Optimal. Leaf size=768 \[ \frac {b^3 g^3 (c+d x)^3 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{3 d^4 i}-\frac {3 b^2 g^3 (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 d^4 i}-\frac {b^2 B g^3 n (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 d^4 i}+\frac {2 B g^3 n (b c-a d)^3 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{d^4 i}+\frac {g^3 (b c-a d)^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{d^4 i}+\frac {6 B g^3 n (b c-a d)^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{d^4 i}-\frac {7 B g^3 n (b c-a d)^3 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 d^4 i}+\frac {3 g^3 (a+b x) (b c-a d)^2 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{d^3 i}+\frac {7 B g^3 n (a+b x) (b c-a d)^2 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 d^3 i}+\frac {6 B^2 g^3 n^2 (b c-a d)^3 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {7 B^2 g^3 n^2 (b c-a d)^3 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{3 d^4 i}-\frac {2 B^2 g^3 n^2 (b c-a d)^3 \text {Li}_3\left (\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {B^2 g^3 n^2 (b c-a d)^3 \log \left (\frac {a+b x}{c+d x}\right )}{3 d^4 i}-\frac {2 B^2 g^3 n^2 (b c-a d)^3 \log (c+d x)}{d^4 i}+\frac {b B^2 g^3 n^2 x (b c-a d)^2}{3 d^3 i} \]
[Out]
________________________________________________________________________________________
Rubi [B] time = 5.59, antiderivative size = 1952, normalized size of antiderivative = 2.54, number of steps used = 101, number of rules used = 28, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.622, Rules used = {2528, 2523, 12, 2524, 2418, 2390, 2301, 2394, 2393, 2391, 2525, 2486, 31, 43, 6688, 6742, 2499, 2396, 2433, 2374, 6589, 2302, 30, 2500, 2375, 2317, 2440, 2434} \[ \text {result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rule 31
Rule 43
Rule 2301
Rule 2302
Rule 2317
Rule 2374
Rule 2375
Rule 2390
Rule 2391
Rule 2393
Rule 2394
Rule 2396
Rule 2418
Rule 2433
Rule 2434
Rule 2440
Rule 2486
Rule 2499
Rule 2500
Rule 2523
Rule 2524
Rule 2525
Rule 2528
Rule 6589
Rule 6688
Rule 6742
Rubi steps
\begin {align*} \int \frac {(a g+b g x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 c+186 d x} \, dx &=\int \left (\frac {b (b c-a d)^2 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}+\frac {(-b c+a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{d^3 (186 c+186 d x)}-\frac {b (b c-a d) g^2 (a g+b g x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^2}+\frac {b g (a g+b g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d}\right ) \, dx\\ &=\frac {(b g) \int (a g+b g x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{186 d}-\frac {\left (b (b c-a d) g^2\right ) \int (a g+b g x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{186 d^2}+\frac {\left (b (b c-a d)^2 g^3\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{186 d^3}-\frac {\left ((b c-a d)^3 g^3\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 c+186 d x} \, dx}{d^3}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {(B n) \int \frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{c+d x} \, dx}{279 d}+\frac {(B (b c-a d) g n) \int \frac {(b c-a d) g^2 (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{c+d x} \, dx}{186 d^2}-\frac {\left (b B (b c-a d)^2 g^3 n\right ) \int \frac {(b c-a d) 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}{93 d^3}+\frac {\left (B (b c-a d)^3 g^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 (186 c+186 d x)}{a+b x} \, dx}{93 d^4}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {\left (B (b c-a d) g^3 n\right ) \int \frac {(a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{c+d x} \, dx}{279 d}+\frac {\left (B (b c-a d)^2 g^3 n\right ) \int \frac {(a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{c+d x} \, dx}{186 d^2}+\frac {\left (B (b c-a d)^3 g^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 (186 c+186 d x)}{(a+b x) (c+d x)} \, dx}{93 d^4}-\frac {\left (b B (b c-a d)^3 g^3 n\right ) \int \frac {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}{93 d^3}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {\left (B (b c-a d) g^3 n\right ) \int \left (-\frac {b (b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{d^2}+\frac {b (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{d}+\frac {(-b c+a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{d^2 (c+d x)}\right ) \, dx}{279 d}+\frac {\left (B (b c-a d)^2 g^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 )}{d}+\frac {(-b c+a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{d (c+d x)}\right ) \, dx}{186 d^2}-\frac {\left (b B (b c-a d)^3 g^3 n\right ) \int \left (-\frac {a \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)}+\frac {c \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{(b c-a d) (c+d x)}\right ) \, dx}{93 d^3}+\frac {\left (B (b c-a d)^4 g^3 n\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (186 c+186 d x)}{(a+b x) (c+d x)} \, dx}{93 d^4}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {\left (b B (b c-a d) g^3 n\right ) \int (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{279 d^2}+\frac {\left (b B (b c-a d)^2 g^3 n\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{279 d^3}+\frac {\left (b B (b c-a d)^2 g^3 n\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{186 d^3}+\frac {\left (a b B (b c-a d)^2 g^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}{93 d^3}-\frac {\left (b B c (b c-a d)^2 g^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{93 d^3}-\frac {\left (B (b c-a d)^3 g^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{279 d^3}-\frac {\left (B (b c-a d)^3 g^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{186 d^3}+\frac {\left (B (b c-a d)^4 g^3 n\right ) \int \left (\frac {d \left (-A-B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (186 c+186 d x)}{(b c-a d) (c+d x)}+\frac {b \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (186 c+186 d x)}{(b c-a d) (a+b x)}\right ) \, dx}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}+\frac {\left (b B^2 (b c-a d)^2 g^3 n\right ) \int \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \, dx}{279 d^3}+\frac {\left (b B^2 (b c-a d)^2 g^3 n\right ) \int \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \, dx}{186 d^3}+\frac {\left (b B (b c-a d)^3 g^3 n\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (186 c+186 d x)}{a+b x} \, dx}{93 d^4}+\frac {\left (B (b c-a d)^3 g^3 n\right ) \int \frac {\left (-A-B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (186 c+186 d x)}{c+d x} \, dx}{93 d^3}+\frac {\left (B^2 (b c-a d) g^3 n^2\right ) \int \frac {(b c-a d) (a+b x)}{c+d x} \, dx}{558 d^2}+\frac {\left (b B^2 c (b c-a d)^2 g^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}{93 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^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}{93 d^3}+\frac {\left (B^2 (b c-a d)^3 g^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}{279 d^4}+\frac {\left (B^2 (b c-a d)^3 g^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}{186 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}+\frac {\left (b B (b c-a d)^3 g^3 n\right ) \int \left (\frac {A \log (186 c+186 d x)}{a+b x}+\frac {B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (186 c+186 d x)}{a+b x}\right ) \, dx}{93 d^4}+\frac {\left (B (b c-a d)^3 g^3 n\right ) \int \left (\frac {A \log (186 c+186 d x)}{-c-d x}+\frac {B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (186 c+186 d x)}{-c-d x}\right ) \, dx}{93 d^3}+\frac {\left (b B^2 c (b c-a d)^2 g^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}{93 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^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}{93 d^3}+\frac {\left (B^2 (b c-a d)^2 g^3 n^2\right ) \int \frac {a+b x}{c+d x} \, dx}{558 d^2}+\frac {\left (B^2 (b c-a d)^3 g^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}{279 d^4}+\frac {\left (B^2 (b c-a d)^3 g^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}{186 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {1}{c+d x} \, dx}{279 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {1}{c+d x} \, dx}{186 d^3}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}+\frac {\left (A b B (b c-a d)^3 g^3 n\right ) \int \frac {\log (186 c+186 d x)}{a+b x} \, dx}{93 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3 n\right ) \int \frac {\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (186 c+186 d x)}{a+b x} \, dx}{93 d^4}+\frac {\left (A B (b c-a d)^3 g^3 n\right ) \int \frac {\log (186 c+186 d x)}{-c-d x} \, dx}{93 d^3}+\frac {\left (B^2 (b c-a d)^3 g^3 n\right ) \int \frac {\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (186 c+186 d x)}{-c-d x} \, dx}{93 d^3}+\frac {\left (b^2 B^2 c (b c-a d)^2 g^3 n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{93 d^4}-\frac {\left (a b B^2 (b c-a d)^2 g^3 n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{93 d^3}-\frac {\left (b B^2 c (b c-a d)^2 g^3 n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{93 d^3}+\frac {\left (B^2 (b c-a d)^2 g^3 n^2\right ) \int \left (\frac {b}{d}+\frac {-b c+a d}{d (c+d x)}\right ) \, dx}{558 d^2}+\frac {\left (a B^2 (b c-a d)^2 g^3 n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{93 d^2}+\frac {\left (b B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{279 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{186 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{279 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{186 d^3}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {\left (A B (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int -\frac {186 \log (x)}{x} \, dx,x,186 c+186 d x\right )}{17298 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3 n\right ) \int \frac {\log \left ((a+b x)^n\right ) \log (186 c+186 d x)}{a+b x} \, dx}{93 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3 n\right ) \int \frac {\log \left ((c+d x)^{-n}\right ) \log (186 c+186 d x)}{a+b x} \, dx}{93 d^4}-\frac {\left (2 A B (b c-a d)^3 g^3 n\right ) \int \frac {\log \left (\frac {186 d (a+b x)}{-186 b c+186 a d}\right )}{186 c+186 d x} \, dx}{d^3}-\frac {\left (b B^2 c (b c-a d)^2 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{93 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{93 d^3}-\frac {\left (a b B^2 (b c-a d)^2 g^3 n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{93 d^3}-\frac {\left (b B^2 c (b c-a d)^2 g^3 n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{93 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{279 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{186 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log ^2(186 c+186 d x)}{a+b x} \, dx}{186 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{279 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{186 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log ^2(186 c+186 d x)}{c+d x} \, dx}{186 d^3}+\frac {\left (b B^2 (b c-a d)^3 g^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 (186 c+186 d x)}{a+b x} \, dx}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {\left (A B (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,186 c+186 d x\right )}{93 d^4}-\frac {\left (A B (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-186 b c+186 a d}\right )}{x} \, dx,x,186 c+186 d x\right )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^n\right ) \log \left (\frac {186 b c-186 a d}{b}+\frac {186 d x}{b}\right )}{x} \, dx,x,a+b x\right )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (\left (-\frac {-b c+a d}{b}+\frac {d x}{b}\right )^{-n}\right ) \log \left (-\frac {-186 b c+186 a d}{b}+\frac {186 d x}{b}\right )}{x} \, dx,x,a+b x\right )}{93 d^4}-\frac {\left (b B^2 c (b c-a d)^2 g^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 )}{93 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^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 )}{93 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {186 \log ^2(x)}{x} \, dx,x,186 c+186 d x\right )}{34596 d^4}-\frac {\left (B^2 (b c-a d)^3 g^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 )}{279 d^4}-\frac {\left (B^2 (b c-a d)^3 g^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 )}{186 d^4}-\frac {\left (2 B^2 (b c-a d)^3 g^3 n^2\right ) \int \frac {\log \left (\frac {186 d (a+b x)}{-186 b c+186 a d}\right ) \log (186 c+186 d x)}{186 c+186 d x} \, dx}{d^3}-\frac {\left (2 B^2 (b c-a d)^3 g^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 \left (\frac {186 d (a+b x)}{-186 b c+186 a d}\right )}{186 c+186 d x} \, dx}{d^3}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \operatorname {Subst}\left (\int \frac {\log ^2\left (x^n\right )}{\frac {186 b c-186 a d}{b}+\frac {186 d x}{b}} \, dx,x,a+b x\right )}{b d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 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 )}{93 b d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,186 c+186 d x\right )}{186 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {186 d \left (\frac {-186 b c+186 a d}{186 d}+\frac {b x}{186 d}\right )}{-186 b c+186 a d}\right )}{x} \, dx,x,186 c+186 d x\right )}{93 d^4}+\frac {\left (2 B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (-\frac {-186 b c+186 a d}{b}+\frac {186 d x}{b}\right )}{-\frac {-186 b c+186 a d}{b}+\frac {186 d x}{b}} \, dx,x,a+b x\right )}{b d^3}-\frac {\left (B^2 (b c-a d)^3 g^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}{-186 b c+186 a d}\right )}{x} \, dx,x,186 c+186 d x\right )}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (186 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^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 )}{93 d^4}-\frac {\left (B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^n\right ) \log \left (1+\frac {186 d x}{186 b c-186 a d}\right )}{x} \, dx,x,a+b x\right )}{93 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,\log (186 (c+d x))\right )}{186 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-186 b c+186 a d}{186 d}+\frac {b x}{186 d}\right )}{x} \, dx,x,186 (c+d x)\right )}{93 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-186 b c+186 a d}\right )}{x} \, dx,x,186 c+186 d x\right )}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (a+b x) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log ^3(186 (c+d x))}{558 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (186 