Optimal. Leaf size=463 \[ -\frac {2 B^2 d^2 i^2 (c+d x)^3}{27 (b c-a d)^3 g^6 (a+b x)^3}+\frac {b B^2 d i^2 (c+d x)^4}{16 (b c-a d)^3 g^6 (a+b x)^4}-\frac {2 b^2 B^2 i^2 (c+d x)^5}{125 (b c-a d)^3 g^6 (a+b x)^5}-\frac {2 B d^2 i^2 (c+d x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{9 (b c-a d)^3 g^6 (a+b x)^3}+\frac {b B d i^2 (c+d x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{4 (b c-a d)^3 g^6 (a+b x)^4}-\frac {2 b^2 B i^2 (c+d x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 (b c-a d)^3 g^6 (a+b x)^5}-\frac {d^2 i^2 (c+d x)^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 (b c-a d)^3 g^6 (a+b x)^3}+\frac {b d i^2 (c+d x)^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 (b c-a d)^3 g^6 (a+b x)^4}-\frac {b^2 i^2 (c+d x)^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 (b c-a d)^3 g^6 (a+b x)^5} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.28, antiderivative size = 463, normalized size of antiderivative = 1.00, number of steps
used = 9, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2562, 2395,
2342, 2341} \begin {gather*} -\frac {b^2 i^2 (c+d x)^5 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac {2 b^2 B i^2 (c+d x)^5 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac {d^2 i^2 (c+d x)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{3 g^6 (a+b x)^3 (b c-a d)^3}-\frac {2 B d^2 i^2 (c+d x)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{9 g^6 (a+b x)^3 (b c-a d)^3}+\frac {b d i^2 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )^2}{2 g^6 (a+b x)^4 (b c-a d)^3}+\frac {b B d i^2 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{4 g^6 (a+b x)^4 (b c-a d)^3}-\frac {2 b^2 B^2 i^2 (c+d x)^5}{125 g^6 (a+b x)^5 (b c-a d)^3}-\frac {2 B^2 d^2 i^2 (c+d x)^3}{27 g^6 (a+b x)^3 (b c-a d)^3}+\frac {b B^2 d i^2 (c+d x)^4}{16 g^6 (a+b x)^4 (b c-a d)^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2341
Rule 2342
Rule 2395
Rule 2562
Rubi steps
\begin {align*} \int \frac {(73 c+73 d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a g+b g x)^6} \, dx &=\int \left (\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g^6 (a+b x)^6}+\frac {10658 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g^6 (a+b x)^5}+\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{b^2 g^6 (a+b x)^4}\right ) \, dx\\ &=\frac {\left (5329 d^2\right ) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^4} \, dx}{b^2 g^6}+\frac {(10658 d (b c-a d)) \int \frac {\left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{(a+b x)^5} \, dx}{b^2 g^6}+\frac {\left (5329 (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+b x)^6} \, dx}{b^2 g^6}\\ &=-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {\left (10658 B d^2\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^4 (c+d x)} \, dx}{3 b^3 g^6}+\frac {(5329 B d (b c-a d)) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^5 (c+d x)} \, dx}{b^3 g^6}+\frac {\left (10658 B (b c-a d)^2\right ) \int \frac {(b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^3 g^6}\\ &=-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {\left (10658 B d^2 (b c-a d)\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4 (c+d x)} \, dx}{3 b^3 g^6}+\frac {\left (5329 B d (b c-a d)^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5 (c+d x)} \, dx}{b^3 g^6}+\frac {\left (10658 B (b c-a d)^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^6 (c+d x)} \, dx}{5 b^3 g^6}\\ &=-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {\left (10658 B d^2 (b c-a d)\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^4}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)}+\frac {d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (c+d x)}\right ) \, dx}{3 b^3 g^6}+\frac {\left (5329 B d (b c-a d)^2\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^5}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)}-\frac {d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (c+d x)}\right ) \, dx}{b^3 g^6}+\frac {\left (10658 B (b c-a d)^3\right ) \int \left (\frac {b \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d) (a+b x)^6}-\frac {b d \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^2 (a+b x)^5}+\frac {b d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^3 (a+b x)^4}-\frac {b d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^4 (a+b x)^3}+\frac {b d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^5 (a+b x)^2}-\frac {b d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (a+b x)}+\frac {d^6 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(b c-a d)^6 (c+d x)}\right ) \, dx}{5 b^3 g^6}\\ &=-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {\left (10658 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{5 b^2 g^6}+\frac {\left (10658 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{3 b^2 g^6}-\frac {\left (5329 B d^2\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^4} \, dx}{b^2 g^6}-\frac {\left (10658 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{5 b^2 (b c-a d)^3 g^6}-\frac {\left (10658 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{3 b^2 (b c-a d)^3 g^6}+\frac {\left (5329 B d^5\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{a+b x} \, dx}{b^2 (b c-a d)^3 g^6}+\frac {\left (10658 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{3 b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B d^6\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{c+d x} \, dx}{b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{5 b^2 (b c-a d)^2 g^6}+\frac {\left (10658 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{3 b^2 (b c-a d)^2 g^6}-\frac {\left (5329 B d^4\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^2} \, dx}{b^2 (b c-a d)^2 g^6}-\frac {\left (10658 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{5 b^2 (b c-a d) g^6}-\frac {\left (10658 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{3 b^2 (b c-a d) g^6}+\frac {\left (5329 B d^3\right ) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^3} \, dx}{b^2 (b c-a d) g^6}-\frac {(10658 B d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{5 b^2 g^6}+\frac {(5329 B d (b c-a d)) \int \frac {A+B \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5} \, dx}{b^2 g^6}+\frac {\left (10658 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)^6} \, dx}{5 b^2 g^6}\\ &=-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{15 b^3 g^6}+\frac {\left (10658 B^2 d^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{9 b^3 g^6}-\frac {\left (5329 B^2 d^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{3 b^3 g^6}+\frac {\left (10658 B^2 d^5\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}{5 b^3 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\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}{3 b^3 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 g^6}+\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{5 b^3 (b c-a d)^2 g^6}+\frac {\left (10658 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{3 b^3 (b c-a d)^2 g^6}-\frac {\left (5329 B^2 d^4\right ) \int \frac {b c-a d}{(a+b x)^2 (c+d x)} \, dx}{b^3 (b c-a d)^2 g^6}-\frac {\left (5329 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{5 b^3 (b c-a d) g^6}-\frac {\left (5329 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{3 b^3 (b c-a d) g^6}+\frac {\left (5329 B^2 d^3\right ) \int \frac {b c-a d}{(a+b x)^3 (c+d x)} \, dx}{2 b^3 (b c-a d) g^6}-\frac {\left (5329 B^2 d (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{10 b^3 g^6}+\frac {\left (5329 B^2 d (b c-a d)\right ) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{4 b^3 g^6}+\frac {\left (10658 B^2 (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^6 (c+d x)} \, dx}{25 b^3 g^6}\\ &=-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^3\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{5 b^3 g^6}-\frac {\left (5329 B^2 d^3\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{3 b^3 g^6}+\frac {\left (5329 B^2 d^3\right ) \int \frac {1}{(a+b x)^3 (c+d x)} \, dx}{2 b^3 g^6}+\frac {\left (10658 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{5 b^3 (b c-a d) g^6}+\frac {\left (10658 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{3 b^3 (b c-a d) g^6}-\frac {\left (5329 B^2 d^4\right ) \int \frac {1}{(a+b x)^2 (c+d x)} \, dx}{b^3 (b c-a d) g^6}+\frac {\left (10658 B^2 d^2 (b c-a d)\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{15 b^3 g^6}+\frac {\left (10658 B^2 d^2 (b c-a d)\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{9 b^3 g^6}-\frac {\left (5329 B^2 d^2 (b c-a d)\right ) \int \frac {1}{(a+b x)^4 (c+d x)} \, dx}{3 b^3 g^6}-\frac {\left (5329 B^2 d (b c-a d)^2\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{10 b^3 g^6}+\frac {\left (5329 B^2 d (b c-a d)^2\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{4 b^3 g^6}+\frac {\left (10658 B^2 (b c-a d)^3\right ) \int \frac {1}{(a+b x)^6 (c+d x)} \, dx}{25 b^3 g^6}+\frac {\left (10658 B^2 d^5\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}{5 b^3 (b c-a d)^3 e g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 e g^6}+\frac {\left (10658 B^2 d^5\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}{3 b^3 (b c-a d)^3 e g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 e g^6}-\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 