Optimal. Leaf size=365 \[ -\frac {b^2 (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac {2 b^2 B (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^2 i^2 (a+b x) (b c-a d)^3}+\frac {d^2 (a+b x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac {2 A B d^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3}-\frac {2 b d \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^3}{3 B g^2 i^2 (b c-a d)^3}-\frac {2 b^2 B^2 (c+d x)}{g^2 i^2 (a+b x) (b c-a d)^3}-\frac {2 B^2 d^2 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{g^2 i^2 (c+d x) (b c-a d)^3}+\frac {2 B^2 d^2 (a+b x)}{g^2 i^2 (c+d x) (b c-a d)^3} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 7.18, antiderivative size = 1521, normalized size of antiderivative = 4.17, number of steps used = 113, number of rules used = 31, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.738, Rules used = {2528, 2525, 12, 44, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 6688, 6742, 2411, 2344, 2317, 2507, 2488, 2506, 6610, 2500, 2433, 2375, 2374, 6589, 2440, 2434, 2499, 2396, 2302, 30} \[ \text {result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rule 44
Rule 2301
Rule 2302
Rule 2317
Rule 2344
Rule 2374
Rule 2375
Rule 2390
Rule 2391
Rule 2393
Rule 2394
Rule 2396
Rule 2411
Rule 2418
Rule 2433
Rule 2434
Rule 2440
Rule 2488
Rule 2499
Rule 2500
Rule 2506
Rule 2507
Rule 2524
Rule 2525
Rule 2528
Rule 6589
Rule 6610
Rule 6688
Rule 6742
Rubi steps
\begin {align*} \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(97 c+97 d x)^2 (a g+b g x)^2} \, dx &=\int \left (\frac {b^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)^2}-\frac {2 b^2 d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)^2}+\frac {2 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2 (c+d x)}\right ) \, dx\\ &=-\frac {\left (2 b^2 d\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b d^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {b^2 \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^2} \, dx}{9409 (b c-a d)^2 g^2}+\frac {d^2 \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(c+d x)^2} \, dx}{9409 (b c-a d)^2 g^2}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {(4 b B d) \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) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{e (a+b x)} \, dx}{9409 (b c-a d)^3 g^2}-\frac {(4 b B d) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{e (a+b x)} \, dx}{9409 (b c-a d)^3 g^2}+\frac {(2 b B) \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}{9409 (b c-a d)^2 g^2}+\frac {(2 B d) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)^2} \, dx}{9409 (b c-a d)^2 g^2}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {(2 b B) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2 (c+d x)} \, dx}{9409 (b c-a d) g^2}+\frac {(2 B d) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^2} \, dx}{9409 (b c-a d) g^2}+\frac {(4 b B d) \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) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{9409 (b c-a d)^3 e g^2}-\frac {(4 b B d) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 e g^2}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {(2 b B) \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}{9409 (b c-a d) g^2}+\frac {(2 B d) \int \left (\frac {b^2 \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 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d 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 (c+d x)}\right ) \, dx}{9409 (b c-a d) g^2}+\frac {(4 b B d) \int \frac {(b c-a d) e \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^3 e g^2}-\frac {(4 b B d) \int \frac {(b c-a d) e \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^3 e g^2}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b^2 B\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{9409 (b c-a d)^2 g^2}+\frac {(4 b B d) \int \frac {\log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}-\frac {(4 b B d) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}-\frac {\left (2 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{9409 (b c-a d)^2 g^2}\\ &=-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b B^2\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}+\frac {(4 b B d) \int \left (\frac {A \log (a+b x)}{(a+b x) (c+d x)}+\frac {B \log (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)}\right ) \, dx}{9409 (b c-a d)^2 g^2}-\frac {(4 b B d) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(b c-a d) (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(b c-a d) (c+d x)}\right ) \, dx}{9409 (b c-a d)^2 g^2}-\frac {\left (2 B^2 d\right ) \int \frac {b c-a d}{(a+b x) (c+d x)^2} \, dx}{9409 (b c-a d)^2 g^2}\\ &=-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b^2 B d\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B d^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {(4 A b B d) \int \frac {\log (a+b x)}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}+\frac {\left (4 b B^2 d\right ) \int \frac {\log (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}+\frac {\left (2 b B^2\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{9409 (b c-a d) g^2}-\frac {\left (2 B^2 d\right ) \int \frac {1}{(a+b x) (c+d x)^2} \, dx}{9409 (b c-a d) g^2}\\ &=\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b^2 B d\right ) \int \left (\frac {A \log (c+d x)}{a+b x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x}\right ) \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (2 b^2 B^2 d\right ) \int \frac {\log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B d^2\right ) \int \left (\frac {A \log (c+d x)}{c+d x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x}\right ) \, dx}{9409 (b c-a d)^3 g^2}+\frac {(4 A B d) \operatorname {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 )}{9409 (b c-a d)^2 g^2}+\frac {\left (2 b B^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}{9409 (b c-a d) g^2}-\frac {\left (2 B^2 d\right ) \int \left (\frac {b^2}{(b c-a d)^2 (a+b x)}-\frac {d}{(b c-a d) (c+d x)^2}-\frac {b d}{(b c-a d)^2 (c+d x)}\right ) \, dx}{9409 (b c-a d) g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {(4 A b B d) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 A b^2 B d\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b^2 B^2 d\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (4 A B d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{\frac {b c-a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 A b B d^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \int \frac {\log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)} \, dx}{9409 (b c-a d)^2 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {(4 A b B d) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}+\frac {(4 A b B d) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (2 b^2 B^2 d\right ) \int \frac {\log ^2(c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b^2 B^2 d\right ) \int \frac {\log (a+b x) \log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b^2 B^2 d\right ) \int \frac {\log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 A b B d^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b B^2 d^2\right ) \int \frac {\log ^2(c+d x)}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d\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}{9409 (b c-a d)^2 g^2}-\frac {\left (4 b^2 B^2 d \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {(4 A b B d) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {b c-a d}{b}+\frac {d x}{b}\right )}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{-\frac {-b c+a d}{b}+\frac {d x}{b}}\right ) \log \left (-\frac {-b c+a d}{b}+\frac {d x}{b}\right )}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right ) \log (c+d x)}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b B^2 d\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {d \left (\frac {-b c+a d}{d}+\frac {b x}{d}\right )}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (2 B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{\frac {b c-a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {1}{-\frac {-b c+a d}{b}+\frac {d x}{b}}\right )}{-\frac {-b c+a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (-\frac {-b c+a d}{b}+\frac {d x}{b}\right )}{-\frac {-b c+a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^3(c+d x)}{28227 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (\frac {-b c+a d}{d}+\frac {b x}{d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c+a d}{d}+\frac {b x}{d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^3(c+d x)}{28227 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b^2 B^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2\left (\frac {1}{x}\right )}{\frac {-b c+a d}{d}+\frac {b x}{d}} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (2 b^2 B^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{\frac {-b c+a d}{d}+\frac {b x}{d}} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^3(c+d x)}{28227 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}+\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}-\frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^3(c+d x)}{28227 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-2 \frac {\left (4 b B^2 d\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9409 (b c-a d)^3 g^2}\\ &=-\frac {2 b B^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {2 B^2 d}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {4 b B^2 d \log (a+b x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(a+b x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9409 (b c-a d)^3 g^2}-\frac {2 b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (a+b x)}+\frac {2 B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (a+b x)}-\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^2 g^2 (c+d x)}-\frac {2 b d \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log ^2(a+b x) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 A b B d \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}-\frac {2 b B^2 d \log (a+b x) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^3(c+d x)}{28227 (b c-a d)^3 g^2}-\frac {4 A b B d \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {2 b B^2 d \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 A b B d \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}+\frac {4 b B^2 d \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \log \left (\frac {e (a+b x)}{c+d x}\right ) \text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{9409 (b c-a d)^3 g^2}-\frac {4 b B^2 d \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{9409 (b c-a d)^3 g^2}\\ \end {align*}
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Mathematica [A] time = 1.10, size = 307, normalized size = 0.84 \[ -\frac {3 B \left (-a^2 B d^2+2 a b d (A (c+d x)-B d x)+b^2 (2 A d x (c+d x)+B c (c+2 d x))\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )-3 d \left (A^2-2 A B+2 B^2\right ) (a+b x) (a d-b c)+3 b \left (A^2+2 A B+2 B^2\right ) (c+d x) (b c-a d)+6 b d \left (A^2+2 B^2\right ) (a+b x) (c+d x) \log (a+b x)-6 b d \left (A^2+2 B^2\right ) (a+b x) (c+d x) \log (c+d x)+6 B (b c-a d) (a A d-a B d+A b c+2 A b d x+b B c) \log \left (\frac {e (a+b x)}{c+d x}\right )+2 b B^2 d (a+b x) (c+d x) \log ^3\left (\frac {e (a+b x)}{c+d x}\right )}{3 g^2 i^2 (a+b x) (c+d x) (b c-a d)^3} \]
Antiderivative was successfully verified.
