R 6 2 7 6 ---R (- 71662500A a b + 4410000B a b)d +--R (45864000A a b - 2822400B a b)d --R * --R 7 --R e --R + ---R 4 3 5 2 8 ---R (3503500A a b - 382200B a b )d +--R 4 3 5 2 8 +--R (- 3503500A a b + 382200B a b )d --R + ---R 5 3 6 2 7 ---R (87587500A a b - 9555000B a b )d +--R 5 3 6 2 7 +--R (- 56056000A a b + 6115200B a b )d --R * --R 6 --R e --R + ---R 3 4 4 3 9 ---R (- 2252250A a b + 400400B a b )d +--R 3 4 4 3 9 +--R (2252250A a b - 400400B a b )d --R + ---R 4 4 5 3 8 ---R (- 56306250A a b + 10010000B a b )d +--R 4 4 5 3 8 +--R (36036000A a b - 6406400B a b )d --R * --R 5 --R e --R + ---R 2 5 3 4 10 ---R (630630A a b - 180180B a b )d +--R 2 5 3 4 10 +--R (- 630630A a b + 180180B a b )d --R + ---R 3 5 4 4 9 ---R (15765750A a b - 4504500B a b )d +--R 3 5 4 4 9 +--R (- 10090080A a b + 2882880B a b )d --R * --R 4 --R e @@ -26213,44 +26593,44 @@ a0:=integrate(t0,x) --R 4 --R x --R + ---R 7 6 8 5 8 ---R (- 168168A a d - 4204200A a d )e +--R 7 6 8 5 8 +--R (168168A a d + 2690688A a d )e --R + ---R 6 7 7 7 8 6 7 ---R ((970200A a b - 25872B a )d + (24255000A a b - 646800B a )d )e +--R 6 7 7 7 8 6 7 +--R ((- 970200A a b + 25872B a )d + (- 15523200A a b + 413952B a )d )e --R + --R 5 2 6 8 ---R (- 2293200A a b + 141120B a b)d ---R + +--R (2293200A a b - 141120B a b)d +--R + --R 6 2 7 7 ---R (- 57330000A a b + 3528000B a b)d +--R (36691200A a b - 2257920B a b)d --R * --R 6 --R e --R + ---R 4 3 5 2 9 ---R (2802800A a b - 305760B a b )d +--R 4 3 5 2 9 +--R (- 2802800A a b + 305760B a b )d --R + ---R 5 3 6 2 8 ---R (70070000A a b - 7644000B a b )d +--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 3 4 4 3 10 +--R (1801800A a b - 320320B a b )d --R + ---R 4 4 5 3 9 ---R (- 45045000A a b + 8008000B a b )d +--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 2 5 3 4 11 +--R (- 504504A a b + 144144B a b )d --R + ---R 3 5 4 4 10 ---R (12612600A a b - 3603600B a b )d +--R 3 5 4 4 10 +--R (- 8072064A a b + 2306304B a b )d --R * --R 3 --R e @@ -26258,44 +26638,44 @@ a0:=integrate(t0,x) --R 3 --R x --R + ---R 7 7 8 6 7 ---R (- 84084A a d - 2102100A a d )e +--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 + (12127500A a b - 323400B a )d )e +--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 (1146600A a b - 70560B a b)d +--R + --R 6 2 7 8 ---R (- 28665000A a b + 1764000B a b)d +--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 4 3 5 2 10 +--R (- 1401400A a b + 152880B a b )d --R + ---R 5 3 6 2 9 ---R (35035000A a b - 3822000B a b )d +--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 3 4 4 3 11 +--R (900900A a b - 160160B a b )d --R + ---R 4 4 5 3 10 ---R (- 22522500A a b + 4004000B a b )d +--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 2 5 3 4 12 +--R (- 252252A a b + 72072B a b )d --R + ---R 3 5 4 4 11 ---R (6306300A a b - 1801800B a b )d +--R 3 5 4 4 11 +--R (- 4036032A a b + 1153152B a b )d --R * --R 2 --R e @@ -26303,193 +26683,192 @@ a0:=integrate(t0,x) --R 2 --R x --R + ---R 7 8 8 7 6 ---R (- 24024A a d - 600600A a d )e +--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 + (3465000A a b - 92400B a )d )e +--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 ---R (- 327600A a b + 20160B a b)d ---R + ---R 6 2 7 9 ---R (- 8190000A a b + 504000B a b)d ---R * ---R 4 ---R e +--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 4 3 5 2 11 +--R (- 400400A a b + 43680B a b )d --R + ---R 5 3 6 2 10 ---R (10010000A a b - 1092000B a b )d +--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 (- 6435000A a b + 1144000B a b )d +--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 3 5 4 4 12 ---R ((72072A a b - 20592B a b )d + (1801800A a b - 514800B a b )d )e +--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 - 75075A a d )e +--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 + (433125A a b - 11550B a )d )e +--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 + (- 1023750A a b + 63000B a b)d )e +--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 + (1251250A a b - 136500B a b )d )e +--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 + (- 804375A a b + 143000B a b )d )e +--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 + (225225A a b - 64350B a b )d +--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 225225a d e - 1351350a b d e + 3378375a b d e +--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 - 4504500a b d e + 3378375a b d e - 1351350a b d e +--R - 3603600a b d e + 2702700a b d e - 1081080a b d e --R + --R 6 14 8 ---R 225225b d e +--R 180180b d e --R * --R 8 --R x --R + ---R 6 9 13 5 10 12 4 2 11 11 ---R 1801800a d e - 10810800a b d e + 27027000a b d e +--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 - 36036000a b d e + 27027000a b d e - 10810800a b d e +--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 1801800b d e +--R 1441440b d e --R * --R 7 --R x --R + --R 6 10 12 5 11 11 4 2 12 10 ---R 6306300a d e - 37837800a b d e + 94594500a b d e +--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 - 126126000a b d e + 94594500a b d e - 37837800a b d e +--R - 100900800a b d e + 75675600a b d e - 30270240a b d e --R + --R 6 16 6 ---R 6306300b d e +--R 5045040b d e --R * --R 6 --R x --R + --R 6 11 11 5 12 10 4 2 13 9 ---R 12612600a d e - 75675600a b d e + 189189000a b d e +--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 - 252252000a b d e + 189189000a b d e - 75675600a b d e +--R - 201801600a b d e + 151351200a b d e - 60540480a b d e --R + --R 6 17 5 ---R 12612600b d e +--R 10090080b d e --R * --R 5 --R x --R + --R 6 12 10 5 13 9 4 2 14 8 ---R 15765750a d e - 94594500a b d e + 236486250a b d e +--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 - 315315000a b d e + 236486250a b d e - 94594500a b d e +--R - 252252000a b d e + 189189000a b d e - 75675600a b d e --R + --R 6 18 4 ---R 15765750b d e +--R 12612600b d e --R * --R 4 --R x --R + --R 6 13 9 5 14 8 4 2 15 7 ---R 12612600a d e - 75675600a b d e + 189189000a b d e +--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 - 252252000a b d e + 189189000a b d e - 75675600a b d e +--R - 201801600a b d e + 151351200a b d e - 60540480a b d e --R + --R 6 19 3 ---R 12612600b d e +--R 10090080b d e --R * --R 3 --R x --R + --R 6 14 8 5 15 7 4 2 16 6 ---R 6306300a d e - 37837800a b d e + 94594500a b d e +--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 - 126126000a b d e + 94594500a b d e - 37837800a b d e +--R - 100900800a b d e + 75675600a b d e - 30270240a b d e --R + --R 6 20 2 ---R 6306300b d e +--R 5045040b d e --R * --R 2 --R x --R + ---R 6 15 7 5 16 6 4 2 17 5 ---R 1801800a d e - 10810800a b d e + 27027000a b d e +--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 - 36036000a b d e + 27027000a b d e - 10810800a b d e +--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 1801800b d e +--R 1441440b d e --R * --R x --R + --R 6 16 6 5 17 5 4 2 18 4 3 3 19 3 ---R 225225a d e - 1351350a b d e + 3378375a b d e - 4504500a b d e +--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 3378375a b d e - 1351350a b d e + 225225b d +--R 2702700a b d e - 1081080a b d e + 180180b d --R Type: Union(Expression(Integer),...) --E 1036 ---S 1037 of 1293 +--S 1037 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (998) ---R 7 8 5 ---R (- 3003A a d - 75075A a )e +--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 + (433125A a b - 11550B a )d)e +--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 + (- 1023750A a b + 63000B a b)d )e +--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 + (1251250A a b - 136500B a b )d )e +--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 + (- 804375A a b + 143000B a b )d )e +--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 + (225225A a b - 64350B a b )d +--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 225225a d e - 1351350a b d e + 3378375a b d e - 4504500a b d e +--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 3378375a b d e - 1351350a b d e + 225225b d +--R 2702700a b d e - 1081080a b d e + 180180b d --R Type: Expression(Integer) --E 1037 @@ -26497,15 +26876,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (999) 0 +--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 (1000) +--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 + @@ -26536,7 +26917,7 @@ 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)/_ sqrt(a+b*x)*sqrt(d+e*x)/(b^4*e^4) --R --R ---R (1001) +--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 + @@ -26628,11 +27009,13 @@ 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)/_ --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 (1002) +--R (1) --R 2 4 2 2 3 --R B b e x + ((A b + 2B a b)e + B b d)x --R + @@ -26659,7 +27042,7 @@ 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)+_ (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 (1003) +--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 + @@ -26736,11 +27119,13 @@ 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)+_ --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 (1004) +--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) @@ -26757,7 +27142,7 @@ r0:=1/5*B*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b*e)+1/128*(b*d-a*e)^4*_ sqrt(a+b*x)*sqrt(d+e*x)/(b^2*e^4) --R --R ---R (1005) +--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 + @@ -26819,15 +27204,17 @@ r0:=1/5*B*(a+b*x)^(7/2)*(d+e*x)^(3/2)/(b*e)+1/128*(b*d-a*e)^4*_ --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 (1006) ---------------------------------------------------------------- ---R +-------+ ---R \|e x + d +--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 @@ -26840,7 +27227,7 @@ 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)/_ (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 (1007) +--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 + @@ -26885,15 +27272,17 @@ 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)/_ --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 (1008) ---------------------------------------------------------------- ---R +-------+ ---R (e x + d)\|e x + d +--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 @@ -26906,7 +27295,7 @@ r0:=-5/8*(b*d-a*e)^2*(7*b*B*d-6*A*b*e-a*B*e)*atanh(sqrt(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 (1009) +--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 + @@ -26951,15 +27340,17 @@ r0:=-5/8*(b*d-a*e)^2*(7*b*B*d-6*A*b*e-a*B*e)*atanh(sqrt(e)*_ --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 (1010) ---------------------------------------------------------------- ---R 2 2 2 +-------+ ---R (e x + 2d e x + d )\|e x + d +--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 @@ -26972,7 +27363,7 @@ 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*(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 (1011) +--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 + @@ -27017,15 +27408,17 @@ r0:=-2/3*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(3/2))+_ --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 (1012) ---------------------------------------------------------------- ---R 3 3 2 2 2 3 +-------+ ---R (e x + 3d e x + 3d e x + d )\|e x + d +--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 @@ -27039,7 +27432,7 @@ r0:=-2/5*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ sqrt(d+e*x)/(e^4*(b*d-a*e)) --R --R ---R (1013) +--R (2) --R 2 3 2 2 2 --R ((30A b + 75B a b)e - 105B b d e )x --R + @@ -27087,15 +27480,17 @@ r0:=-2/5*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(5/2))-_ --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 (1014) ---------------------------------------------------------------- ---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 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 @@ -27106,7 +27501,7 @@ r0:=-2/7*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))-_ (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 (1015) +--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 + @@ -27157,15 +27552,17 @@ r0:=-2/7*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(7/2))-_ --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 (1016) ---------------------------------------------------------------- ---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 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 @@ -27174,7 +27571,7 @@ 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 (1017) +--R (2) --R 4 3 4 4 --R ((4A b - 18B a b )e + 14B b d)x --R + @@ -27210,99 +27607,105 @@ r0:=-2/9*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ --R Type: Expression(Integer) --E 1080 ---S 1081 of 1293 +--S 1081 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1018) +--R (3) --R 4 3 5 4 6 4 ---R ((12A b - 54B a b )d e + 42B b d )x +--R ((16A b - 72B a b )d e + 56B b d )x --R + --R 3 2 2 5 4 3 6 3 ---R ((- 6A a b - 162B a b )d e + (54A b + 114B a b )d )x +--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 ((- 90A a b - 162B a b)d e + (162A a b + 90B a b )d )x +--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 ((- 114A a b - 54B a )d e + (162A a b + 6B a b)d )x - 42A a d e +--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 (54A a b - 12B a )d +--R (72A a b - 16B a )d --R * --R +-------+ +-------+ --R \|b x + a \|e x + d --R + ---R 4 5 6 3 4 2 4 5 5 5 ---R ((- 7A a d - 63A a )e + ((9A a b - 2B a )d + (81A a b - 18B a )d)e )x +--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 - 315A a d)e +--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 + (405A a b - 90B a )d )e +--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 - 630A a d )e +--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 + (810A a b - 180B a )d )e +--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 - 630A a d )e +--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 + (810A a b - 180B a )d )e +--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 - 315A a d )e +--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 + (405A a b - 90B a )d )e +--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 - 63A a d )e + (9A a b - 2B a )d + (81A a b - 18B a )d +--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 (189a d e - 378a b d e + 189b d e )x +--R (252a d e - 504a b d e + 252b d e )x --R + ---R 2 6 6 7 5 2 8 4 4 ---R (945a d e - 1890a b d e + 945b d e )x +--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 (1890a d e - 3780a b d e + 1890b d e )x +--R (2520a d e - 5040a b d e + 2520b d e )x --R + --R 2 8 4 9 3 2 10 2 2 ---R (1890a