Optimal. Leaf size=525 \[ -\frac{b^3 (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{2 b^3 B (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{b^2 d \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^3}{B g^2 i^3 (b c-a d)^4}+\frac{3 b d^2 (a+b x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{d^3 (a+b x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}+\frac{B d^3 (a+b x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{2 g^2 i^3 (c+d x)^2 (b c-a d)^4}-\frac{6 A b B d^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{2 b^3 B^2 (c+d x)}{g^2 i^3 (a+b x) (b c-a d)^4}-\frac{6 b B^2 d^2 (a+b x) \log \left (\frac{e (a+b x)}{c+d x}\right )}{g^2 i^3 (c+d x) (b c-a d)^4}+\frac{6 b B^2 d^2 (a+b x)}{g^2 i^3 (c+d x) (b c-a d)^4}-\frac{B^2 d^3 (a+b x)^2}{4 g^2 i^3 (c+d x)^2 (b c-a d)^4} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 8.41743, antiderivative size = 2071, normalized size of antiderivative = 3.94, 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 2528
Rule 2525
Rule 12
Rule 44
Rule 2524
Rule 2418
Rule 2390
Rule 2301
Rule 2394
Rule 2393
Rule 2391
Rule 6688
Rule 6742
Rule 2411
Rule 2344
Rule 2317
Rule 2507
Rule 2488
Rule 2506
Rule 6610
Rule 2500
Rule 2433
Rule 2375
Rule 2374
Rule 6589
Rule 2440
Rule 2434
Rule 2499
Rule 2396
Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(105 c+105 d x)^3 (a g+b g x)^2} \, dx &=\int \left (\frac{b^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)^2}-\frac{b^3 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^2 g^2 (c+d x)^3}+\frac{2 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)^2}+\frac{b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2 (c+d x)}\right ) \, dx\\ &=-\frac{\left (b^3 d\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}+\frac{\left (b^2 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}{385875 (b c-a d)^4 g^2}+\frac{b^3 \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^2} \, dx}{1157625 (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)^2} \, dx}{1157625 (b c-a d)^3 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)^3} \, dx}{1157625 (b c-a d)^2 g^2}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^2 (c+d x)} \, dx}{1157625 (b c-a d)^3 g^2}+\frac{(4 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) (c+d x)^2} \, dx}{1157625 (b c-a d)^3 g^2}+\frac{(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)^3} \, dx}{1157625 (b c-a d)^2 g^2}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 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 (c+d x)} \, dx}{1157625 (b c-a d)^2 g^2}+\frac{(4 b 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}{1157625 (b c-a d)^2 g^2}+\frac{(B d) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^3} \, dx}{1157625 (b c-a d) g^2}+\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 e g^2}-\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 e g^2}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^2}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (c+d x)}\right ) \, dx}{1157625 (b c-a d)^2 g^2}+\frac{(4 b 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}{1157625 (b c-a d)^2 g^2}+\frac{(B d) \int \left (\frac{b^3 \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 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d 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 (c+d x)^2}-\frac{b^2 d \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}{1157625 (b c-a d) g^2}+\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 e g^2}-\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^4 e g^2}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{\left (b^3 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^3 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (4 b^3 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^3 B\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{1157625 (b c-a d)^3 g^2}+\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^3 g^2}-\frac{\left (2 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) (c+d x)} \, dx}{385875 (b c-a d)^3 g^2}-\frac{\left (b B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{1157625 (b c-a d)^3 g^2}-\frac{\left (4 b B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{1157625 (b c-a d)^3 g^2}-\frac{\left (B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^3} \, dx}{1157625 (b c-a d)^2 g^2}\\ &=-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}+\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}+\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{1157625 (b c-a d)^3 g^2}+\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^3 g^2}-\frac{\left (2 b^2 B d\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}{385875 (b c-a d)^3 g^2}-\frac{\left (b B^2 d\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{1157625 (b c-a d)^3 g^2}-\frac{\left (4 b B^2 d\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{1157625 (b c-a d)^3 g^2}-\frac{\left (B^2 d\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^3} \, dx}{2315250 (b c-a d)^2 g^2}\\ &=-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^3 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}{385875 (b c-a d)^4 g^2}+\frac{\left (2 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)}{c+d x} \, dx}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d\right ) \int \frac{\log (a+b x)}{(a+b x) (c+d x)} \, dx}{385875 (b c-a d)^3 g^2}+\frac{\left (2 b^2 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}{385875 (b c-a d)^3 g^2}+\frac{\left (2 b^2 B^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{1157625 (b c-a d)^2 g^2}-\frac{\left (b B^2 d\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{1157625 (b c-a d)^2 g^2}-\frac{\left (4 b B^2 d\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{1157625 (b c-a d)^2 g^2}-\frac{\left (B^2 d\right ) \int \frac{1}{(a+b x) (c+d x)^3} \, dx}{2315250 (b c-a d) g^2}-\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}-\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}-\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}\\ &=\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^3 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}{385875 (b c-a d)^4 g^2}-\frac{\left (b^3 B^2 d\right ) \int \frac{\log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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}{385875 (b c-a d)^4 g^2}+\frac{(2 A b 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 )}{385875 (b c-a d)^3 g^2}+\frac{\left (2 b^2 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}{1157625 (b c-a d)^2 g^2}-\frac{\left (b 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}{1157625 (b c-a d)^2 g^2}-\frac{\left (4 b 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}{1157625 (b c-a d)^2 g^2}-\frac{\left (B^2 d\right ) \int \left (\frac{b^3}{(b c-a d)^3 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^3}-\frac{b d}{(b c-a d)^2 (c+d x)^2}-\frac{b^2 d}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2315250 (b c-a d) g^2}-\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}-\frac{\left (2 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}-\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}+\frac{\left (4 b^2 B^2 