Optimal. Leaf size=373 \[ -\frac {b^3 (c+d x)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{3 g^4 i (a+b x)^3 (b c-a d)^4}+\frac {3 b^2 d (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{2 g^4 i (a+b x)^2 (b c-a d)^4}-\frac {d^3 \log \left (\frac {a+b x}{c+d x}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^4 i (b c-a d)^4}-\frac {3 b d^2 (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^4 i (a+b x) (b c-a d)^4}-\frac {b^3 B (c+d x)^3}{9 g^4 i (a+b x)^3 (b c-a d)^4}+\frac {3 b^2 B d (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}+\frac {B d^3 \log ^2\left (\frac {a+b x}{c+d x}\right )}{2 g^4 i (b c-a d)^4}-\frac {3 b B d^2 (c+d x)}{g^4 i (a+b x) (b c-a d)^4} \]
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Rubi [C] time = 1.08, antiderivative size = 620, normalized size of antiderivative = 1.66, number of steps used = 32, number of rules used = 11, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.275, Rules used = {2528, 2525, 12, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391} \[ -\frac {B d^3 \text {PolyLog}\left (2,-\frac {d (a+b x)}{b c-a d}\right )}{g^4 i (b c-a d)^4}-\frac {B d^3 \text {PolyLog}\left (2,\frac {b (c+d x)}{b c-a d}\right )}{g^4 i (b c-a d)^4}-\frac {d^3 \log (a+b x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^4 i (b c-a d)^4}+\frac {d^3 \log (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^4 i (b c-a d)^4}-\frac {d^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^4 i (a+b x) (b c-a d)^3}+\frac {d \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{2 g^4 i (a+b x)^2 (b c-a d)^2}-\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right )+A}{3 g^4 i (a+b x)^3 (b c-a d)}-\frac {11 B d^2}{6 g^4 i (a+b x) (b c-a d)^3}+\frac {B d^3 \log ^2(a+b x)}{2 g^4 i (b c-a d)^4}+\frac {B d^3 \log ^2(c+d x)}{2 g^4 i (b c-a d)^4}-\frac {11 B d^3 \log (a+b x)}{6 g^4 i (b c-a d)^4}-\frac {B d^3 \log (c+d x) \log \left (-\frac {d (a+b x)}{b c-a d}\right )}{g^4 i (b c-a d)^4}+\frac {11 B d^3 \log (c+d x)}{6 g^4 i (b c-a d)^4}-\frac {B d^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{g^4 i (b c-a d)^4}+\frac {5 B d}{12 g^4 i (a+b x)^2 (b c-a d)^2}-\frac {B}{9 g^4 i (a+b x)^3 (b c-a d)} \]
Antiderivative was successfully verified.
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Rule 12
Rule 44
Rule 2301
Rule 2390
Rule 2391
Rule 2393
Rule 2394
Rule 2418
Rule 2524
Rule 2525
Rule 2528
Rubi steps
\begin {align*} \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(38 c+38 d x) (a g+b g x)^4} \, dx &=\int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d) g^4 (a+b x)^4}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^2 g^4 (a+b x)^3}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)^2}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4 (a+b x)}+\frac {d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4 (c+d x)}\right ) \, dx\\ &=-\frac {\left (b d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{38 (b c-a d)^4 g^4}+\frac {d^4 \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{38 (b c-a d)^4 g^4}+\frac {\left (b d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{38 (b c-a d)^3 g^4}-\frac {(b d) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{38 (b c-a d)^2 g^4}+\frac {b \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{38 (b c-a d) g^4}\\ &=-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {\left (B d^3\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{38 (b c-a d)^4 g^4}-\frac {\left (B d^3\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{38 (b c-a d)^4 g^4}+\frac {\left (B d^2\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{38 (b c-a d)^3 g^4}-\frac {(B d) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{76 (b c-a d)^2 g^4}+\frac {B \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{114 (b c-a d) g^4}\\ &=-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {B \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{114 g^4}+\frac {\left (B d^2\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{38 (b c-a d)^2 g^4}-\frac {(B d) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{76 (b c-a d) g^4}+\frac {\left (B d^3\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{38 (b c-a d)^4 e g^4}-\frac {\left (B d^3\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{38 (b c-a d)^4 e g^4}\\ &=-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {B \int \left (\frac {b}{(b c-a d) (a+b x)^4}-\frac {b d}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3}{(b c-a d)^4 (a+b x)}+\frac {d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{114 g^4}+\frac {\left (B d^2\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^2}-\frac {b d}{(b c-a d)^2 (a+b