Optimal. Leaf size=644 \[ -\frac {4 B^2 d (b c-a d) i^3 n^2 (c+d x)}{b^3 g^3 (a+b x)}-\frac {B^2 (b c-a d) i^3 n^2 (c+d x)^2}{4 b^2 g^3 (a+b x)^2}-\frac {4 B d (b c-a d) i^3 n (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^3 g^3 (a+b x)}-\frac {B (b c-a d) i^3 n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{2 b^2 g^3 (a+b x)^2}+\frac {d^3 i^3 (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {2 d (b c-a d) i^3 (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3 (a+b x)}-\frac {(b c-a d) i^3 (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{2 b^2 g^3 (a+b x)^2}+\frac {2 B d^2 (b c-a d) i^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log \left (\frac {b c-a d}{b (c+d x)}\right )}{b^4 g^3}-\frac {3 d^2 (b c-a d) i^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right )}{b^4 g^3}+\frac {2 B^2 d^2 (b c-a d) i^3 n^2 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{b^4 g^3}+\frac {6 B d^2 (b c-a d) i^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^4 g^3}+\frac {6 B^2 d^2 (b c-a d) i^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^4 g^3} \]
[Out]
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Rubi [A]
time = 0.45, antiderivative size = 644, normalized size of antiderivative = 1.00, number of steps
used = 13, number of rules used = 10, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2561, 2395,
2342, 2341, 2355, 2354, 2438, 2379, 2421, 6724} \begin {gather*} \frac {6 B d^2 i^3 n (b c-a d) \text {PolyLog}\left (2,\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{b^4 g^3}+\frac {2 B^2 d^2 i^3 n^2 (b c-a d) \text {PolyLog}\left (2,\frac {d (a+b x)}{b (c+d x)}\right )}{b^4 g^3}+\frac {6 B^2 d^2 i^3 n^2 (b c-a d) \text {PolyLog}\left (3,\frac {b (c+d x)}{d (a+b x)}\right )}{b^4 g^3}+\frac {d^3 i^3 (a+b x) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{b^4 g^3}+\frac {2 B d^2 i^3 n (b c-a d) \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{b^4 g^3}-\frac {3 d^2 i^3 (b c-a d) \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{b^4 g^3}-\frac {2 d i^3 (c+d x) (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{b^3 g^3 (a+b x)}-\frac {4 B d i^3 n (c+d x) (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{b^3 g^3 (a+b x)}-\frac {i^3 (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 b^2 g^3 (a+b x)^2}-\frac {B i^3 n (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{2 b^2 g^3 (a+b x)^2}-\frac {4 B^2 d i^3 n^2 (c+d x) (b c-a d)}{b^3 g^3 (a+b x)}-\frac {B^2 i^3 n^2 (c+d x)^2 (b c-a d)}{4 b^2 g^3 (a+b x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2341
Rule 2342
Rule 2354
Rule 2355
Rule 2379
Rule 2395
Rule 2421
Rule 2438
Rule 2561
Rule 6724
Rubi steps
\begin {align*} \int \frac {(184 c+184 d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{(a g+b g x)^3} \, dx &=\int \left (\frac {6229504 d^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}+\frac {6229504 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3 (a+b x)^3}+\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3 (a+b x)^2}+\frac {18688512 d^2 (b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3 (a+b x)}\right ) \, dx\\ &=\frac {\left (6229504 d^3\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{b^3 g^3}+\frac {\left (18688512 d^2 (b c-a d)\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{a+b x} \, dx}{b^3 g^3}+\frac {\left (18688512 d (b c-a d)^2\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{(a+b x)^2} \, dx}{b^3 g^3}+\frac {\left (6229504 (b c-a d)^3\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{(a+b x)^3} \, dx}{b^3 g^3}\\ &=\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {\left (12459008 B d^3 n\right ) \int \frac {(b c-a d) x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{b^3 g^3}-\frac {\left (37377024 B d^2 (b c-a d) n\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{b^4 g^3}+\frac {\left (37377024 B d (b c-a d)^2 n\right ) \int \frac {(b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (6229504 B (b c-a d)^3 n\right ) \int \frac {(b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^3}\\ &=\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {\left (37377024 B d^2 (b c-a d) n\right ) \int \frac {(b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{b^4 g^3}-\frac {\left (12459008 B d^3 (b c-a d) n\right ) \int \frac {x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{b^3 g^3}+\frac {\left (37377024 B d (b c-a d)^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (6229504 B (b c-a d)^4 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^3}\\ &=\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {\left (12459008 B d^3 (b c-a d) n\right ) \int \left (-\frac {a \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)}+\frac {c \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (c+d x)}\right ) \, dx}{b^3 g^3}-\frac {\left (37377024 B d^2 (b c-a d)^2 n\right ) \int \frac {\log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{b^4 g^3}+\frac {\left (37377024 B d (b c-a d)^3 n\right ) \int \left (\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)^2}-\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (a+b x)}+\frac {d^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^4 g^3}+\frac {\left (6229504 B (b c-a d)^4 n\right ) \int \left (\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)^3}-\frac {b d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (a+b