Optimal. Leaf size=523 \[ -\frac {b^3 (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{2 g^3 i^2 (a+b x)^2 (b c-a d)^4}-\frac {b^3 B (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{2 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac {3 b^2 d (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac {6 b^2 B d (c+d x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{g^3 i^2 (a+b x) (b c-a d)^4}-\frac {d^3 (a+b x) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac {2 A B d^3 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4}+\frac {b d^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^3}{B g^3 i^2 (b c-a d)^4}-\frac {b^3 B^2 (c+d x)^2}{4 g^3 i^2 (a+b x)^2 (b c-a d)^4}+\frac {6 b^2 B^2 d (c+d x)}{g^3 i^2 (a+b x) (b c-a d)^4}+\frac {2 B^2 d^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{g^3 i^2 (c+d x) (b c-a d)^4}-\frac {2 B^2 d^3 (a+b x)}{g^3 i^2 (c+d x) (b c-a d)^4} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 8.46, antiderivative size = 2071, normalized size of antiderivative = 3.96, number of steps used = 143, 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}{(98 c+98 d x)^2 (a g+b g x)^3} \, dx &=\int \left (\frac {b^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^2 g^3 (a+b x)^3}-\frac {b^2 d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)^2}+\frac {3 b^2 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3 (a+b x)}-\frac {d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)^2}-\frac {3 b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3 (c+d x)}\right ) \, dx\\ &=\frac {\left (3 b^2 d^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (3 b d^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (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)^2} \, dx}{4802 (b c-a d)^3 g^3}-\frac {d^3 \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(c+d x)^2} \, dx}{9604 (b c-a d)^3 g^3}+\frac {b^2 \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^3} \, dx}{9604 (b c-a d)^2 g^3}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {\left (3 b B d^2\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) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{e (a+b x)} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^4 g^3}-\frac {(b 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)^2 (c+d x)} \, dx}{2401 (b c-a d)^3 g^3}-\frac {\left (B 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) (c+d x)^2} \, dx}{4802 (b c-a d)^3 g^3}+\frac {(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)^3 (c+d x)} \, dx}{9604 (b c-a d)^2 g^3}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {(b B d) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2 (c+d x)} \, dx}{2401 (b c-a d)^2 g^3}-\frac {\left (B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^2} \, dx}{4802 (b c-a d)^2 g^3}+\frac {(b B) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3 (c+d x)} \, dx}{9604 (b c-a d) g^3}-\frac {\left (3 b B d^2\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) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{4802 (b c-a d)^4 e g^3}+\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^4 e g^3}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {(b B d) \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}{2401 (b c-a d)^2 g^3}-\frac {\left (B d^2\right ) \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}{4802 (b c-a d)^2 g^3}+\frac {(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)^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}{9604 (b c-a d) g^3}-\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^4 e g^3}+\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^4 e g^3}\\ &=-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {\left (b^2 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (b^2 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (b^2 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{2401 (b c-a d)^4 g^3}-\frac {\left (b B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}+\frac {\left (b B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (b B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{2401 (b c-a d)^4 g^3}-\frac {\left (b^2 B d\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{9604 (b c-a d)^3 g^3}-\frac {\left (b^2 B d\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{2401 (b c-a d)^3 g^3}-\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^3 g^3}+\frac {\left (3 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)}{(a+b x) (c+d x)} \, dx}{4802 (b c-a d)^3 g^3}+\frac {\left (B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{4802 (b c-a d)^3 g^3}+\frac {\left (b^2 B\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{9604 (b c-a d)^2 g^3}\\ &=-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 g^3}-\frac {\left (b B^2 d\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{9604 (b c-a d)^3 g^3}-\frac {\left (b B^2 d\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{2401 (b c-a d)^3 g^3}-\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^3 g^3}+\frac {\left (3 b B d^2\right ) \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}{4802 (b c-a d)^3 g^3}+\frac {\left (B^2 d^2\right ) \int \frac {b c-a d}{(a+b x) (c+d x)^2} \, dx}{4802 (b c-a d)^3 g^3}+\frac {\left (b B^2\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{19208 (b c-a d)^2 g^3}\\ &=-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {\left (3 b^2 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)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B d^3\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}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^2\right ) \int \frac {\log (a+b x)}{(a+b x) (c+d x)} \, dx}{4802 (b c-a d)^3 g^3}-\frac {\left (3 b B^2 d^2\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}{4802 (b c-a d)^3 g^3}-\frac {\left (b B^2 d\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{9604 (b c-a d)^2 g^3}-\frac {\left (b B^2 d\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{2401 (b c-a d)^2 g^3}+\frac {\left (B^2 d^2\right ) \int \frac {1}{(a+b x) (c+d x)^2} \, dx}{4802 (b c-a d)^2 g^3}+\frac {\left (b B^2\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{19208 (b c-a d) g^3}-\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 e g^3}-\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 e g^3}-\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 e g^3}\\ &=-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B d^2\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}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B^2 d^2\right ) \int \frac {\log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (3 b B d^3\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}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A B d^2\right ) \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 )}{4802 (b c-a d)^3 g^3}-\frac {\left (b B^2 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}{9604 (b c-a d)^2 g^3}-\frac {\left (b B^2 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}{2401 (b c-a d)^2 g^3}+\frac {\left (B^2 d^2\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}{4802 (b c-a d)^2 g^3}+\frac {\left (b B^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}{19208 (b c-a d) g^3}-\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{9604 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 e g^3}-\frac {\left (b B^2 d^2\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}{4802 (b c-a d)^4 e g^3}-\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 e g^3}+\frac {\left (b B^2 d^2\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}{2401 (b c-a d)^4 e g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 A b^2 B d^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}+\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}+\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{2401 (b c-a d)^4 g^3}+\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{2401 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B^2 d^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (3 A B d^3\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{\frac {b c-a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^3\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^3\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^3\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{2401 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{2401 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^3\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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}{4802 (b c-a d)^3 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{9604 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{2401 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{2401 (b c-a d)^4 g^3}-\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}+\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B^2 d^2\right ) \int \frac {\log ^2(c+d x)}{a+b x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (b^2 B^2 d^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{2401 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B^2 d^2\right ) \int \frac {\log (a+b x) \log (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b^2 B^2 d^2\right ) \int \frac {\log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^3\right ) \int \frac {\log ^2(c+d x)}{c+d x} \, dx}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{2401 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\right ) \int \frac {\text {Li}_2\left (1+\frac {b c-a d}{d (a+b x)}\right )}{(a+b x) (c+d x)} \, dx}{4802 (b c-a d)^3 g^3}+\frac {\left (3 b^2 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 (c+d x)}{a+b x} \, dx}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 A b B d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9604 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}+\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,c+d x\right )}{9604 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{2401 (b c-a d)^4 g^3}-\frac {\left (b B^2 d^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{2401 (b c-a d)^4 g^3}+\frac {\left (3 b 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 )}{x} \, dx,x,a+b x\right )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right ) \log (c+d x)}{c+d x} \, dx}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^3 \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}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{9604 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 B^2 d^3\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 )}{9604 (b c-a d)^4 g^3}-\frac {\left (3 B^2 d^3\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 )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 B^2 d^3\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 )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 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 ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {b B^2 d^2 \log ^3(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 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 ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {b B^2 d^2 \log ^3(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 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 ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b^2 B^2 d\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 )}{9604 (b c-a d)^4 g^3}-\frac {\left (3 b^2 B^2 d\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 )}{9604 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {b B^2 d^2 \log ^3(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 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 ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (c+d x) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}-\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}+\frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {b B^2 d^2 \log ^3(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}-\frac {3 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 ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}+2 \frac {\left (3 b B^2 d^2\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 )}{4802 (b c-a d)^4 g^3}\\ &=-\frac {b B^2}{38416 (b c-a d)^2 g^3 (a+b x)^2}+\frac {11 b B^2 d}{19208 (b c-a d)^3 g^3 (a+b x)}+\frac {B^2 d^2}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {15 b B^2 d^2 \log (a+b x)}{19208 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(a+b x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (-\frac {b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )}{9604 (b c-a d)^4 g^3}-\frac {b B \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {5 b B d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^3 g^3 (a+b x)}-\frac {B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4802 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b B d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9604 (b c-a d)^4 g^3}-\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{19208 (b c-a d)^2 g^3 (a+b x)^2}+\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{4802 (b c-a d)^3 g^3 (a+b x)}+\frac {d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^3 g^3 (c+d x)}+\frac {3 b d^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{9604 (b c-a d)^4 g^3}-\frac {15 b B^2 d^2 \log (c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log ^2(a+b x) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (c+d x)}{4802 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \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)}{4802 (b c-a d)^4 g^3}-\frac {3 b B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 A b B d^2 \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(c+d x)}{19208 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9604 (b c-a d)^4 g^3}-\frac {b B^2 d^2 \log ^3(c+d x)}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}-\frac {3 b B^2 d^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 A b B d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{9604 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}-\frac {3 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 ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \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 )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{4802 (b c-a d)^4 g^3}+\frac {3 b B^2 d^2 \text {Li}_3\left (1+\frac {b c-a d}{d (a+b x)}\right )}{4802 (b c-a d)^4 g^3}\\ \end {align*}
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Mathematica [A] time = 1.53, size = 466, normalized size = 0.89 \[ \frac {-2 B \left (2 a^3 B d^3-6 a^2 b d^2 (A (c+d x)-B d x)-6 a b^2 d (2 A d x (c+d x)+B c (c+2 d x))+b^3 \left (B \left (c^3-3 c^2 d x-9 c d^2 x^2-3 d^3 x^3\right )-6 A d^2 x^2 (c+d x)\right )\right ) \log ^2\left (\frac {e (a+b x)}{c+d x}\right )+4 d^2 \left (A^2-2 A B+2 B^2\right ) (a+b x)^2 (b c-a d)+6 b d^2 \left (2 A^2+2 A B+5 B^2\right ) (a+b x)^2 (c+d x) \log (a+b x)-6 b d^2 \left (2 A^2+2 A B+5 B^2\right ) (a+b x)^2 (c+d x) \log (c+d x)-b \left (2 A^2+2 A B+B^2\right ) (c+d x) (b c-a d)^2+2 b d \left (4 A^2+10 A B+11 B^2\right ) (a+b x) (c+d x) (b c-a d)+2 B (b c-a d) \left (2 b d (4 A+5 B) (a+b x) (c+d x)-b (2 A+B) (c+d x) (b c-a d)+4 d^2 (A-B) (a+b x)^2\right ) \log \left (\frac {e (a+b x)}{c+d x}\right )+4 b B^2 d^2 (a+b x)^2 (c+d x) \log ^3\left (\frac {e (a+b x)}{c+d x}\right )}{4 g^3 i^2 (a+b x)^2 (c+d x) (b c-a d)^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.32, size = 1005, normalized size = 1.92 \[ -\frac {{\left (2 \, A^{2} + 2 \, A B + B^{2}\right )} b^{3} c^{3} - 12 \, {\left (A^{2} + 2 \, A B + 2 \, B^{2}\right )} a b^{2} c^{2} d + 3 \, {\left (2 \, A^{2} + 10 \, A B + 5 \, B^{2}\right )} a^{2} b c d^{2} + 4 \, {\left (A^{2} - 2 \, A B + 2 \, B^{2}\right )} a^{3} d^{3} - 4 \, {\left (B^{2} b^{3} d^{3} x^{3} + B^{2} a^{2} b c d^{2} + {\left (B^{2} b^{3} c d^{2} + 2 \, B^{2} a b^{2} d^{3}\right )} x^{2} + {\left (2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{3} - 6 \, {\left ({\left (2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right )} b^{3} c d^{2} - {\left (2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right )} a b^{2} d^{3}\right )} x^{2} - 2 \, {\left (3 \, {\left (2 \, A B + B^{2}\right )} b^{3} d^{3} x^{3} - B^{2} b^{3} c^{3} + 6 \, B^{2} a b^{2} c^{2} d + 6 \, A B a^{2} b c d^{2} - 2 \, B^{2} a^{3} d^{3} + 3 \, {\left (4 \, A B a b^{2} d^{3} + {\left (2 \, A B + 3 \, B^{2}\right )} b^{3} c d^{2}\right )} x^{2} + 3 \, {\left (B^{2} b^{3} c^{2} d + 4 \, {\left (A B + B^{2}\right )} a b^{2} c d^{2} + 2 \, {\left (A B - B^{2}\right )} a^{2} b d^{3}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} - 3 \, {\left ({\left (2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right )} b^{3} c^{2} d + 2 \, {\left (2 \, A^{2} - 2 \, A B + 3 \, B^{2}\right )} a b^{2} c d^{2} - {\left (6 \, A^{2} + 2 \, A B + 13 \, B^{2}\right )} a^{2} b d^{3}\right )} x - 2 \, {\left (3 \, {\left (2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right )} b^{3} d^{3} x^{3} + 6 \, A^{2} a^{2} b c d^{2} - {\left (2 \, A B + B^{2}\right )} b^{3} c^{3} + 12 \, {\left (A B + B^{2}\right )} a b^{2} c^{2} d - 4 \, {\left (A B - B^{2}\right )} a^{3} d^{3} + 3 \, {\left ({\left (2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right )} b^{3} c d^{2} + 4 \, {\left (A^{2} + 2 \, B^{2}\right )} a b^{2} d^{3}\right )} x^{2} + 3 \, {\left ({\left (2 \, A B + 3 \, B^{2}\right )} b^{3} c^{2} d + 4 \, {\left (A^{2} + 2 \, A B + 2 \, B^{2}\right )} a b^{2} c d^{2} + 2 \, {\left (A^{2} - 2 \, A B + 2 \, B^{2}\right )} a^{2} b d^{3}\right )} x\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{4 \, {\left ({\left (b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right )} g^{3} i^{2} x^{3} + {\left (b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right )} g^{3} i^{2} x^{2} + {\left (2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right )} g^{3} i^{2} x + {\left (a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4}\right )} g^{3} 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 = 0.05, size = 3538, normalized size = 6.76 \[ \text {output too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 4.89, size = 4187, normalized size = 8.01 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 11.47, size = 1497, normalized size = 2.86 \[ \text {result too large to display} \]
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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