Optimal. Leaf size=543 \[ -\frac{b^3 (c+d x)^3 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{3 g^4 i (a+b x)^3 (b c-a d)^4}-\frac{2 b^3 B n (c+d x)^3 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{9 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 d (c+d x)^2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 g^4 i (a+b x)^2 (b c-a d)^4}+\frac{3 b^2 B d n (c+d x)^2 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{2 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{3 b d^2 (c+d x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^2}{g^4 i (a+b x) (b c-a d)^4}-\frac{6 b B d^2 n (c+d x) \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )}{g^4 i (a+b x) (b c-a d)^4}-\frac{d^3 \left (B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+A\right )^3}{3 B g^4 i n (b c-a d)^4}-\frac{2 b^3 B^2 n^2 (c+d x)^3}{27 g^4 i (a+b x)^3 (b c-a d)^4}+\frac{3 b^2 B^2 d n^2 (c+d x)^2}{4 g^4 i (a+b x)^2 (b c-a d)^4}-\frac{6 b B^2 d^2 n^2 (c+d x)}{g^4 i (a+b x) (b c-a d)^4} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 8.35375, antiderivative size = 2180, normalized size of antiderivative = 4.01, number of steps used = 143, number of rules used = 31, integrand size = 45, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.689, 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 (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{(193 c+193 d x) (a g+b g x)^4} \, dx &=\int \left (\frac{b \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d) g^4 (a+b x)^4}-\frac{b d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^2 g^4 (a+b x)^3}+\frac{b d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)^2}-\frac{b d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4 (a+b x)}+\frac{d^4 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4 (c+d x)}\right ) \, dx\\ &=-\frac{\left (b d^3\right ) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{d^4 \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (b d^2\right ) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{(a+b x)^2} \, dx}{193 (b c-a d)^3 g^4}-\frac{(b d) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{(a+b x)^3} \, dx}{193 (b c-a d)^2 g^4}+\frac{b \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{(a+b x)^4} \, dx}{193 (b c-a d) g^4}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^3 n\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B d^3 n\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^2 n\right ) \int \frac{(b c-a d) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^3 g^4}-\frac{(B d n) \int \frac{(b c-a d) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(a+b x)^3 (c+d x)} \, dx}{193 (b c-a d)^2 g^4}+\frac{(2 B n) \int \frac{(b c-a d) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(a+b x)^4 (c+d x)} \, dx}{579 (b c-a d) g^4}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{(2 B n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^4 (c+d x)} \, dx}{579 g^4}+\frac{\left (2 B d^3 n\right ) \int \frac{(b c-a d) \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B d^3 n\right ) \int \frac{(b c-a d) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^2 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^2 g^4}-\frac{(B d n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^3 (c+d x)} \, dx}{193 (b c-a d) g^4}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{(2 B n) \int \left (\frac{b \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)^4}-\frac{b d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (a+b x)^3}+\frac{b d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (a+b x)^2}-\frac{b d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^4 (a+b x)}+\frac{d^4 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^4 (c+d x)}\right ) \, dx}{579 g^4}+\frac{\left (2 B d^3 n\right ) \int \frac{\log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}-\frac{\left (2 B d^3 n\right ) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B d^2 n\right ) \int \left (\frac{b \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)^2}-\frac{b d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (a+b x)}+\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (c+d x)}\right ) \, dx}{193 (b c-a d)^2 g^4}-\frac{(B d n) \int \left (\frac{b \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (a+b x)^3}-\frac{b d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (a+b x)}-\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{193 (b c-a d) g^4}\\ &=-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B d^3 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (b B d^3 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B d^3 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^4 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (B d^4 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^4 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 b B d^2 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{579 (b c-a d)^3 g^4}+\frac{\left (b B d^2 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 b B d^2 n\right ) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^2} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B d^3 n\right ) \int \left (\frac{A \log (a+b x)}{(a+b x) (c+d x)}+\frac{B \log (a+b x) \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)}\right ) \, dx}{193 (b c-a d)^3 g^4}-\frac{\left (2 B d^3 n\right ) \int \left (\frac{b \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{(b c-a d) (a+b x)}-\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{(b c-a d) (c+d x)}\right ) \, dx}{193 (b c-a d)^3 g^4}-\frac{(2 b B d n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^3} \, dx}{579 (b c-a d)^2 g^4}-\frac{(b B d n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^3} \, dx}{193 (b c-a d)^2 g^4}+\frac{(2 b B n) \int \frac{A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x)^4} \, dx}{579 (b c-a d) g^4}\\ &=-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B d^3 n\right ) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^4 n\right ) \int \frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\right ) \int \frac{\log (a+b x)}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B^2 d^3 n\right ) \int \frac{\log (a+b x) \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \int \frac{(c+d x) \left (-\frac{d (a+b x)}{(c+d x)^2}+\frac{b}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^2 n^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{579 (b c-a d)^3 g^4}+\frac{\left (B^2 d^2 n^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B^2 d^2 n^2\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^3 g^4}-\frac{\left (B^2 d n^2\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{579 (b c-a d)^2 g^4}-\frac{\left (B^2 d n^2\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{386 (b c-a d)^2 g^4}+\frac{\left (2 B^2 n^2\right ) \int \frac{b c-a d}{(a+b x)^4 (c+d x)} \, dx}{1737 (b c-a d) g^4}\\ &=\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{\left (b B^2 d^3\right ) \int \frac{\log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B d^3 n\right ) \int \left (\frac{A \log (c+d x)}{a+b x}+\frac{B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log (c+d x)}{a+b x}\right ) \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B d^4 n\right ) \int \left (\frac{A \log (c+d x)}{c+d x}+\frac{B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log (c+d x)}{c+d x}\right ) \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\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 )}{193 b (b c-a d)^3 g^4}+\frac{\left (2 B^2 n^2\right ) \int \frac{1}{(a+b x)^4 (c+d x)} \, dx}{1737 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \int \left (\frac{b \log (a+b x)}{a+b x}-\frac{d \log (a+b x)}{c+d x}\right ) \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \int \left (\frac{b \log (c+d x)}{a+b x}-\frac{d \log (c+d x)}{c+d x}\right ) \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \int \left (\frac{b \log (a+b x)}{a+b x}-\frac{d \log (a+b x)}{c+d x}\right ) \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (B^2 d^3 n^2\right ) \int \left (\frac{b \log (c+d x)}{a+b x}-\frac{d \log (c+d x)}{c+d x}\right ) \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \int \left (\frac{b \log (a+b x)}{a+b x}-\frac{d \log (a+b x)}{c+d x}\right ) \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \int \left (\frac{b \log (c+d x)}{a+b x}-\frac{d \log (c+d x)}{c+d x}\right ) \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^2 n^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{579 (b c-a d)^2 g^4}+\frac{\left (B^2 d^2 n^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^2 g^4}+\frac{\left (2 B^2 d^2 n^2\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{193 (b c-a d)^2 g^4}-\frac{\left (B^2 d n^2\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{579 (b c-a d) g^4}-\frac{\left (B^2 d n^2\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{386 (b c-a d) g^4}\\ &=\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 A b B d^3 n\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B^2 d^3 n\right ) \int \frac{\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^4 n\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 A B d^4 n\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{\frac{b c-a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{193 b (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n\right ) \int \frac{\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n\right ) \int \frac{\log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}+\frac{\left (2 B^2 n^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}{1737 g^4}+\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (b B^2 d^3 n^2\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (b B^2 d^3 n^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log (a+b x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (B^2 d^4 n^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^4 n^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log (a+b x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^2 n^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}{579 (b c-a d)^2 g^4}+\frac{\left (B^2 d^2 n^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}{193 (b c-a d)^2 g^4}+\frac{\left (2 B^2 d^2 n^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}{193 (b c-a d)^2 g^4}-\frac{\left (B^2 d n^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{579 (b c-a d) g^4}-\frac{\left (B^2 