Optimal. Leaf size=299 \[ -\frac {b i^3 (c+d x)^5 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{5 g^6 (a+b x)^5 (b c-a d)^2}-\frac {2 b B i^3 (c+d x)^5 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{25 g^6 (a+b x)^5 (b c-a d)^2}+\frac {d i^3 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{4 g^6 (a+b x)^4 (b c-a d)^2}+\frac {B d i^3 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{8 g^6 (a+b x)^4 (b c-a d)^2}-\frac {2 b B^2 i^3 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^2}+\frac {B^2 d i^3 (c+d x)^4}{32 g^6 (a+b x)^4 (b c-a d)^2} \]
[Out]
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Rubi [C] time = 5.20, antiderivative size = 1061, normalized size of antiderivative = 3.55, number of steps used = 146, number of rules used = 11, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.262, Rules used = {2528, 2525, 12, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391} \[ -\frac {B^2 i^3 \log ^2(a+b x) d^5}{20 b^4 (b c-a d)^2 g^6}-\frac {B^2 i^3 \log ^2(c+d x) d^5}{20 b^4 (b c-a d)^2 g^6}+\frac {9 B^2 i^3 \log (a+b x) d^5}{200 b^4 (b c-a d)^2 g^6}+\frac {B i^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^5}{10 b^4 (b c-a d)^2 g^6}-\frac {9 B^2 i^3 \log (c+d x) d^5}{200 b^4 (b c-a d)^2 g^6}+\frac {B^2 i^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x) d^5}{10 b^4 (b c-a d)^2 g^6}-\frac {B i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac {B^2 i^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac {B^2 i^3 \text {PolyLog}\left (2,-\frac {d (a+b x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac {B^2 i^3 \text {PolyLog}\left (2,\frac {b (c+d x)}{b c-a d}\right ) d^5}{10 b^4 (b c-a d)^2 g^6}+\frac {B i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^4}{10 b^4 (b c-a d) g^6 (a+b x)}+\frac {9 B^2 i^3 d^4}{200 b^4 (b c-a d) g^6 (a+b x)}-\frac {i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d^3}{2 b^4 g^6 (a+b x)^2}-\frac {B i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^3}{20 b^4 g^6 (a+b x)^2}+\frac {11 B^2 i^3 d^3}{400 b^4 g^6 (a+b x)^2}-\frac {(b c-a d) i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d^2}{b^4 g^6 (a+b x)^3}-\frac {3 B (b c-a d) i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^2}{10 b^4 g^6 (a+b x)^3}-\frac {7 B^2 (b c-a d) i^3 d^2}{200 b^4 g^6 (a+b x)^3}-\frac {3 (b c-a d)^2 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d}{4 b^4 g^6 (a+b x)^4}-\frac {11 B (b c-a d)^2 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d}{40 b^4 g^6 (a+b x)^4}-\frac {39 B^2 (b c-a d)^2 i^3 d}{800 b^4 g^6 (a+b x)^4}-\frac {(b c-a d)^3 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {2 B (b c-a d)^3 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {2 B^2 (b c-a d)^3 i^3}{125 b^4 g^6 (a+b x)^5} \]
Antiderivative was successfully verified.
