Optimal. Leaf size=762 \[ \frac {2 B i^3 n (b c-a d)^3 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{b^4 g}+\frac {d i^3 (a+b x) (b c-a d)^2 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{b^4 g}-\frac {5 B d i^3 n (a+b x) (b c-a d)^2 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 b^4 g}+\frac {2 B i^3 n (b c-a d)^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{b^4 g}-\frac {i^3 (b c-a d)^3 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{b^4 g}+\frac {5 B i^3 n (b c-a d)^3 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 b^4 g}+\frac {i^3 (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{2 b^2 g}-\frac {B i^3 n (c+d x)^2 (b c-a d) \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )}{3 b^2 g}+\frac {i^3 (c+d x)^3 \left (B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+A\right )^2}{3 b g}+\frac {2 B^2 i^3 n^2 (b c-a d)^3 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{b^4 g}-\frac {5 B^2 i^3 n^2 (b c-a d)^3 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{3 b^4 g}+\frac {2 B^2 i^3 n^2 (b c-a d)^3 \text {Li}_3\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^4 g}+\frac {B^2 i^3 n^2 (b c-a d)^3 \log \left (\frac {a+b x}{c+d x}\right )}{3 b^4 g}+\frac {2 B^2 i^3 n^2 (b c-a d)^3 \log (c+d x)}{b^4 g}+\frac {B^2 d i^3 n^2 x (b c-a d)^2}{3 b^3 g} \]
[Out]
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Rubi [B] time = 5.62, antiderivative size = 1995, normalized size of antiderivative = 2.62, 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, 6688, 6742, 2500, 2440, 2434, 2433, 2375, 2317, 2374, 6589, 2499, 2302, 30, 2396, 2525, 2486, 31, 43} \[ \text {result too large to display} \]
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 {(182 c+182 d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{a g+b g x} \, dx &=\int \left (\frac {6028568 d (b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {33124 d (b c-a d) (182 c+182 d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {182 d (182 c+182 d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 (a g+b g x)}\right ) \, dx\\ &=\frac {\left (6028568 (b c-a d)^3\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{a g+b g x} \, dx}{b^3}+\frac {(182 d) \int (182 c+182 d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{b g}+\frac {(33124 d (b c-a d)) \int (182 c+182 d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{b^2 g}+\frac {\left (6028568 d (b c-a d)^2\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \, dx}{b^3 g}\\ &=\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {(2 B n) \int \frac {6028568 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{3 b g}-\frac {(182 B (b c-a d) n) \int \frac {33124 (b c-a d) (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (12057136 B d (b c-a d)^2 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}{b^3 g}-\frac {\left (12057136 B (b c-a d)^3 n\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^4 g}\\ &=\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {(12057136 B (b c-a d) n) \int \frac {(c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{3 b g}-\frac {\left (6028568 B (b c-a d)^2 n\right ) \int \frac {(c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (12057136 B (b c-a d)^3 n\right ) \int \frac {(b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^4 g}-\frac {\left (12057136 B d (b c-a d)^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}{b^3 g}\\ &=\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {(12057136 B (b c-a d) n) \int \left (\frac {d (b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^2}+\frac {(b c-a d)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^2 (a+b x)}+\frac {d (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b}\right ) \, dx}{3 b g}-\frac {\left (6028568 B (b c-a d)^2 n\right ) \int \left (\frac {d \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b}+\frac {(b c-a d) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b (a+b x)}\right ) \, dx}{b^2 g}-\frac {\left (12057136 B d (b c-a d)^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}{b^3 g}-\frac {\left (12057136 B (b c-a d)^4 n\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^4 g}\\ &=\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {(12057136 B d (b c-a d) n) \int (c+d x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{3 b^2 g}-\frac {\left (12057136 B d (b c-a d)^2 n\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{3 b^3 g}-\frac {\left (6028568 