Optimal. Leaf size=682 \[ -\frac{6 b^2 d^2 (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{12 b^2 B d^2 (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{b^4 (c+d x)^3 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{3 g^4 i^2 (a+b x)^3 (b c-a d)^5}-\frac{2 b^4 B (c+d x)^3 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{9 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{2 b^3 d (c+d x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}+\frac{2 b^3 B d (c+d x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{4 b d^3 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^3}{3 B g^4 i^2 (b c-a d)^5}+\frac{d^4 (a+b x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{2 A B d^4 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5}-\frac{12 b^2 B^2 d^2 (c+d x)}{g^4 i^2 (a+b x) (b c-a d)^5}-\frac{2 b^4 B^2 (c+d x)^3}{27 g^4 i^2 (a+b x)^3 (b c-a d)^5}+\frac{b^3 B^2 d (c+d x)^2}{g^4 i^2 (a+b x)^2 (b c-a d)^5}-\frac{2 B^2 d^4 (a+b x) \log \left (\frac{e (a+b x)}{c+d x}\right )}{g^4 i^2 (c+d x) (b c-a d)^5}+\frac{2 B^2 d^4 (a+b x)}{g^4 i^2 (c+d x) (b c-a d)^5} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 9.47853, antiderivative size = 2222, normalized size of antiderivative = 3.26, number of steps used = 177, 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}{(99 c+99 d x)^2 (a g+b g x)^4} \, dx &=\int \left (\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^2 g^4 (a+b x)^4}-\frac{2 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^3}+\frac{b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)^2}-\frac{4 b^2 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4 (a+b x)}+\frac{d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)^2}+\frac{4 b d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4 (c+d x)}\right ) \, dx\\ &=-\frac{\left (4 b^2 d^3\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (4 b d^4\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}+\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}{(a+b x)^2} \, dx}{3267 (b c-a d)^4 g^4}+\frac{d^4 \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(c+d x)^2} \, dx}{9801 (b c-a d)^4 g^4}-\frac{\left (2 b^2 d\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^3} \, dx}{9801 (b c-a d)^3 g^4}+\frac{b^2 \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^4} \, dx}{9801 (b c-a d)^2 g^4}\\ &=-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b 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)^2 (c+d x)} \, dx}{3267 (b c-a d)^4 g^4}+\frac{\left (2 B d^3\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)^2} \, dx}{9801 (b c-a d)^4 g^4}-\frac{(2 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)^3 (c+d x)} \, dx}{9801 (b c-a d)^3 g^4}+\frac{(2 b B) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^4 (c+d x)} \, dx}{29403 (b c-a d)^2 g^4}\\ &=-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2 (c+d x)} \, dx}{3267 (b c-a d)^3 g^4}+\frac{\left (2 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^2} \, dx}{9801 (b c-a d)^3 g^4}-\frac{(2 b B d) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3 (c+d x)} \, dx}{9801 (b c-a d)^2 g^4}+\frac{(2 b B) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^4 (c+d x)} \, dx}{29403 (b c-a d) g^4}+\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 e g^4}-\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 e g^4}\\ &=-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B d^2\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^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}{3267 (b c-a d)^3 g^4}+\frac{\left (2 B d^3\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}{9801 (b c-a d)^3 g^4}-\frac{(2 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)^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}{9801 (b c-a d)^2 g^4}+\frac{(2 b B) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^4}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)}+\frac{d^4 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (c+d x)}\right ) \, dx}{29403 (b c-a d) g^4}+\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 e g^4}-\frac{\left (8 b B d^3\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}{9801 (b c-a d)^5 e g^4}\\ &=-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{\left (2 b^2 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{29403 (b c-a d)^5 g^4}-\frac{\left (2 b^2 B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{29403 (b c-a d)^4 g^4}+\frac{\left (2 b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{9801 (b c-a d)^4 g^4}+\frac{\left (2 b^2 B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{3267 (b c-a d)^4 g^4}+\frac{\left (8 b B d^3\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}{9801 (b c-a d)^4 g^4}-\frac{\left (8 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)}{(a+b x) (c+d x)} \, dx}{9801 (b c-a d)^4 g^4}-\frac{\left (2 B d^4\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{9801 (b c-a d)^4 g^4}-\frac{\left (2 b^2 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{29403 (b c-a d)^3 g^4}-\frac{\left (2 b^2 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{9801 (b c-a d)^3 g^4}+\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)^4} \, dx}{29403 (b c-a d)^2 g^4}\\ &=-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 g^4}-\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 g^4}-\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{29403 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{9801 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{3267 (b c-a d)^4 g^4}+\frac{\left (8 b B d^3\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}{9801 (b c-a d)^4 g^4}-\frac{\left (8 b B d^3\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}{9801 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{9801 (b c-a d)^4 g^4}-\frac{\left (b B^2 