Optimal. Leaf size=711 \[ \frac {3 B^2 (b c-a d)^5 g^3 i^2 x}{20 b^2 d^3}+\frac {B^2 (b c-a d)^2 g^3 i^2 (a+b x)^4}{60 b^3}-\frac {3 B^2 (b c-a d)^4 g^3 i^2 (c+d x)^2}{40 b d^4}+\frac {B^2 (b c-a d)^3 g^3 i^2 (c+d x)^3}{60 d^4}-\frac {B (b c-a d)^3 g^3 i^2 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{90 b^3 d}-\frac {B (b c-a d)^2 g^3 i^2 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3}-\frac {B (b c-a d) g^3 i^2 (a+b x)^4 (c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^2}+\frac {(b c-a d)^2 g^3 i^2 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{60 b^3}+\frac {(b c-a d) g^3 i^2 (a+b x)^4 (c+d x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{15 b^2}+\frac {g^3 i^2 (a+b x)^4 (c+d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{6 b}+\frac {B (b c-a d)^4 g^3 i^2 (a+b x)^2 \left (3 A+B+3 B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{180 b^3 d^2}-\frac {B (b c-a d)^5 g^3 i^2 (a+b x) \left (6 A+5 B+6 B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{180 b^3 d^3}-\frac {B (b c-a d)^6 g^3 i^2 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (6 A+11 B+6 B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{180 b^3 d^4}-\frac {B^2 (b c-a d)^6 g^3 i^2 \log (c+d x)}{20 b^3 d^4}-\frac {B^2 (b c-a d)^6 g^3 i^2 \text {Li}_2\left (\frac {d (a+b x)}{b (c+d x)}\right )}{30 b^3 d^4} \]
[Out]
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Rubi [A]
time = 0.67, antiderivative size = 711, normalized size of antiderivative = 1.00, number of steps
used = 17, number of rules used = 13, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.310, Rules used = {2562, 2383,
2381, 2384, 2354, 2438, 2373, 45, 47, 37, 2382, 12, 79} \begin {gather*} -\frac {B^2 g^3 i^2 (b c-a d)^6 \text {PolyLog}\left (2,\frac {d (a+b x)}{b (c+d x)}\right )}{30 b^3 d^4}-\frac {B g^3 i^2 (b c-a d)^6 \log \left (\frac {b c-a d}{b (c+d x)}\right ) \left (6 B \log \left (\frac {e (a+b x)}{c+d x}\right )+6 A+11 B\right )}{180 b^3 d^4}-\frac {B g^3 i^2 (a+b x) (b c-a d)^5 \left (6 B \log \left (\frac {e (a+b x)}{c+d x}\right )+6 A+5 B\right )}{180 b^3 d^3}+\frac {B g^3 i^2 (a+b x)^2 (b c-a d)^4 \left (3 B \log \left (\frac {e (a+b x)}{c+d x}\right )+3 A+B\right )}{180 b^3 d^2}-\frac {B g^3 i^2 (a+b x)^3 (b c-a d)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{90 b^3 d}+\frac {g^3 i^2 (a+b x)^4 (b c-a d)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{60 b^3}-\frac {B g^3 i^2 (a+b x)^4 (b c-a d)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{20 b^3}+\frac {g^3 i^2 (a+b x)^4 (c+d x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{15 b^2}-\frac {B g^3 i^2 (a+b x)^4 (c+d x) (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{15 b^2}+\frac {g^3 i^2 (a+b x)^4 (c+d x)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{6 b}-\frac {B^2 g^3 i^2 (b c-a d)^6 \log (c+d x)}{20 b^3 d^4}+\frac {B^2 g^3 i^2 (a+b x)^4 (b c-a d)^2}{60 b^3}+\frac {3 B^2 g^3 i^2 x (b c-a d)^5}{20 b^2 d^3}-\frac {3 B^2 g^3 i^2 (c+d x)^2 (b c-a d)^4}{40 b d^4}+\frac {B^2 g^3 i^2 (c+d x)^3 (b c-a d)^3}{60 d^4} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 37
Rule 45
Rule 47
Rule 79
Rule 2354
Rule 2373
Rule 2381
Rule 2382
Rule 2383
Rule 2384
Rule 2438
Rule 2562
Rubi steps
