Optimal. Leaf size=147 \[ -\frac {i^3 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{4 g^5 (a+b x)^4 (b c-a d)}-\frac {B i^3 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{8 g^5 (a+b x)^4 (b c-a d)}-\frac {B^2 i^3 (c+d x)^4}{32 g^5 (a+b x)^4 (b c-a d)} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 4.54, antiderivative size = 970, normalized size of antiderivative = 6.60, number of steps used = 130, 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} \[ \frac {B^2 i^3 \log ^2(a+b x) d^4}{4 b^4 (b c-a d) g^5}+\frac {B^2 i^3 \log ^2(c+d x) d^4}{4 b^4 (b c-a d) g^5}-\frac {B^2 i^3 \log (a+b x) d^4}{8 b^4 (b c-a d) g^5}-\frac {B i^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^4}{2 b^4 (b c-a d) g^5}+\frac {B^2 i^3 \log (c+d x) d^4}{8 b^4 (b c-a d) g^5}-\frac {B^2 i^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x) d^4}{2 b^4 (b c-a d) g^5}+\frac {B i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x) d^4}{2 b^4 (b c-a d) g^5}-\frac {B^2 i^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right ) d^4}{2 b^4 (b c-a d) g^5}-\frac {B^2 i^3 \text {PolyLog}\left (2,-\frac {d (a+b x)}{b c-a d}\right ) d^4}{2 b^4 (b c-a d) g^5}-\frac {B^2 i^3 \text {PolyLog}\left (2,\frac {b (c+d x)}{b c-a d}\right ) d^4}{2 b^4 (b c-a d) g^5}-\frac {i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d^3}{b^4 g^5 (a+b x)}-\frac {B i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^3}{2 b^4 g^5 (a+b x)}-\frac {B^2 i^3 d^3}{8 b^4 g^5 (a+b x)}-\frac {3 (b c-a d) i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d^2}{2 b^4 g^5 (a+b x)^2}-\frac {3 B (b c-a d) i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d^2}{4 b^4 g^5 (a+b x)^2}-\frac {3 B^2 (b c-a d) i^3 d^2}{16 b^4 g^5 (a+b x)^2}-\frac {(b c-a d)^2 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 d}{b^4 g^5 (a+b x)^3}-\frac {B (b c-a d)^2 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) d}{2 b^4 g^5 (a+b x)^3}-\frac {B^2 (b c-a d)^2 i^3 d}{8 b^4 g^5 (a+b x)^3}-\frac {(b c-a d)^3 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {B (b c-a d)^3 i^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {B^2 (b c-a d)^3 i^3}{32 b^4 g^5 (a+b x)^4} \]
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 {(81 c+81 d x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^5} \, dx &=\int \left (\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^5 (a+b x)^5}+\frac {1594323 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^5 (a+b x)^4}+\frac {1594323 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^5 (a+b x)^3}+\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3 g^5 (a+b x)^2}\right ) \, dx\\ &=\frac {\left (531441 d^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^2} \, dx}{b^3 g^5}+\frac {\left (1594323 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)^3} \, dx}{b^3 g^5}+\frac {\left (1594323 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)^4} \, dx}{b^3 g^5}+\frac {\left (531441 (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)^5} \, dx}{b^3 g^5}\\ &=-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}+\frac {\left (1062882 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)^2 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1594323 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)^3 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1062882 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)^4 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (531441 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)^5 (c+d x)} \, dx}{2 b^4 g^5}\\ &=-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}+\frac {\left (1062882 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)^2 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1594323 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)^3 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1062882 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)^4 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (531441 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)^5 (c+d x)} \, dx}{2 b^4 g^5}\\ &=-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}+\frac {\left (1062882 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)^2}-\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)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^4 g^5}+\frac {\left (1594323 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)^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^5}+\frac {\left (1062882 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)^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^5}+\frac {\left (531441 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)^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}{2 b^4 g^5}\\ &=-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {\left (531441 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{2 b^3 g^5}+2 \frac {\left (1062882 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 g^5}-\frac {\left (1594323 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^3 g^5}+\frac {\left (531441 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{2 b^3 (b c-a d) g^5}-2 \frac {\left (1062882 B d^4\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) g^5}+\frac {\left (1594323 B d^4\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) g^5}-\frac {\left (531441 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{2 b^4 (b c-a d) g^5}+2 \frac {\left (1062882 B d^5\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) g^5}-\frac {\left (1594323 B