d\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{29403 (b c-a d)^3 g^4}-\frac{\left (b B^2 d\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{9801 (b c-a d)^3 g^4}+\frac{\left (2 b B^2\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{88209 (b c-a d)^2 g^4}\\ &=-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b^2 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)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B d^4\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}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^3\right ) \int \frac{\log (a+b x)}{(a+b x) (c+d x)} \, dx}{9801 (b c-a d)^4 g^4}+\frac{\left (8 b B^2 d^3\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}{9801 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{29403 (b c-a d)^3 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{9801 (b c-a d)^3 g^4}+\frac{\left (2 b B^2 d^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{3267 (b c-a d)^3 g^4}-\frac{\left (2 B^2 d^3\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{9801 (b c-a d)^3 g^4}-\frac{\left (b B^2 d\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{29403 (b c-a d)^2 g^4}-\frac{\left (b B^2 d\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{9801 (b c-a d)^2 g^4}+\frac{\left (2 b B^2\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{88209 (b c-a d) g^4}+\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 e g^4}-\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 e g^4}+\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 e g^4}-\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 e g^4}\\ &=\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b^2 B d^3\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}{9801 (b c-a d)^5 g^4}-\frac{\left (4 b^2 B^2 d^3\right ) \int \frac{\log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B d^4\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}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A B d^3\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 )}{9801 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^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}{29403 (b c-a d)^3 g^4}+\frac{\left (2 b B^2 d^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}{9801 (b c-a d)^3 g^4}+\frac{\left (2 b B^2 d^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}{3267 (b c-a d)^3 g^4}-\frac{\left (2 B^2 d^3\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}{9801 (b c-a d)^3 g^4}-\frac{\left (b B^2 d\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{29403 (b c-a d)^2 g^4}-\frac{\left (b B^2 d\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{9801 (b c-a d)^2 g^4}+\frac{\left (2 b B^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^4}-\frac{b d}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3}{(b c-a d)^4 (a+b x)}+\frac{d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{88209 (b c-a d) g^4}+\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 e g^4}-\frac{\left (2 b B^2 d^3\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}{29403 (b c-a d)^5 e g^4}+\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 e g^4}-\frac{\left (2 b B^2 d^3\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}{3267 (b c-a d)^5 e g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 A b^2 B d^3\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{29403 (b c-a d)^5 g^4}-\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{3267 (b c-a d)^5 g^4}-\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{3267 (b c-a d)^5 g^4}-\frac{\left (8 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}-\frac{\left (8 A B d^4\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{\frac{b c-a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^4\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}-\frac{\left (2 b B^2 d^4\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^4\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{29403 (b c-a d)^5 g^4}-\frac{\left (2 b B^2 d^4\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^4\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{3267 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^4\right ) \int \frac{\log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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}{9801 (b c-a d)^4 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{29403 (b c-a d)^5 g^4}-\frac{\left (4 b^2 B^2 d^3\right ) \int \frac{\log ^2(c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3267 (b c-a d)^5 g^4}-\frac{\left (8 b^2 B^2 d^3\right ) \int \frac{\log (a+b x) \log (c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^4\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^4\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{29403 (b c-a d)^5 g^4}+\frac{\left (4 b B^2 d^4\right ) \int \frac{\log ^2(c+d x)}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^4\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3267 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^3\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}{9801 (b c-a d)^4 g^4}-\frac{\left (8 b^2 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 (c+d x)}{a+b x} \, dx}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 A b B d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{29403 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{29403 (b c-a d)^5 g^4}+\frac{\left (4 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{x} \, dx,x,c+d x\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3267 (b c-a d)^5 g^4}+\frac{\left (2 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{3267 (b c-a d)^5 g^4}-\frac{\left (8 b 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 )}{x} \, dx,x,a+b x\right )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^4\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right ) \log (c+d x)}{c+d