Optimal. Leaf size=685 \[ \frac{2 b^2 d^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^3}{B g^3 i^3 (b c-a d)^5}-\frac{b^4 (c+d x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{2 g^3 i^3 (a+b x)^2 (b c-a d)^5}-\frac{b^4 B (c+d x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{2 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{4 b^3 d (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{8 b^3 B d (c+d x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{g^3 i^3 (a+b x) (b c-a d)^5}-\frac{4 b d^3 (a+b x) \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{g^3 i^3 (c+d x) (b c-a d)^5}+\frac{d^4 (a+b x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )^2}{2 g^3 i^3 (c+d x)^2 (b c-a d)^5}-\frac{B d^4 (a+b x)^2 \left (B \log \left (\frac{e (a+b x)}{c+d x}\right )+A\right )}{2 g^3 i^3 (c+d x)^2 (b c-a d)^5}+\frac{8 A b B d^3 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{b^4 B^2 (c+d x)^2}{4 g^3 i^3 (a+b x)^2 (b c-a d)^5}+\frac{8 b^3 B^2 d (c+d x)}{g^3 i^3 (a+b x) (b c-a d)^5}+\frac{8 b B^2 d^3 (a+b x) \log \left (\frac{e (a+b x)}{c+d x}\right )}{g^3 i^3 (c+d x) (b c-a d)^5}-\frac{8 b B^2 d^3 (a+b x)}{g^3 i^3 (c+d x) (b c-a d)^5}+\frac{B^2 d^4 (a+b x)^2}{4 g^3 i^3 (c+d x)^2 (b c-a d)^5} \]
[Out]
________________________________________________________________________________________
Rubi [C] time = 9.57928, antiderivative size = 1921, normalized size of antiderivative = 2.8, number of steps used = 173, 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}{(106 c+106 d x)^3 (a g+b g x)^3} \, dx &=\int \left (\frac{b^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^3 g^3 (a+b x)^3}-\frac{3 b^3 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)^2}+\frac{3 b^3 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3 (a+b x)}-\frac{d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^3 g^3 (c+d x)^3}-\frac{3 b d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)^2}-\frac{3 b^2 d^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3 (c+d x)}\right ) \, dx\\ &=\frac{\left (3 b^3 d^2\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{a+b x} \, dx}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 d^3\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{c+d x} \, dx}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^3 d\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^2} \, dx}{1191016 (b c-a d)^4 g^3}-\frac{\left (3 b d^3\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(c+d x)^2} \, dx}{1191016 (b c-a d)^4 g^3}+\frac{b^3 \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^3} \, dx}{1191016 (b c-a d)^3 g^3}-\frac{d^3 \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{(c+d x)^3} \, dx}{1191016 (b c-a d)^3 g^3}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B d^2\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{e (a+b x)} \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B d^2\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{e (a+b x)} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B d\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}{595508 (b c-a d)^4 g^3}-\frac{\left (3 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) (c+d x)^2} \, dx}{595508 (b c-a d)^4 g^3}+\frac{\left (b^2 B\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x)^3 (c+d x)} \, dx}{1191016 (b c-a d)^3 g^3}-\frac{\left (B d^2\right ) \int \frac{(b c-a d) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)^3} \, dx}{1191016 (b c-a d)^3 g^3}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2 (c+d x)} \, dx}{595508 (b c-a d)^3 g^3}-\frac{\left (3 b B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^2} \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b^2 B\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3 (c+d x)} \, dx}{1191016 (b c-a d)^2 g^3}-\frac{\left (B d^2\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)^3} \, dx}{1191016 (b c-a d)^2 g^3}-\frac{\left (3 b^2 B d^2\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{297754 (b c-a d)^5 e g^3}+\frac{\left (3 b^2 B d^2\right ) \int \frac{(c+d x) \left (-\frac{d e (a+b x)}{(c+d x)^2}+\frac{b e}{c+d x}\right ) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 e g^3}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B d\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}{595508 (b c-a d)^3 g^3}-\frac{\left (3 b B d^2\right ) \int \left (\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d x)^2}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (c+d x)}\right ) \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b^2 B\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^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}{1191016 (b c-a d)^2 g^3}-\frac{\left (B d^2\right ) \int \left (\frac{b^3 