x)}-\frac {d^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^3}\\ &=\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}+\frac {\left (12459008 a B d^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (12459008 B c d^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{b^3 g^3}+\frac {\left (6229504 B d^2 (b c-a d) n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (37377024 B d^2 (b c-a d) n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (6229504 B d^3 (b c-a d) n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{b^4 g^3}+\frac {\left (37377024 B d^3 (b c-a d) n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{b^4 g^3}-\frac {\left (6229504 B d (b c-a d)^2 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{b^3 g^3}+\frac {\left (37377024 B d (b c-a d)^2 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{b^3 g^3}-\frac {\left (37377024 B d^2 (b c-a d)^2 n\right ) \int \left (\frac {A \log (a+b x)}{(a+b x) (c+d x)}+\frac {B \log (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)}\right ) \, dx}{b^4 g^3}+\frac {\left (6229504 B (b c-a d)^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x)^3} \, dx}{b^3 g^3}\\ &=-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}-\frac {\left (37377024 A B d^2 (b c-a d)^2 n\right ) \int \frac {\log (a+b x)}{(a+b x) (c+d x)} \, dx}{b^4 g^3}-\frac {\left (37377024 B^2 d^2 (b c-a d)^2 n\right ) \int \frac {\log (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)} \, dx}{b^4 g^3}+\frac {\left (12459008 B^2 c d^2 n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^3 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 g^3}+\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 g^3}-\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d (b c-a d)^2 n^2\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d (b c-a d)^2 n^2\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (3114752 B^2 (b c-a d)^3 n^2\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^3}\\ &=-\frac {18688512 B^2 d^2 (b c-a d) \log (a+b x) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}+\frac {\left (18688512 B^2 d^2 (b c-a d)\right ) \int \frac {\log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (37377024 A B d^2 (b c-a d)^2 n\right ) \text {Subst}\left (\int \frac {\log (x)}{x \left (\frac {b c-a d}{b}+\frac {d x}{b}\right )} \, dx,x,a+b x\right )}{b^5 g^3}+\frac {\left (12459008 B^2 c d^2 n^2\right ) \int \left (\frac {b \log (c+d x)}{a+b x}-\frac {d \log (c+d x)}{c+d x}\right ) \, dx}{b^3 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{b^4 g^3}+\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \left (\frac {b \log (c+d x)}{a+b x}-\frac {d \log (c+d x)}{c+d x}\right ) \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{b^4 g^3}-\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \left (\frac {b \log (c+d x)}{a+b x}-\frac {d \log (c+d x)}{c+d x}\right ) \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d (b c-a d)^3 n^2\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d (b c-a d)^3 n^2\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^3}+\frac {\left (3114752 B^2 (b c-a d)^4 n^2\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^3}\\ &=-\frac {18688512 B^2 d^2 (b c-a d) \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log (a+b x) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}-\frac {\left (37377024 A B d^2 (b c-a d) n\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g^3}+\frac {\left (37377024 A B d^3 (b c-a d) n\right ) \text {Subst}\left (\int \frac {\log (x)}{\frac {b c-a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{b^5 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d)^2 n\right ) \int \frac {\log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)} \, dx}{b^4 g^3}+\frac {\left (12459008 B^2 c d^2 n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^2 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 g^3}-\frac {\left (12459008 B^2 c d^3 n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^3 g^3}+\frac {\left (12459008 a B^2 d^4 n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 g^3}+\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 g^3}-\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 g^3}+\frac {\left (6229504 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 g^3}-\frac {\left (37377024 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 g^3}-\frac {\left (6229504 B^2 d (b c-a d)^3 n^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}{b^4 g^3}+\frac {\left (37377024 B^2 d (b c-a d)^3 n^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}{b^4 g^3}+\frac {\left (3114752 B^2 (b c-a d)^4 n^2\right ) \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}{b^4 g^3}\\ &=-\frac {1557376 B^2 (b c-a d)^3 n^2}{b^4 g^3 (a+b x)^2}-\frac {28032768 B^2 d (b c-a d)^2 n^2}{b^4 g^3 (a+b x)}-\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (a+b x)}{b^4 g^3}-\frac {18688512 A B d^2 (b c-a d) n \log ^2(a+b x)}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log (a+b x) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}+\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (c+d x)}{b^4 g^3}+\frac {12459008 B^2 c d^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}+\frac {37377024 A B d^2 (b c-a d) n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {12459008 a B^2 d^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {37377024 