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^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 )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {\left (b B^2 (b c-a d)^3 g^3\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 )}{186 d^5}-\frac {\left (b B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{\frac {-186 b c+186 a d}{186 d}+\frac {b x}{186 d}} \, dx,x,186 (c+d x)\right )}{34596 d^5}+\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {186 d x}{186 b c-186 a d}\right )}{x} \, dx,x,a+b x\right )}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (a+b x) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log ^3(186 (c+d x))}{558 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (186 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {\left (B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (1+\frac {b x}{-186 b c+186 a d}\right )}{x} \, dx,x,186 (c+d x)\right )}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (a+b x) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log ^3(186 (c+d x))}{558 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-186 b c+186 a d}\right )}{x} \, dx,x,186 (c+d x)\right )}{93 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 n x}{558 d^3}+\frac {b B^2 (b c-a d)^2 g^3 n^2 x}{558 d^3}-\frac {a B^2 (b c-a d)^2 g^3 n^2 \log ^2(a+b x)}{186 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{558 d^3}-\frac {B (b c-a d) g^3 n (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{558 d^2}+\frac {a B (b c-a d)^2 g^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{93 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{186 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{372 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{558 d}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log (c+d x)}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{558 d^4}-\frac {b B c (b c-a d)^2 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{93 d^4}-\frac {5 B (b c-a d)^3 g^3 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{558 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 n^2 \log ^2(c+d x)}{186 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 n^2 \log ^2(c+d x)}{1116 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log (186 (c+d x))}{186 d^4}-\frac {A B (b c-a d)^3 g^3 n \log ^2(186 (c+d x))}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log (a+b x) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 (c+d x))}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n^2 \log ^3(186 (c+d x))}{558 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{186 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log (a+b x) \log (186 (c+d x)) \log \left ((c+d x)^{-n}\right )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{186 d^4}+\frac {A B (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (186 c+186 d x)}{93 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \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 ) \log (186 c+186 d x)}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(186 c+186 d x)}{186 d^4}-\frac {B^2 (b c-a d)^3 g^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(186 c+186 d x)}{186 d^4}+\frac {a B^2 (b c-a d)^2 g^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^3}-\frac {B^2 (b c-a d)^3 g^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}+\frac {A B (b c-a d)^3 g^3 n \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{558 d^4}+\frac {B^2 (b c-a d)^3 g^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}-\frac {B^2 (b c-a d)^3 g^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 )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{93 d^4}+\frac {B^2 (b c-a d)^3 g^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{93 d^4}\\ \end {align*}
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Mathematica [B] time = 4.33, size = 3265, normalized size = 4.25 \[ \text {Result too large to show} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.93, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left (B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right )} \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right )^{2} + 2 \, {\left (A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right )} \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right )}{d i x + c i}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.47, size = 0, normalized size = 0.00 \[ \int \frac {\left (b g x +a g \right )^{3} \left (B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )+A \right )^{2}}{d i x +c i}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {{\left (a\,g+b\,g\,x\right )}^3\,{\left (A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )\right )}^2}{c\,i+d\,i\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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