d e - 3780a b d e + 1890b d e )x +--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 (945a d e - 1890a b d e + 945b d e)x + 189a d e - 378a b d e +--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 189b d +--R 252b d --R Type: Union(Expression(Integer),...) --E 1081 ---S 1082 of 1293 +--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 - 63A a )e + (9A a b - 2B a )d + (81A a b - 18B a )d ---R (1019) --------------------------------------------------------------- ---R 2 5 2 6 2 7 ---R 189a d e - 378a b d e + 189b d +--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 @@ -27310,15 +27713,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1020) 0 +--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 (1021) +--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 ------------------------------------------------------------------------- @@ -27334,7 +27739,7 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ (e*(b*d-a*e)^3*(d+e*x)^(7/2)) --R --R ---R (1022) +--R (2) --R 5 4 2 5 5 --R ((- 16A b + 44B a b )e - 28B b d e)x --R + @@ -27396,168 +27801,174 @@ r0:=-2/11*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(11/2))+_ --R Type: Expression(Integer) --E 1085 ---S 1086 of 1293 +--S 1086 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1023) +--R (3) --R 5 4 6 2 5 7 5 ---R ((- 16A b + 44B a b )d e - 28B b d e)x +--R ((- 32A b + 88B a b )d e - 56B b d e)x --R + ---R 4 2 3 6 2 5 4 7 5 8 4 ---R ((8A a b - 22B a b )d e + (- 88A b + 256B a b )d e - 154B b d )x +--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 (- 6A a b - 330B a b )d e + (44A a b + 908B a b )d e +--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 (- 198A b - 418B a b )d +--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 (- 226A a b - 418B a b)d e + (660A a b + 908B a b )d e +--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 (- 594A a b - 330B a b )d +--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 (- 322A a b - 154B a )d e + (836A a b + 256B a b)d e +--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 (- 594A a b - 22B a b )d +--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 - 126A a d e + (308A a b - 28B a )d e + (- 198A a b + 44B a b)d +--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 + 63A a )e +--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 + (- 154A a b + 14B a )d)e +--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 + (99A a b - 22B a b)d )e +--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 + 378A a d)e +--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 + (- 924A a b + 84B a )d )e +--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 + (594A a b - 132B a b)d )e +--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 + 945A a d )e +--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 + (- 2310A a b + 210B a )d )e +--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 + (1485A a b - 330B a b)d )e +--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 + 1260A a d )e +--R (1260A a d + 5040A a d )e --R + ---R 4 5 5 5 6 4 4 ---R ((- 3080A a b + 280B a )d + (- 3080A a b + 280B a )d )e +--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 + (1980A a b - 440B a b)d )e +--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 + 945A a d )e +--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 + (- 2310A a b + 210B a )d )e +--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 + (1485A a b - 330B a b)d )e +--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 + 378A a d )e +--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 + (- 924A a b + 84B a )d )e +--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 + (594A a b - 132B a b)d )e +--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 + 63A a d )e +--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 + (- 154A a b + 14B a )d )e +--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 + (99A a b - 22B a b)d +--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 (693a d e - 2079a b d e + 2079a b d e - 693b d e )x +--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 (4158a d e - 12474a b d e + 12474a b d e - 4158b d e )x +--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 (10395a d e - 31185a b d e + 31185a b d e - 10395b d e )x +--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 (13860a d e - 41580a b d e + 41580a b d e - 13860b d e )x +--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 (10395a d e - 31185a b d e + 31185a b d e - 10395b d e )x +--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 (4158a d e - 12474a b d e + 12474a b d e - 4158b d e)x +--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 693a d e - 2079a b d e + 2079a b d e - 693b d +--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 +--S 1087 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1024) ---R 5 6 2 ---R (63A a d + 63A a )e +--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 + (- 154A a b + 14B a )d)e +--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 + (99A a b - 22B a b)d +--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 693a d e - 2079a b d e + 2079a b d e - 693b d +--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 @@ -27565,15 +27976,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1025) 0 +--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 (1026) +--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 / @@ -27596,7 +28009,7 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ (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 (1027) +--R (2) --R 6 5 3 6 2 6 --R ((96A b - 208B a b )e + 112B b d e )x --R + @@ -27714,284 +28127,272 @@ r0:=-2/13*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(13/2))+_ --R Type: Expression(Integer) --E 1090 ---S 1091 of 1293 +--S 1091 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1028) +--R (3) --R 6 5 7 3 6 8 2 6 ---R ((288A b - 624B a b )d e + 336B b d e )x +--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 (- 144A a b + 312B a b )d e + (1872A b - 4224B a b )d e +--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 2184B b d e +--R 1456B b d e --R * --R 5 --R x --R + ---R 2 4 3 3 7 3 5 2 4 8 2 ---R (108A a b - 234B a b )d e + (- 936A a b + 2154B a b )d e +--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 (5148A b - 12246B a b )d e + 6006B b d +--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 (- 90A a b - 8814B a b )d e + (702A a b + 34410B a b )d e +--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 (- 2574A a b - 47658B a b )d e + (7722A b + 16302B a b )d +--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 (- 6678A a b - 12558B a b)d e + (26442A a b + 43026B a b )d e +--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 (- 38610A a b - 47658B a b )d e + (23166A a b + 12870B a b )d +--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 (- 10206A a b - 4914B a )d e + (37674A a b + 14574B a b)d e +--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 (- 48906A a b - 12246B a b )d e + (23166A a b + 858B a b )d +--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 - 4158A a d e + (14742A a b - 756B a )d e +--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 (- 18018A a b + 2184B a b)d e + (7722A a b - 1716B a b )d +--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 - 6237A a )e +--R (- 693A a d - 2772A a )e --R + ---R 5 6 2 6 7 9 ---R ((2457A a b - 126B a )d + (22113A a b - 1134B a )d)e +--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 + (- 27027A a b + 3276B a b)d )e +--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 + (11583A a b - 2574B a b )d )e +--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 - 43659A a d)e +--R (- 4851A a d - 19404A a d)e --R + ---R 5 6 3 6 7 2 8 ---R ((17199A a b - 882B a )d + (154791A a b - 7938B a )d )e +--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 + (- 189189A a b + 22932B a b)d )e +--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 + (81081A a b - 18018B a b )d )e +--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 - 130977A a d )e +--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 + (464373A a b - 23814B a )d )e +--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 + (- 567567A a b + 68796B a b)d )e +--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 + (243243A a b - 54054B a b )d )e +--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 - 218295A a d )e +--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 + (773955A a b - 39690B a )d )e +--R ((85995A a b - 4410B a )d + (343980A a b - 17640B a )d )e --R + ---R 4 2 5 6 ---R (- 105105A a b + 12740B a b)d ---R + ---R 5 2 6 5 ---R (- 945945A a b + 114660B a b)d ---R * ---R 5 ---R e +--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 + (405405A a b - 90090B a b )d )e +--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 - 218295A a d )e +--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 + (773955A a b - 39690B a )d )e +--R ((85995A a b - 4410B a )d + (343980A a b - 17640B a )d )e --R + ---R 4 2 5 7 ---R (- 105105A a b + 12740B a b)d ---R + ---R 5 2 6 6 ---R (- 945945A a b + 114660B a b)d ---R * ---R 4 ---R e +--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 + (405405A a b - 90090B a b )d )e +--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 - 130977A a d )e +--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 + (464373A a b - 23814B a )d )e +--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 + (- 567567A a b + 68796B a b)d )e +--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 + (243243A a b - 54054B a b )d )e +--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 - 43659A a d )e +--R (- 4851A a d - 19404A a d )e --R + ---R 5 6 8 6 7 7 3 ---R ((17199A a b - 882B a )d + (154791A a b - 7938B a )d )e +--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 + (- 189189A a b + 22932B a b)d )e +--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 + (81081A a b - 18018B a b )d )e +--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 - 6237A a d )e +--R (- 693A a d - 2772A a d )e --R + ---R 5 6 9 6 7 8 2 ---R ((2457A a b - 126B a )d + (22113A a b - 1134B a )d )e +--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 + (- 27027A a b + 3276B a b)d )e +--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 + (11583A a b - 2574B a b )d +--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 27027a d e - 108108a b d e + 162162a b d e - 108108a b d e +--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 27027b d e +--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 189189a d e - 756756a b d e + 1135134a b d e - 756756a b d e +--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 189189b d e +--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 567567a d e - 2270268a b d e + 3405402a b d e - 2270268a b d e +--R 378378a d e - 1513512a b d e + 2270268a b d e - 1513512a b d e --R + --R 4 13 5 ---R 567567b d e +--R 378378b d e --R * --R 5 --R x --R + --R 4 10 8 3 11 7 2 2 12 6 ---R 945945a d e - 3783780a b d e + 5675670a b d e +--R 630630a d e - 2522520a b d e + 3783780a b d e --R + --R 3 13 5 4 14 4 ---R - 3783780a b d e + 945945b d e +--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 945945a d e - 3783780a b d e + 5675670a b d e +--R 630630a d e - 2522520a b d e + 3783780a b d e --R + --R 3 14 4 4 15 3 ---R - 3783780a b d e + 945945b d e +--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 567567a d e - 2270268a b d e + 3405402a b d e +--R 378378a d e - 1513512a b d e + 2270268a b d e --R + --R 3 15 3 4 16 2 ---R - 2270268a b d e + 567567b d e +--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 189189a d e - 756756a b d e + 1135134a b d e - 756756a b d e +--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 189189b d e +--R 126126b d e --R * --R x --R + ---R 4 14 4 3 15 3 2 2 16 2 3 17 ---R 27027a d e - 108108a b d e + 162162a b d e - 108108a b d e +--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 27027b d +--R 18018b d --R Type: Union(Expression(Integer),...) --E 1091 ---S 1092 of 1293 +--S 1092 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1029) +--R (4) --R 6 7 3 ---R (- 693A a d - 6237A a )e +--R (- 693A a d - 2772A a )e --R + ---R 5 6 2 6 7 2 ---R ((2457A a b - 126B a )d + (22113A a b - 1134B a )d)e +--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 + (- 27027A a b + 3276B a b)d )e +--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 + (11583A a b - 2574B a b )d +--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 27027a d e - 108108a b d e + 162162a b d e - 108108a b d e + 27027b d +--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 @@ -27999,15 +28400,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1030) 0 +--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 (1031) +--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 / @@ -28032,7 +28435,7 @@ r0:=-2/15*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ (a+b*x)^(7/2)/(e*(b*d-a*e)^5*(d+e*x)^(7/2)) --R --R ---R (1032) +--R (2) --R 7 6 4 7 3 7 --R ((- 256A b + 480B a b )e - 224B b d e )x --R + @@ -28186,419 +28589,401 @@ r0:=-2/15*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(15/2))+_ --R Type: Expression(Integer) --E 1095 ---S 1096 of 1293 +--S 1096 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1033) ---R 7 6 8 4 7 9 3 7 ---R ((- 1024A b + 1920B a b )d e - 896B b d e )x +--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 (512A a b - 960B a b )d e + (- 7680A b + 14848B a b )d e +--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 - 6720B b d e +--R - 3360B b d e --R * --R 6 --R x --R + --R 2 5 3 4 8 4 6 2 5 9 3 ---R (- 384A a b + 720B a b )d e + (3840A a b - 7536B a b )d e +--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 (- 24960A b + 50160B a b )d e - 21840B b d e +--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 (320A a b - 600B a b )d e + (- 2880A a b + 5680B a b )d e +--R (160A a b - 300B a b )d e + (- 1440A a b + 2840B a b )d e --R + ---R 6 2 5 10 2 ---R (12480A a b - 25920B a b )d e +--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 6 11 7 12 ---R (- 45760A b + 96720B a b )d e - 40040B b d +--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 (- 280A a b - 44520B a b )d e + (2400A a b + 220480B a b )d e +--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 (- 9360A a b - 430800B a b )d e +--R (- 4680A a b - 215400B a b )d e --R + ---R 6 2 5 11 7 6 12 ---R (22880A a b + 399360B a