B^2 d^2 (b c-a d) n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b^4 g^3}-\frac {\left (37377024 A B d^2 (b c-a d) n\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g^3}-\frac {\left (12459008 B^2 c d^2 n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^3 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (12459008 B^2 c d^3 n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^3 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 g^3}-\frac {\left (6229504 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 g^3}+\frac {\left (37377024 B^2 d^3 (b c-a d) n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 g^3}-\frac {\left (37377024 B^2 d^2 (b c-a d)^2 n^2\right ) \int \frac {\text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{(a+b x) (c+d x)} \, dx}{b^4 g^3}\\ &=-\frac {1557376 B^2 (b c-a d)^3 n^2}{b^4 g^3 (a+b x)^2}-\frac {28032768 B^2 d (b c-a d)^2 n^2}{b^4 g^3 (a+b x)}-\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (a+b x)}{b^4 g^3}-\frac {18688512 A B d^2 (b c-a d) n \log ^2(a+b x)}{b^4 g^3}-\frac {6229504 a B^2 d^3 n^2 \log ^2(a+b x)}{b^4 g^3}+\frac {15573760 B^2 d^2 (b c-a d) n^2 \log ^2(a+b x)}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log (a+b x) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}+\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (c+d x)}{b^4 g^3}+\frac {12459008 B^2 c d^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}-\frac {6229504 B^2 c d^2 n^2 \log ^2(c+d x)}{b^3 g^3}+\frac {15573760 B^2 d^2 (b c-a d) n^2 \log ^2(c+d x)}{b^4 g^3}+\frac {37377024 A B d^2 (b c-a d) n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {12459008 a B^2 d^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {37377024 A B d^2 (b c-a d) n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g^3}+\frac {37377024 B^2 d^2 (b c-a d) n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b^4 g^3}+\frac {37377024 B^2 d^2 (b c-a d) n^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b^4 g^3}-\frac {\left (12459008 B^2 c d^2 n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^3 g^3}-\frac {\left (12459008 a B^2 d^3 n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g^3}-\frac {\left (6229504 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g^3}+\frac {\left (37377024 B^2 d^2 (b c-a d) n^2\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 g^3}\\ &=-\frac {1557376 B^2 (b c-a d)^3 n^2}{b^4 g^3 (a+b x)^2}-\frac {28032768 B^2 d (b c-a d)^2 n^2}{b^4 g^3 (a+b x)}-\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (a+b x)}{b^4 g^3}-\frac {18688512 A B d^2 (b c-a d) n \log ^2(a+b x)}{b^4 g^3}-\frac {6229504 a B^2 d^3 n^2 \log ^2(a+b x)}{b^4 g^3}+\frac {15573760 B^2 d^2 (b c-a d) n^2 \log ^2(a+b x)}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {18688512 B^2 d^2 (b c-a d) \log (a+b x) \log ^2\left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{b^4 g^3}-\frac {3114752 B (b c-a d)^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)^2}-\frac {31147520 B d (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3 (a+b x)}+\frac {12459008 a B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}-\frac {31147520 B d^2 (b c-a d) n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g^3}+\frac {6229504 d^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g^3}-\frac {3114752 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)^2}-\frac {18688512 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3 (a+b x)}+\frac {18688512 d^2 (b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^4 g^3}+\frac {28032768 B^2 d^2 (b c-a d) n^2 \log (c+d x)}{b^4 g^3}+\frac {12459008 B^2 c d^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 g^3}-\frac {12459008 B c d^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g^3}+\frac {31147520 B d^2 (b c-a d) n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^4 g^3}-\frac {6229504 B^2 c d^2 n^2 \log ^2(c+d x)}{b^3 g^3}+\frac {15573760 B^2 d^2 (b c-a d) n^2 \log ^2(c+d x)}{b^4 g^3}+\frac {37377024 A B d^2 (b c-a d) n \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {12459008 a B^2 d^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {37377024 A B d^2 (b c-a d) n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g^3}+\frac {12459008 a B^2 d^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g^3}+\frac {12459008 B^2 c d^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g^3}-\frac {31147520 B^2 d^2 (b c-a d) n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g^3}+\frac {37377024 B^2 d^2 (b c-a d) n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b^4 g^3}+\frac {37377024 B^2 d^2 (b c-a d) n^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{b^4 g^3}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(6226\) vs. \(2(644)=1288\).
time = 21.17, size = 6226, normalized size = 9.67 \begin {gather*} \text {Result too large to show} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.17, size = 0, normalized size = 0.00 \[\int \frac {\left (d i x +c i \right )^{3} \left (A +B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )\right )^{2}}{\left (b g x +a g \right )^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (c\,i+d\,i\,x\right )}^3\,{\left (A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )\right )}^2}{{\left (a\,g+b\,g\,x\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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