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d x)^3}-\frac{b d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (c+d x)^2}-\frac{b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (c+d x)}\right ) \, dx}{1191016 (b c-a d)^2 g^3}-\frac{\left (3 b^2 B d^2\right ) \int \frac{(b c-a d) e \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^5 e g^3}+\frac{\left (3 b^2 B d^2\right ) \int \frac{(b c-a d) e \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^5 e g^3}\\ &=-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (b^3 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{1191016 (b c-a d)^4 g^3}-\frac{\left (3 b^3 B d\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{595508 (b c-a d)^4 g^3}-\frac{\left (3 b^2 B d^2\right ) \int \frac{\log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}+\frac{\left (3 b^2 B d^2\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}+\frac{\left (b B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{1191016 (b c-a d)^4 g^3}+\frac{\left (3 b B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^2} \, dx}{595508 (b c-a d)^4 g^3}+\frac{\left (b^3 B\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{1191016 (b c-a d)^3 g^3}+\frac{\left (B d^3\right ) \int \frac{A+B \log \left (\frac{e (a+b x)}{c+d x}\right )}{(c+d x)^3} \, dx}{1191016 (b c-a d)^3 g^3}\\ &=-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (b^2 B^2 d\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{1191016 (b c-a d)^4 g^3}-\frac{\left (3 b^2 B^2 d\right ) \int \frac{b c-a d}{(a+b x)^2 (c+d x)} \, dx}{595508 (b c-a d)^4 g^3}-\frac{\left (3 b^2 B d^2\right ) \int \left (\frac{A \log (a+b x)}{(a+b x) (c+d x)}+\frac{B \log (a+b x) \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)}\right ) \, dx}{297754 (b c-a d)^4 g^3}+\frac{\left (3 b^2 B d^2\right ) \int \left (\frac{b \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(b c-a d) (a+b x)}-\frac{d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{(b c-a d) (c+d x)}\right ) \, dx}{297754 (b c-a d)^4 g^3}+\frac{\left (b B^2 d^2\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{1191016 (b c-a d)^4 g^3}+\frac{\left (3 b B^2 d^2\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^2} \, dx}{595508 (b c-a d)^4 g^3}+\frac{\left (b^2 B^2\right ) \int \frac{b c-a d}{(a+b x)^3 (c+d x)} \, dx}{2382032 (b c-a d)^3 g^3}+\frac{\left (B^2 d^2\right ) \int \frac{b c-a d}{(a+b x) (c+d x)^3} \, dx}{2382032 (b c-a d)^3 g^3}\\ &=-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B d^2\right ) \int \frac{\left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 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)}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^2\right ) \int \frac{\log (a+b x)}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \int \frac{\log (a+b x) \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}-\frac{\left (b^2 B^2 d\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{1191016 (b c-a d)^3 g^3}-\frac{\left (3 b^2 B^2 d\right ) \int \frac{1}{(a+b x)^2 (c+d x)} \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b B^2 d^2\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{1191016 (b c-a d)^3 g^3}+\frac{\left (3 b B^2 d^2\right ) \int \frac{1}{(a+b x) (c+d x)^2} \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b^2 B^2\right ) \int \frac{1}{(a+b x)^3 (c+d x)} \, dx}{2382032 (b c-a d)^2 g^3}+\frac{\left (B^2 d^2\right ) \int \frac{1}{(a+b x) (c+d x)^3} \, dx}{2382032 (b c-a d)^2 g^3}\\ &=-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B d^2\right ) \int \left (\frac{A \log (c+d x)}{a+b x}+\frac{B \log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x}\right ) \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B^2 d^2\right ) \int \frac{\log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B d^3\right ) \int \left (\frac{A \log (c+d x)}{c+d x}+\frac{B \log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x}\right ) \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b B d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x \left (\frac{b c-a d}{b}+\frac{d x}{b}\right )} \, dx,x,a+b x\right )}{297754 (b c-a d)^4 g^3}-\frac{\left (b^2 B^2 d\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{1191016 (b c-a d)^3 g^3}-\frac{\left (3 b^2 B^2 d\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^2}-\frac{b d}{(b c-a d)^2 (a+b x)}+\frac{d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b B^2 d^2\right ) \int \left (\frac{b^2}{(b c-a d)^2 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^2}-\frac{b d}{(b c-a d)^2 (c+d x)}\right ) \, dx}{1191016 (b c-a d)^3 g^3}+\frac{\left (3 b B^2 d^2\right ) \int \left (\frac{b^2}{(b c-a d)^2 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^2}-\frac{b d}{(b c-a d)^2 (c+d x)}\right ) \, dx}{595508 (b c-a d)^3 g^3}+\frac{\left (b^2 B^2\right ) \int \left (\frac{b}{(b c-a d) (a+b x)^3}-\frac{b d}{(b c-a d)^2 (a+b x)^2}+\frac{b d^2}{(b c-a d)^3 (a+b x)}-\frac{d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2382032 (b c-a d)^2 g^3}+\frac{\left (B^2 d^2\right ) \int \left (\frac{b^3}{(b c-a d)^3 (a+b x)}-\frac{d}{(b c-a d) (c+d x)^3}-\frac{b d}{(b c-a d)^2 (c+d x)^2}-\frac{b^2 d}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2382032 (b c-a d)^2 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 A b^3 B d^2\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B^2 d^2\right ) \int \frac{\log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 A b B d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{\frac{b c-a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^3\right ) \int \frac{\log (c+d x)}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{e (a+b x)}{c+d x}\right ) \log (c+d x)}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \int \frac{\log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log \left (\frac{e (a+b x)}{c+d x}\right )}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B^2 d^2\right ) \int \frac{\log ^2(c+d x)}{a+b x} \, dx}{595508 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B^2 d^2\right ) \int \frac{\log (a+b x) \log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^3 B^2 d^2\right ) \int \frac{\log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^3\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^3\right ) \int \frac{\log ^2(c+d x)}{c+d x} \, dx}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \int \frac{\text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{(a+b x) (c+d x)} \, dx}{297754 (b c-a d)^4 g^3}+\frac{\left (3 b^3 B^2 d^2 \left (-\log (a+b x)-\log \left (\frac{1}{c+d x}\right )+\log \left (\frac{e (a+b x)}{c+d x}\right )\right )\right ) \int \frac{\log (c+d x)}{a+b x} \, dx}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 A b^2 B d^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{x} \, dx,x,c+d x\right )}{595508 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{b c-a d}{b}+\frac{d x}{b}\right )}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (\frac{1}{-\frac{-b c+a d}{b}+\frac{d x}{b}}\right ) \log \left (-\frac{-b c+a d}{b}+\frac{d x}{b}\right )}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^3\right ) \int \frac{\log \left (\frac{d (a+b x)}{-b c+a d}\right ) \log (c+d x)}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}-\frac{\left (3 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 \left (\frac{d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int x^2 \, dx,x,\log (c+d x)\right )}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{d \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{\frac{b c-a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b B^2 d^3\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{1}{-\frac{-b c+a d}{b}+\frac{d x}{b}}\right )}{-\frac{-b c+a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 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 )}{-\frac{-b c+a d}{b}+\frac{d x}{b}} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2 \left (-\log (a+b x)-\log \left (\frac{1}{c+d x}\right )+\log \left (\frac{e (a+b x)}{c+d x}\right )\right )\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{b^2 B^2 d^2 \log ^3(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (\frac{1}{x}\right ) \log \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (\frac{-b c+a d}{d}+\frac{b x}{d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (1+\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{b^2 B^2 d^2 \log ^3(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^3 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log ^2\left (\frac{1}{x}\right )}{\frac{-b c+a d}{d}+\frac{b x}{d}} \, dx,x,c+d x\right )}{595508 (b c-a d)^5 g^3}-\frac{\left (3 b^3 B^2 d\right ) \operatorname{Subst}\left (\int \frac{\log ^2(x)}{\frac{-b c+a d}{d}+\frac{b x}{d}} \, dx,x,c+d x\right )}{595508 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{b^2 B^2 d^2 \log ^3(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (c+d x) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}-\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (\frac{1}{x}\right ) \log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}+\frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\log (x) \log \left (1+\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{b^2 B^2 d^2 \log ^3(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{1}{c+d x}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+2 \frac{\left (3 b^2 B^2 d^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{297754 (b c-a d)^5 g^3}\\ &=-\frac{b^2 B^2}{4764064 (b c-a d)^3 g^3 (a+b x)^2}+\frac{15 b^2 B^2 d}{2382032 (b c-a d)^4 g^3 (a+b x)}+\frac{B^2 d^2}{4764064 (b c-a d)^3 g^3 (c+d x)^2}+\frac{15 b B^2 d^2}{2382032 (b c-a d)^4 g^3 (c+d x)}+\frac{15 b^2 B^2 d^2 \log (a+b x)}{1191016 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(a+b x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac{1}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{b c-a d}{d (a+b x)}\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )}{595508 (b c-a d)^5 g^3}-\frac{b^2 B \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{7 b^2 B d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (a+b x)}-\frac{B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{2382032 (b c-a d)^3 g^3 (c+d x)^2}-\frac{7 b B d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )}{1191016 (b c-a d)^4 g^3 (c+d x)}-\frac{b^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (a+b x)^2}+\frac{3 b^2 d \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (a+b x)}+\frac{d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{2382032 (b c-a d)^3 g^3 (c+d x)^2}+\frac{3 b d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{1191016 (b c-a d)^4 g^3 (c+d x)}+\frac{3 b^2 d^2 \log (a+b x) \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2}{595508 (b c-a d)^5 g^3}-\frac{15 b^2 B^2 d^2 \log (c+d x)}{1191016 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log (c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log \left (\frac{1}{c+d x}\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (-\frac{d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 d^2 \left (A+B \log \left (\frac{e (a+b x)}{c+d x}\right )\right )^2 \log (c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 A b^2 B d^2 \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log (a+b x) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \log ^2(c+d x)}{595508 (b c-a d)^5 g^3}-\frac{b^2 B^2 d^2 \log ^3(c+d x)}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \log (a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log ^2(a+b x) \log \left (\frac{b (c+d x)}{b c-a d}\right )}{595508 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \log (a+b x) \text{Li}_2\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 A b^2 B d^2 \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{1}{c+d x}\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}-\frac{3 b^2 B^2 d^2 \left (\log (a+b x)+\log \left (\frac{1}{c+d x}\right )-\log \left (\frac{e (a+b x)}{c+d x}\right )\right ) \text{Li}_2\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \log \left (\frac{e (a+b x)}{c+d x}\right ) \text{Li}_2\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (-\frac{d (a+b x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (\frac{b (c+d x)}{b c-a d}\right )}{297754 (b c-a d)^5 g^3}+\frac{3 b^2 B^2 d^2 \text{Li}_3\left (1+\frac{b c-a d}{d (a+b x)}\right )}{297754 (b c-a d)^5 g^3}\\ \end{align*}
Mathematica [A] time = 1.96067, size = 611, normalized size = 0.89 \[ \frac{-2 B \left (-6 a^2 b^2 d^2 \left (2 A (c+d x)^2-B d x (4 c+3 d x)\right )+4 a^3 b B d^3 (2 c+d x)-a^4 B d^4-4 a b^3 d \left (6 A d x (c+d x)^2+B \left (6 c^2 d x+2 c^3-3 d^3 x^3\right )\right )+b^4 \left (B c \left (-4 c^2 d x+c^3-18 c d^2 x^2-12 d^3 x^3\right )-12 A d^2 x^2 (c+d x)^2\right )\right ) \log ^2\left (\frac{e (a+b x)}{c+d x}\right )+12 b^2 d^2 \left (2 A^2+5 B^2\right ) (a+b x)^2 (c+d x)^2 \log (a+b x)-12 b^2 d^2 \left (2 A^2+5 B^2\right ) (a+b x)^2 (c+d x)^2 \log (c+d x)-b^2 \left (2 A^2+2 A B+B^2\right ) (c+d x)^2 (b c-a d)^2+2 b^2 d \left (6 A^2+14 A B+15 B^2\right ) (a+b x) (c+d x)^2 (b c-a d)+d^2 \left (2 A^2-2 A B+B^2\right ) (a+b x)^2 (b c-a d)^2+2 b d^2 \left (6 A^2-14 A B+15 B^2\right ) (a+b x)^2 (c+d x) (b c-a d)+2 B (b c-a d) \left (2 b^2 d (6 A+7 B) (a+b x) (c+d x)^2-b^2 (2 A+B) (c+d x)^2 (b c-a d)+d^2 (2 A-B) (a+b x)^2 (b c-a d)+2 b d^2 (6 A-7 B) (a+b x)^2 (c+d x)\right ) \log \left (\frac{e (a+b x)}{c+d x}\right )+8 b^2 B^2 d^2 (a+b x)^2 (c+d x)^2 \log ^3\left (\frac{e (a+b x)}{c+d x}\right )}{4 g^3 i^3 (a+b x)^2 (c+d x)^2 (b c-a d)^5} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.058, size = 4782, normalized size = 7. \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 3.48238, size = 7537, normalized size = 11. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.698954, size = 3056, normalized size = 4.46 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 142.653, size = 3720, normalized size = 5.43 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (B \log \left (\frac{{\left (b x + a\right )} e}{d x + c}\right ) + A\right )}^{2}}{{\left (b g x + a g\right )}^{3}{\left (d i x + c i\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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