[In]
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fricas [A] time = 0.92, size = 515, normalized size = 1.41 \[ \frac {12 \, A B a b c d - 3 \, {\left (A^{2} + 2 \, A B + 2 \, B^{2}\right )} b^{2} c^{2} + 3 \, {\left (A^{2} - 2 \, A B + 2 \, B^{2}\right )} a^{2} d^{2} - 2 \, {\left (B^{2} b^{2} d^{2} x^{2} + B^{2} a b c d + {\left (B^{2} b^{2} c d + B^{2} a b d^{2}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{3} - 3 \, {\left (2 \, A B b^{2} d^{2} x^{2} + B^{2} b^{2} c^{2} + 2 \, A B a b c d - B^{2} a^{2} d^{2} + 2 \, {\left ({\left (A B + B^{2}\right )} b^{2} c d + {\left (A B - B^{2}\right )} a b d^{2}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} - 6 \, {\left ({\left (A^{2} + 2 \, B^{2}\right )} b^{2} c d - {\left (A^{2} + 2 \, B^{2}\right )} a b d^{2}\right )} x - 6 \, {\left ({\left (A^{2} + 2 \, B^{2}\right )} b^{2} d^{2} x^{2} + A^{2} a b c d + {\left (A B + B^{2}\right )} b^{2} c^{2} - {\left (A B - B^{2}\right )} a^{2} d^{2} + {\left ({\left (A^{2} + 2 \, A B + 2 \, B^{2}\right )} b^{2} c d + {\left (A^{2} - 2 \, A B + 2 \, B^{2}\right )} a b d^{2}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{3 \, {\left ({\left (b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right )} g^{2} i^{2} x^{2} + {\left (b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right )} g^{2} i^{2} x + {\left (a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right )} g^{2} i^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 2572, normalized size = 7.05 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.61, size = 1995, normalized size = 5.47 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.20, size = 731, normalized size = 2.00 \[ \frac {2\,B^2\,b\,d\,{\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}^3}{3\,g^2\,i^2\,{\left (a\,d-b\,c\right )}^3}-\frac {\frac {A^2\,a\,d+A^2\,b\,c+2\,B^2\,a\,d+2\,B^2\,b\,c-2\,A\,B\,a\,d+2\,A\,B\,b\,c}{a\,d-b\,c}+\frac {2\,x\,\left (b\,d\,A^2+2\,b\,d\,B^2\right )}{a\,d-b\,c}}{x\,\left (a^2\,d^2\,g^2\,i^2-b^2\,c^2\,g^2\,i^2\right )+x^2\,\left (a\,b\,d^2\,g^2\,i^2-b^2\,c\,d\,g^2\,i^2\right )-a\,b\,c^2\,g^2\,i^2+a^2\,c\,d\,g^2\,i^2}-\frac {\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\,\left (\frac {2\,\left (B^2\,b\,c-B^2\,a\,d+A\,B\,a\,d+A\,B\,b\,c\right )}{g^2\,i^2\,\left (a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right )}+\frac {4\,A\,B\,x}{g^2\,i^2\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}\right )}{x^2+\frac {x\,\left (a\,d+b\,c\right )}{b\,d}+\frac {a\,c}{b\,d}}-{\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )}^2\,\left (\frac {\frac {B^2\,\left (a\,d+b\,c\right )}{g^2\,i^2\,\left (a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right )}+\frac {2\,B^2\,x}{g^2\,i^2\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}}{x^2+\frac {x\,\left (a\,d+b\,c\right )}{b\,d}+\frac {a\,c}{b\,d}}-\frac {2\,A\,B\,b\,d}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^3}\right )-\frac {b\,d\,\mathrm {atan}\left (\frac {b\,d\,\left (A^2+2\,B^2\right )\,\left (\frac {a^3\,d^3\,g^2\,i^2-a^2\,b\,c\,d^2\,g^2\,i^2-a\,b^2\,c^2\,d\,g^2\,i^2+b^3\,c^3\,g^2\,i^2}{a^2\,d^2\,g^2\,i^2-2\,a\,b\,c\,d\,g^2\,i^2+b^2\,c^2\,g^2\,i^2}+2\,b\,d\,x\right )\,\left (a^2\,d^2\,g^2\,i^2-2\,a\,b\,c\,d\,g^2\,i^2+b^2\,c^2\,g^2\,i^2\right )\,2{}\mathrm {i}}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^3\,\left (2\,b\,d\,A^2+4\,b\,d\,B^2\right )}\right )\,\left (A^2+2\,B^2\right )\,4{}\mathrm {i}}{g^2\,i^2\,{\left (a\,d-b\,c\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 9.76, size = 1404, normalized size = 3.85 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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