\begin {align*} \int (64 c+64 d x)^2 (a g+b g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx &=\int \left (\frac {4096 (b c-a d)^2 (a g+b g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2}+\frac {8192 d (b c-a d) (a g+b g x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g}+\frac {4096 d^2 (a g+b g x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g^2}\right ) \, dx\\ &=\frac {\left (4096 (b c-a d)^2\right ) \int (a g+b g x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b^2}+\frac {\left (4096 d^2\right ) \int (a g+b g x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b^2 g^2}+\frac {(8192 d (b c-a d)) \int (a g+b g x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2 \, dx}{b^2 g}\\ &=\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}-\frac {\left (4096 B d^2\right ) \int \frac {(b c-a d) g^6 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{3 b^3 g^3}-\frac {(16384 B d (b c-a d)) \int \frac {(b c-a d) g^5 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{5 b^3 g^2}-\frac {\left (2048 B (b c-a d)^2\right ) \int \frac {(b c-a d) g^4 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{b^3 g}\\ &=\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}-\frac {\left (4096 B d^2 (b c-a d) g^3\right ) \int \frac {(a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{3 b^3}-\frac {\left (16384 B d (b c-a d)^2 g^3\right ) \int \frac {(a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{5 b^3}-\frac {\left (2048 B (b c-a d)^3 g^3\right ) \int \frac {(a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{c+d x} \, dx}{b^3}\\ &=\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}-\frac {\left (4096 B d^2 (b c-a d) g^3\right ) \int \left (\frac {b (b c-a d)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^5}-\frac {b (b c-a d)^3 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^4}+\frac {b (b c-a d)^2 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^3}-\frac {b (b c-a d) (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^2}+\frac {b (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d}+\frac {(-b c+a d)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^5 (c+d x)}\right ) \, dx}{3 b^3}-\frac {\left (16384 B d (b c-a d)^2 g^3\right ) \int \left (-\frac {b (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^4}+\frac {b (b c-a d)^2 (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^3}-\frac {b (b c-a d) (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^2}+\frac {b (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d}+\frac {(-b c+a d)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^4 (c+d x)}\right ) \, dx}{5 b^3}-\frac {\left (2048 B (b c-a d)^3 g^3\right ) \int \left (\frac {b (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^3}-\frac {b (b c-a d) (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^2}+\frac {b (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d}+\frac {(-b c+a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{d^3 (c+d x)}\right ) \, dx}{b^3}\\ &=\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}-\frac {\left (4096 B d (b c-a d) g^3\right ) \int (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{3 b^2}+\frac {\left (4096 B (b c-a d)^2 g^3\right ) \int (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{3 b^2}-\frac {\left (16384 B (b c-a d)^2 g^3\right ) \int (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{5 b^2}-\frac {\left (4096 B (b c-a d)^3 g^3\right ) \int (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{3 b^2 d}-\frac {\left (2048 B (b c-a d)^3 g^3\right ) \int (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{b^2 