x)}+\frac {d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{38 (b c-a d)^2 g^4}-\frac {(B d) \int \left (\frac {b}{(b c-a d) (a+b x)^3}-\frac {b d}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2}{(b c-a d)^3 (a+b x)}-\frac {d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{76 (b c-a d) g^4}+\frac {\left (B d^3\right ) \int \left (\frac {b e \log (a+b x)}{a+b x}-\frac {d e \log (a+b x)}{c+d x}\right ) \, dx}{38 (b c-a d)^4 e g^4}-\frac {\left (B d^3\right ) \int \left (\frac {b e \log (c+d x)}{a+b x}-\frac {d e \log (c+d x)}{c+d x}\right ) \, dx}{38 (b c-a d)^4 e g^4}\\ &=-\frac {B}{342 (b c-a d) g^4 (a+b x)^3}+\frac {5 B d}{456 (b c-a d)^2 g^4 (a+b x)^2}-\frac {11 B d^2}{228 (b c-a d)^3 g^4 (a+b x)}-\frac {11 B d^3 \log (a+b x)}{228 (b c-a d)^4 g^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {11 B d^3 \log (c+d x)}{228 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {\left (b B d^3\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{38 (b c-a d)^4 g^4}-\frac {\left (b B d^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{38 (b c-a d)^4 g^4}-\frac {\left (B d^4\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{38 (b c-a d)^4 g^4}+\frac {\left (B d^4\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{38 (b c-a d)^4 g^4}\\ &=-\frac {B}{342 (b c-a d) g^4 (a+b x)^3}+\frac {5 B d}{456 (b c-a d)^2 g^4 (a+b x)^2}-\frac {11 B d^2}{228 (b c-a d)^3 g^4 (a+b x)}-\frac {11 B d^3 \log (a+b x)}{228 (b c-a d)^4 g^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {11 B d^3 \log (c+d x)}{228 (b c-a d)^4 g^4}-\frac {B d^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}-\frac {B d^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{38 (b c-a d)^4 g^4}+\frac {\left (B d^3\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{38 (b c-a d)^4 g^4}+\frac {\left (B d^3\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{38 (b c-a d)^4 g^4}+\frac {\left (b B d^3\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{38 (b c-a d)^4 g^4}+\frac {\left (B d^4\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{38 (b c-a d)^4 g^4}\\ &=-\frac {B}{342 (b c-a d) g^4 (a+b x)^3}+\frac {5 B d}{456 (b c-a d)^2 g^4 (a+b x)^2}-\frac {11 B d^2}{228 (b c-a d)^3 g^4 (a+b x)}-\frac {11 B d^3 \log (a+b x)}{228 (b c-a d)^4 g^4}+\frac {B d^3 \log ^2(a+b x)}{76 (b c-a d)^4 g^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {11 B d^3 \log (c+d x)}{228 (b c-a d)^4 g^4}-\frac {B d^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {B d^3 \log ^2(c+d x)}{76 (b c-a d)^4 g^4}-\frac {B d^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{38 (b c-a d)^4 g^4}+\frac {\left (B d^3\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{38 (b c-a d)^4 g^4}+\frac {\left (B d^3\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{38 (b c-a d)^4 g^4}\\ &=-\frac {B}{342 (b c-a d) g^4 (a+b x)^3}+\frac {5 B d}{456 (b c-a d)^2 g^4 (a+b x)^2}-\frac {11 B d^2}{228 (b c-a d)^3 g^4 (a+b x)}-\frac {11 B d^3 \log (a+b x)}{228 (b c-a d)^4 g^4}+\frac {B d^3 \log ^2(a+b x)}{76 (b c-a d)^4 g^4}-\frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{114 (b c-a d) g^4 (a+b x)^3}+\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{76 (b c-a d)^2 g^4 (a+b x)^2}-\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^3 g^4 (a+b x)}-\frac {d^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{38 (b c-a d)^4 g^4}+\frac {11 B d^3 \log (c+d x)}{228 (b c-a d)^4 g^4}-\frac {B d^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{38 (b c-a d)^4 g^4}+\frac {B d^3 \log ^2(c+d x)}{76 (b c-a d)^4 g^4}-\frac {B d^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{38 (b c-a d)^4 g^4}-\frac {B d^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{38 (b c-a d)^4 g^4}-\frac {B d^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{38 (b c-a d)^4 g^4}\\ \end {align*}
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Mathematica [C] time = 0.71, size = 492, normalized size = 1.32 \[ \frac {\frac {36 A d^2 (a d-b c)}{a+b x}+\frac {18 A d (b c-a d)^2}{(a+b x)^2}-\frac {12 A (b c-a d)^3}{(a+b x)^3}-36 A d^3 \log (a+b x)-36 B d^3 \log (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )+36 B d^3 \log (c+d x) \log \left (\frac {e (a+b x)}{c+d x}\right )-36 B d^3 \text {Li}_2\left (\frac {d (a+b x)}{a d-b c}\right )-36 B d^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )-36 B d^3 \log (c+d x) \log \left (\frac {d (a+b x)}{a d-b c}\right )-36 B d^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )+\frac {36 B d^2 (a d-b c) \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x}+\frac {66 B d^2 (a d-b c)}{a+b x}+\frac {18 B d (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2}-\frac {12 B (b c-a d)^3 \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3}+\frac {15 B d (b c-a d)^2}{(a+b x)^2}-\frac {4 B (b c-a d)^3}{(a+b x)^3}+18 B d^3 \log ^2(a+b x)-66 B d^3 \log (a+b x)+36 A d^3 \log (c+d x)+18 B d^3 \log ^2(c+d x)+66 B d^3 \log (c+d x)}{36 g^4 i (b c-a d)^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 611, normalized size = 1.64 \[ -\frac {4 \, {\left (3 \, A + B\right )} b^{3} c^{3} - 27 \, {\left (2 \, A + B\right )} a b^{2} c^{2} d + 108 \, {\left (A + B\right )} a^{2} b c d^{2} - {\left (66 \, A + 85 \, B\right )} a^{3} d^{3} + 6 \, {\left ({\left (6 \, A + 11 \, B\right )} b^{3} c d^{2} - {\left (6 \, A + 11 \, B\right )} a b^{2} d^{3}\right )} x^{2} + 18 \, {\left (B b^{3} d^{3} x^{3} + 3 \, B a b^{2} d^{3} x^{2} + 3 \, B a^{2} b d^{3} x + B a^{3} d^{3}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} - 3 \, {\left ({\left (6 \, A + 5 \, B\right )} b^{3} c^{2} d - 18 \, {\left (2 \, A + 3 \, B\right )} a b^{2} c d^{2} + {\left (30 \, A + 49 \, B\right )} a^{2} b d^{3}\right )} x + 6 \, {\left ({\left (6 \, A + 11 \, B\right )} b^{3} d^{3} x^{3} + 2 \, B b^{3} c^{3} - 9 \, B a b^{2} c^{2} d + 18 \, B a^{2} b c d^{2} + 6 \, A a^{3} d^{3} + 3 \, {\left (2 \, B b^{3} c d^{2} + 3 \, {\left (2 \, A + 3 \, B\right )} a b^{2} d^{3}\right )} x^{2} - 3 \, {\left (B b^{3} c^{2} d - 6 \, B a b^{2} c d^{2} - 6 \, {\left (A + B\right )} a^{2} b d^{3}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{36 \, {\left ({\left (b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right )} g^{4} i x^{3} + 3 \, {\left (a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right )} g^{4} i x^{2} + 3 \, {\left (a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right )} g^{4} i x + {\left (a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right )} g^{4} i\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 1474, normalized size = 3.95 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.41, size = 1469, normalized size = 3.94 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.51, size = 970, normalized size = 2.60 \[ \frac {11\,A\,a^2\,d^2}{6\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}-\frac {B\,d^3\,{\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}^2}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^4}+\frac {A\,b^2\,c^2}{3\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {85\,B\,a^2\,d^2}{36\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {B\,b^2\,c^2}{9\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {11\,B\,a^3\,d^3\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{6\,g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}-\frac {B\,b^3\,c^3\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{3\,g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}+\frac {A\,b^2\,d^2\,x^2}{g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {11\,B\,b^2\,d^2\,x^2}{6\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}-\frac {7\,A\,a\,b\,c\,d}{6\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}-\frac {23\,B\,a\,b\,c\,d}{36\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {5\,A\,a\,b\,d^2\,x}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {49\,B\,a\,b\,d^2\,x}{12\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}-\frac {A\,b^2\,c\,d\,x}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}-\frac {5\,B\,b^2\,c\,d\,x}{12\,g^4\,i\,{\left (a\,d-b\,c\right )}^3\,{\left (a+b\,x\right )}^3}+\frac {3\,B\,a\,b^2\,c^2\,d\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}-\frac {3\,B\,a^2\,b\,c\,d^2\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}+\frac {5\,B\,a^2\,b\,d^3\,x\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}+\frac {B\,b^3\,c^2\,d\,x\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{2\,g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}+\frac {B\,a\,b^2\,d^3\,x^2\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}-\frac {B\,b^3\,c\,d^2\,x^2\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}-\frac {3\,B\,a\,b^2\,c\,d^2\,x\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}{g^4\,i\,{\left (a\,d-b\,c\right )}^4\,{\left (a+b\,x\right )}^3}+\frac {A\,d^3\,\mathrm {atan}\left (\frac {a\,d\,1{}\mathrm {i}+b\,c\,1{}\mathrm {i}+b\,d\,x\,2{}\mathrm {i}}{a\,d-b\,c}\right )\,2{}\mathrm {i}}{g^4\,i\,{\left (a\,d-b\,c\right )}^4}+\frac {B\,d^3\,\mathrm {atan}\left (\frac {a\,d\,1{}\mathrm {i}+b\,c\,1{}\mathrm {i}+b\,d\,x\,2{}\mathrm {i}}{a\,d-b\,c}\right )\,11{}\mathrm {i}}{3\,g^4\,i\,{\left (a\,d-b\,c\right )}^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 20.69, size = 1392, normalized size = 3.73 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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