Optimal. Leaf size=718 \[ \frac {b B^2 (b c-a d)^2 g^3 x}{3 d^3 i}+\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {a+b x}{c+d x}\right )}{3 d^4 i}+\frac {7 B (b c-a d)^2 g^3 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 d^3 i}-\frac {b^2 B (b c-a d) g^3 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 d^4 i}+\frac {6 B (b c-a d)^3 g^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^4 i}+\frac {3 (b c-a d)^2 g^3 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{d^3 i}-\frac {3 b^2 (b c-a d) g^3 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 d^4 i}+\frac {b^3 g^3 (c+d x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 d^4 i}+\frac {(b c-a d)^3 g^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{d^4 i}-\frac {2 B^2 (b c-a d)^3 g^3 \log (c+d x)}{d^4 i}-\frac {7 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log \left (1-\frac {b (c+d x)}{d (a+b x)}\right )}{3 d^4 i}+\frac {6 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {2 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {7 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{d (a+b x)}\right )}{3 d^4 i}-\frac {2 B^2 (b c-a d)^3 g^3 \text {Li}_3\left (\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.64, antiderivative size = 718, normalized size of antiderivative = 1.00, number
of steps used = 25, number of rules used = 13, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.310, Rules
used = {2562, 2395, 2356, 2389, 2379, 2438, 2351, 31, 46, 2355, 2354, 2421, 6724}
\begin {gather*} \frac {2 B g^3 (b c-a d)^3 \text {PolyLog}\left (2,\frac {d (a+b x)}{b (c+d x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{d^4 i}+\frac {6 B^2 g^3 (b c-a d)^3 \text {PolyLog}\left (2,\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {7 B^2 g^3 (b c-a d)^3 \text {PolyLog}\left (2,\frac {b (c+d x)}{d (a+b x)}\right )}{3 d^4 i}-\frac {2 B^2 g^3 (b c-a d)^3 \text {PolyLog}\left (3,\frac {d (a+b x)}{b (c+d x)}\right )}{d^4 i}+\frac {b^3 g^3 (c+d x)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{3 d^4 i}-\frac {3 b^2 g^3 (c+d x)^2 (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{2 d^4 i}-\frac {b^2 B g^3 (c+d x)^2 (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{3 d^4 i}+\frac {g^3 (b c-a d)^3 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{d^4 i}+\frac {6 B g^3 (b c-a d)^3 \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 )}{d^4 i}-\frac {7 B g^3 (b c-a d)^3 \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 )}{3 d^4 i}+\frac {3 g^3 (a+b x) (b c-a d)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{d^3 i}+\frac {7 B g^3 (a+b x) (b c-a d)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{3 d^3 i}+\frac {B^2 g^3 (b c-a d)^3 \log \left (\frac {a+b x}{c+d x}\right )}{3 d^4 i}-\frac {2 B^2 g^3 (b c-a d)^3 \log (c+d x)}{d^4 i}+\frac {b B^2 g^3 x (b c-a d)^2}{3 d^3 i} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 46
Rule 2351
Rule 2354
Rule 2355
Rule 2356
Rule 2379
Rule 2389
Rule 2395
Rule 2421
Rule 2438
Rule 2562
Rule 6724
Rubi steps
\begin {align*} \int \frac {(a g+b g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 c+84 d x} \, dx &=\int \left (\frac {b (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}+\frac {(-b c+a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{d^3 (84 c+84 d x)}-\frac {b (b c-a d) g^2 (a g+b g x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^2}+\frac {b g (a g+b g x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d}\right ) \, dx\\ &=\frac {(b g) \int (a g+b g x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{84 d}-\frac {\left (b (b c-a d) g^2\right ) \int (a g+b g x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{84 d^2}+\frac {\left (b (b c-a d)^2 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{84 d^3}-\frac {\left ((b c-a d)^3 g^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 c+84 d x} \, dx}{d^3}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}-\frac {B \int \frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{126 d}+\frac {(B (b c-a d) g) \int \frac {(b c-a d) g^2 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{84 d^2}-\frac {\left (b B (b c-a d)^2 g^3\right ) \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}{42 d^3}+\frac {\left (B (b c-a d)^3 g^3\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 (84 c+84 d x)}{e (a+b x)} \, dx}{42 d^4}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}-\frac {\left (B (b c-a d) g^3\right ) \int \frac {(a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{126 d}+\frac {\left (B (b c-a d)^2 g^3\right ) \int \frac {(a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{84 d^2}-\frac {\left (b B (b c-a d)^3 g^3\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}{42 d^3}+\frac {\left (B (b c-a d)^3 g^3\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 (84 c+84 d x)}{a+b x} \, dx}{42 d^4 e}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}-\frac {\left (B (b c-a d) g^3\right ) \int \left (-\frac {b (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^2}+\frac {b (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d}+\frac {(-b c+a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^2 (c+d x)}\right ) \, dx}{126 d}+\frac {\left (B (b c-a d)^2 g^3\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d}+\frac {(-b c+a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d (c+d x)}\right ) \, dx}{84 d^2}-\frac {\left (b B (b c-a d)^3 g^3\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}{42 d^3}+\frac {\left (B (b c-a d)^3 g^3\right ) \int \frac {(b c-a d) e \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{(a+b x) (c+d x)} \, dx}{42 d^4 e}\\ &=\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}-\frac {\left (b B (b c-a d) g^3\right ) \int (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{126 d^2}+\frac {\left (b B (b c-a d)^2 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{126 d^3}+\frac {\left (b B (b c-a d)^2 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{84 d^3}+\frac {\left (a b B (b c-a d)^2 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{42 d^3}-\frac {\left (b B c (b c-a d)^2 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{42 d^3}-\frac {\left (B (b c-a d)^3 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{126 d^3}-\frac {\left (B (b c-a d)^3 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{84 d^3}+\frac {\left (B (b c-a d)^4 g^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{(a+b x) (c+d x)} \, dx}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {\left (B^2 (b c-a d) g^3\right ) \int \frac {(b c-a d) (a+b x)}{c+d x} \, dx}{252 d^2}+\frac {\left (b B^2 c (b c-a d)^2 g^3\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}{42 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^3\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}{42 d^3}+\frac {\left (b B^2 (b c-a d)^2 g^3\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{126 d^3}+\frac {\left (b B^2 (b c-a d)^2 g^3\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{84 d^3}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{126 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{84 d^4}+\frac {\left (B (b c-a d)^4 g^3\right ) \int \left (\frac {d \left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d 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 (84 c+84 d x)}{(b c-a d) (a+b x)}\right ) \, dx}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {\left (B^2 (b c-a d)^2 g^3\right ) \int \frac {a+b x}{c+d x} \, dx}{252 d^2}+\frac {\left (b B (b c-a d)^3 g^3\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}+\frac {\left (B (b c-a d)^3 g^3\right ) \int \frac {\left (-A-B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{c+d x} \, dx}{42 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {1}{c+d x} \, dx}{126 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {1}{c+d x} \, dx}{84 d^3}+\frac {\left (b B^2 c (b c-a d)^2 g^3\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}{42 d^4 e}-\frac {\left (a B^2 (b c-a d)^2 g^3\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}{42 d^3 e}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{126 d^4 e}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{84 d^4 e}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {5 B^2 (b c-a d)^3 g^3 \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {\left (B^2 (b c-a d)^2 g^3\right ) \int \left (\frac {b}{d}+\frac {-b c+a d}{d (c+d x)}\right ) \, dx}{252 d^2}+\frac {\left (b B (b c-a d)^3 g^3\right ) \int \left (\frac {A \log (84 c+84 d x)}{a+b x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (84 c+84 d x)}{a+b x}\right ) \, dx}{42 d^4}+\frac {\left (B (b c-a d)^3 g^3\right ) \int \left (\frac {A \log (84 c+84 d x)}{-c-d x}+\frac {B \log \left (\frac {e (a+b x)}{c+d x}\right ) \log (84 c+84 d x)}{-c-d x}\right ) \, dx}{42 d^3}+\frac {\left (b B^2 c (b c-a d)^2 g^3\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}{42 d^4 e}-\frac {\left (a B^2 (b c-a d)^2 g^3\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}{42 d^3 e}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{126 d^4 e}+\frac {\left (B^2 (b c-a d)^3 g^3\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}{84 d^4 e}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {\left (b^2 B^2 c (b c-a d)^2 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{42 d^4}-\frac {\left (a b B^2 (b c-a d)^2 g^3\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{42 d^3}-\frac {\left (b B^2 c (b c-a d)^2 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{42 d^3}+\frac {\left (a B^2 (b c-a d)^2 g^3\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{42 d^2}+\frac {\left (A b B (b c-a d)^3 g^3\right ) \int \frac {\log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{126 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{84 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}+\frac {\left (A B (b c-a d)^3 g^3\right ) \int \frac {\log (84 c+84 d x)}{-c-d x} \, dx}{42 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{126 