Optimal. Leaf size=535 \[ \frac {2 B i^2 (b c-a d)^2 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {d i^2 (a+b x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{b^3 g}-\frac {B d i^2 (a+b x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {2 B i^2 (b c-a d)^2 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}-\frac {i^2 (b c-a d)^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{b^3 g}+\frac {B i^2 (b c-a d)^2 \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{b^3 g}+\frac {i^2 (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{2 b g}+\frac {2 B^2 i^2 (b c-a d)^2 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{b^3 g}-\frac {B^2 i^2 (b c-a d)^2 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {2 B^2 i^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{d (a+b x)}\right )}{b^3 g}+\frac {B^2 i^2 (b c-a d)^2 \log (c+d x)}{b^3 g} \]
[Out]
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Rubi [B] time = 5.12, antiderivative size = 1676, normalized size of antiderivative = 3.13, number of steps used = 86, number of rules used = 27, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.643, 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} \[ \text {result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rule 31
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 {(68 c+68 d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{a g+b g x} \, dx &=\int \left (\frac {4624 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {68 d (68 c+68 d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 (a g+b g x)}\right ) \, dx\\ &=\frac {\left (4624 (b c-a d)^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{a g+b g x} \, dx}{b^2}+\frac {(68 d) \int (68 c+68 d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b g}+\frac {(4624 d (b c-a d)) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b^2 g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {B \int \frac {4624 (b c-a d) (c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{b g}-\frac {(9248 B d (b c-a d)) \int \frac {(b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{e (a+b x)} \, dx}{b^3 g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B (b c-a d)) \int \frac {(c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{a+b x} \, dx}{b g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \frac {x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x) (c+d x)} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^3 e g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B (b c-a d)) \int \left (\frac {d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b}+\frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b (a+b x)}\right ) \, dx}{b g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \left (-\frac {a \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)}+\frac {c \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (c+d x)}\right ) \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {(b c-a d) e \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^3 e g}\\ &=\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {(4624 B d (b c-a d)) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{b^2 g}+\frac {(9248 a B d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^2 g}-\frac {(9248 B c d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^2 g}-\frac {\left (4624 B (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B (b c-a d)^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(a+b x) (c+d x)} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{e (a+b x)} \, dx}{b^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{e (a+b x)} \, dx}{b^3 g}-\frac {\left (9248 B (b c-a d)^3\right ) \int \left (\frac {d \left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(b c-a d) (c+d x)}+\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{(b c-a d) (a+b x)}\right ) \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \frac {\left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (a g+b g x)}{c+d x} \, dx}{b^3 g}+\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {1}{c+d x} \, dx}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (c+d x)}{a+b x} \, dx}{b^2 e g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^3 e g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {(c+d x) \left (-\frac {d e (a+b x)}{(c+d x)^2}+\frac {b e}{c+d x}\right ) \log (a+b x)}{a+b x} \, dx}{b^3 e g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}-\frac {\left (9248 B (b c-a d)^2\right ) \int \left (\frac {A \log (a g+b g x)}{a+b x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{a+b x}\right ) \, dx}{b^2 g}-\frac {\left (9248 B d (b c-a d)^2\right ) \int \left (\frac {A \log (a g+b g x)}{-c-d x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{-c-d x}\right ) \, dx}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \left (\frac {b e \log (c+d x)}{a+b x}-\frac {d e \log (c+d x)}{c+d x}\right ) \, dx}{b^2 e g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \left (\frac {b e \log (a+b x)}{a+b x}-\frac {d e \log (a+b x)}{c+d x}\right ) \, dx}{b^3 e g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \left (\frac {b e \log (a+b x)}{a+b x}-\frac {d e \log (a+b x)}{c+d x}\right ) \, dx}{b^3 e g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 c (b c-a d)\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 c d (b c-a d)\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^2 g}+\frac {\left (9248 a B^2 d^2 (b c-a d)\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \int \frac {\log (a g+b g x)}{a+b x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 A