d}+\frac {\left (16384 B (b c-a d)^3 g^3\right ) \int (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{5 b^2 d}+\frac {\left (4096 B (b c-a d)^4 g^3\right ) \int (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{3 b^2 d^2}+\frac {\left (2048 B (b c-a d)^4 g^3\right ) \int (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{b^2 d^2}-\frac {\left (16384 B (b c-a d)^4 g^3\right ) \int (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{5 b^2 d^2}-\frac {\left (4096 B (b c-a d)^5 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{3 b^2 d^3}-\frac {\left (2048 B (b c-a d)^5 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{b^2 d^3}+\frac {\left (16384 B (b c-a d)^5 g^3\right ) \int \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \, dx}{5 b^2 d^3}+\frac {\left (4096 B (b c-a d)^6 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{3 b^3 d^3}+\frac {\left (2048 B (b c-a d)^6 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^3 d^3}-\frac {\left (16384 B (b c-a d)^6 g^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{5 b^3 d^3}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {\left (4096 B^2 d (b c-a d) g^3\right ) \int \frac {(b c-a d) (a+b x)^4}{c+d x} \, dx}{15 b^3}-\frac {\left (1024 B^2 (b c-a d)^2 g^3\right ) \int \frac {(b c-a d) (a+b x)^3}{c+d x} \, dx}{3 b^3}+\frac {\left (4096 B^2 (b c-a d)^2 g^3\right ) \int \frac {(b c-a d) (a+b x)^3}{c+d x} \, dx}{5 b^3}+\frac {\left (4096 B^2 (b c-a d)^3 g^3\right ) \int \frac {(b c-a d) (a+b x)^2}{c+d x} \, dx}{9 b^3 d}+\frac {\left (2048 B^2 (b c-a d)^3 g^3\right ) \int \frac {(b c-a d) (a+b x)^2}{c+d x} \, dx}{3 b^3 d}-\frac {\left (16384 B^2 (b c-a d)^3 g^3\right ) \int \frac {(b c-a d) (a+b x)^2}{c+d x} \, dx}{15 b^3 d}-\frac {\left (2048 B^2 (b c-a d)^4 g^3\right ) \int \frac {(b c-a d) (a+b x)}{c+d x} \, dx}{3 b^3 d^2}-\frac {\left (1024 B^2 (b c-a d)^4 g^3\right ) \int \frac {(b c-a d) (a+b x)}{c+d x} \, dx}{b^3 d^2}+\frac {\left (8192 B^2 (b c-a d)^4 g^3\right ) \int \frac {(b c-a d) (a+b x)}{c+d x} \, dx}{5 b^3 d^2}-\frac {\left (4096 B^2 (b c-a d)^5 g^3\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{3 b^2 d^3}-\frac {\left (2048 B^2 (b c-a d)^5 g^3\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{b^2 d^3}+\frac {\left (16384 B^2 (b c-a d)^5 g^3\right ) \int \log \left (\frac {e (a+b x)}{c+d x}\right ) \, dx}{5 b^2 d^3}-\frac {\left (4096 B^2 (b c-a d)^6 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}{3 b^3 d^4}-\frac {\left (2048 B^2 (b c-a d)^6 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}{b^3 d^4}+\frac {\left (16384 B^2 (b c-a d)^6 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}{5 b^3 d^4}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {\left (4096 B^2 d (b c-a d)^2 g^3\right ) \int \frac {(a+b x)^4}{c+d x} \, dx}{15 b^3}-\frac {\left (1024 B^2 (b c-a d)^3 g^3\right ) \int \frac {(a+b x)^3}{c+d x} \, dx}{3 b^3}+\frac {\left (4096 B^2 (b c-a d)^3 g^3\right ) \int \frac {(a+b x)^3}{c+d x} \, dx}{5 b^3}+\frac {\left (4096 B^2 (b c-a d)^4 g^3\right ) \int \frac {(a+b x)^2}{c+d x} \, dx}{9 b^3 d}+\frac {\left (2048 B^2 (b c-a d)^4 g^3\right ) \int \frac {(a+b x)^2}{c+d x} \, dx}{3 b^3 d}-\frac {\left (16384 B^2 (b c-a d)^4 g^3\right ) \int \frac {(a+b x)^2}{c+d x} \, dx}{15 b^3 d}-\frac {\left (2048 B^2 (b c-a d)^5 g^3\right ) \int \frac {a+b x}{c+d x} \, dx}{3 b^3 d^2}-\frac {\left (1024 B^2 (b c-a d)^5 g^3\right ) \int \frac {a+b x}{c+d x} \, dx}{b^3 d^2}+\frac {\left (8192 B^2 (b c-a d)^5 g^3\right ) \int \frac {a+b x}{c+d x} \, dx}{5 b^3 d^2}+\frac {\left (4096 B^2 (b c-a d)^6 g^3\right ) \int \frac {1}{c+d x} \, dx}{3 b^3 d^3}+\frac {\left (2048 B^2 (b c-a d)^6 g^3\right ) \int \frac {1}{c+d x} \, dx}{b^3 d^3}-\frac {\left (16384 B^2 (b c-a d)^6 g^3\right ) \int \frac {1}{c+d x} \, dx}{5 b^3 d^3}-\frac {\left (4096 B^2 (b c-a d)^6 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}{3 b^3 d^4 e}-\frac {\left (2048 B^2 (b c-a d)^6 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}{b^3 d^4 e}+\frac {\left (16384 B^2 (b c-a d)^6 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}{5 b^3 d^4 e}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B^2 (b c-a d)^6 g^3 \log (c+d x)}{15 b^3 d^4}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {\left (4096 B^2 d (b c-a d)^2 g^3\right ) \int \left (-\frac {b (b c-a d)^3}{d^4}+\frac {b (b c-a d)^2 (a+b x)}{d^3}-\frac {b (b c-a d) (a+b x)^2}{d^2}+\frac {b (a+b x)^3}{d}+\frac {(-b c+a d)^4}{d^4 (c+d x)}\right ) \, dx}{15 b^3}-\frac {\left (1024 B^2 (b c-a d)^3 g^3\right ) \int \left (\frac {b (b c-a d)^2}{d^3}-\frac {b (b c-a d) (a+b x)}{d^2}+\frac {b (a+b x)^2}{d}+\frac {(-b c+a d)^3}{d^3 (c+d x)}\right ) \, dx}{3 b^3}+\frac {\left (4096 B^2 (b c-a d)^3 g^3\right ) \int \left (\frac {b (b c-a d)^2}{d^3}-\frac {b (b c-a d) (a+b x)}{d^2}+\frac {b (a+b x)^2}{d}+\frac {(-b c+a d)^3}{d^3 (c+d x)}\right ) \, dx}{5 b^3}+\frac {\left (4096 B^2 (b c-a d)^4 g^3\right ) \int \left (-\frac {b (b c-a d)}{d^2}+\frac {b (a+b x)}{d}+\frac {(-b c+a d)^2}{d^2 (c+d x)}\right ) \, dx}{9 b^3 d}+\frac {\left (2048 B^2 (b c-a d)^4 g^3\right ) \int \left (-\frac {b (b c-a d)}{d^2}+\frac {b (a+b x)}{d}+\frac {(-b c+a d)^2}{d^2 (c+d x)}\right ) \, dx}{3 b^3 d}-\frac {\left (16384 B^2 (b c-a d)^4 g^3\right ) \int \left (-\frac {b (b c-a d)}{d^2}+\frac {b (a+b x)}{d}+\frac {(-b c+a d)^2}{d^2 (c+d x)}\right ) \, dx}{15 b^3 d}-\frac {\left (2048 B^2 (b c-a d)^5 g^3\right ) \int \left (\frac {b}{d}+\frac {-b c+a d}{d (c+d x)}\right ) \, dx}{3 b^3 d^2}-\frac {\left (1024 B^2 (b c-a d)^5 g^3\right ) \int \left (\frac {b}{d}+\frac {-b c+a d}{d (c+d x)}\right ) \, dx}{b^3 d^2}+\frac {\left (8192 B^2 (b c-a d)^5 g^3\right ) \int \left (\frac {b}{d}+\frac {-b c+a d}{d (c+d x)}\right ) \, dx}{5 b^3 d^2}-\frac {\left (4096 B^2 (b c-a d)^6 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}{3 b^3 d^4 e}-\frac {\left (2048 B^2 (b c-a d)^6 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}{b^3 d^4 e}+\frac {\left (16384 B^2 (b c-a d)^6 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}{5 b^3 d^4 e}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}+\frac {4096 B^2 (b c-a d)^5 g^3 x}{45 b^2 d^3}-\frac {3584 B^2 (b c-a d)^4 g^3 (a+b x)^2}{45 b^3 d^2}+\frac {1024 B^2 (b c-a d)^3 g^3 (a+b x)^3}{15 b^3 d}+\frac {1024 B^2 (b c-a d)^2 g^3 (a+b x)^4}{15 b^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B^2 (b c-a d)^6 g^3 \log (c+d x)}{45 b^3 d^4}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}-\frac {\left (4096 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{3 b^2 d^4}-\frac {\left (2048 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^2 d^4}+\frac {\left (16384 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{5 b^2 d^4}+\frac {\left (4096 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{3 b^3 d^3}+\frac {\left (2048 