d^5\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) g^5}+\frac {\left (531441 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)^3} \, dx}{2 b^3 g^5}-\frac {\left (1062882 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)^3} \, dx}{b^3 g^5}+\frac {\left (1594323 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)^3} \, dx}{b^3 g^5}-\frac {\left (531441 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)^4} \, dx}{2 b^3 g^5}+\frac {\left (1062882 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)^4} \, dx}{b^3 g^5}+\frac {\left (531441 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)^5} \, dx}{2 b^3 g^5}\\ &=-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{2 b^4 g^5}+2 \left (-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {\left (1062882 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^5}\right )-\frac {\left (1594323 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^5}-\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) g^5}+\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) g^5}-2 \left (\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) g^5}\right )+2 \left (\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) g^5}\right )-\frac {\left (1594323 B^2 d^4\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) g^5}+\frac {\left (1594323 B^2 d^4\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) g^5}+\frac {\left (531441 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{4 b^4 g^5}-\frac {\left (531441 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1594323 B^2 d^2 (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{2 b^4 g^5}-\frac {\left (177147 B^2 d (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{2 b^4 g^5}+\frac {\left (354294 B^2 d (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (531441 B^2 (b c-a d)^3\right ) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{8 b^4 g^5}\\ &=-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{2 b^4 g^5}+2 \left (-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {\left (1062882 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^5}\right )-\frac {\left (1594323 B^2 d^3 (b c-a d)\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (531441 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{4 b^4 g^5}-\frac {\left (531441 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (1594323 B^2 d^2 (b c-a d)^2\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{2 b^4 g^5}-\frac {\left (177147 B^2 d (b c-a d)^3\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{2 b^4 g^5}+\frac {\left (354294 B^2 d (b c-a d)^3\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{b^4 g^5}+\frac {\left (531441 B^2 (b c-a d)^4\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{8 b^4 g^5}-\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) e g^5}+\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) e g^5}-2 \left (\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) e g^5}\right )+2 \left (\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) e g^5}\right )-\frac {\left (1594323 B^2 d^4\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) e g^5}+\frac {\left (1594323 B^2 d^4\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) e g^5}\\ &=-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^3 (b c-a d)\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}{2 b^4 g^5}+2 \left (-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {\left (1062882 B^2 d^3 (b c-a d)\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^5}\right )-\frac {\left (1594323 B^2 d^3 (b c-a d)\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^5}+\frac {\left (531441 B^2 d^2 (b c-a d)^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}{4 b^4 g^5}-\frac {\left (531441 B^2 d^2 (b c-a d)^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^5}+\frac {\left (1594323 B^2 d^2 (b c-a d)^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}{2 b^4 g^5}-\frac {\left (177147 B^2 d (b c-a d)^3\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}{2 b^4 g^5}+\frac {\left (354294 B^2 d (b c-a d)^3\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^5}+\frac {\left (531441 B^2 (b c-a d)^4\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}{8 b^4 g^5}-\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) e g^5}+\frac {\left (531441 B^2 d^4\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}{2 b^4 (b c-a d) e g^5}-2 \left (\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) e g^5}\right )+2 \left (\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) e g^5}\right )-\frac {\left (1594323 B^2 d^4\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) e g^5}+\frac {\left (1594323 B^2 d^4\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) e g^5}\\ &=-\frac {531441 B^2 (b c-a d)^3}{32 b^4 g^5 (a+b x)^4}-\frac {531441 B^2 d (b c-a d)^2}{8 b^4 g^5 (a+b x)^3}-\frac {1594323 B^2 d^2 (b c-a d)}{16 b^4 g^5 (a+b x)^2}+\frac {16474671 B^2 d^3}{8 b^4 g^5 (a+b x)}+\frac {16474671 B^2 d^4 \log (a+b x)}{8 b^4 (b c-a d) g^5}-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {16474671 B^2 d^4 \log (c+d x)}{8 b^4 (b c-a d) g^5}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^3}{b^4 g^5 (a+b x)}-\frac {1062882 B^2 d^4 \log (a+b x)}{b^4 (b c-a d) g^5}-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {1062882 B^2 d^4 \log (c+d x)}{b^4 (b c-a d) g^5}\right )-\frac {\left (531441 B^2 d^4\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{2 b^3 (b c-a d) g^5}+\frac {\left (531441 B^2 