[In]
[Out]
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 {(82 c+82 d x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^6} \, dx &=\int \left (\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^6}+\frac {1654104 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^5}+\frac {1654104 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^4}+\frac {551368 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^6 (a+b x)^3}\right ) \, dx\\ &=\frac {\left (551368 d^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^3} \, dx}{b^3 g^6}+\frac {\left (1654104 d^2 (b c-a d)\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^4} \, dx}{b^3 g^6}+\frac {\left (1654104 d (b c-a d)^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^5} \, dx}{b^3 g^6}+\frac {\left (551368 (b c-a d)^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^6} \, dx}{b^3 g^6}\\ &=-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac {\left (551368 B d^3\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B d^2 (b c-a d)\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (827052 B d (b c-a d)^2\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B (b c-a d)^3\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^4 g^6}\\ &=-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac {\left (551368 B d^3 (b c-a d)\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B d^2 (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (827052 B d (b c-a d)^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B (b c-a d)^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^4 g^6}\\ &=-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}+\frac {\left (551368 B d^3 (b c-a d)\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^3}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)}-\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac {\left (1102736 B d^2 (b c-a d)^2\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^4}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)}+\frac {d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac {\left (827052 B d (b c-a d)^3\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^5}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)}-\frac {d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac {\left (1102736 B (b c-a d)^4\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^6}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^5}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^4}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^3}+\frac {b d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)^2}-\frac {b d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (a+b x)}+\frac {d^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (c+d x)}\right ) \, dx}{5 b^4 g^6}\\ &=-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {\left (1102736 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{5 b^3 g^6}+\frac {\left (551368 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}+\frac {\left (827052 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}-\frac {\left (1102736 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^3 g^6}-\frac {\left (1102736 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}+\frac {\left (551368 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (827052 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (1102736 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (1102736 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{5 b^3 (b c-a d) g^6}-\frac {\left (551368 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}-\frac {\left (827052 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}+\frac {\left (1102736 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 (b c-a d) g^6}+\frac {\left (1102736 B d^2 (b c-a d)\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{5 b^3 g^6}-\frac {\left (827052 B d^2 (b c-a d)\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{b^3 g^6}+\frac {\left (1102736 B d^2 (b c-a d)\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{b^3 g^6}-\frac {\left (1102736 B d (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{5 b^3 g^6}+\frac {\left (827052 B d (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{b^3 g^6}+\frac {\left (1102736 B (b c-a d)^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^6} \, dx}{5 b^3 g^6}\\ &=-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 g^6}+\frac {\left (275684 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (413526 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}-\frac {\left (551368 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}+\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}+\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 (b c-a d) g^6}-\frac {\left (551368 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}-\frac {\left (827052 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}+\frac {\left (1102736 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 (b c-a d) g^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{15 b^4 g^6}-\frac {\left (275684 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{3 b^4 g^6}-\frac {\left (275684 B^2 d (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{5 b^4 g^6}+\frac {\left (206763 B^2 d (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 (b c-a d)^3\right ) \int \frac {b c-a d}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^6}\\ &=-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{5 b^4 g^6}-\frac {\left (551368 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}-\frac {\left (827052 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^6}-\frac {\left (551368 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{5 b^4 g^6}+\frac {\left (275684 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (413526 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}-\frac {\left (551368 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{15 