x} \, dx}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^4 \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}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (4 b B^2 d^3\right ) \operatorname{Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (4 B^2 d^4\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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 B^2 d^4\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 )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 B^2 d^4\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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 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 ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^3(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^3(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (4 b^2 B^2 d^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 )}{9801 (b c-a d)^5 g^4}+\frac{\left (4 b^2 B^2 d^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 )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^3(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}+\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}-\frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^3(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log \left (\frac{1}{c+d x}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}+\frac{8 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}-2 \frac{\left (8 b B^2 d^3\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 )}{9801 (b c-a d)^5 g^4}\\ &=-\frac{2 b B^2}{264627 (b c-a d)^2 g^4 (a+b x)^3}+\frac{7 b B^2 d}{88209 (b c-a d)^3 g^4 (a+b x)^2}-\frac{92 b B^2 d^2}{88209 (b c-a d)^4 g^4 (a+b x)}-\frac{2 B^2 d^3}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{10 b B^2 d^3 \log (a+b x)}{8019 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(a+b x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(a+b x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{9801 (b c-a d)^5 g^4}-\frac{2 b B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{88209 (b c-a d)^2 g^4 (a+b x)^3}+\frac{4 b B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^3 g^4 (a+b x)^2}-\frac{26 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^4 g^4 (a+b x)}+\frac{2 B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{20 b B d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{29403 (b c-a d)^5 g^4}-\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{29403 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{3267 (b c-a d)^4 g^4 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^4 g^4 (c+d x)}-\frac{4 b d^3 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log (c+d x)}{8019 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log ^2(a+b x) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \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)}{9801 (b c-a d)^5 g^4}+\frac{20 b B d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{29403 (b c-a d)^5 g^4}+\frac{4 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 A b B d^3 \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{10 b B^2 d^3 \log ^2(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{4 b B^2 d^3 \log (a+b x) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{9801 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^3(c+d x)}{29403 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{4 b B^2 d^3 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}+\frac{8 b B^2 d^3 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 A b B d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{20 b B^2 d^3 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{29403 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \log \left (\frac{1}{c+d x}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}+\frac{8 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 ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \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 )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{9801 (b c-a d)^5 g^4}-\frac{8 b B^2 d^3 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{9801 (b c-a d)^5 g^4}\\ \end{align*}
Mathematica [A] time = 2.10637, size = 613, normalized size = 0.9 \[ -\frac{9 B \left (18 a^2 b^2 d^2 (2 A d x (c+d x)+B c (c+2 d x))+12 a^3 b d^3 (A (c+d x)-B d x)-3 a^4 B d^4+6 a b^3 d \left (6 A d^2 x^2 (c+d x)+B \left (3 c^2 d x-c^3+9 c d^2 x^2+3 d^3 x^3\right )\right )+b^4 \left (12 A d^3 x^3 (c+d x)+B \left (6 c^2 d^2 x^2-2 c^3 d x+c^4+22 c d^3 x^3+10 d^4 x^4\right )\right )\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )+3 b d^2 \left (27 A^2+78 A B+92 B^2\right ) (a+b x)^2 (c+d x) (b c-a d)-27 d^3 \left (A^2-2 A B+2 B^2\right ) (a+b x)^3 (a d-b c)+6 b d^3 \left (18 A^2+30 A B+55 B^2\right ) (a+b x)^3 (c+d x) \log (a+b x)-6 b d^3 \left (18 A^2+30 A B+55 B^2\right ) (a+b x)^3 (c+d x) \log (c+d x)+b \left (9 A^2+6 A B+2 B^2\right ) (c+d x) (b c-a d)^3-3 b d \left (9 A^2+12 A B+7 B^2\right ) (a+b x) (c+d x) (b c-a d)^2+6 B (b c-a d) \left (3 b d^2 (9 A+13 B) (a+b x)^2 (c+d x)-3 b d (3 A+2 B) (a+b x) (c+d x) (b c-a d)+b (3 A+B) (c+d x) (b c-a d)^2+9 d^3 (A-B) (a+b x)^3\right ) \log \left (\frac{e (a+b x)}{c+d x}\right )+36 b B^2 d^3 (a+b x)^3 (c+d x) \log ^3\left (\frac{e (a+b x)}{c+d x}\right )}{27 g^4 i^2 (a+b x)^3 (c+d x) (b c-a d)^5} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.065, size = 4487, normalized size = 6.6 \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 = 4.42911, size = 8316, normalized size = 12.19 \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 [B] time = 0.694092, size = 3193, normalized size = 4.68 \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 [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 )}^{4}{\left (d i x + c i\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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