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{84 d^3}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {e (a+b x)}{c+d x}\right ) \log (84 c+84 d x)}{-c-d x} \, dx}{42 d^3}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {\left (b B^2 c (b c-a d)^2 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{42 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{42 d^3}-\frac {\left (a b B^2 (b c-a d)^2 g^3\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{42 d^3}-\frac {\left (b B^2 c (b c-a d)^2 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{42 d^3}+\frac {\left (A B (b c-a d)^3 g^3\right ) \text {Subst}\left (\int -\frac {84 \log (x)}{x} \, dx,x,84 c+84 d x\right )}{3528 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{126 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{84 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log ^2(84 c+84 d x)}{a+b x} \, dx}{84 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log (a+b x) \log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}+\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {1}{c+d x}\right ) \log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}-\frac {\left (2 A B (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {84 d (a+b x)}{-84 b c+84 a d}\right )}{84 c+84 d x} \, dx}{d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{126 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{84 d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \int \frac {\log ^2(84 c+84 d x)}{c+d x} \, dx}{84 d^3}+\frac {\left (b B^2 (b c-a d)^3 g^3 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log (84 c+84 d x)}{a+b x} \, dx}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {\left (b B^2 c (b c-a d)^2 g^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{42 d^4}-\frac {\left (a B^2 (b c-a d)^2 g^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{42 d^3}-\frac {\left (A B (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,84 c+84 d x\right )}{42 d^4}-\frac {\left (A B (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-84 b c+84 a d}\right )}{x} \, dx,x,84 c+84 d x\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {84 \log ^2(x)}{x} \, dx,x,84 c+84 d x\right )}{7056 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{126 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{84 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {84 b c-84 a d}{b}+\frac {84 d x}{b}\right )}{x} \, dx,x,a+b x\right )}{42 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {1}{-\frac {-b c+a d}{b}+\frac {d x}{b}}\right ) \log \left (-\frac {-84 b c+84 a d}{b}+\frac {84 d x}{b}\right )}{x} \, dx,x,a+b x\right )}{42 d^4}-\frac {\left (2 B^2 (b c-a d)^3 g^3\right ) \int \frac {\log \left (\frac {84 d (a+b x)}{-84 b c+84 a d}\right ) \log (84 c+84 d x)}{84 c+84 d x} \, dx}{d^3}-\frac {\left (2 B^2 (b c-a d)^3 g^3 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \int \frac {\log \left (\frac {84 d (a+b x)}{-84 b c+84 a d}\right )}{84 c+84 d x} \, dx}{d^3}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{x} \, dx,x,84 c+84 d x\right )}{84 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {84 d \left (\frac {-84 b c+84 a d}{84 d}+\frac {b x}{84 d}\right )}{-84 b c+84 a d}\right )}{x} \, dx,x,84 c+84 d x\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {1}{-\frac {-b c+a d}{b}+\frac {d x}{b}}\right )}{-\frac {-b c+a d}{b}+\frac {d x}{b}} \, dx,x,a+b x\right )}{42 b d^3}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{\frac {84 b c-84 a d}{b}+\frac {84 d x}{b}} \, dx,x,a+b x\right )}{b d^3}+\frac {\left (2 B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (-\frac {-84 b c+84 a d}{b}+\frac {84 d x}{b}\right )}{-\frac {-84 b c+84 a d}{b}+\frac {84 d x}{b}} \, dx,x,a+b x\right )}{b d^3}-\frac {\left (B^2 (b c-a d)^3 g^3 \left (-\log (a+b x)-\log \left (\frac {1}{c+d x}\right )+\log \left (\frac {e (a+b x)}{c+d x}\right )\right )\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {b x}{-84 b c+84 a d}\right )}{x} \, dx,x,84 c+84 d x\right )}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{84 d^4}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}-\frac {B^2 (b c-a d)^3 g^3 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (84 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int x^2 \, dx,x,\log (84 (c+d x))\right )}{84 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (\frac {-84 b c+84 a d}{84 d}+\frac {b x}{84 d}\right )}{x} \, dx,x,84 (c+d x)\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (\frac {-b c+a d}{d}+\frac {b x}{d}\right )}{x} \, dx,x,c+d x\right )}{42 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (1+\frac {84 d x}{84 b c-84 a d}\right )}{x} \, dx,x,a+b x\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-84 b c+84 a d}\right )}{x} \, dx,x,84 c+84 d x\right )}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log ^3(84 (c+d x))}{252 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{84 d^4}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}-\frac {B^2 (b c-a d)^3 g^3 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (84 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log ^2(x)}{\frac {-84 b c+84 a d}{84 d}+\frac {b x}{84 d}} \, dx,x,84 (c+d x)\right )}{7056 d^5}-\frac {\left (b B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log ^2\left (\frac {1}{x}\right )}{\frac {-b c+a d}{d}+\frac {b x}{d}} \, dx,x,c+d x\right )}{84 d^5}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {84 d x}{84 b c-84 a d}\right )}{x} \, dx,x,a+b x\right )}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log ^3(84 (c+d x))}{252 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{84 d^4}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}-\frac {B^2 (b c-a d)^3 g^3 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (84 (c+d x)) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log \left (\frac {1}{x}\right ) \log \left (1+\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{42 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\log (x) \log \left (1+\frac {b x}{-84 b c+84 a d}\right )}{x} \, dx,x,84 (c+d x)\right )}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log ^3(84 (c+d x))}{252 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{84 d^4}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-b c+a d}\right )}{x} \, dx,x,c+d x\right )}{42 d^4}+\frac {\left (B^2 (b c-a d)^3 g^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {b x}{-84 b c+84 a d}\right )}{x} \, dx,x,84 (c+d x)\right )}{42 d^4}\\ &=\frac {5 A b B (b c-a d)^2 g^3 x}{252 d^3}+\frac {b B^2 (b c-a d)^2 g^3 x}{252 d^3}-\frac {a B^2 (b c-a d)^2 g^3 \log ^2(a+b x)}{84 d^3}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2\left (\frac {1}{c+d x}\right )}{84 d^4}+\frac {5 B^2 (b c-a d)^2 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{252 d^3}-\frac {B (b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{252 d^2}+\frac {a B (b c-a d)^2 g^3 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{42 d^3}+\frac {b (b c-a d)^2 g^3 x \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{84 d^3}-\frac {(b c-a d) g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{168 d^2}+\frac {g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{252 d}-\frac {B^2 (b c-a d)^3 g^3 \log (c+d x)}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{252 d^4}-\frac {b B c (b c-a d)^2 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{42 d^4}-\frac {5 B (b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{252 d^4}-\frac {b B^2 c (b c-a d)^2 g^3 \log ^2(c+d x)}{84 d^4}-\frac {5 B^2 (b c-a d)^3 g^3 \log ^2(c+d x)}{504 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log (84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log \left (\frac {1}{c+d x}\right ) \log (84 (c+d x))}{42 d^4}-\frac {A B (b c-a d)^3 g^3 \log ^2(84 (c+d x))}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 (c+d x))}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log ^3(84 (c+d x))}{252 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log ^2(a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{84 d^4}+\frac {A B (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (84 c+84 d x)}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (84 c+84 d x)}{42 d^4}-\frac {(b c-a d)^3 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \log (84 c+84 d x)}{84 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log ^2(84 c+84 d x)}{84 d^4}-\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {e (a+b x)}{c+d x}\right ) \log ^2(84 c+84 d x)}{84 d^4}+\frac {a B^2 (b c-a d)^2 g^3 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^3}-\frac {B^2 (b c-a d)^3 g^3 \log (a+b x) \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}+\frac {b B^2 c (b c-a d)^2 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {A B (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {5 B^2 (b c-a d)^3 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{252 d^4}+\frac {B^2 (b c-a d)^3 g^3 \log \left (\frac {1}{c+d x}\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}-\frac {B^2 (b c-a d)^3 g^3 \left (\log (a+b x)+\log \left (\frac {1}{c+d x}\right )-\log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (-\frac {d (a+b x)}{b c-a d}\right )}{42 d^4}+\frac {B^2 (b c-a d)^3 g^3 \text {Li}_3\left (\frac {b (c+d x)}{b c-a d}\right )}{42 d^4}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(4802\) vs. \(2(718)=1436\).
time = 1.19, size = 4802, normalized size = 6.69 \begin {gather*} \text {Result too large to show} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.36, size = 0, normalized size = 0.00 \[\int \frac {\left (b g x +a g \right )^{3} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}}{d i x +c i}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\left (a\,g+b\,g\,x\right )}^3\,{\left (A+B\,\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\right )}^2}{c\,i+d\,i\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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