b )d e + (- 51480A b - 108680B a b )d +--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 (- 35784A a b - 68040B a b)d e +--R (- 17892A a b - 34020B a b)d e --R + ---R 4 3 5 2 9 3 ---R (178080A a b + 310464B a b )d e +--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 (- 352560A a b - 534480B a b )d e +--R (- 176280A a b - 267240B a b )d e --R + --R 2 5 3 4 11 ---R (343200A a b + 399360B a b )d e +--R (171600A a b + 199680B a b )d e --R + ---R 6 2 5 12 ---R (- 154440A a b - 85800B a b )d +--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 (- 57288A a b - 27720B a )d e + (272160A a b + 115248B a b)d e +--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 (- 502320A a b - 171360B a b )d e +--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 (434720A a b + 96720B a b )d e + (- 154440A a b - 5720B a b )d +--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 - 24024A a d e + (110880A a b - 3696B a )d e +--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 (- 196560A a b + 15120B a b)d e + (160160A a b - 21840B a b )d e +--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 (- 51480A a b + 11440B a b )d +--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 + 48048A a )e +--R (3003A a d + 12012A a )e --R + ---R 6 7 2 7 8 11 ---R ((- 13860A a b + 462B a )d + (- 221760A a b + 7392B a )d)e +--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 + (393120A a b - 30240B a b)d )e +--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 + (- 320320A a b + 43680B a b )d )e +--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 + (102960A a b - 22880B a b )d )e +--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 + 384384A a d)e +--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 + (- 1774080A a b + 59136B a )d )e +--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 + (3144960A a b - 241920B a b)d )e +--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 (- 2562560A a b + 349440B a b )d +--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 + (823680A a b - 183040B a b )d )e +--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 + 1345344A a d )e +--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 + (- 6209280A a b + 206976B a )d )e +--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 + (11007360A a b - 846720B a b)d )e +--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 (- 8968960A a b + 1223040B a b )d +--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 + (2882880A a b - 640640B a b )d )e +--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 + 2690688A a d )e +--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 + (- 12418560A a b + 413952B a )d )e +--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 ---R (1375920A a b - 105840B a b)d ---R + ---R 6 2 7 5 ---R (22014720A a b - 1693440B a b)d ---R * ---R 7 ---R e +--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 (- 17937920A a b + 2446080B a b )d +--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 + (5765760A a b - 1281280B a b )d )e +--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 + 3363360A a d )e +--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 + (- 15523200A a b + 517440B a )d )e +--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 ---R (1719900A a b - 132300B a b)d ---R + ---R 6 2 7 6 ---R (27518400A a b - 2116800B a b)d ---R * ---R 6 ---R e +--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 (- 22422400A a b + 3057600B a b )d +--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 + (7207200A a b - 1601600B a b )d )e +--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 + 2690688A a d )e +--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 + (- 12418560A a b + 413952B a )d )e +--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 ---R (1375920A a b - 105840B a b)d ---R + ---R 6 2 7 7 ---R (22014720A a b - 1693440B a b)d ---R * ---R 5 ---R e +--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 (- 17937920A a b + 2446080B a b )d +--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 + (5765760A a b - 1281280B a b )d )e +--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 + 1345344A a d )e +--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 + (- 6209280A a b + 206976B a )d )e +--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 + (11007360A a b - 846720B a b)d )e +--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 (- 8968960A a b + 1223040B a b )d +--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 + (2882880A a b - 640640B a b )d )e +--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 + 384384A a d )e +--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 + (- 1774080A a b + 59136B a )d )e +--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 + (3144960A a b - 241920B a b)d )e +--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 (- 2562560A a b + 349440B a b )d +--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 + (823680A a b - 183040B a b )d )e +--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 + 48048A a d )e +--R (3003A a d + 12012A a d )e --R + ---R 6 7 10 7 8 9 3 ---R ((- 13860A a b + 462B a )d + (- 221760A a b + 7392B a )d )e +--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 + (393120A a b - 30240B a b)d )e +--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 + (- 320320A a b + 43680B a b )d )e +--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 + (102960A a b - 22880B a b )d +--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 ---R 180180a d e - 900900a b d e + 1801800a b d e +--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 2 3 11 10 4 12 9 5 13 8 ---R - 1801800a b d e + 900900a b d e - 180180b d e +--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 1441440a d e - 7207200a b d e + 14414400a b d e +--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 - 14414400a b d e + 7207200a b d e - 1441440b d e +--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 5045040a d e - 25225200a b d e + 50450400a b d e +--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 - 50450400a b d e + 25225200a b d e - 5045040b d e +--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 10090080a d e - 50450400a b d e + 100900800a b d e +--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 - 100900800a b d e + 50450400a b d e - 10090080b d e +--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 12612600a d e - 63063000a b d e + 126126000a b d e +--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 - 126126000a b d e + 63063000a b d e - 12612600b d e +--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 10090080a d e - 50450400a b d e + 100900800a b d e +--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 - 100900800a b d e + 50450400a b d e - 10090080b d e +--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 5045040a d e - 25225200a b d e + 50450400a b d e +--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 - 50450400a b d e + 25225200a b d e - 5045040b d e +--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 1441440a d e - 7207200a b d e + 14414400a b d e +--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 - 14414400a b d e + 7207200a b d e - 1441440b d e +--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 180180a d e - 900900a b d e + 1801800a b d e - 1801800a b d e +--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 900900a b d e - 180180b d +--R 4 20 5 21 +--R 450450a b d e - 90090b d --R Type: Union(Expression(Integer),...) --E 1096 ---S 1097 of 1293 +--S 1097 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1034) +--R (4) --R 7 8 4 ---R (3003A a d + 48048A a )e +--R (3003A a d + 12012A a )e --R + ---R 6 7 2 7 8 3 ---R ((- 13860A a b + 462B a )d + (- 221760A a b + 7392B a )d)e +--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 + (393120A a b - 30240B a b)d )e +--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 + (- 320320A a b + 43680B a b )d )e +--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 + (102960A a b - 22880B a b )d +--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 180180a d e - 900900a b d e + 1801800a b d e - 1801800a b d e +--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 900900a b d e - 180180b d +--R 4 12 5 13 +--R 450450a b d e - 90090b d --R Type: Expression(Integer) --E 1097 @@ -28606,15 +28991,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1035) 0 +--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 (1036) +--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 / @@ -28641,7 +29028,7 @@ r0:=-2/17*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(17/2))+_ (e*(b*d-a*e)^6*(d+e*x)^(7/2)) --R --R ---R (1037) +--R (2) --R 8 7 5 8 4 8 --R ((2560A b - 4352B a b )e + 1792B b d e )x --R + @@ -28858,258 +29245,273 @@ r0:=-2/17*(B*d-A*e)*(a+b*x)^(7/2)/(e*(b*d-a*e)*(d+e*x)^(17/2))+_ --R Type: Expression(Integer) --E 1100 ---S 1101 of 1293 +--S 1101 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1038) ---R 8 7 9 5 8 10 4 8 ---R ((5120A b - 8704B a b )d e + 3584B b d e )x +--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 (- 2560A a b + 4352B a b )d e + (43520A b - 75776B a b )d e +--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 30464B b d e +--R 45696B b d e --R * --R 7 --R x --R + --R 2 6 3 5 9 5 ---R (1920A a b - 3264B a b )d e +--R (2880A a b - 4896B a b )d e --R + --R 7 2 6 10 4 ---R (- 21760A a b + 38336B a b )d e +--R (- 32640A a b + 57504B a b )d e --R + --R 8 7 11 3 8 12 2 ---R (163200A b - 292672B a b )d e + 114240B b d e +--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 (- 1600A a b + 2720B a b )d e +--R (- 2400A a b + 4080B a b )d e --R + --R 2 6 3 5 10 4 ---R (16320A a b - 28864B a b )d e +--R (24480A a b - 43296B a b )d e --R + ---R 7 2 6 11 3 ---R (- 81600A a b + 150144B a b )d e +--R 7 2 6 11 3 +--R (- 122400A a b + 225216B a b )d e --R + --R 8 7 12 2 8 13 ---R (353600A b - 658240B a b )d e + 247520B b d e +--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 (1400A a b - 2380B a b )d e +--R (2100A a b - 3570B a b )d e --R + --R 3 5 4 4 10 4 ---R (- 13600A a b + 24100B a b )d e +--R (- 20400A a b + 36150B a b )d e --R + --R 2 6 3 5 11 3 ---R (61200A a b - 113560B a b )d e +--R (91800A a b - 170340B a b )d e --R + --R 7 2 6 12 2 ---R (- 176800A a b + 343400B a b )d e +--R (- 265200A a b + 515100B a b )d e --R + ---R 8 7 13 8 14 ---R (486200A b - 950300B a b )d e + 340340B b d +--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 (- 1260A a b - 304164B a b )d e +--R (- 1890A a b - 456246B a b )d e --R + --R 4 4 5 3 10 4 ---R (11900A a b + 1816724B a b )d e +--R (17850A a b + 2725086B a b )d e --R + --R 3 5 4 4 11 3 ---R (- 51000A a b - 4499560B a b )d e +--R (- 76500A a b - 6749340B a b )d e --R + --R 2 6 3 5 12 2 ---R (132600A a b + 5865000B a b )d e +--R (198900A a b + 8797500B a b )d e --R + --R 7 2 6 13 ---R (- 243100A a b - 4088500B a b )d e +--R (- 364650A a b - 6132750B a b )d e --R + ---R 8 7 14 ---R (437580A b + 923780B a b )d +--R 8 7 14 +--R (656370A b + 1385670B a b )d --R * --R 3 --R x --R + --R 6 2 7 9 5 ---R (- 254100A a b - 486948B a b)d e +--R (- 381150A a b - 730422B a b)d e --R + --R 5 3 6 2 10 4 ---R (1520820A a b + 2750244B a b )d e +--R (2281230A a b + 4125366B a b )d e --R + --R 4 4 5 3 11 3 ---R (- 3784200A a b - 6286056B a b )d e +--R (- 5676300A a b - 9429084B a b )d e --R + ---R 3 5 4 4 12 2 ---R (4994600A a b + 7238600B a b )d e +--R 3 5 4 4 12 2 +--R (7491900A a b + 10857900B a b )d e --R + --R 2 6 3 5 13 ---R (- 3646500A a b - 4088500B a b )d e +--R (- 5469750A a b - 6132750B a b )d e --R + ---R 7 2 6 14 ---R (1312740A a b + 729300B a b )d +--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 (- 420420A a b - 204204B a )d e +--R (- 630630A a b - 306306B a )d e --R + --R 6 2 7 10 4 ---R (2434740A a b + 1080156B a b)d e +--R (3652110A a b + 1620234B a b)d e --R + --R 5 3 6 2 11 3 ---R (- 5783400A a b - 2247672B a b )d e +--R (- 8675100A a b - 3371508B a b )d e --R + ---R 4 4 5 3 12 2 ---R (7116200A a b + 2232440B a b )d e +--R 4 4 5 3 12 2 +--R (10674300A a b + 3348660B a b )d e --R + ---R 3 5 4 4 13 ---R (- 4618900A a b - 950300B a b )d e +--R 3 5 4 4 13 +--R (- 6928350A a b - 1425450B a b )d e --R + --R 2 6 3 5 14 ---R (1312740A a b + 48620B a b )d +--R (1969110A a b + 72930B a b )d --R * --R x --R + --R 8 9 5 7 8 10 4 ---R - 180180A a d e + (1021020A a b - 24024B a )d e +--R - 270270A a d e + (1531530A a b - 36036B a )d e --R + --R 6 2 7 11 3 ---R (- 2356200A a b + 125664B a b)d e +--R (- 3534300A a b + 188496B a b)d e --R + --R 5 3 6 2 12 2 ---R (2784600A a b - 257040B a b )d e +--R (4176900A a b - 385560B a b )d e --R + ---R 4 4 5 3 13 3 5 4 4 14 ---R (- 1701700A a b + 247520B a b )d e + (437580A a b - 97240B a b )d +--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 - 180180A a )e +--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 + (1021020A a b - 24024B a )d)e +--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 ---R (- 589050A a b + 31416B a b)d ---R + ---R 7 2 8 2 ---R (- 2356200A a b + 125664B a b)d ---R * ---R 12 ---R e +--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 6 3 7 2 3 ---R ((696150A a b - 64260B a b )d + (2784600A a b - 257040B a b )d ) +--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 ---R (- 425425A a b + 61880B a b )d ---R + ---R 5 4 6 3 4 ---R (- 1701700A a b + 247520B a b )d +--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 4 5 5 4 5 9 ---R ((109395A a b - 24310B a b )d + (437580A a b - 97240B a b )d )e +--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 - 1621620A a d)e +--R 8 2 9 13 +--R (405405A a d + 3648645A a d)e --R + ---R 7 8 3 8 9 2 12 ---R ((2297295A a b - 54054B a )d + (9189180A a b - 216216B a )d )e +--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 (5301450A a b - 282744B a b)d +--R + --R 7 2 8 3 ---R (- 21205800A a b + 1130976B a b)d +--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 5 3 6 2 5 +--R (- 6265350A a b + 578340B a b )d --R + ---R 6 3 7 2 4 ---R (25061400A a b - 2313360B a b )d +--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 4 4 5 3 6 +--R (3828825A a b - 556920B a b )d --R + ---R 5 4 6 3 5 ---R (- 15315300A a b + 2227680B a b )d +--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 4 5 5 4 6 8 ---R ((984555A a b - 218790B a b )d + (3938220A a b - 875160B a b )d )e +--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 - 6486480A a d )e +--R 8 3 9 2 12 +--R (1621620A a d + 14594580A a