b^4 g^6}-\frac {\left (275684 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{3 b^4 g^6}-\frac {\left (275684 B^2 d (b c-a d)^3\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{5 b^4 g^6}+\frac {\left (206763 B^2 d (b c-a d)^3\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 (b c-a d)^4\right ) \int \frac {1}{(a+b x)^6 (c+d x)} \, dx}{25 b^4 g^6}+\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 e g^6}-\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 e g^6}-\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}-\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}-\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}\\ &=-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^4\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}{5 b^4 g^6}-\frac {\left (551368 B^2 d^4\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^6}-\frac {\left (827052 B^2 d^4\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^6}+\frac {\left (1102736 B^2 d^4\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^6}-\frac {\left (551368 B^2 d^3 (b c-a d)\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}{5 b^4 g^6}+\frac {\left (275684 B^2 d^3 (b c-a d)\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^6}+\frac {\left (413526 B^2 d^3 (b c-a d)\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^6}-\frac {\left (551368 B^2 d^3 (b c-a d)\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^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)^2\right ) \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}{15 b^4 g^6}-\frac {\left (275684 B^2 d^2 (b c-a d)^2\right ) \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}{b^4 g^6}+\frac {\left (1102736 B^2 d^2 (b c-a d)^2\right ) \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}{3 b^4 g^6}-\frac {\left (275684 B^2 d (b c-a d)^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^5}-\frac {b d}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4}{(b c-a d)^5 (a+b x)}-\frac {d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{5 b^4 g^6}+\frac {\left (206763 B^2 d (b c-a d)^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^5}-\frac {b d}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4}{(b c-a d)^5 (a+b x)}-\frac {d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{b^4 g^6}+\frac {\left (1102736 B^2 (b c-a d)^4\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^6}-\frac {b d}{(b c-a d)^2 (a+b x)^5}+\frac {b d^2}{(b c-a d)^3 (a+b x)^4}-\frac {b d^3}{(b c-a d)^4 (a+b x)^3}+\frac {b d^4}{(b c-a d)^5 (a+b x)^2}-\frac {b d^5}{(b c-a d)^6 (a+b x)}+\frac {d^6}{(b c-a d)^6 (c+d x)}\right ) \, dx}{25 b^4 g^6}+\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 e g^6}-\frac {\left (1102736 B^2 d^5\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}{5 b^4 (b c-a d)^2 e g^6}-\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (551368 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}-\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (827052 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}+\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}-\frac {\left (1102736 B^2 d^5\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}{b^4 (b c-a d)^2 e g^6}\\ &=-\frac {1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac {2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac {482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac {758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac {620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac {620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (551368 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (827052 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (551368 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac {\left (827052 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}\\ &=-\frac {1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac {2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac {482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac {758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac {620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac {620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{5 b^3 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^4 (b c-a d)^2 g^6}\\ &=-\frac {1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac {2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac {482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac {758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac {620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac {620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac {137842 B^2 d^5 \log ^2(a+b x)}{5 b^4 (b c-a d)^2 g^6}-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {137842 B^2 d^5 \log ^2(c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (551368 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}-\frac {\left (827052 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d)^2 g^6}+\frac {\left (1102736 B^2 d^5\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d)^2 g^6}\\ &=-\frac {1102736 B^2 (b c-a d)^3}{125 b^4 g^6 (a+b x)^5}-\frac {2687919 B^2 d (b c-a d)^2}{100 b^4 g^6 (a+b x)^4}-\frac {482447 B^2 d^2 (b c-a d)}{25 b^4 g^6 (a+b x)^3}+\frac {758131 B^2 d^3}{50 b^4 g^6 (a+b x)^2}+\frac {620289 B^2 d^4}{25 b^4 (b c-a d) g^6 (a+b x)}+\frac {620289 B^2 d^5 \log (a+b x)}{25 b^4 (b c-a d)^2 g^6}-\frac {137842 B^2 d^5 \log ^2(a+b x)}{5 b^4 (b c-a d)^2 g^6}-\frac {1102736 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^4 g^6 (a+b x)^5}-\frac {758131 B d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^4}-\frac {827052 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^3}-\frac {137842 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 g^6 (a+b x)^2}+\frac {275684 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d) g^6 (a+b x)}+\frac {275684 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^4 (b c-a d)^2 g^6}-\frac {551368 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^4 g^6 (a+b x)^5}-\frac {413526 d (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^4}-\frac {551368 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^3}-\frac {275684 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^6 (a+b x)^2}-\frac {620289 B^2 d^5 \log (c+d x)}{25 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {275684 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{5 b^4 (b c-a d)^2 g^6}-\frac {137842 B^2 d^5 \log ^2(c+d x)}{5 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}+\frac {275684 B^2 d^5 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{5 b^4 (b c-a d)^2 g^6}\\ \end {align*}