B d (b c-a d)^2 n\right ) \int \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \, dx}{b^3 g}+\frac {\left (12057136 a B d (b c-a d)^2 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B c d (b c-a d)^2 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{c+d x} \, dx}{b^3 g}-\frac {\left (12057136 B (b c-a d)^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{3 b^3 g}-\frac {\left (6028568 B (b c-a d)^3 n\right ) \int \frac {A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B (b c-a d)^4 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 (a g+b g 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 (a g+b g x)}{(b c-a d) (a+b x)}\right ) \, dx}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {\left (12057136 B^2 d (b c-a d)^2 n\right ) \int \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \, dx}{3 b^3 g}-\frac {\left (6028568 B^2 d (b c-a d)^2 n\right ) \int \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \, dx}{b^3 g}-\frac {\left (12057136 B (b c-a d)^3 n\right ) \int \frac {\left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B d (b c-a d)^3 n\right ) \int \frac {\left (-A-B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (a g+b g x)}{c+d x} \, dx}{b^4 g}+\frac {\left (6028568 B^2 (b c-a d) n^2\right ) \int \frac {(b c-a d) (c+d x)}{a+b x} \, dx}{3 b^2 g}+\frac {\left (12057136 B^2 c (b c-a d)^2 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}{b^3 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 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}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{3 b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \int \frac {(c+d x) \left (-\frac {d (a+b x)}{(c+d x)^2}+\frac {b}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {\left (12057136 B (b c-a d)^3 n\right ) \int \left (\frac {A \log (a g+b g x)}{a+b x}+\frac {B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (a g+b g x)}{a+b x}\right ) \, dx}{b^3 g}-\frac {\left (12057136 B d (b c-a d)^3 n\right ) \int \left (\frac {A \log (a g+b g x)}{-c-d x}+\frac {B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (a g+b g x)}{-c-d x}\right ) \, dx}{b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^2 n^2\right ) \int \frac {c+d x}{a+b x} \, dx}{3 b^2 g}+\frac {\left (12057136 B^2 c (b c-a d)^2 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}{b^3 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 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}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{3 b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \int \left (\frac {b \log (a+b x)}{a+b x}-\frac {d \log (a+b x)}{c+d x}\right ) \, dx}{b^4 g}+\frac {\left (12057136 B^2 d (b c-a d)^3 n^2\right ) \int \frac {1}{c+d x} \, dx}{3 b^4 g}+\frac {\left (6028568 B^2 d (b c-a d)^3 n^2\right ) \int \frac {1}{c+d x} \, dx}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}-\frac {\left (12057136 A B (b c-a d)^3 n\right ) \int \frac {\log (a g+b g x)}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \int \frac {\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (a g+b g x)}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 A B d (b c-a d)^3 n\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^4 g}-\frac {\left (12057136 B^2 d (b c-a d)^3 n\right ) \int \frac {\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^2 n^2\right ) \int \left (\frac {d}{b}+\frac {b c-a d}{b (a+b x)}\right ) \, dx}{3 b^2 g}+\frac {\left (12057136 B^2 c (b c-a d)^2 n^2\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^2 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B^2 c d (b c-a d)^2 n^2\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^3 g}+\frac {\left (12057136 a B^2 d^2 (b c-a d)^2 n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{3 b^3 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B^2 d (b c-a d)^3 n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{3 b^4 g}-\frac {\left (6028568 B^2 d (b c-a d)^3 n^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {\left (12057136 A B (b c-a d)^3 n\right ) \int \frac {\log \left (\frac {b g (-c-d x)}{-b c g+a d g}\right )}{a g+b g x} \, dx}{b^3}-\frac {\left (12057136 A B (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {g \log (x)}{x} \, dx,x,a g+b g x\right )}{b^4 g^2}-\frac {\left (12057136 B^2 d (b c-a d)^3 n\right ) \int \frac {\log \left ((a+b x)^n\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^4 g}-\frac {\left (12057136 B^2 d (b c-a