d )e --R + ---R 7 8 4 8 9 3 11 ---R ((9189180A a b - 216216B a )d + (36756720A a b - 864864B a )d )e +--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 6 2 7 5 +--R (21205800A a b - 1130976B a b)d --R + ---R 7 2 8 4 ---R (- 84823200A a b + 4523904B a b)d +--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 5 3 6 2 6 +--R (- 25061400A a b + 2313360B a b )d --R + ---R 6 3 7 2 5 ---R (100245600A a b - 9253440B a b )d +--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 4 4 5 3 7 +--R (15315300A a b - 2227680B a b )d --R + ---R 5 4 6 3 6 ---R (- 61261200A a b + 8910720B a b )d +--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 3 5 4 4 8 +--R (- 3938220A a b + 875160B a b )d --R + ---R 4 5 5 4 7 ---R (15752880A a b - 3500640B a b )d +--R 4 5 5 4 7 +--R (- 35443980A a b + 7876440B a b )d --R * --R 7 --R e @@ -29117,44 +29519,50 @@ a0:=integrate(t0,x) --R 7 --R x --R + ---R 8 4 9 3 11 ---R (- 3783780A a d - 15135120A a d )e +--R 8 4 9 3 11 +--R (3783780A a d + 34054020A a d )e --R + ---R 7 8 5 8 9 4 10 ---R ((21441420A a b - 504504B a )d + (85765680A a b - 2018016B a )d )e +--R 7 8 5 +--R (- 21441420A a b + 504504B a )d +--R + +--R 8 9 4 +--R (- 192972780A a b + 4540536B a )d +--R * +--R 10 +--R e --R + ---R 6 2 7 6 ---R (- 49480200A a b + 2638944B a b)d +--R 6 2 7 6 +--R (49480200A a b - 2638944B a b)d --R + ---R 7 2 8 5 ---R (- 197920800A a b + 10555776B a b)d +--R 7 2 8 5 +--R (445321800A a b - 23750496B a b)d --R * --R 9 --R e --R + ---R 5 3 6 2 7 ---R (58476600A a b - 5397840B a b )d +--R 5 3 6 2 7 +--R (- 58476600A a b + 5397840B a b )d --R + ---R 6 3 7 2 6 ---R (233906400A a b - 21591360B a b )d +--R 6 3 7 2 6 +--R (- 526289400A a b + 48580560B a b )d --R * --R 8 --R e --R + ---R 4 4 5 3 8 ---R (- 35735700A a b + 5197920B a b )d +--R 4 4 5 3 8 +--R (35735700A a b - 5197920B a b )d --R + ---R 5 4 6 3 7 ---R (- 142942800A a b + 20791680B a b )d +--R 5 4 6 3 7 +--R (321621300A a b - 46781280B a b )d --R * --R 7 --R e --R + ---R 3 5 4 4 9 ---R (9189180A a b - 2042040B a b )d +--R 3 5 4 4 9 +--R (- 9189180A a b + 2042040B a b )d --R + ---R 4 5 5 4 8 ---R (36756720A a b - 8168160B a b )d +--R 4 5 5 4 8 +--R (- 82702620A a b + 18378360B a b )d --R * --R 6 --R e @@ -29162,44 +29570,50 @@ a0:=integrate(t0,x) --R 6 --R x --R + ---R 8 5 9 4 10 ---R (- 5675670A a d - 22702680A a d )e +--R 8 5 9 4 10 +--R (5675670A a d + 51081030A a d )e --R + ---R 7 8 6 8 9 5 9 ---R ((32162130A a b - 756756B a )d + (128648520A a b - 3027024B a )d )e +--R 7 8 6 +--R (- 32162130A a b + 756756B a )d +--R + +--R 8 9 5 +--R (- 289459170A a b + 6810804B a )d +--R * +--R 9 +--R e --R + ---R 6 2 7 7 ---R (- 74220300A a b + 3958416B a b)d +--R 6 2 7 7 +--R (74220300A a b - 3958416B a b)d --R + ---R 7 2 8 6 ---R (- 296881200A a b + 15833664B a b)d +--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 5 3 6 2 8 +--R (- 87714900A a b + 8096760B a b )d --R + ---R 6 3 7 2 7 ---R (350859600A a b - 32387040B a b )d +--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 4 4 5 3 9 +--R (53603550A a b - 7796880B a b )d --R + ---R 5 4 6 3 8 ---R (- 214414200A a b + 31187520B a b )d +--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 3 5 4 4 10 +--R (- 13783770A a b + 3063060B a b )d --R + ---R 4 5 5 4 9 ---R (55135080A a b - 12252240B a b )d +--R 4 5 5 4 9 +--R (- 124053930A a b + 27567540B a b )d --R * --R 5 --R e @@ -29207,44 +29621,50 @@ a0:=integrate(t0,x) --R 5 --R x --R + ---R 8 6 9 5 9 ---R (- 5675670A a d - 22702680A a d )e +--R 8 6 9 5 9 +--R (5675670A a d + 51081030A a d )e --R + ---R 7 8 7 8 9 6 8 ---R ((32162130A a b - 756756B a )d + (128648520A a b - 3027024B a )d )e +--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 6 2 7 8 +--R (74220300A a b - 3958416B a b)d --R + ---R 7 2 8 7 ---R (- 296881200A a b + 15833664B a b)d +--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 5 3 6 2 9 +--R (- 87714900A a b + 8096760B a b )d --R + ---R 6 3 7 2 8 ---R (350859600A a b - 32387040B a b )d +--R 6 3 7 2 8 +--R (- 789434100A a b + 72870840B a b )d --R * --R 6 --R e --R + ---R 4 4 5 3 10 ---R (- 53603550A a b + 7796880B a b )d +--R 4 4 5 3 10 +--R (53603550A a b - 7796880B a b )d --R + ---R 5 4 6 3 9 ---R (- 214414200A a b + 31187520B a b )d +--R 5 4 6 3 9 +--R (482431950A a b - 70171920B a b )d --R * --R 5 --R e --R + ---R 3 5 4 4 11 ---R (13783770A a b - 3063060B a b )d +--R 3 5 4 4 11 +--R (- 13783770A a b + 3063060B a b )d --R + ---R 4 5 5 4 10 ---R (55135080A a b - 12252240B a b )d +--R 4 5 5 4 10 +--R (- 124053930A a b + 27567540B a b )d --R * --R 4 --R e @@ -29252,44 +29672,50 @@ a0:=integrate(t0,x) --R 4 --R x --R + ---R 8 7 9 6 8 ---R (- 3783780A a d - 15135120A a d )e +--R 8 7 9 6 8 +--R (3783780A a d + 34054020A a d )e --R + ---R 7 8 8 8 9 7 7 ---R ((21441420A a b - 504504B a )d + (85765680A a b - 2018016B a )d )e +--R 7 8 8 +--R (- 21441420A a b + 504504B a )d +--R + +--R 8 9 7 +--R (- 192972780A a b + 4540536B a )d +--R * +--R 7 +--R e --R + ---R 6 2 7 9 ---R (- 49480200A a b + 2638944B a b)d +--R 6 2 7 9 +--R (49480200A a b - 2638944B a b)d --R + ---R 7 2 8 8 ---R (- 197920800A a b + 10555776B a b)d +--R 7 2 8 8 +--R (445321800A a b - 23750496B a b)d --R * --R 6 --R e --R + ---R 5 3 6 2 10 ---R (58476600A a b - 5397840B a b )d +--R 5 3 6 2 10 +--R (- 58476600A a b + 5397840B a b )d --R + ---R 6 3 7 2 9 ---R (233906400A a b - 21591360B a b )d +--R 6 3 7 2 9 +--R (- 526289400A a b + 48580560B a b )d --R * --R 5 --R e --R + ---R 4 4 5 3 11 ---R (- 35735700A a b + 5197920B a b )d +--R 4 4 5 3 11 +--R (35735700A a b - 5197920B a b )d --R + ---R 5 4 6 3 10 ---R (- 142942800A a b + 20791680B a b )d +--R 5 4 6 3 10 +--R (321621300A a b - 46781280B a b )d --R * --R 4 --R e --R + ---R 3 5 4 4 12 ---R (9189180A a b - 2042040B a b )d +--R 3 5 4 4 12 +--R (- 9189180A a b + 2042040B a b )d --R + ---R 4 5 5 4 11 ---R (36756720A a b - 8168160B a b )d +--R 4 5 5 4 11 +--R (- 82702620A a b + 18378360B a b )d --R * --R 3 --R e @@ -29297,44 +29723,50 @@ a0:=integrate(t0,x) --R 3 --R x --R + ---R 8 8 9 7 7 ---R (- 1621620A a d - 6486480A a d )e +--R 8 8 9 7 7 +--R (1621620A a d + 14594580A a d )e --R + ---R 7 8 9 8 9 8 6 ---R ((9189180A a b - 216216B a )d + (36756720A a b - 864864B a )d )e +--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 6 2 7 10 +--R (21205800A a b - 1130976B a b)d --R + ---R 7 2 8 9 ---R (- 84823200A a b + 4523904B a b)d +--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 5 3 6 2 11 +--R (- 25061400A a b + 2313360B a b )d --R + ---R 6 3 7 2 10 ---R (100245600A a b - 9253440B a b )d +--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 4 4 5 3 12 +--R (15315300A a b - 2227680B a b )d --R + ---R 5 4 6 3 11 ---R (- 61261200A a b + 8910720B a b )d +--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 3 5 4 4 13 +--R (- 3938220A a b + 875160B a b )d --R + ---R 4 5 5 4 12 ---R (15752880A a b - 3500640B a b )d +--R 4 5 5 4 12 +--R (- 35443980A a b + 7876440B a b )d --R * --R 2 --R e @@ -29342,210 +29774,222 @@ a0:=integrate(t0,x) --R 2 --R x --R + ---R 8 9 9 8 6 ---R (- 405405A a d - 1621620A a d )e +--R 8 9 9 8 6 +--R (405405A a d + 3648645A a d )e --R + ---R 7 8 10 8 9 9 5 ---R ((2297295A a b - 54054B a )d + (9189180A a b - 216216B a )d )e +--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 6 2 7 11 +--R (5301450A a b - 282744B a b)d --R + ---R 7 2 8 10 ---R (- 21205800A a b + 1130976B a b)d +--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 5 3 6 2 12 +--R (- 6265350A a b + 578340B a b )d --R + ---R 6 3 7 2 11 ---R (25061400A a b - 2313360B a b )d +--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 4 4 5 3 13 +--R (3828825A a b - 556920B a b )d --R + ---R 5 4 6 3 12 ---R (- 15315300A a b + 2227680B a b )d +--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 4 5 5 4 13 ---R ((984555A a b - 218790B a b )d + (3938220A a b - 875160B a b )d )e +--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 - 180180A a d )e +--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 + (1021020A a b - 24024B a )d )e +--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 + (- 2356200A a b + 125664B a b)d )e +--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 6 3 7 2 12 2 ---R ((696150A a b - 64260B a b )d + (2784600A a b - 257040B a b )d )e ---R + ---R 4 4 5 3 14 ---R (- 425425A a b + 61880B a b )d +--R 5 3 6 2 13 +--R (- 696150A a b + 64260B a b )d --R + ---R 5 4 6 3 13 ---R (- 1701700A a b + 247520B a b )d +--R 6 3 7 2 12 +--R (- 6265350A a b + 578340B a b )d --R * +--R 2 --R e --R + ---R 3 5 4 4 15 4 5 5 4 14 ---R (109395A a b - 24310B a b )d + (437580A a b - 97240B a b )d +--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 1531530a d e - 9189180a b d e + 22972950a b d e +--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 - 30630600a b d e + 22972950a b d e - 9189180a b d e +--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 1531530b d e +--R 2297295b d e --R * --R 9 --R x --R + ---R 6 10 14 5 11 13 4 2 12 12 ---R 13783770a d e - 82702620a b d e + 206756550a b d e +--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 - 275675400a b d e + 206756550a b d e - 82702620a b d e +--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 13783770b d e +--R 20675655b d e --R * --R 8 --R x --R + ---R 6 11 13 5 12 12 4 2 13 11 ---R 55135080a d e - 330810480a b d e + 827026200a b d e +--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 - 1102701600a b d e + 827026200a b d e - 330810480a b d e +--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 55135080b d e +--R 82702620b d e --R * --R 7 --R x --R + ---R 6 12 12 5 13 11 4 2 14 10 ---R 128648520a d e - 771891120a b d e + 1929727800a b d e +--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 - 2572970400a b d e + 1929727800a b d e - 771891120a b d e +--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 128648520b d e +--R 192972780b d e --R * --R 6 --R x --R + --R 6 13 11 5 14 10 4 2 15 9 ---R 192972780a d e - 1157836680a b d e + 2894591700a b d e +--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 - 3859455600a b d e + 2894591700a b d e - 1157836680a b d e +--R - 5789183400a b d e + 4341887550a b d e - 1736755020a b d e --R + --R 6 19 5 ---R 192972780b d e +--R 289459170b d e --R * --R 5 --R x --R + --R 6 14 10 5 15 9 4 2 16 8 ---R 192972780a d e - 1157836680a b d e + 2894591700a b d e +--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 - 3859455600a b d e + 2894591700a b d e - 1157836680a b d e +--R - 5789183400a b d e + 4341887550a b d e - 1736755020a b d e --R + --R 6 20 4 ---R 192972780b d e +--R 289459170b d e --R * --R 4 --R x --R + ---R 6 15 9 5 16 8 4 2 17 7 ---R 128648520a d e - 771891120a b d e + 1929727800a b d e +--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 - 2572970400a b d e + 1929727800a b d e - 771891120a b d e +--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 128648520b d e +--R 192972780b d e --R * --R 3 --R x --R + ---R 6 16 8 5 17 7 4 2 18 6 ---R 55135080a d e - 330810480a b d e + 827026200a b d e +--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 - 1102701600a b d e + 827026200a b d e - 330810480a b d e +--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 55135080b d e +--R 82702620b d e --R * --R 2 --R x --R + ---R 6 17 7 5 18 6 4 2 19 5 ---R 13783770a d e - 82702620a b d e + 206756550a b d e +--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 - 275675400a b d e + 206756550a b d e - 82702620a b d e +--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 13783770b d e +--R 20675655b d e --R * --R x --R + ---R 6 18 6 5 19 5 4 2 20 4 3 3 21 3 ---R 1531530a d e - 9189180a b d e + 22972950a b d e - 30630600a b d e +--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 2 4 22 2 5 23 6 24 ---R 22972950a b d e - 9189180a b d e + 1531530b d +--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 +--S 1102 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1039) ---R 8 9 5 ---R (- 45045A a d - 180180A a )e +--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 + (1021020A a b - 24024B a )d)e +--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 + (- 2356200A a b + 125664B a b)d )e +--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 + (2784600A a b - 257040B a b )d )e +--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 + (- 1701700A a b + 247520B a b )d )e +--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 + (437580A a b - 97240B a b )d +--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 1531530a d e - 9189180a b d e + 22972950a b d e - 30630600a b d e +--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 22972950a b d e - 9189180a b d e + 1531530b d +--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 @@ -29553,19 +29997,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1040) 0 +--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 (1041) ---------------------------------------------------------------- ---R +-------+ ---R \|b x + a +--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 @@ -29578,7 +30024,7 @@ r0:=-5/64*(b*d-a*e)^3*(b*B*d-8*A*b*e+7*a*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 (1042) +--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 + @@ -29623,15 +30069,17 @@ r0:=-5/64*(b*d-a*e)^3*(b*B*d-8*A*b*e+7*a*B*e)*_ --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 (1043) --------------------------------------- ---R +-------+ ---R \|b x + a +--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 @@ -29643,7 +30091,7 @@ r0:=-1/8*(b*d-a*e)^2*(b*B*d-6*A*b*e+5*a*B*e)*atanh(sqrt(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 (1044) +--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 + @@ -29682,15 +30130,17 @@ r0:=-1/8*(b*d-a*e)^2*(b*B*d-6*A*b*e+5*a*B*e)*atanh(sqrt(e)*_ --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 (1045) ------------------- ---R +-------+ ---R \|b x + a +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +-------+ +--R \|b x + a --R Type: Expression(Integer) --E 1114 @@ -29701,7 +30151,7 @@ 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(d+e*x)/(b^2*e) --R --R ---R (1046) +--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 * @@ -29731,14 +30181,16 @@ r0:=-1/4*(b*d-a*e)*(b*B*d-4*A*b*e+3*a*B*e)*atanh(sqrt(e)*_ --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 (1047) -------------------- ---R +-------+ +-------+ ---R \|b x + a \|e x + d +--R B x + A +--R (1) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|e x + d --R Type: Expression(Integer) --E 1119 @@ -29747,7 +30199,7 @@ 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 (1048) +--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 @@ -29771,14 +30223,16 @@ r0:=(2*A*b*e-B*(b*d+a*e))*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ --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 (1049) ----------------------------- ---R +-------+ +-------+ ---R (e x + d)\|b x + a \|e x + d +--R B x + A +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (e x + d)\|b x + a \|e x + d --R Type: Expression(Integer) --E 1124 @@ -29787,7 +30241,7 @@ 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 (1050) +--R (2) --R +-+ +-------+ --R +-------+ \|e \|b x + a --R (2B a e - 2B b d)\|e x + d atanh(--------------) @@ -29814,14 +30268,16 @@ r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/(e^(3/2)*sqrt(b))-_ --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 (1051) ---------------------------------------- ---R 2 2 2 +-------+ +-------+ ---R (e x + 2d e x + d )\|b x + a \|e x + d +--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 @@ -29830,34 +30286,33 @@ 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 (1052) ---R +-------+ ---R (((4A b - 6B a)e + 2B b d)x - 2A a e + (6A b - 4B a)d)\|b x + a ---R ---------------------------------------------------------------------- ---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 +-------+ +--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 +--S 1131 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1053) +--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 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 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 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 @@ -29867,15 +30322,15 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 1131 ---S 1132 of 1293 +--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 (1054) ------------------------------------------------------- ---R 2 2 2 3 2 4 ---R 3a d e - 6a b d e + 3b d +--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 @@ -29883,18 +30338,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1055) 0 +--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 (1056) -------------------------------------------------- ---R 3 3 2 2 2 3 +-------+ +-------+ ---R (e x + 3d e x + 3d e x + d )\|b x + a \|e x + d +--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 @@ -29904,7 +30361,7 @@ r0:=-2/5*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ 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 (1057) +--R (2) --R 2 2 2 2 --R ((- 16A b + 20B a b)e - 4B b d e)x --R + @@ -29931,88 +30388,94 @@ r0:=-2/5*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2))+_ --R Type: Expression(Integer) --E 1135 ---S 1136 of 1293 +--S 1136 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1058) +--R (3) --R 2 3 2 2 4 2 ---R ((- 48A b + 60B a b)d e - 12B b d e)x +--R ((- 64A b + 80B a b)d e - 16B b d e)x --R + --R 2 3 2 2 4 2 5 ---R ((24A a b - 30B a )d e + (- 120A b + 156B a b)d e - 30B b d )x +--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 - 18A a d e + (60A a b - 12B a )d e + (- 90A b + 60B a b)d +--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 2 2 2 3 4 ---R (- 3A a d - 27A a )e + ((10A a b - 2B a )d + (90A a b - 18B a )d)e +--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 + (- 135A a b + 90B a b)d )e +--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 - 81A a d)e +--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 + (270A a b - 54B a )d )e +--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 + (- 405A a b + 270B a b)d )e +--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 - 81A a d )e +--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 + (270A a b - 54B a )d )e +--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 + (- 405A a b + 270B a b)d )e +--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 2 5 2 3 4 ---R (- 3A a d - 27A a d )e + ((10A a b - 2B a )d + (90A a b - 18B a )d )e +--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 6 2 2 5 ---R (- 15A b + 10B a b)d + (- 135A a b + 90B a b)d +--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 (45a d e - 135a b d e + 135a b d e - 45b d e )x +--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 (135a d e - 405a b d e + 405a b d e - 135b d e )x +--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 (135a d e - 405a b d e + 405a b d e - 135b d e)x + 45a d e +--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 - 135a b d e + 135a b d e - 45b d +--R - 180a b d e + 180a b d e - 60b d --R Type: Union(Expression(Integer),...) --E 1136 ---S 1137 of 1293 +--S 1137 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1059) ---R 2 3 2 2 2 2 3 ---R (- 3A a d - 27A a )e + ((10A a b - 2B a )d + (90A a b - 18B a )d)e +--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 + (- 135A a b + 90B a b)d +--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 45a d e - 135a b d e + 135a b d e - 45b d +--R 60a d e - 180a b d e + 180a b d e - 60b d --R Type: Expression(Integer) --E 1137 @@ -30020,18 +30483,20 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1060) 0 +--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 (1061) ------------------------------------------------------------ ---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 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 @@ -30043,7 +30508,7 @@ r0:=-2/7*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ sqrt(a+b*x)/(e*(b*d-a*e)^4*sqrt(d+e*x)) --R --R ---R (1062) +--R (2) --R 3 2 3 3 2 3 --R ((96A b - 112B a b )e + 16B b d e )x --R + @@ -30084,150 +30549,138 @@ r0:=-2/7*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(7/2))+_ --R Type: Expression(Integer) --E 1140 ---S 1141 of 1293 +--S 1141 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1063) ---R 3 2 4 3 3 5 2 3 ---R ((384A b - 448B a b )d e + 64B b d e )x +--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 (- 192A a b + 224B a b)d e + (1344A b - 1600B a b )d e ---R + ---R 3 6 ---R 224B b d e +--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 (144A a b - 168B a )d e + (- 672A a b + 808B a b)d e +--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 (1680A b - 2072B a b )d e + 280B b d +--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 - 120A a d e + (504A a b - 48B a )d e + (- 840A a b + 224B a b)d e +--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 (840A b - 560B a b )d +--R (210A b - 140B a b )d --R * --R +-------+ +-------+ --R \|b x + a \|e x + d --R + ---R 3 4 7 ---R (- 15A a d - 240A a )e +--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 3 2 3 4 6 ---R ((63A a b - 6B a )d + (1008A a b - 96B a )d)e +--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 2 2 3 2 2 3 2 5 ---R ((- 105A a b + 28B a b)d + (- 1680A a b + 448B a b)d )e ---R + ---R 3 2 4 3 2 2 3 4 ---R ((105A b - 70B a b )d + (1680A a b - 1120B a b )d )e +--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 - 960A a d)e +--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 + (4032A a b - 384B a )d )e +--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 + (- 6720A a b + 1792B a b)d )e +--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 + (6720A a b - 4480B a b )d )e +--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 - 1440A a d )e +--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 + (6048A a b - 576B a )d )e +--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 + (- 10080A a b + 2688B a b)d )e +--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 + (10080A a b - 6720B a b )d )e +--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 - 960A a d )e +--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 + (4032A a b - 384B a )d )e +--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 + (- 6720A a b + 1792B a b)d )e +--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 + (6720A a b - 4480B a b )d )e +--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 ---R (- 15A a d - 240A a d )e ---R + ---R 2 3 6 3 4 5 2 ---R ((63A a b - 6B a )d + (1008A a b - 96B a )d )e +--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 + (- 1680A a b + 448B a b)d )e +--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 + (1680A a b - 1120B a b )d +--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 (420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d e )x +--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 (1680a d e - 6720a b d e + 10080a b d e - 6720a b d e + 1680b d e )x +--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 ---R 2520a d e - 10080a b d e + 15120a b d e - 10080a b d e ---R + ---R 4 10 2 ---R 2520b d e ---R * ---R 2 ---R x +--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 (1680a d e - 6720a b d e + 10080a b d e - 6720a b d e + 1680b d e)x +--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 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--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 +--S 1142 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1064) ---R 3 4 3 2 3 2 3 4 2 ---R (- 15A a d - 240A a )e + ((63A a b - 6B a )d + (1008A a b - 96B a )d)e +--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 + (- 1680A a b + 448B a b)d )e +--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 + (1680A a b - 1120B a b )d +--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 420a d e - 1680a b d e + 2520a b d e - 1680a b d e + 420b d +--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 @@ -30235,15 +30688,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1065) 0 +--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 (1066) +--R (1) --R B x + A --R ------------------------------------------------------------------------ --R 5 5 4 4 2 3 3 3 2 2 4 5 +-------+ +-------+ @@ -30260,7 +30715,7 @@ r0:=-2/9*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ 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 (1067) +--R (2) --R 4 3 4 4 3 4 --R ((- 256A b + 288B a b )e - 32B b d e )x --R + @@ -30348,11 +30803,11 @@ r0:=-2/9*(B*d-A*e)*sqrt(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(9/2))+_ --R Type: Expression(Integer) --E 1145 ---S 1146 of 1293 +--S 1146 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1068) +--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 + @@ -30553,11 +31008,11 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 1146 ---S 1147 of 1293 +--S 1147 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1069) +--R (4) --R 4 5 4 --R (- 35A a d - 315A a )e --R + @@ -30585,19 +31040,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1070) 0 +--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 (1071) ---------------------------------------------------------------- ---R +-------+ ---R (b x + a)\|b x + a +--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 @@ -30610,7 +31067,7 @@ r0:=5/8*(b*d-a*e)^2*(b*B*d+6*A*b*e-7*a*B*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 (1072) +--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 + @@ -30655,15 +31112,17 @@ r0:=5/8*(b*d-a*e)^2*(b*B*d+6*A*b*e-7*a*B*e)*_ --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 (1073) --------------------------------------- ---R +-------+ ---R (b x + a)\|b x + a +--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 @@ -30675,7 +31134,7 @@ 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(a+b*x)*sqrt(d+e*x)/b^3 --R --R ---R (1074) +--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 * @@ -30711,15 +31170,17 @@ 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)/_ --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 (1075) ------------------- ---R +-------+ ---R (b x + a)\|b x + a +--R +-------+ +--R (B x + A)\|e x + d +--R (1) ------------------- +--R +-------+ +--R (b x + a)\|b x + a --R Type: Expression(Integer) --E 1159 @@ -30730,7 +31191,7 @@ r0:=(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ sqrt(d+e*x)/(b^2*(b*d-a*e)) --R --R ---R (1076) +--R (2) --R +-+ +-------+ --R +-------+ \|e \|b x + a --R ((2A b - 3B a)e + B b d)\|b x + a atanh(--------------) @@ -30757,14 +31218,16 @@ r0:=(b*B*d+2*A*b*e-3*a*B*e)*atanh(sqrt(e)*sqrt(a+b*x)/_ --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 (1077) ----------------------------- ---R +-------+ +-------+ ---R (b x + a)\|b x + a \|e x + d +--R B x + A +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (b x + a)\|b x + a \|e x + d --R Type: Expression(Integer) --E 1164 @@ -30773,7 +31236,7 @@ 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 (1078) +--R (2) --R +-+ +-------+ --R +-------+ \|e \|b x + a --R (2B a e - 2B b d)\|b x + a atanh(--------------) @@ -30800,14 +31263,16 @@ r0:=2*B*atanh(sqrt(e)*sqrt(a+b*x)/(sqrt(b)*sqrt(d+e*x)))/_ --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 (1079) ------------------------------------------------- ---R 2 +-------+ +-------+ ---R (b e x + (a e + b d)x + a d)\|b x + a \|e x + d +--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 @@ -30816,64 +31281,64 @@ 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 (1080) -------------------------------------------------------- ---R 2 2 2 2 +-------+ +-------+ ---R (a e - 2a b d e + b d )\|b x + a \|e x + d +--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 +--S 1171 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1081) ---R 2 2 2 ---R ((- 12A a b + 6B a )d e + 6B a b d )x - 6A a d e ---R + ---R 2 2 ---R (- 6A a b + 12B a )d +--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 - 9A a b)e ---R + ---R 2 2 2 2 ---R ((- A b + 2B a b)d + (- 9A a b + 18B a b)d)e +--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 - 9A a )e + ((- 2A a b + 2B a )d + (- 18A a b + 18B a )d)e +--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 + (- 9A a b + 18B a b)d +--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 - 9A a d)e + (- A a b + 2B a )d + (- 9A a b + 18B a )d +--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 (3a b d e - 6a b d e + 3a b d e)x +--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 (3a d e - 3a b d e - 3a b d e + 3a b d )x + 3a d e - 6a b d e + 3a b d +--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 +--S 1172 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R 2 2 2 ---R (- A a d - 9A a )e + (- A b + 2B a)d + (- 9A a b + 18B a )d ---R (1082) ------------------------------------------------------------ ---R 3 2 2 2 2 3 ---R 3a d e - 6a b d e + 3a b d +--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 @@ -30881,15 +31346,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1083) 0 +--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 (1084) +--R (1) --R B x + A --R -------------------------------------------------------------------------- --R 2 3 2 2 2 2 +-------+ +-------+ @@ -30903,7 +31370,7 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a+b*x))+_ 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 (1085) +--R (2) --R 2 2 2 2 --R ((16A b - 12B a b)e - 4B b d e)x --R + @@ -30924,94 +31391,94 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a+b*x))+_ --R Type: Expression(Integer) --E 1175 ---S 1176 of 1293 +--S 1176 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1086) ---R 2 2 2 2 2 3 2 ---R ((64A a b - 48B a b)d e - 16B a b d e)x +--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 ((32A a b - 24B a )d e + (96A a b - 80B a b)d e - 24B a b d )x +--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 - 8A a d e + (48A a b - 16B a )d e + (24A a b - 48B a b)d +--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 + 16A a b)e +--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 + (- 96A a b + 32B a b)d)e +--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 + (- 48A a b + 96B a b )d )e +--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 + 16A a )e + ((- 4A a b + 2B a )d + (- 64A a b + 32B a )d)e +--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 + (- 240A a b + 160B a b)d )e +--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 + (- 96A a b + 192B a b )d )e +--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 + 32A a d)e +--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 + (- 176A a b + 64B a )d )e +--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 + (- 192A a b + 224B a b)d )e +--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 + (- 48A a b + 96B a b )d +--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 + 16A a d )e + ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d )e +--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 + (- 48A a b + 96B a b)d +--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 (12a b d e - 36a b d e + 36a b d e - 12a b d e )x +--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 (12a d e - 12a b d e - 36a b d e + 60a b d e - 24a b d e)x +--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 (24a d e - 60a b d e + 36a b d e + 12a b d e - 12a b d )x + 12a d e +--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 - 36a b d e + 36a b d e - 12a b d +--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 +--S 1177 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1087) ---R 2 3 2 2 2 2 3 ---R (A a d + 16A a )e + ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d)e +--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 + (- 48A a b + 96B a b)d +--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 12a d e - 36a b d e + 36a b d e - 12a b d +--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 @@ -31019,15 +31486,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1088) 0 +--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 (1089) +--R (1) --R B x + A --R / --R 3 4 3 2 3 2 2 2 2 3 @@ -31048,7 +31517,7 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a+b*x))+_ 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 (1090) +--R (2) --R 3 2 3 3 2 3 --R ((- 96A b + 80B a b )e + 16B b d e )x --R + @@ -31083,164 +31552,170 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a+b*x))+_ --R Type: Expression(Integer) --E 1180 ---S 1181 of 1293 +--S 1181 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1091) ---R 3 2 2 3 3 3 4 2 3 ---R ((- 96A a b + 80B a b )d e + 16B a b d e )x +--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 (- 48A a b + 40B a b)d e + (- 240A a b + 208B a b )d e +--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 40B a b d e +--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 (12A a b - 10B a )d e + (- 120A a b + 98B a b)d e +--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 (- 180A a b + 170B a b )d e + 30B a b d +--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 - 6A a d e + (30A a b - 4B a )d e + (- 90A a b + 40B a b)d e +--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 (- 30A a b + 60B a b )d +--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 + 3A a b)e +--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 + (- 15A a b + 2B a b)d)e +--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 + (45A a b - 20B a b )d )e +--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 + (15A a b - 30B a b )d )e +--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 3 4 2 4 5 5 ---R (3A a d + 3A a )e + ((- 6A a b + 2B a )d + (- 6A a b + 2B a )d)e +--R 4 5 6 +--R (3A a d + 48A a )e --R + ---R 3 3 4 2 4 ---R (- 14B a b d - 14B a b d )e +--R 3 4 2 4 5 5 +--R ((- 6A a b + 2B a )d + (- 96A a b + 32B a )d)e --R + ---R 3 2 2 4 2 3 3 2 3 3 ---R ((150A a b - 90B a b )d + (150A a b - 90B a b )d )e +--R 3 3 4 2 4 +--R (- 14B a b d - 224B a b d )e --R + ---R 4 3 5 4 2 3 4 2 ---R ((45A b - 90B a b )d + (45A a b - 90B a b )d )e +--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 + 9A a d)e +--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 + (- 36A a b + 6B a )d )e +--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 + (90A a b - 54B a b)d )e +--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 + (180A a b - 150B a b )d )e +--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 + (45A a b - 90B a b )d )e +--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 + 9A a d )e +--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 + (- 42A a b + 6B a )d )e +--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 + (120A a b - 58B a b)d )e +--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 + (90A a b - 110B a b )d )e +--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 + (15A a b - 30B a b )d +--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 3 4 5 4 5 4 2 ---R (3A a d + 3A a d )e + ((- 15A a b + 2B a )d + (- 15A a b + 2B a )d )e +--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 + (45A a b - 20B a b)d )e +--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 + (15A a b - 30B a b )d +--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 (15a b d e - 60a b d e + 90a b d e - 60a b d e + 15a b d e )x +--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 15a d e - 15a b d e - 90a b d e + 210a b d e - 165a b d e +--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 45a b d e +--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 45a d e - 135a b d e + 90a b d e + 90a b d e - 135a b d e +--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 45a b d e +--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 45a d e - 165a b d e + 210a b d e - 90a b d e - 15a b d e +--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 15a b d +--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 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--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 +--S 1182 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1092) ---R 3 4 3 2 3 2 3 4 2 ---R (3A a d + 3A a )e + ((- 15A a b + 2B a )d + (- 15A a b + 2B a )d)e +--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 + (45A a b - 20B a b)d )e +--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 + (15A a b - 30B a b )d +--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 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--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 @@ -31248,15 +31723,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1093) 0 +--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 (1094) +--R (1) --R B x + A --R / --R 4 5 4 3 4 3 2 2 3 @@ -31278,7 +31755,7 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a+b*x))+_ 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 (1095) +--R (2) --R 4 3 4 4 3 4 --R ((256A b - 224B a b )e - 32B b d e )x --R + @@ -31342,11 +31819,11 @@ r0:=-2*(A*b-a*B)/(b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a+b*x))+_ --R Type: Expression(Integer) --E 1185 ---S 1186 of 1293 +--S 1186 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1096) +--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 + @@ -31388,115 +31865,115 @@ a0:=integrate(t0,x) --R +-------+ +-------+ --R \|b x + a \|e x + d --R + ---R 4 5 8 ---R (5A a b d + 5A a b)e +--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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 @@ -31550,22 +32027,22 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 1186 ---S 1187 of 1293 +--S 1187 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1097) ---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 (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 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 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 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 @@ -31576,15 +32053,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1098) 0 +--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 (1099) +--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 + @@ -31610,7 +32089,7 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ sqrt(a+b*x)*sqrt(d+e*x)/b^5 --R --R ---R (1100) +--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 + @@ -31671,15 +32150,17 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ --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 (1101) ---------------------------------------------------------------- ---R 2 2 2 +-------+ ---R (b x + 2a b x + a )\|b x + a +--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 @@ -31692,7 +32173,7 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ 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 (1102) +--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 + @@ -31737,15 +32218,17 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ --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 (1103) --------------------------------------- ---R 2 2 2 +-------+ ---R (b x + 2a b x + a )\|b x + a +--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 @@ -31757,7 +32240,7 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ sqrt(a+b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)) --R --R ---R (1104) +--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 * @@ -31793,15 +32276,17 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ --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 (1105) ------------------------------ ---R 2 2 2 +-------+ ---R (b x + 2a b x + a )\|b x + a +--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 @@ -31811,7 +32296,7 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ 2*B*sqrt(d+e*x)/(b^2*sqrt(a+b*x)) --R --R ---R (1106) +--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 * @@ -31841,14 +32326,16 @@ r0:=-2/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^(3/2))+_ --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 (1107) ---------------------------------------- ---R 2 2 2 +-------+ +-------+ ---R (b x + 2a b x + a )\|b x + a \|e x + d +--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 @@ -31857,63 +32344,51 @@ 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 (1108) ---R +-------+ ---R (((4A b + 2B a)e - 6B b d)x + 6A a e + (- 2A b - 4B a)d)\|e x + d ---R ---------------------------------------------------------------------- ---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 +-------+ +--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 +--S 1211 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1109) ---R 2 3 2 3 2 3 ---R (((12A a b + 6B a )e - 18B a b d)x + 18A a e + (- 6A a b - 12B a )d) +--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 ---R (3A a b d + 27A a b )e + (- A b - 2B a b )d ---R + ---R 3 2 2 ---R (- 9A a b - 18B a b )d ---R * ---R 2 ---R x +--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 ---R (6A a b d + 54A a b)e + (- 2A a b - 4B a b)d ---R + ---R 2 2 3 ---R (- 18A a b - 36B a b)d ---R * ---R x +--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 + 27A a )e + (- A a b - 2B a )d + (- 9A a b - 18B a )d +--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 (9a b e - 18a b d e + 9a b d )x + (18a b e - 36a b d e + 18a b d )x +--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 9a e - 18a b d e + 9a b d +--R 6a e - 12a b d e + 6a b d --R Type: Union(Expression(Integer),...) --E 1211 ---S 1212 of 1293 +--S 1212 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R 2 2 2 ---R (3A a d + 27A a )e + (- A b - 2B a)d + (- 9A a b - 18B a )d ---R (1110) ------------------------------------------------------------ ---R 4 2 3 2 2 2 ---R 9a e - 18a b d e + 9a b d +--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 @@ -31921,15 +32396,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1111) 0 +--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 (1112) +--R (1) --R B x + A --R ----------------------------------------------------------------------- --R 2 3 2 2 2 2 +-------+ +-------+ @@ -31943,7 +32420,7 @@ r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*sqrt(d+e*x))+_ 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 (1113) +--R (2) --R 2 2 2 2 --R ((- 16A b + 4B a b)e + 12B b d e)x --R + @@ -31964,94 +32441,100 @@ r0:=-2*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*sqrt(d+e*x))+_ --R Type: Expression(Integer) --E 1215 ---S 1216 of 1293 +--S 1216 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1114) ---R 2 2 3 2 2 2 2 2 ---R ((- 16A a b + 4B a b)d e + 12B a b d e)x +--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 ((- 24A a b + 6B a )d e + (- 8A a b + 20B a b)d e + 6B a b d )x +--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 - 6A a d e + (- 12A a b + 12B a )d e + (2A a b + 4B a b)d +--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 + 3A a b )e +--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 + (6A a b - 6B a b )d)e +--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 + (- A a b - 2B a b )d )e +--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 + 6A a b)e +--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 + (15A a b - 12B a b)d)e +--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 + (4A a b - 10B a b )d )e +--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 + (- A a b - 2B a b )d +--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 3 4 2 4 5 2 ---R (3A a d + 3A a )e + ((12A a b - 6B a )d + (12A a b - 6B a )d)e +--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 + (11A a b - 14B a b)d )e +--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 + (- 2A a b - 4B a b )d +--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 3 4 3 4 5 2 ---R (3A a d + 3A a d)e + ((6A a b - 6B a )d + (6A a b - 6B a )d )e +--R 4 2 5 2 +--R (- 3A a d - 48A a d)e --R + ---R 2 2 3 4 3 2 4 3 ---R (- A a b - 2B a b)d + (- A a b - 2B a b)d +--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 (3a b d e - 9a b d e + 9a b d e - 3a b d e)x +--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 (6a b d e - 15a b d e + 9a b d e + 3a b d e - 3a b d )x +--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 (3a d e - 3a b d e - 9a b d e + 15a b d e - 6a b d )x + 3a d e +--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 - 9a b d e + 9a b d e - 3a b d +--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 -m0:=a0-r0 +--S 1217 of 1293 ok to fail, differs by a constant +m0:=a0-r0 --R --R ---R (1115) ---R 2 3 2 2 2 2 3 ---R (3A a d + 3A a )e + ((6A a b - 6B a )d + (6A a b - 6B a )d)e +--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 + (- A a b - 2B a b)d +--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 3a d e - 9a b d e + 9a b d e - 3a b d +--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 @@ -32059,15 +32542,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1116) 0 +--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 (1117) +--R (1) --R B x + A --R / --R 2 2 4 2 2 3 2 2 2 2 2 @@ -32088,7 +32573,7 @@ r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2))+_ 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 (1118) +--R (2) --R 3 2 3 3 2 3 --R ((32A b - 16B a b )e - 16B b d e )x --R + @@ -32123,156 +32608,156 @@ r0:=-2/3*(B*d-A*e)/(e*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(3/2))+_ --R Type: Expression(Integer) --E 1220 ---S 1221 of 1293 +--S 1221 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1119) ---R 2 3 3 2 2 3 2 3 3 2 3 ---R ((160A a b - 80B a b )d e - 80B a b d e )x +--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 (240A a b - 120B a b)d e + (240A a b - 240B a b )d e ---R + ---R 2 3 4 ---R - 120B a b d e +--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 (60A a b - 30B a )d e + (360A a b - 210B a b)d e +--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 (60A a b - 210B a b )d e - 30B a b d +--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 - 10A a d e + (90A a b - 20B a )d e + (90A a b - 120B a b)d e +--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 (- 10A a b - 20B a b )d +--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 - 25A a b )e +--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 + (225A a b - 50B a b )d)e +--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 + (225A a b - 300B a b )d )e +--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 + (- 25A a b - 50B a b )d )e +--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 - 50A a b)e +--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 + (400A a b - 100B a b)d)e +--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 + (900A a b - 700B a b )d )e +--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 + (400A a b - 700B a b )d )e +--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 + (- 50A a b - 100B a b )d )e +--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 - 25A a )e + ((5A a b - 2B a )d + (125A a b - 50B a )d)e +--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 + (1100A a b - 500B a b)d )e +--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 + (1100A a b - 1300B a b )d )e +--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 + (125A a b - 500B a b )d )e +--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 + (- 25A a b - 50B a b )d +--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 - 50A a d)e +--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 + (400A a b - 100B a )d )e +--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 + (900A a b - 700B a b)d )e +--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 + (400A a b - 700B a b )d )e +--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 + (- 50A a b - 100B a b )d +--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 - 25A a d )e + ((9A a b - 2B a )d + (225A a b - 50B a )d )e +--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 + (225A a b - 300B a b)d )e +--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 + (- 25A a b - 50B a b )d +--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 (15a b d e - 60a b d e + 90a b d e - 60a b d e + 15a b d e )x +--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 30a b d e - 90a b d e + 60a b d e + 60a b d e - 90a b d e +--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 30a b d e +--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 (15a d e - 135a b d e + 240a b d e - 135a b d e + 15a b d )x +--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 (30a d e - 90a b d e + 60a b d e + 60a b d e - 90a b d e + 30a b d )x +--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 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--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 +--S 1222 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1120) ---R 3 4 3 2 3 2 3 4 2 ---R (- A a d - 25A a )e + ((9A a b - 2B a )d + (225A a b - 50B a )d)e +--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 + (225A a b - 300B a b)d )e +--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 + (- 25A a b - 50B a b )d +--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 15a d e - 60a b d e + 90a b d e - 60a b d e + 15a b d +--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 @@ -32280,15 +32765,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1121) 0 +--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 (1122) +--R (1) --R B x + A --R / --R 2 3 5 3 2 2 4 2 3 2 2 2 3 @@ -32311,7 +32798,7 @@ r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2))-_ 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 (1123) +--R (2) --R 4 3 4 4 3 4 --R ((- 256A b + 160B a b )e + 96B b d e )x --R + @@ -32381,242 +32868,245 @@ r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(5/2))-_ --R Type: Expression(Integer) --E 1225 ---S 1226 of 1293 +--S 1226 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1124) ---R 2 4 3 3 3 4 2 4 4 3 4 ---R ((- 1024A a b + 640B a b )d e + 384B a b d e )x +--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 (- 1536A a b + 960B a b )d e + (- 2560A a b + 2176B a b )d e +--R (- 1152A a b + 720B a b )d e + (- 1920A a b + 1632B a b )d e --R + --R 2 4 5 2 ---R 960B a b d e +--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 (- 384A a b + 240B a b)d e + (- 3840A a b + 2544B a b )d e +--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 (- 1920A a b + 2640B a b )d e + 720B a b d e +--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 (64A a b - 40B a )d e + (- 960A a b + 576B a b)d e +--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 (- 2880A a b + 2160B a b )d e + (- 320A a b + 1280B a b )d e +--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 120B a b d +--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 - 24A a d e + (160A a b - 16B a )d e + (- 720A a b + 240B a b)d e +--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 (- 480A a b + 720B a b )d e + (40A a b + 80B a b )d +--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 - 48A a b )e +--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 + (320A a b - 32B a b )d)e +--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 + (- 1440A a b + 480B a b )d )e +--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 + (- 960A a b + 1440B a b )d )e +--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 + (80A a b + 160B a b )d )e +--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 - 96A a b)e +--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 + (496A a b - 64B a b)d)e +--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 + (- 1920A a b + 864B a b )d )e +--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 + (- 6240A a b + 4320B a b )d )e +--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 + (- 2720A a b + 4640B a b )d )e +--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 + (240A a b + 480B a b )d )e +--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 5 6 2 6 7 6 ---R (- 3A a d - 48A a )e + ((2A a b - 2B a )d + (32A a b - 32B a )d)e +--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 + (336A a b + 288B a b)d )e +--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 + (- 8640A a b + 4224B a b )d )e +--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 + (- 10000A a b + 10240B a b )d )e +--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 + (- 2400A a b + 5280B a b )d )e +--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 + (240A a b + 480B a b )d )e +--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 - 144A a d)e +--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 + (672A a b - 96B a )d )e +--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 + (- 2448A a b + 1248B a b)d )e +--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 + (- 11200A a b + 7168B a b )d )e +--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 + (- 6960A a b + 9600B a b )d )e +--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 + (- 480A a b + 2400B a b )d )e +--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 + (80A a b + 160B a b )d +--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 - 144A a d )e +--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 + (864A a b - 96B a )d )e +--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 + (- 3680A a b + 1376B a b)d )e +--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 + (- 5760A a b + 5280B a b )d )e +--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 + (- 1680A a b + 3360B a b )d )e +--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 + (160A a b + 320B a b )d +--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 - 48A a d )e +--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 + (320A a b - 32B a )d )e +--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 + (- 1440A a b + 480B a b)d )e +--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 + (- 960A a b + 1440B a b )d )e +--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 + (80A a b + 160B a b )d +--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 60a b d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--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 - 60a b d e +--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 120a b d e - 420a b d e + 300a b d e + 600a b d e - 1200a b d e +--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 780a b d e - 180a b d e +--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 60a d e + 60a b d e - 1020a b d e + 2100a b d e - 1500a b d e +--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 - 60a b d e + 540a b d e - 180a b d e +--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 180a d e - 540a b d e + 60a b d e + 1500a b d e - 2100a b d e +--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 1020a b d e - 60a b d e - 60a b d +--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 180a d e - 780a b d e + 1200a b d e - 600a b d e - 300a b d e +--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 420a b d e - 120a b d +--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 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e +--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 - 60a b d +--R - 45a b d --R Type: Union(Expression(Integer),...) --E 1226 ---S 1227 of 1293 +--S 1227 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1125) ---R 4 5 4 3 4 2 4 5 3 ---R (- 3A a d - 48A a )e + ((20A a b - 2B a )d + (320A a b - 32B a )d)e +--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 + (- 1440A a b + 480B a b)d )e +--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 + (- 960A a b + 1440B a b )d )e +--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 + (80A a b + 160B a b )d +--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 60a d e - 300a b d e + 600a b d e - 600a b d e + 300a b d e - 60a b d +--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 @@ -32624,15 +33114,17 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1126) 0 +--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 (1127) +--R (1) --R B x + A --R / --R 2 4 6 4 2 3 5 2 4 3 2 2 2 4 @@ -32660,7 +33152,7 @@ r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(7/2))-_ ((b*d-a*e)^6*sqrt(d+e*x)) --R --R ---R (1128) +--R (2) --R 5 4 5 5 4 5 --R ((2560A b - 1792B a b )e - 768B b d e )x --R + @@ -32760,332 +33252,332 @@ r0:=-2/3*(A*b-a*B)/(b*(b*d-a*e)*(a+b*x)^(3/2)*(d+e*x)^(7/2))-_ --R Type: Expression(Integer) --E 1230 ---S 1231 of 1293 +--S 1231 of 1293 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R ---R (1129) +--R (3) --R 2 5 3 4 4 5 2 5 5 4 5 ---R ((10240A a b - 7168B a b )d e - 3072B a b d e )x +--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 (15360A a b - 10752B a b )d e + (35840A a b - 29696B a b )d e +--R (19200A a b - 13440B a b )d e + (44800A a b - 37120B a b )d e --R + --R 2 5 6 3 ---R - 10752B a b d e +--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 (3840A a b - 2688B a b )d e + (53760A a b - 38784B a b )d e +--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 (44800A a b - 47488B a b )d e - 13440B a b d e +--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 (- 640A a b + 448B a b)d e + (13440A a b - 9216B a b )d e +--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 (67200A a b - 51072B a b )d e + (22400A a b - 35840B a b )d e +--R (84000A a b - 63840B a b )d e + (28000A a b - 44800B a b )d e --R + --R 2 5 8 ---R - 6720B a b d e +--R - 8400B a b d e --R * --R 2 --R x --R + --R 6 7 4 5 5 2 6 5 4 ---R (240A a b - 168B a )d e + (- 2240A a b + 1496B a b)d e +--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 (16800A a b - 11088B a b )d e + (33600A a b - 28560B a b )d e +--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 (2800A a b - 12040B a b )d e - 840B a b d +--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 - 120A a d e + (840A a b - 48B a )d e +--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 (- 