d\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}{1157625 (b c-a d)^4 e g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 A b^3 B d\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}-\frac{\left (b^3 B^2 d\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (b^3 B^2 d\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^3 B^2 d\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^3 B^2 d\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^3 B^2 d\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (4 b^3 B^2 d\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^3 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}{385875 (b c-a d)^4 g^2}-\frac{\left (2 A b 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{385875 (b c-a d)^4 g^2}+\frac{\left (b^2 B^2 d^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^2 B^2 d^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (4 b^2 B^2 d^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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}{385875 (b c-a d)^3 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{385875 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^3 B^2 d\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^3 B^2 d\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^3 B^2 d\right ) \int \frac{\log ^2(c+d x)}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}-\frac{\left (4 b^3 B^2 d\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^3 B^2 d\right ) \int \frac{\log (a+b x) \log (c+d x)}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^3 B^2 d\right ) \int \frac{\log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{385875 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (b^2 B^2 d^2\right ) \int \frac{\log ^2(c+d x)}{c+d x} \, dx}{385875 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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}{385875 (b c-a d)^3 g^2}-\frac{\left (2 b^3 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}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 A b^2 B d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{385875 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}+\frac{\left (2 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}+\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{x} \, dx,x,c+d x\right )}{385875 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (4 b^2 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{1157625 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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}{385875 (b c-a d)^4 g^2}+\frac{\left (2 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 \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (b^2 B^2 d\right ) \operatorname{Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (b 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 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 )}{-\frac{-b c+a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 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 ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^3(c+d x)}{1157625 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^3(c+d x)}{1157625 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (b^3 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 )}{385875 (b c-a d)^4 g^2}+\frac{\left (b^3 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^3(c+d x)}{1157625 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}+\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^3(c+d x)}{1157625 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{2 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}-2 \frac{\left (2 b^2 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 )}{385875 (b c-a d)^4 g^2}\\ &=-\frac{2 b^2 B^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{B^2 d}{4630500 (b c-a d)^2 g^2 (c+d x)^2}-\frac{11 b B^2 d}{2315250 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 B^2 d \log (a+b x)}{154350 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(a+b x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1157625 (b c-a d)^3 g^2 (a+b x)}+\frac{B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2315250 (b c-a d)^2 g^2 (c+d x)^2}+\frac{b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{231525 (b c-a d)^3 g^2 (c+d x)}+\frac{b^2 B d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{385875 (b c-a d)^4 g^2}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2315250 (b c-a d)^2 g^2 (c+d x)^2}-\frac{2 b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1157625 (b c-a d)^3 g^2 (c+d x)}-\frac{b^2 d \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (c+d x)}{154350 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(a+b x) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 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)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{385875 (b c-a d)^4 g^2}+\frac{A b^2 B d \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log ^2(c+d x)}{771750 (b c-a d)^4 g^2}-\frac{b^2 B^2 d \log (a+b x) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^3(c+d x)}{1157625 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{2 b^2 B^2 d \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 A b^2 B d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}+\frac{b^2 B^2 d \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}+\frac{2 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 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 )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{385875 (b c-a d)^4 g^2}-\frac{2 b^2 B^2 d \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{385875 (b c-a d)^4 g^2}\\ \end{align*}
Mathematica [A] time = 1.50747, size = 453, normalized size = 0.86 \[ -\frac{2 B \left (-3 a^2 b B d^2 (2 c+d x)+a^3 B d^3+3 a b^2 d \left (2 A (c+d x)^2-B d x (4 c+3 d x)\right )+b^3 \left (6 A d x (c+d x)^2+B \left (6 c^2 d x+2 c^3-3 d^3 x^3\right )\right )\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )+4 b^2 \left (A^2+2 A B+2 B^2\right ) (c+d x)^2 (b c-a d)+6 b^2 d \left (2 A^2-2 A B+5 B^2\right ) (a+b x) (c+d x)^2 \log (a+b x)-6 b^2 d \left (2 A^2-2 A B+5 B^2\right ) (a+b x) (c+d x)^2 \log (c+d x)+d \left (2 A^2-2 A B+B^2\right ) (a+b x) (b c-a d)^2+2 b d \left (4 A^2-10 A B+11 B^2\right ) (a+b x) (c+d x) (b c-a d)+2 B (b c-a d) \left (2 b d (4 A-5 B) (a+b x) (c+d x)+d (2 A-B) (a+b x) (b c-a d)+4 b^2 (A+B) (c+d x)^2\right ) \log \left (\frac{e (a+b x)}{c+d x}\right )+4 b^2 B^2 d (a+b x) (c+d x)^2 \log ^3\left (\frac{e (a+b x)}{c+d x}\right )}{4 g^2 i^3 (a+b x) (c+d x)^2 (b c-a d)^4} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.06, size = 3802, normalized size = 7.2 \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 3.26861, size = 5654, normalized size = 10.77 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.561856, size = 2061, normalized size = 3.93 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 72.3652, size = 2683, normalized size = 5.11 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}^{2}}{{\left (b g x + a g\right )}^{2}{\left (d i x + c i\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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