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Mathematica [C] time = 4.20, size = 2289, normalized size = 7.66 \[ \text {Result too large to show} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.95, size = 1045, normalized size = 3.49 \[ \frac {20 \, {\left ({\left (20 \, A B + 9 \, B^{2}\right )} b^{5} c d^{4} - {\left (20 \, A B + 9 \, B^{2}\right )} a b^{4} d^{5}\right )} i^{3} x^{4} - 10 \, {\left ({\left (200 \, A^{2} + 20 \, A B - 11 \, B^{2}\right )} b^{5} c^{2} d^{3} - 50 \, {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{4} c d^{4} + {\left (200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right )} a^{2} b^{3} d^{5}\right )} i^{3} x^{3} - 10 \, {\left (2 \, {\left (200 \, A^{2} + 60 \, A B + 7 \, B^{2}\right )} b^{5} c^{3} d^{2} - 75 \, {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{4} c^{2} d^{3} + {\left (200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right )} a^{3} b^{2} d^{5}\right )} i^{3} x^{2} - 5 \, {\left ({\left (600 \, A^{2} + 220 \, A B + 39 \, B^{2}\right )} b^{5} c^{4} d - 100 \, {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{4} c^{3} d^{2} + {\left (200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right )} a^{4} b d^{5}\right )} i^{3} x - {\left (32 \, {\left (25 \, A^{2} + 10 \, A B + 2 \, B^{2}\right )} b^{5} c^{5} - 125 \, {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{4} c^{4} d + {\left (200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right )} a^{5} d^{5}\right )} i^{3} + 200 \, {\left (B^{2} b^{5} d^{5} i^{3} x^{5} + 5 \, B^{2} a b^{4} d^{5} i^{3} x^{4} - 10 \, {\left (B^{2} b^{5} c^{2} d^{3} - 2 \, B^{2} a b^{4} c d^{4}\right )} i^{3} x^{3} - 10 \, {\left (2 \, B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3}\right )} i^{3} x^{2} - 5 \, {\left (3 \, B^{2} b^{5} c^{4} d - 4 \, B^{2} a b^{4} c^{3} d^{2}\right )} i^{3} x - {\left (4 \, B^{2} b^{5} c^{5} - 5 \, B^{2} a b^{4} c^{4} d\right )} i^{3}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} + 20 \, {\left ({\left (20 \, A B + 9 \, B^{2}\right )} b^{5} d^{5} i^{3} x^{5} + 5 \, {\left (4 \, B^{2} b^{5} c d^{4} + 5 \, {\left (4 \, A B + B^{2}\right )} a b^{4} d^{5}\right )} i^{3} x^{4} - 10 \, {\left ({\left (20 \, A B + B^{2}\right )} b^{5} c^{2} d^{3} - 10 \, {\left (4 \, A B + B^{2}\right )} a b^{4} c d^{4}\right )} i^{3} x^{3} - 10 \, {\left (2 \, {\left (20 \, A B + 3 \, B^{2}\right )} b^{5} c^{3} d^{2} - 15 \, {\left (4 \, A B + B^{2}\right )} a b^{4} c^{2} d^{3}\right )} i^{3} x^{2} - 5 \, {\left ({\left (60 \, A B + 11 \, B^{2}\right )} b^{5} c^{4} d - 20 \, {\left (4 \, A B + B^{2}\right )} a b^{4} c^{3} d^{2}\right )} i^{3} x - {\left (16 \, {\left (5 \, A B + B^{2}\right )} b^{5} c^{5} - 25 \, {\left (4 \, A B + B^{2}\right )} a b^{4} c^{4} d\right )} i^{3}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{4000 \, {\left ({\left (b^{11} c^{2} - 2 \, a b^{10} c d + a^{2} b^{9} d^{2}\right )} g^{6} x^{5} + 5 \, {\left (a b^{10} c^{2} - 2 \, a^{2} b^{9} c d + a^{3} b^{8} d^{2}\right )} g^{6} x^{4} + 10 \, {\left (a^{2} b^{9} c^{2} - 2 \, a^{3} b^{8} c d + a^{4} b^{7} d^{2}\right )} g^{6} x^{3} + 10 \, {\left (a^{3} b^{8} c^{2} - 2 \, a^{4} b^{7} c d + a^{5} b^{6} d^{2}\right )} g^{6} x^{2} + 5 \, {\left (a^{4} b^{7} c^{2} - 2 \, a^{5} b^{6} c d + a^{6} b^{5} d^{2}\right )} g^{6} x + {\left (a^{5} b^{6} c^{2} - 2 \, a^{6} b^{5} c d + a^{7} b^{4} d^{2}\right )} g^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 4.34, size = 437, normalized size = 1.46 \[ \frac {{\left (800 \, B^{2} b i e^{6} \log \left (\frac {b x e + a e}{d x + c}\right )^{2} - \frac {1000 \, {\left (b x e + a e\right )} B^{2} d i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )^{2}}{d x + c} + 1600 \, A B b i e^{6} \log \left (\frac {b x e + a e}{d x + c}\right ) + 320 \, B^{2} b i e^{6} \log \left (\frac {b x e + a e}{d x + c}\right ) - \frac {2000 \, {\left (b x e + a e\right )} A B d i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} - \frac {500 \, {\left (b x e + a e\right )} B^{2} d i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} + 800 \, A^{2} b i e^{6} + 320 \, A B b i e^{6} + 64 \, B^{2} b i e^{6} - \frac {1000 \, {\left (b x e + a e\right )} A^{2} d i e^{5}}{d x + c} - \frac {500 \, {\left (b x e + a e\right )} A B d i e^{5}}{d x + c} - \frac {125 \, {\left (b x e + a e\right )} B^{2} d i e^{5}}{d x + c}\right )} {\left (\frac {b c}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}} - \frac {a d}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}}\right )}}{4000 \, {\left (\frac {{\left (b x e + a e\right )}^{5} b c g^{6}}{{\left (d x + c\right )}^{5}} - \frac {{\left (b x e + a e\right )}^{5} a d g^{6}}{{\left (d x + c\right )}^{5}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 1814, normalized size = 6.07 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 16.44, size = 15765, normalized size = 52.73 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 12.64, size = 3720, normalized size = 12.44 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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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