d)^3 n\right ) \int \frac {\log \left ((c+d x)^{-n}\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^4 g}-\frac {\left (12057136 B^2 c (b c-a d)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^3 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 g}-\frac {\left (12057136 B^2 c d (b c-a d)^2 n^2\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^3 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{3 b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 b^3 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^3 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log ^2(a g+b g x)}{a+b x} \, dx}{b^3 g}-\frac {\left (6028568 B^2 d (b c-a d)^3 n^2\right ) \int \frac {\log ^2(a g+b g x)}{c+d x} \, dx}{b^4 g}-\frac {\left (12057136 B^2 d (b c-a d)^3 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\right )\right )\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {\left (12057136 A B (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a g+b g x\right )}{b^4 g}-\frac {\left (12057136 A B (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (\left (\frac {-b c+a d}{d}-\frac {b x}{d}\right )^n\right ) \log \left (\frac {-b c g+a d g}{d}-\frac {b g x}{d}\right )}{x} \, dx,x,-c-d x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^{-n}\right ) \log \left (\frac {-b c g+a d g}{d}+\frac {b g x}{d}\right )}{x} \, dx,x,c+d x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \int \frac {\log \left (\frac {b g (c+d x)}{b c g-a d g}\right ) \log (a g+b g x)}{a g+b g x} \, dx}{b^3}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {g \log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^4 g^2}-\frac {\left (12057136 B^2 c (b c-a d)^2 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 )}{b^3 g}-\frac {\left (12057136 a B^2 d (b c-a d)^2 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 )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3 b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\right )\right )\right ) \int \frac {\log \left (\frac {b g (-c-d x)}{-b c g+a d g}\right )}{a g+b g x} \, dx}{b^3}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {\left (6028568 B^2 (b c-a d)^3\right ) \operatorname {Subst}\left (\int \frac {\log ^2\left (x^{-n}\right )}{\frac {-b c g+a d g}{d}+\frac {b g x}{d}} \, dx,x,c+d x\right )}{b^3 d}+\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\left (\frac {-b c+a d}{d}-\frac {b x}{d}\right )^n\right )}{\frac {-b c+a d}{d}-\frac {b x}{d}} \, dx,x,-c-d x\right )}{b^3 d g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c g+a d g}{d}-\frac {b g x}{d}\right )}{\frac {-b c g+a d g}{d}-\frac {b g x}{d}} \, dx,x,-c-d x\right )}{b^3 d}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {b g \left (\frac {b c g-a d g}{b g}+\frac {d x}{b g}\right )}{b c g-a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n \left (-\log \left ((a+b x)^n\right )+\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )-\log \left ((c+d x)^{-n}\right )\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^n\right ) \log \left (\frac {-b c+a d}{b}-\frac {d x}{b}\right )}{x} \, dx,x,a+b x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^{-n}\right ) \log \left (1+\frac {b g x}{-b c g+a d g}\right )}{x} \, dx,x,c+d x\right )}{b^4 g}+\frac {\left (6028568 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,\log (g (a+b x))\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c g+a d g}{b g}-\frac {d x}{b g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}+\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {d x}{b c g-a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^3(g (a+b x))}{3 b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {\left (6028568 B^2 d (b c-a d)^3\right ) \operatorname {Subst}\left (\int \frac {\log ^2\left (x^n\right )}{\frac {-b c+a d}{b}-\frac {d x}{b}} \, dx,x,a+b x\right )}{b^5 g}-\frac {\left (6028568 B^2 d (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{\frac {-b c g+a d g}{b g}-\frac {d x}{b g}} \, dx,x,a g+b g x\right )}{b^5 g^2}-\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b g x}{-b c g+a d g}\right )}{x} \, dx,x,c+d x\right )}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^3(g (a+b x))}{3 b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n\right ) \operatorname {Subst}\left (\int \frac {\log \left (x^n\right ) \log \left (1-\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^3(g (a+b x))}{3 b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^4 g}-\frac {\left (12057136 B^2 (b c-a d)^3 n^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^4 g}\\ &=-\frac {30142840 A B d (b c-a d)^2 n x}{3 b^3 g}+\frac {6028568 B^2 d (b c-a d)^2 n^2 x}{3 b^3 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log (a+b x)}{3 b^4 g}-\frac {6028568 a B^2 d (b c-a d)^2 n^2 \log ^2(a+b x)}{b^4 g}+\frac {15071420 B^2 (b c-a d)^3 n^2 \log ^2(a+b x)}{3 b^4 g}-\frac {6028568 A B (b c-a d)^3 n \log ^2(g (a+b x))}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^3(g (a+b x))}{3 b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log (g (a+b x)) \log \left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log (-c-d x)}{b^4 g}-\frac {30142840 B^2 d (b c-a d)^2 n (a+b x) \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )}{3 b^4 g}-\frac {6028568 B (b c-a d) n (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^2 g}+\frac {12057136 a B d (b c-a d)^2 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{b^4 g}-\frac {30142840 B (b c-a d)^3 n \log (a+b x) \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )}{3 b^4 g}+\frac {6028568 d (b c-a d)^2 x \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^3 g}+\frac {3014284 (b c-a d) (c+d x)^2 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{b^2 g}+\frac {6028568 (c+d x)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2}{3 b g}+\frac {30142840 B^2 (b c-a d)^3 n^2 \log (c+d x)}{3 b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^3 g}-\frac {12057136 B c (b c-a d)^2 n \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right ) \log (c+d x)}{b^3 g}-\frac {6028568 B^2 c (b c-a d)^2 n^2 \log ^2(c+d x)}{b^3 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{3 b^4 g}+\frac {6028568 B^2 (b c-a d)^3 n^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log ^2\left ((a+b x)^n\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}+\frac {6028568 B^2 (b c-a d)^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 \log (g (a+b x)) \log ^2\left ((c+d x)^{-n}\right )}{b^4 g}+\frac {6028568 (b c-a d)^3 \left (A+B \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )\right )^2 \log (a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left (\frac {b (c+d 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 (a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n \log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right ) \log ^2(a g+b g x)}{b^4 g}-\frac {6028568 B^2 (b c-a d)^3 n^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^4 g}+\frac {12057136 A B (b c-a d)^3 n \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 a B^2 d (b c-a d)^2 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {30142840 B^2 (b c-a d)^3 n^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{3 b^4 g}+\frac {12057136 B^2 (b c-a d)^3 n \log \left ((a+b x)^n\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n \left (\log \left ((a+b x)^n\right )-\log \left (e \left (\frac {a+b x}{c+d x}\right )^n\right )+\log \left ((c+d x)^{-n}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}+\frac {12057136 B^2 c (b c-a d)^2 n^2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {12057136 B^2 (b c-a d)^3 n \log \left ((c+d x)^{-n}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^4 g}-\frac {12057136 B^2 (b c-a d)^3 n^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^4 g}\\ \end {align*}
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Mathematica [B] time = 5.20, size = 2941, normalized size = 3.86 \[ \text {Result too large to show} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.74, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left (B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right )} \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right )^{2} + 2 \, {\left (A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right )} \log \left (e \left (\frac {b x + a}{d x + c}\right )^{n}\right )}{b g x + a g}, x\right ) \]
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 = 0.45, size = 0, normalized size = 0.00 \[ \int \frac {\left (d i x +c i \right )^{3} \left (B \ln \left (e \left (\frac {b x +a}{d x +c}\right )^{n}\right )+A \right )^{2}}{b g x +a g}\, dx \]
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 \[ \int \frac {{\left (c\,i+d\,i\,x\right )}^3\,{\left (A+B\,\ln \left (e\,{\left (\frac {a+b\,x}{c+d\,x}\right )}^n\right )\right )}^2}{a\,g+b\,g\,x} \,d x \]
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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