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^3 d^3}-\frac {\left (16384 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{5 b^3 d^3}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}+\frac {4096 B^2 (b c-a d)^5 g^3 x}{45 b^2 d^3}-\frac {3584 B^2 (b c-a d)^4 g^3 (a+b x)^2}{45 b^3 d^2}+\frac {1024 B^2 (b c-a d)^3 g^3 (a+b x)^3}{15 b^3 d}+\frac {1024 B^2 (b c-a d)^2 g^3 (a+b x)^4}{15 b^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B^2 (b c-a d)^6 g^3 \log (c+d x)}{45 b^3 d^4}-\frac {2048 B^2 (b c-a d)^6 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 d^4}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {\left (4096 B^2 (b c-a d)^6 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{3 b^3 d^4}+\frac {\left (2048 B^2 (b c-a d)^6 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^3 d^4}-\frac {\left (16384 B^2 (b c-a d)^6 g^3\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{5 b^3 d^4}+\frac {\left (4096 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 b^3 d^3}+\frac {\left (2048 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^3 d^3}-\frac {\left (16384 B^2 (b c-a d)^6 g^3\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{5 b^3 d^3}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}+\frac {4096 B^2 (b c-a d)^5 g^3 x}{45 b^2 d^3}-\frac {3584 B^2 (b c-a d)^4 g^3 (a+b x)^2}{45 b^3 d^2}+\frac {1024 B^2 (b c-a d)^3 g^3 (a+b x)^3}{15 b^3 d}+\frac {1024 B^2 (b c-a d)^2 g^3 (a+b x)^4}{15 b^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B^2 (b c-a d)^6 g^3 \log (c+d x)}{45 b^3 d^4}-\frac {2048 B^2 (b c-a d)^6 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 d^4}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {1024 B^2 (b c-a d)^6 g^3 \log ^2(c+d x)}{15 b^3 d^4}+\frac {\left (4096 B^2 (b c-a d)^6 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 )}{3 b^3 d^4}+\frac {\left (2048 B^2 (b c-a d)^6 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 )}{b^3 d^4}-\frac {\left (16384 B^2 (b c-a d)^6 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 )}{5 b^3 d^4}\\ &=-\frac {2048 A B (b c-a d)^5 g^3 x}{15 b^2 d^3}+\frac {4096 B^2 (b c-a d)^5 g^3 x}{45 b^2 d^3}-\frac {3584 B^2 (b c-a d)^4 g^3 (a+b x)^2}{45 b^3 d^2}+\frac {1024 B^2 (b c-a d)^3 g^3 (a+b x)^3}{15 b^3 d}+\frac {1024 B^2 (b c-a d)^2 g^3 (a+b x)^4}{15 b^3}-\frac {2048 B^2 (b c-a d)^5 g^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )}{15 b^3 d^3}+\frac {1024 B (b c-a d)^4 g^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 d^2}-\frac {2048 B (b c-a d)^3 g^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 d}-\frac {7168 B (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}-\frac {4096 B d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3}+\frac {1024 (b c-a d)^2 g^3 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^3}+\frac {8192 d (b c-a d) g^3 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3}+\frac {2048 d^2 g^3 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3}+\frac {2048 B^2 (b c-a d)^6 g^3 \log (c+d x)}{45 b^3 d^4}-\frac {2048 B^2 (b c-a d)^6 g^3 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 d^4}+\frac {2048 B (b c-a d)^6 g^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 d^4}+\frac {1024 B^2 (b c-a d)^6 g^3 \log ^2(c+d x)}{15 b^3 d^4}-\frac {2048 B^2 (b c-a d)^6 g^3 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{15 b^3 d^4}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1559\) vs. \(2(711)=1422\).