d^4\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{2 b^3 (b c-a d) g^5}-\frac {\left (1594323 B^2 d^4\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d) g^5}+\frac {\left (1594323 B^2 d^4\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d) g^5}+\frac {\left (531441 B^2 d^5\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^5\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{2 b^4 (b c-a d) g^5}-2 \left (\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 (b c-a d) g^5}+\frac {\left (1062882 B^2 d^5\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d) g^5}\right )+2 \left (\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^3 (b c-a d) g^5}+\frac {\left (1062882 B^2 d^5\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d) g^5}\right )+\frac {\left (1594323 B^2 d^5\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 (b c-a d) g^5}-\frac {\left (1594323 B^2 d^5\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^4 (b c-a d) g^5}\\ &=-\frac {531441 B^2 (b c-a d)^3}{32 b^4 g^5 (a+b x)^4}-\frac {531441 B^2 d (b c-a d)^2}{8 b^4 g^5 (a+b x)^3}-\frac {1594323 B^2 d^2 (b c-a d)}{16 b^4 g^5 (a+b x)^2}+\frac {16474671 B^2 d^3}{8 b^4 g^5 (a+b x)}+\frac {16474671 B^2 d^4 \log (a+b x)}{8 b^4 (b c-a d) g^5}-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {16474671 B^2 d^4 \log (c+d x)}{8 b^4 (b c-a d) g^5}+\frac {3720087 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^3}{b^4 g^5 (a+b x)}-\frac {1062882 B^2 d^4 \log (a+b x)}{b^4 (b c-a d) g^5}-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {1062882 B^2 d^4 \log (c+d x)}{b^4 (b c-a d) g^5}\right )+\frac {3720087 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{2 b^4 (b c-a d) g^5}-\frac {\left (1594323 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d) g^5}-\frac {\left (1594323 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^4\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{2 b^3 (b c-a d) g^5}-2 \left (\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}+\frac {1062882 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) g^5}\right )-\frac {\left (1594323 B^2 d^4\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) g^5}-\frac {\left (531441 B^2 d^5\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{2 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {\left (1062882 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^4 (b c-a d) g^5}+\frac {\left (1062882 B^2 d^5\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) g^5}\right )-\frac {\left (1594323 B^2 d^5\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) g^5}\\ &=-\frac {531441 B^2 (b c-a d)^3}{32 b^4 g^5 (a+b x)^4}-\frac {531441 B^2 d (b c-a d)^2}{8 b^4 g^5 (a+b x)^3}-\frac {1594323 B^2 d^2 (b c-a d)}{16 b^4 g^5 (a+b x)^2}+\frac {16474671 B^2 d^3}{8 b^4 g^5 (a+b x)}+\frac {16474671 B^2 d^4 \log (a+b x)}{8 b^4 (b c-a d) g^5}-\frac {3720087 B^2 d^4 \log ^2(a+b x)}{4 b^4 (b c-a d) g^5}-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {16474671 B^2 d^4 \log (c+d x)}{8 b^4 (b c-a d) g^5}+\frac {3720087 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {3720087 B^2 d^4 \log ^2(c+d x)}{4 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^3}{b^4 g^5 (a+b x)}-\frac {1062882 B^2 d^4 \log (a+b x)}{b^4 (b c-a d) g^5}-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {1062882 B^2 d^4 \log (c+d x)}{b^4 (b c-a d) g^5}\right )+\frac {3720087 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{2 b^4 (b c-a d) g^5}-\frac {\left (531441 B^2 d^4\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{2 b^4 (b c-a d) g^5}-2 \left (-\frac {531441 B^2 d^4 \log ^2(a+b x)}{b^4 (b c-a d) g^5}+\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}+\frac {1062882 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 (b c-a d) g^5}-\frac {\left (1062882 B^2 d^4\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) g^5}\right )+2 \left (-\frac {1062882 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {531441 B^2 d^4 \log ^2(c+d x)}{b^4 (b c-a d) g^5}+\frac {\left (1062882 B^2 d^4\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) g^5}\right )-\frac {\left (1594323 B^2 d^4\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) g^5}-\frac {\left (1594323 B^2 d^4\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) g^5}\\ &=-\frac {531441 B^2 (b c-a d)^3}{32 b^4 g^5 (a+b x)^4}-\frac {531441 B^2 d (b c-a d)^2}{8 b^4 g^5 (a+b x)^3}-\frac {1594323 B^2 d^2 (b c-a d)}{16 b^4 g^5 (a+b x)^2}+\frac {16474671 B^2 d^3}{8 b^4 g^5 (a+b x)}+\frac {16474671 B^2 d^4 \log (a+b x)}{8 b^4 (b c-a d) g^5}-\frac {3720087 B^2 d^4 \log ^2(a+b x)}{4 b^4 (b c-a d) g^5}-\frac {531441 B (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{8 b^4 g^5 (a+b x)^4}-\frac {531441 B 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^5 (a+b x)^3}-\frac {1594323 B d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 b^4 g^5 (a+b x)^2}+\frac {3720087 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 g^5 (a+b x)}+\frac {3720087 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^4 (b c-a d) g^5}-\frac {531441 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4 b^4 g^5 (a+b x)^4}-\frac {531441 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^5 (a+b x)^3}-\frac {1594323 d^2 (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^4 g^5 (a+b x)^2}-\frac {531441 d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^4 g^5 (a+b x)}-\frac {16474671 B^2 d^4 \log (c+d x)}{8 b^4 (b c-a d) g^5}+\frac {3720087 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {3720087 