B d (b c-a d)^2\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\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^2}-\frac {\left (9248 A B (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {g \log (x)}{x} \, dx,x,a g+b g x\right )}{b^3 g^2}-\frac {\left (9248 B^2 c (b c-a d)\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 a B^2 d (b c-a d)\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^2 g}-\frac {\left (9248 B^2 c d (b c-a d)\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^3 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \int \frac {\log ^2(a g+b g x)}{a+b x} \, dx}{b^2 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \int \frac {\log ^2(a g+b g x)}{c+d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log (a+b x) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2\right ) \int \frac {\log \left (\frac {1}{c+d x}\right ) \log (a g+b g x)}{-c-d x} \, dx}{b^3 g}-\frac {\left (9248 B^2 d (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log (a g+b g x)}{-c-d x} \, dx}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^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^2}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {g \log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^3 g^2}-\frac {\left (9248 B^2 c (b c-a d)\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^2 g}-\frac {\left (9248 a B^2 d (b c-a d)\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^3 g}-\frac {\left (9248 A B (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a g+b g x\right )}{b^3 g}-\frac {\left (9248 A B (b c-a d)^2\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^3 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {-b c+a d}{d}-\frac {b x}{d}\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^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{x}\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^3 g}-\frac {\left (9248 B^2 (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log \left (\frac {b g (-c-d x)}{-b c g+a d g}\right )}{a g+b g x} \, dx}{b^2}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2\left (\frac {1}{x}\right )}{\frac {-b c g+a d g}{d}+\frac {b g x}{d}} \, dx,x,c+d x\right )}{b^2 d}+\frac {\left (9248 B^2 (b c-a d)^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^2 d}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,a g+b g x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^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^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c+a d}{d}-\frac {b x}{d}\right )}{\frac {-b c+a d}{d}-\frac {b x}{d}} \, dx,x,-c-d x\right )}{b^2 d g}-\frac {\left (9248 B^2 (b c-a d)^2 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \operatorname {Subst}\left (\int \frac {\log \left (1-\frac {d x}{-b c g+a d g}\right )}{x} \, dx,x,a g+b g x\right )}{b^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}+\frac {\left (4624 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int x^2 \, dx,x,\log (g (a+b x))\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (\frac {-b c+a d}{b}-\frac {d x}{b}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^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^3 g}+\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (1+\frac {b g x}{-b c g+a d g}\right )}{x} \, dx,x,c+d x\right )}{b^3 g}+\frac {\left (9248 B^2 (b c-a d)^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^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {\left (4624 B^2 d (b c-a d)^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^4 g^2}-\frac {\left (9248 B^2 (b c-a d)^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^3 g}-\frac {\left (4624 B^2 d (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log ^2(x)}{\frac {-b c+a d}{b}-\frac {d x}{b}} \, dx,x,a+b x\right )}{b^4 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \log (g (a+b x)) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\log (x) \log \left (1-\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^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^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^2\right ) \operatorname {Subst}\left (\int \frac {\text {Li}_2\left (\frac {d x}{-b c+a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 g}-\frac {\left (9248 B^2 (b c-a d)^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^3 g}\\ &=-\frac {4624 A B d (b c-a d) x}{b^2 g}-\frac {4624 a B^2 d (b c-a d) \log ^2(a+b x)}{b^3 g}+\frac {2312 B^2 (b c-a d)^2 \log ^2(a+b x)}{b^3 g}-\frac {4624 A B (b c-a d)^2 \log ^2(g (a+b x))}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^3(g (a+b x))}{3 b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log (-c-d x)}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \log (g (a+b x)) \log (-c-d x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log (-c-d x)}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (g (a+b x)) \log ^2\left (\frac {1}{c+d x}\right )}{b^3 g}-\frac {4624 B^2 d (b c-a d) (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{b^3 g}+\frac {9248 a B d (b c-a d) \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}-\frac {4624 B (b c-a d)^2 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^3 g}+\frac {4624 d (b c-a d) x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {2312 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b g}+\frac {4624 B^2 (b c-a d)^2 \log (c+d x)}{b^3 g}+\frac {9248 B^2 c (b c-a d) \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{b^2 g}-\frac {9248 B c (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{b^2 g}-\frac {4624 B^2 c (b c-a d) \log ^2(c+d x)}{b^2 g}+\frac {9248 a B^2 d (b c-a d) \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 B^2 (b c-a d)^2 \log ^2(g (a+b x)) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}+\frac {4624 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (a g+b g x)}{b^3 g}+\frac {9248 A B (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log (a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(a g+b g x)}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \log \left (\frac {b (c+d x)}{b c-a d}\right ) \log ^2(a g+b g x)}{b^3 g}+\frac {9248 a B^2 d (b c-a d) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 A B (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {4624 B^2 (b c-a d)^2 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 (b c-a d)^2 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}+\frac {9248 B^2 c (b c-a d) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^2 g}-\frac {9248 B^2 (b c-a d)^2 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{b^3 g}-\frac {9248 B^2 (b c-a d)^2 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{b^3 g}\\ \end {align*}
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Mathematica [B] time = 3.67, size = 1987, normalized size = 3.71 \[ \text {result too large to display} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.79, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left (B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )^{2} + 2 \, {\left (A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{b g x + a g}, x\right ) \]
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 = 2.11, size = 0, normalized size = 0.00 \[ \int \frac {\left (d i x +c i \right )^{2} \left (B \ln \left (\frac {\left (b x +a \right ) e}{d x +c}\right )+A \right )^{2}}{b g x +a g}\, dx \]
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 \[ 2 \, A^{2} c d i^{2} {\left (\frac {x}{b g} - \frac {a \log \left (b x + a\right )}{b^{2} g}\right )} + \frac {1}{2} \, A^{2} d^{2} i^{2} {\left (\frac {2 \, a^{2} \log \left (b x + a\right )}{b^{3} g} + \frac {b x^{2} - 2 \, a x}{b^{2} g}\right )} + \frac {A^{2} c^{2} i^{2} \log \left (b g x + a g\right )}{b g} + \frac {{\left (B^{2} b^{2} d^{2} i^{2} x^{2} + 2 \, {\left (2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right )} B^{2} x + 2 \, {\left (b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right )} B^{2} \log \left (b x + a\right )\right )} \log \left (d x + c\right )^{2}}{2 \, b^{3} g} - \int -\frac {B^{2} b^{3} c^{3} i^{2} \log \relax (e)^{2} + 2 \, A B b^{3} c^{3} i^{2} \log \relax (e) + {\left (B^{2} b^{3} d^{3} i^{2} \log \relax (e)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log \relax (e)\right )} x^{3} + 3 \, {\left (B^{2} b^{3} c d^{2} i^{2} \log \relax (e)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log \relax (e)\right )} x^{2} + {\left (B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right )} \log \left (b x + a\right )^{2} + 3 \, {\left (B^{2} b^{3} c^{2} d i^{2} \log \relax (e)^{2} + 2 \, A B b^{3} c^{2} d i^{2} \log \relax (e)\right )} x + 2 \, {\left (B^{2} b^{3} c^{3} i^{2} \log \relax (e) + A B b^{3} c^{3} i^{2} + {\left (B^{2} b^{3} d^{3} i^{2} \log \relax (e) + A B b^{3} d^{3} i^{2}\right )} x^{3} + 3 \, {\left (B^{2} b^{3} c d^{2} i^{2} \log \relax (e) + A B b^{3} c d^{2} i^{2}\right )} x^{2} + 3 \, {\left (B^{2} b^{3} c^{2} d i^{2} \log \relax (e) + A B b^{3} c^{2} d i^{2}\right )} x\right )} \log \left (b x + a\right ) - {\left (2 \, B^{2} b^{3} c^{3} i^{2} \log \relax (e) + 2 \, A B b^{3} c^{3} i^{2} + {\left (2 \, A B b^{3} d^{3} i^{2} + {\left (2 \, i^{2} \log \relax (e) + i^{2}\right )} B^{2} b^{3} d^{3}\right )} x^{3} + {\left (6 \, A B b^{3} c d^{2} i^{2} - {\left (a b^{2} d^{3} i^{2} - 2 \, {\left (3 \, i^{2} \log \relax (e) + 2 \, i^{2}\right )} b^{3} c d^{2}\right )} B^{2}\right )} x^{2} + 2 \, {\left (3 \, A B b^{3} c^{2} d i^{2} + {\left (3 \, b^{3} c^{2} d i^{2} \log \relax (e) + 2 \, a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2}\right )} B^{2}\right )} x + 2 \, {\left (B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + {\left (4 \, b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right )} B^{2} x + {\left (b^{3} c^{3} i^{2} + a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right )} B^{2}\right )} \log \left (b x + a\right )\right )} \log \left (d x + c\right )}{b^{4} d g x^{2} + a b^{3} c g + {\left (b^{4} c g + a b^{3} d g\right )} x}\,{d x} \]
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 \[ \int \frac {{\left (c\,i+d\,i\,x\right )}^2\,{\left (A+B\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\right )}^2}{a\,g+b\,g\,x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {i^{2} \left (\int \frac {A^{2} c^{2}}{a + b x}\, dx + \int \frac {A^{2} d^{2} x^{2}}{a + b x}\, dx + \int \frac {B^{2} c^{2} \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}^{2}}{a + b x}\, dx + \int \frac {2 A B c^{2} \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}}{a + b x}\, dx + \int \frac {2 A^{2} c d x}{a + b x}\, dx + \int \frac {B^{2} d^{2} x^{2} \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}^{2}}{a + b x}\, dx + \int \frac {2 A B d^{2} x^{2} \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}}{a + b x}\, dx + \int \frac {2 B^{2} c d x \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}^{2}}{a + b x}\, dx + \int \frac {4 A B c d x \log {\left (\frac {a e}{c + d x} + \frac {b e x}{c + d x} \right )}}{a + b x}\, dx\right )}{g} \]
Verification of antiderivative is not currently implemented for this CAS.
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