d n^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{386 (b c-a d) g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B^2 d^3 n\right ) \int \frac{\log \left ((a+b x)^n\right ) \log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}-\frac{\left (2 b B^2 d^3 n\right ) \int \frac{\log (c+d x) \log \left ((c+d x)^{-n}\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^4 n\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{579 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{579 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{579 (b c-a d)^4 g^4}-\frac{\left (b B^2 d^3 n^2\right ) \int \frac{\log ^2(c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (b B^2 d^3 n^2\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 b B^2 d^3 n^2\right ) \int \frac{\log \left (\frac{b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{579 (b c-a d)^4 g^4}+\frac{\left (B^2 d^4 n^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^4 n^2\right ) \int \frac{\log ^2(c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \int \frac{\text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{(a+b x) (c+d x)} \, dx}{193 (b c-a d)^3 g^4}-\frac{\left (2 b B^2 d^3 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\right )\right )\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 A B d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (x^n\right ) \log \left (\frac{b c-a d}{b}+\frac{d x}{b}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (-\frac{-b c+a d}{b}+\frac{d x}{b}\right ) \log \left (\left (-\frac{-b c+a d}{b}+\frac{d x}{b}\right )^{-n}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{579 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{579 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n^2\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right ) \log (c+d x)}{c+d x} \, dx}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\right )\right )\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (B^2 d^4\right ) \operatorname{Subst}\left (\int \frac{\log ^2\left (x^n\right )}{\frac{b c-a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{193 b (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^4 n\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\left (-\frac{-b c+a d}{b}+\frac{d x}{b}\right )^{-n}\right )}{-\frac{-b c+a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{193 b (b c-a d)^4 g^4}+\frac{\left (B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{d \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^4 n^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 )}{193 b (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\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 )}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n^2 \log ^3(c+d x)}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (x^{-n}\right ) \log \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (x^n\right ) \log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log (a+b x) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n^2 \log ^3(c+d x)}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left ((a+b x)^n\right ) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (b B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log ^2\left (x^{-n}\right )}{\frac{-b c+a d}{d}+\frac{b x}{d}} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}+\frac{\left (b B^2 d^2 n^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 )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log (a+b x) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n^2 \log ^3(c+d x)}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left ((a+b x)^n\right ) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}+\frac{\left (2 B^2 d^3 n\right ) \operatorname{Subst}\left (\int \frac{\log \left (x^{-n}\right ) \log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}-\frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log (a+b x) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n^2 \log ^3(c+d x)}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left ((a+b x)^n\right ) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left ((c+d x)^{-n}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-2 \frac{\left (2 B^2 d^3 n^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{193 (b c-a d)^4 g^4}\\ &=-\frac{2 B^2 n^2}{5211 (b c-a d) g^4 (a+b x)^3}+\frac{19 B^2 d n^2}{6948 (b c-a d)^2 g^4 (a+b x)^2}-\frac{85 B^2 d^2 n^2}{3474 (b c-a d)^3 g^4 (a+b x)}-\frac{85 B^2 d^3 n^2 \log (a+b x)}{3474 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(a+b x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(a+b x)}{1158 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log (a+b x) \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )}{193 (b c-a d)^4 g^4}-\frac{2 B n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1737 (b c-a d) g^4 (a+b x)^3}+\frac{5 B d n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{1158 (b c-a d)^2 g^4 (a+b x)^2}-\frac{11 B d^2 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^3 g^4 (a+b x)}-\frac{11 B d^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )}{579 (b c-a d)^4 g^4}-\frac{\left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{579 (b c-a d) g^4 (a+b x)^3}+\frac{d \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{386 (b c-a d)^2 g^4 (a+b x)^2}-\frac{d^2 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^3 g^4 (a+b x)}-\frac{d^3 \log (a+b x) \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2}{193 (b c-a d)^4 g^4}+\frac{85 B^2 d^3 n^2 \log (c+d x)}{3474 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B d^3 n \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{579 (b c-a d)^4 g^4}+\frac{d^3 \left (A+B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )\right )^2 \log (c+d x)}{193 (b c-a d)^4 g^4}+\frac{A B d^3 n \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{11 B^2 d^3 n^2 \log ^2(c+d x)}{1158 (b c-a d)^4 g^4}-\frac{B^2 d^3 n^2 \log (a+b x) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \log ^2(c+d x)}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 n^2 \log ^3(c+d x)}{579 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log (a+b x) \log (c+d x) \log \left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}-\frac{B^2 d^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{B^2 d^3 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x) \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \log \left ((a+b x)^n\right ) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 A B d^3 n \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{11 B^2 d^3 n^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{579 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left ((c+d x)^{-n}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}+\frac{2 B^2 d^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{193 (b c-a d)^4 g^4}-\frac{2 B^2 d^3 n^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{193 (b c-a d)^4 g^4}\\ \end{align*}
Mathematica [B] time = 1.898, size = 1295, normalized size = 2.38 \[ -\frac{4 \left (9 A^2+6 B n A+2 B^2 n^2+9 B^2 \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+9 B^2 n^2 \log ^2\left (\frac{a+b x}{c+d x}\right )-6 B n (3 A+B n) \log \left (\frac{a+b x}{c+d x}\right )+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \left (3 A+B n-3 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right ) (b c-a d)^3-3 d (a+b x) \left (18 A^2+30 B n A+19 B^2 n^2+18 B^2 \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+18 B^2 n^2 \log ^2\left (\frac{a+b x}{c+d x}\right )-6 B n (6 A+5 B n) \log \left (\frac{a+b x}{c+d x}\right )+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \left (6 A+5 B n-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right ) (b c-a d)^2+6 d^2 (a+b x)^2 \left (18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+18 B^2 n^2 \log ^2\left (\frac{a+b x}{c+d x}\right )-6 B n (6 A+11 B n) \log \left (\frac{a+b x}{c+d x}\right )+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \left (6 A+11 B n-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right ) (b c-a d)+6 B n \log \left (\frac{a+b x}{c+d x}\right ) \left (4 \left (3 A+B n+3 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-3 B n \log \left (\frac{a+b x}{c+d x}\right )\right ) (b c-a d)^2+3 d (a d-b c) (a+b x) \left (6 A+5 B n+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )+6 d^2 (a+b x)^2 \left (6 A+11 B n+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right ) (b c-a d)+36 B^2 d^3 n^2 (a+b x)^3 \log ^3\left (\frac{a+b x}{c+d x}\right )+18 B n \log ^2\left (\frac{a+b x}{c+d x}\right ) \left (6 A d^3 x^3 b^3+11 B d^3 n x^3 b^3+6 B c d^2 n x^2 b^3+2 B c^3 n b^3-3 B c^2 d n x b^3+18 a A d^3 x^2 b^2+27 a B d^3 n x^2 b^2-9 a B c^2 d n b^2+18 a B c d^2 n x b^2+18 a^2 B c d^2 n b+18 a^2 A d^3 x b+18 a^2 B d^3 n x b+6 a^3 A d^3+6 B d^3 (a+b x)^3 \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right )-6 B d^3 n (a+b x)^3 \log \left (\frac{a+b x}{c+d x}\right )\right )+6 d^3 (a+b x)^3 \log (a+b x) \left (18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+18 B^2 n^2 \log ^2\left (\frac{a+b x}{c+d x}\right )-6 B n (6 A+11 B n) \log \left (\frac{a+b x}{c+d x}\right )+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \left (6 A+11 B n-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right )-6 d^3 (a+b x)^3 \left (18 A^2+66 B n A+85 B^2 n^2+18 B^2 \log ^2\left (e \left (\frac{a+b x}{c+d x}\right )^n\right )+18 B^2 n^2 \log ^2\left (\frac{a+b x}{c+d x}\right )-6 B n (6 A+11 B n) \log \left (\frac{a+b x}{c+d x}\right )+6 B \log \left (e \left (\frac{a+b x}{c+d x}\right )^n\right ) \left (6 A+11 B n-6 B n \log \left (\frac{a+b x}{c+d x}\right )\right )\right ) \log (c+d x)}{108 (b c-a d)^4 g^4 i (a+b x)^3} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.71, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( bgx+ag \right ) ^{4} \left ( dix+ci \right ) } \left ( A+B\ln \left ( e \left ({\frac{bx+a}{dx+c}} \right ) ^{n} \right ) \right ) ^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 2.82677, size = 4651, normalized size = 8.57 \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 = 0.693763, size = 3987, normalized size = 7.34 \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 (e \left (\frac{b x + a}{d x + c}\right )^{n}\right ) + A\right )}^{2}}{{\left (b g x + a g\right )}^{4}{\left (d i x + c i\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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