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{2 b^4 (b c-a d) g^5}-\frac {3720087 B^2 d^4 \log ^2(c+d x)}{4 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^3}{b^4 g^5 (a+b x)}-\frac {1062882 B^2 d^4 \log (a+b x)}{b^4 (b c-a d) g^5}-\frac {1062882 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 g^5 (a+b x)}+\frac {1062882 B^2 d^4 \log (c+d x)}{b^4 (b c-a d) g^5}\right )+\frac {3720087 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{2 b^4 (b c-a d) g^5}+\frac {3720087 B^2 d^4 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{2 b^4 (b c-a d) g^5}-2 \left (-\frac {531441 B^2 d^4 \log ^2(a+b x)}{b^4 (b c-a d) g^5}+\frac {1062882 B d^4 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^4 (b c-a d) g^5}+\frac {1062882 B^2 d^4 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 (b c-a d) g^5}+\frac {1062882 B^2 d^4 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 (b c-a d) g^5}\right )+\frac {3720087 B^2 d^4 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{2 b^4 (b c-a d) g^5}+2 \left (-\frac {1062882 B^2 d^4 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {1062882 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^4 (b c-a d) g^5}+\frac {531441 B^2 d^4 \log ^2(c+d x)}{b^4 (b c-a d) g^5}-\frac {1062882 B^2 d^4 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 (b c-a d) g^5}\right )\\ \end {align*}
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Mathematica [C] time = 1.44, size = 2470, normalized size = 16.80 \[ \text {Result too large to show} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.89, size = 559, normalized size = 3.80 \[ -\frac {4 \, {\left ({\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} b^{4} c d^{3} - {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{3} d^{4}\right )} i^{3} x^{3} + 6 \, {\left ({\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} b^{4} c^{2} d^{2} - {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a^{2} b^{2} d^{4}\right )} i^{3} x^{2} + 4 \, {\left ({\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} b^{4} c^{3} d - {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a^{3} b d^{4}\right )} i^{3} x + {\left ({\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} b^{4} c^{4} - {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a^{4} d^{4}\right )} i^{3} + 8 \, {\left (B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} + 4 \, {\left ({\left (4 \, A B + B^{2}\right )} b^{4} d^{4} i^{3} x^{4} + 4 \, {\left (4 \, A B + B^{2}\right )} b^{4} c d^{3} i^{3} x^{3} + 6 \, {\left (4 \, A B + B^{2}\right )} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, {\left (4 \, A B + B^{2}\right )} b^{4} c^{3} d i^{3} x + {\left (4 \, A B + B^{2}\right )} b^{4} c^{4} i^{3}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{32 \, {\left ({\left (b^{9} c - a b^{8} d\right )} g^{5} x^{4} + 4 \, {\left (a b^{8} c - a^{2} b^{7} d\right )} g^{5} x^{3} + 6 \, {\left (a^{2} b^{7} c - a^{3} b^{6} d\right )} g^{5} x^{2} + 4 \, {\left (a^{3} b^{6} c - a^{4} b^{5} d\right )} g^{5} x + {\left (a^{4} b^{5} c - a^{5} b^{4} d\right )} g^{5}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.22, size = 185, normalized size = 1.26 \[ \frac {{\left (8 \, B^{2} i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )^{2} + 16 \, A B i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right ) + 4 \, B^{2} i e^{5} \log \left (\frac {b x e + a e}{d x + c}\right ) + 8 \, A^{2} i e^{5} + 4 \, A B i e^{5} + B^{2} i e^{5}\right )} {\left (d x + c\right )}^{4} {\left (\frac {b c}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}} - \frac {a d}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}}\right )}}{32 \, {\left (b x e + a e\right )}^{4} g^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 890, normalized size = 6.05 \[ \frac {B^{2} a d \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )^{2}}{4 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {B^{2} b c \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )^{2}}{4 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}+\frac {A B a d \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )}{2 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {A B b c \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )}{2 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}+\frac {B^{2} a d \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )}{8 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {B^{2} b c \,e^{4} i^{3} \ln \left (\frac {b e}{d}+\frac {\left (a d -b c \right ) e}{\left (d x +c \right ) d}\right )}{8 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}+\frac {A^{2} a d \,e^{4} i^{3}}{4 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {A^{2} b c \,e^{4} i^{3}}{4 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}+\frac {A B a d \,e^{4} i^{3}}{8 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {A B b c \,e^{4} i^{3}}{8 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}+\frac {B^{2} a d \,e^{4} i^{3}}{32 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}}-\frac {B^{2} b c \,e^{4} i^{3}}{32 \left (a d -b c \right )^{2} \left (\frac {a e}{d x +c}-\frac {b c e}{\left (d x +c \right ) d}+\frac {b e}{d}\right )^{4} g^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 11.34, size = 11688, normalized size = 79.51 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 10.43, size = 1565, normalized size = 10.65 \[ \text {result too large to display} \]
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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