time = 0.91, size = 1559, normalized size = 2.19 \begin {gather*} \frac {g^3 i^2 \left (15 (b c-a d)^2 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2+24 d (b c-a d) (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2+10 d^2 (a+b x)^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2-\frac {5 B (b c-a d)^3 \left (6 A b d (b c-a d)^2 x+6 B d (b c-a d)^2 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )+3 d^2 (-b c+a d) (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )+2 d^3 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )-6 B (b c-a d)^3 \log (c+d x)-6 (b c-a d)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)+B (b c-a d) \left (2 b d (b c-a d) x-d^2 (a+b x)^2-2 (b c-a d)^2 \log (c+d x)\right )+3 B (b c-a d)^2 (b d x+(-b c+a d) \log (c+d x))+3 B (b c-a d)^3 \left (\left (2 \log \left (\frac {d (a+b x)}{-b c+a d}\right )-\log (c+d x)\right ) \log (c+d x)+2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )\right )\right )}{d^4}+\frac {2 B (b c-a d)^2 \left (24 A b d (b c-a d)^3 x+24 B d (b c-a d)^3 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )-12 d^2 (b c-a d)^2 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )+8 d^3 (b c-a d) (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )-6 d^4 (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )-24 B (b c-a d)^4 \log (c+d x)-24 (b c-a d)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)+4 B (b c-a d)^2 \left (2 b d (b c-a d) x-d^2 (a+b x)^2-2 (b c-a d)^2 \log (c+d x)\right )+B (b c-a d) \left (6 b d (b c-a d)^2 x+3 d^2 (-b c+a d) (a+b x)^2+2 d^3 (a+b x)^3-6 (b c-a d)^3 \log (c+d x)\right )+12 B (b c-a d)^3 (b d x+(-b c+a d) \log (c+d x))+12 B (b c-a d)^4 \left (\left (2 \log \left (\frac {d (a+b x)}{-b c+a d}\right )-\log (c+d x)\right ) \log (c+d x)+2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )\right )\right )}{d^4}-\frac {B (b c-a d) \left (24 b^2 B c d (b c-a d)^3 x+120 A b d (b c-a d)^4 x+130 b B d (b c-a d)^4 x+24 a b B d^2 (-b c+a d)^3 x-12 b B c d^2 (b c-a d)^2 (a+b x)^2+12 a B d^3 (b c-a d)^2 (a+b x)^2+35 B d^2 (-b c+a d)^3 (a+b x)^2+8 b B c d^3 (b c-a d) (a+b x)^3+10 B d^3 (b c-a d)^2 (a+b x)^3+8 a B d^4 (-b c+a d) (a+b x)^3-6 b B c d^4 (a+b x)^4+6 a B d^5 (a+b x)^4+120 B d (b c-a d)^4 (a+b x) \log \left (\frac {e (a+b x)}{c+d x}\right )+60 d^2 (-b c+a d)^3 (a+b x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )+40 d^3 (b c-a d)^2 (a+b x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )+30 d^4 (-b c+a d) (a+b x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )+24 d^5 (a+b x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )-24 b B c (b c-a d)^4 \log (c+d x)+24 a B d (b c-a d)^4 \log (c+d x)-250 B (b c-a d)^5 \log (c+d x)-120 (b c-a d)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)+60 B (b c-a d)^5 \left (\left (2 \log \left (\frac {d (a+b x)}{-b c+a d}\right )-\log (c+d x)\right ) \log (c+d x)+2 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )\right )\right )}{6 d^4}\right )}{60 b^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.55, size = 0, normalized size = 0.00 \[\int \left (b g x +a g \right )^{3} \left (d i x +c i \right )^{2} \left (A +B \ln \left (\frac {e \left (b x +a \right )}{d x +c}\right )\right )^{2}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 4015 vs.
\(2 (644) = 1288\).
time = 0.44, size = 4015, normalized size = 5.65 \begin {gather*} \text {Too large to display} \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 {\left (a\,g+b\,g\,x\right )}^3\,{\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 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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