2800A a b + 448B a b)d e + (8400A a b - 3360B a b )d e +--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 (4200A a b - 6720B a b )d e + (- 280A a b - 560B a b )d +--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 - 240A a b )e +--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 + (1680A a b - 96B a b )d)e +--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 + (- 5600A a b + 896B a b )d )e +--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 + (16800A a b - 6720B a b )d )e +--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 + (8400A a b - 13440B a b )d )e +--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 + (- 560A a b - 1120B a b )d )e +--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 - 480A a b)e +--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 + (2400A a b - 192B a b)d)e +--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 + (- 4480A a b + 1408B a b )d )e +--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 + (11200A a b - 9856B a b )d )e +--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 + (84000A a b - 53760B a b )d )e +--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 + (32480A a b - 56000B a b )d )e +--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 + (- 2240A a b - 4480B a b )d )e +--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 - 240A a )e +--R (- 15A a d - 375A a )e --R + ---R 6 7 2 7 8 8 ---R ((- 15A a b - 6B a )d + (- 240A a b - 96B a )d)e +--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 + (6400A a b + 128B a b)d )e +--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 + (- 17920A a b - 128B a b )d )e +--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 + (109200A a b - 61824B a b )d )e +--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 + (167440A a b - 148960B a b )d )e +--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 + (45920A a b - 89600B a b )d )e +--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 + (- 3360A a b - 6720B a b )d )e +--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 - 960A a d)e +--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 + (3840A a b - 384B a )d )e +--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 + (- 3200A a b + 2432B a b)d )e +--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 + (6720A a b - 16512B a b )d )e +--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 + (212800A a b - 130816B a b )d )e +--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 + (165760A a b - 192640B a b )d )e +--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 + (26880A a b - 67200B a b )d )e +--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 + (- 2240A a b - 4480B a b )d )e +--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 - 1440A a d )e +--R (- 90A a d - 2250A a d )e --R + ---R 6 7 4 7 8 3 6 ---R ((510A a b - 36B a )d + (8160A a b - 576B a )d )e +--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 + (- 20400A a b + 4608B a b)d )e +--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 + (57680A a b - 33248B a b )d )e +--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 + (179200A a b - 133504B a b )d )e +--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 + (80640A a b - 120960B a b )d )e +--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 + (3920A a b - 22400B a b )d )e +--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 + (- 560A a b - 1120B a b )d +--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 - 960A a d )e +--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 + (6240A a b - 384B a )d )e +--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 + (- 19040A a b + 3392B a b)d )e +--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 + (56000A a b - 25088B a b )d )e +--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 + (67200A a b - 67200B a b )d )e +--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 + (14560A a b - 31360B a b )d )e +--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 + (- 1120A a b - 2240B a b )d +--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 - 240A a d )e +--R (- 15A a d - 375A a d )e --R + ---R 6 7 6 7 8 5 4 ---R ((105A a b - 6B a )d + (1680A a b - 96B a )d )e +--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 + (- 5600A a b + 896B a b)d )e +--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 + (16800A a b - 6720B a b )d )e +--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 + (8400A a b - 13440B a b )d )e +--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 + (- 560A a b - 1120B a b )d +--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 420a b d e - 2520a b d e + 6300a b d e - 8400a b d e +--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 6300a b d e - 2520a b d e + 420a b d e +--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 840a b d e - 3360a b d e + 2520a b d e + 8400a b d e +--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 - 21000a b d e + 20160a b d e - 9240a b d e + 1680a b d e +--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 420a d e + 840a b d e - 11340a b d e + 26880a b d e +--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 - 23100a b d e - 2520a b d e + 18060a b d e - 11760a b d e +--R - 28875a b d e - 3150a b d e + 22575a b d e - 14700a b d e --R + --R 2 8 12 2 ---R 2520a b d e +--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 1680a d e - 5040a b d e - 3360a b d e + 31920a b d e +--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 - 50400a b d e + 31920a b d e - 3360a b d e - 5040a b d e +--R - 63000a b d e + 39900a b d e - 4200a b d e - 6300a b d e --R + --R 2 8 13 ---R 1680a b d e +--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 2520a d e - 11760a b d e + 18060a b d e - 2520a b d e +--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 - 23100a b d e + 26880a b d e - 11340a b d e + 840a b d e +--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 420a b d +--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 1680a d e - 9240a b d e + 20160a b d e - 21000a b d e +--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 8400a b d e + 2520a b d e - 3360a b d e + 840a b d +--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 6 4 12 2 ---R 420a d e - 2520a b d e + 6300a b d e - 8400a b d e + 6300a b d e +--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 5 5 13 4 6 14 ---R - 2520a b d e + 420a b d +--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 +--S 1232 of 1293 ok to fail, differs by a constant m0:=a0-r0 --R --R ---R (1130) +--R (4) --R 5 6 5 ---R (- 15A a d - 240A a )e +--R (- 15A a d - 375A a )e --R + ---R 4 5 2 5 6 4 ---R ((105A a b - 6B a )d + (1680A a b - 96B a )d)e +--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 + (- 5600A a b + 896B a b)d )e +--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 + (16800A a b - 6720B a b )d )e +--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 + (8400A a b - 13440B a b )d )e +--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 + (- 560A a b - 1120B a b )d +--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 420a d e - 2520a b d e + 6300a b d e - 8400a b d e + 6300a b d e +--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 - 2520a b d e + 420a b d +--R - 3150a b d e + 525a b d --R Type: Expression(Integer) --E 1232 @@ -33093,19 +33585,21 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1131) 0 +--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 (1132) ------------------- ---R n ---R (f x + e) +--R n +--R (b x + a)(d x + c) +--R (1) ------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1234 @@ -33128,15 +33622,17 @@ t0:=(a+b*x)*(c+d*x)^n/(e+f*x)^n --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 (1133) ----------------------- ---R n ---R (f x + e) +--R n - 1 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1239 @@ -33159,15 +33655,17 @@ t0:=(a+b*x)*(c+d*x)^(-1+n)/(e+f*x)^n --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 (1134) ----------------------- ---R n ---R (f x + e) +--R n - 2 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1244 @@ -33190,15 +33688,17 @@ t0:=(a+b*x)*(c+d*x)^(-2+n)/(e+f*x)^n --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 (1135) ----------------------- ---R n ---R (f x + e) +--R n - 3 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1249 @@ -33208,7 +33708,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(2-n))+_ (e+f*x)^(1-n)/(d*(d*e-c*f)^2*(1-n)*(2-n)) --R --R ---R (1136) +--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 + @@ -33236,7 +33736,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-2+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(2-n))+_ a0:=integrate(t0,x) --R --R ---R (1137) +--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 + @@ -33278,7 +33778,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1138) +--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 + @@ -33335,7 +33835,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1139) +--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 + @@ -33388,15 +33888,17 @@ d0:=D(m0,x) --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 (1140) ----------------------- ---R n ---R (f x + e) +--R n - 4 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1254 @@ -33407,7 +33909,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(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 (1141) +--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 + @@ -33467,7 +33969,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-3+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(3-n))+_ a0:=integrate(t0,x) --R --R ---R (1142) +--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 + @@ -33564,7 +34066,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1143) +--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 + @@ -33702,7 +34204,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1144) +--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 * @@ -33837,15 +34339,17 @@ d0:=D(m0,x) --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 (1145) ----------------------- ---R n ---R (f x + e) +--R n - 5 +--R (b x + a)(d x + c) +--R (1) ----------------------- +--R n +--R (f x + e) --R Type: Expression(Integer) --E 1259 @@ -33858,7 +34362,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-4+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(4-n))+_ (e+f*x)^(1-n)/(d*(d*e-c*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) --R --R ---R (1146) +--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 + @@ -33962,7 +34466,7 @@ r0:=(b*c-a*d)*(c+d*x)^(-4+n)*(e+f*x)^(1-n)/(d*(d*e-c*f)*(4-n))+_ a0:=integrate(t0,x) --R --R ---R (1147) +--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 + @@ -34126,7 +34630,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1148) +--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 * @@ -34381,7 +34885,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1149) +--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 * @@ -34625,15 +35129,17 @@ d0:=D(m0,x) --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 (1150) ------------------- ---R n ---R (b x + a) +--R n +--R (d x + c)(f x + e) +--R (1) ------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1264 @@ -34655,15 +35161,17 @@ t0:=(c+d*x)*(e+f*x)^n/(a+b*x)^n --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 (1151) ----------------------- ---R n ---R (b x + a) +--R n - 1 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1269 @@ -34686,15 +35194,17 @@ t0:=(c+d*x)*(e+f*x)^(-1+n)/(a+b*x)^n --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 (1152) ----------------------- ---R n ---R (b x + a) +--R n - 2 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1274 @@ -34717,15 +35227,17 @@ t0:=(c+d*x)*(e+f*x)^(-2+n)/(a+b*x)^n --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 (1153) ----------------------- ---R n ---R (b x + a) +--R n - 3 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1279 @@ -34735,7 +35247,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)*(2-n))-_ (f*(b*e-a*f)^2*(1-n)*(2-n)) --R --R ---R (1154) +--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 * @@ -34763,7 +35275,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-2+n)/(f*(b*e-a*f)*(2-n))-_ a0:=integrate(t0,x) --R --R ---R (1155) +--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 + @@ -34805,7 +35317,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1156) +--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 + @@ -34865,7 +35377,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1157) +--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 + @@ -34921,15 +35433,17 @@ d0:=D(m0,x) --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 (1158) ----------------------- ---R n ---R (b x + a) +--R n - 4 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1284 @@ -34941,7 +35455,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)*(3-n))+_ (2-n)*(3-n)) --R --R ---R (1159) +--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 * @@ -34990,7 +35504,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-3+n)/(f*(b*e-a*f)*(3-n))+_ a0:=integrate(t0,x) --R --R ---R (1160) +--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 + @@ -35084,7 +35598,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1161) +--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 + @@ -35211,7 +35725,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1162) +--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 + @@ -35346,15 +35860,17 @@ d0:=D(m0,x) --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 (1163) ----------------------- ---R n ---R (b x + a) +--R n - 5 +--R (d x + c)(f x + e) +--R (1) ----------------------- +--R n +--R (b x + a) --R Type: Expression(Integer) --E 1289 @@ -35367,7 +35883,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-4+n)/(f*(b*e-a*f)*(4-n))+_ (f*(b*e-a*f)^4*(1-n)*(2-n)*(3-n)*(4-n)) --R --R ---R (1164) +--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 * @@ -35471,7 +35987,7 @@ r0:=-(d*e-c*f)*(a+b*x)^(1-n)*(e+f*x)^(-4+n)/(f*(b*e-a*f)*(4-n))+_ a0:=integrate(t0,x) --R --R ---R (1165) +--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 + @@ -35635,7 +36151,7 @@ a0:=integrate(t0,x) m0:=a0-r0 --R --R ---R (1166) +--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 + @@ -35884,7 +36400,7 @@ m0:=a0-r0 d0:=D(m0,x) --R --R ---R (1167) +--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 +