e g^6}+\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 e g^6}\\ &=-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^3}-\frac {b d}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2}{(b c-a d)^3 (a+b x)}-\frac {d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{5 b^3 g^6}-\frac {\left (5329 B^2 d^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^3}-\frac {b d}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2}{(b c-a d)^3 (a+b x)}-\frac {d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{3 b^3 g^6}+\frac {\left (5329 B^2 d^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^3}-\frac {b d}{(b c-a d)^2 (a+b x)^2}+\frac {b d^2}{(b c-a d)^3 (a+b x)}-\frac {d^3}{(b c-a d)^3 (c+d x)}\right ) \, dx}{2 b^3 g^6}+\frac {\left (10658 B^2 d^4\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^2}-\frac {b d}{(b c-a d)^2 (a+b x)}+\frac {d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{5 b^3 (b c-a d) g^6}+\frac {\left (10658 B^2 d^4\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^2}-\frac {b d}{(b c-a d)^2 (a+b x)}+\frac {d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{3 b^3 (b c-a d) g^6}-\frac {\left (5329 B^2 d^4\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^2}-\frac {b d}{(b c-a d)^2 (a+b x)}+\frac {d^2}{(b c-a d)^2 (c+d x)}\right ) \, dx}{b^3 (b c-a d) g^6}+\frac {\left (10658 B^2 d^2 (b c-a d)\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^4}-\frac {b d}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3}{(b c-a d)^4 (a+b x)}+\frac {d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{15 b^3 g^6}+\frac {\left (10658 B^2 d^2 (b c-a d)\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^4}-\frac {b d}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3}{(b c-a d)^4 (a+b x)}+\frac {d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{9 b^3 g^6}-\frac {\left (5329 B^2 d^2 (b c-a d)\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^4}-\frac {b d}{(b c-a d)^2 (a+b x)^3}+\frac {b d^2}{(b c-a d)^3 (a+b x)^2}-\frac {b d^3}{(b c-a d)^4 (a+b x)}+\frac {d^4}{(b c-a d)^4 (c+d x)}\right ) \, dx}{3 b^3 g^6}-\frac {\left (5329 B^2 d (b c-a d)^2\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^5}-\frac {b d}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4}{(b c-a d)^5 (a+b x)}-\frac {d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{10 b^3 g^6}+\frac {\left (5329 B^2 d (b c-a d)^2\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^5}-\frac {b d}{(b c-a d)^2 (a+b x)^4}+\frac {b d^2}{(b c-a d)^3 (a+b x)^3}-\frac {b d^3}{(b c-a d)^4 (a+b x)^2}+\frac {b d^4}{(b c-a d)^5 (a+b x)}-\frac {d^5}{(b c-a d)^5 (c+d x)}\right ) \, dx}{4 b^3 g^6}+\frac {\left (10658 B^2 (b c-a d)^3\right ) \int \left (\frac {b}{(b c-a d) (a+b x)^6}-\frac {b d}{(b c-a d)^2 (a+b x)^5}+\frac {b d^2}{(b c-a d)^3 (a+b x)^4}-\frac {b d^3}{(b c-a d)^4 (a+b x)^3}+\frac {b d^4}{(b c-a d)^5 (a+b x)^2}-\frac {b d^5}{(b c-a d)^6 (a+b x)}+\frac {d^6}{(b c-a d)^6 (c+d x)}\right ) \, dx}{25 b^3 g^6}+\frac {\left (10658 B^2 d^5\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}{5 b^3 (b c-a d)^3 e g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 e g^6}+\frac {\left (10658 B^2 d^5\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}{3 b^3 (b c-a d)^3 e g^6}-\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 e g^6}-\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 e g^6}+\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 e g^6}\\ &=-\frac {10658 B^2 (b c-a d)^2}{125 b^3 g^6 (a+b x)^5}-\frac {37303 B^2 d (b c-a d)}{400 b^3 g^6 (a+b x)^4}+\frac {229147 B^2 d^2}{2700 b^3 g^6 (a+b x)^3}-\frac {69277 B^2 d^3}{1800 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {250463 B^2 d^4}{900 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {250463 B^2 d^5 \log (a+b x)}{900 b^3 (b c-a d)^3 g^6}-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {250463 B^2 d^5 \log (c+d x)}{900 b^3 (b c-a d)^3 g^6}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{5 b^2 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{5 b^2 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{3 b^2 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{3 b^2 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\right ) \int \frac {\log (a+b x)}{a+b x} \, dx}{b^2 (b c-a d)^3 g^6}+\frac {\left (5329 B^2 d^5\right ) \int \frac {\log (c+d x)}{a+b x} \, dx}{b^2 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{5 b^3 (b c-a d)^3 g^6}-\frac {\left (10658 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{3 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{3 b^3 (b c-a d)^3 g^6}+\frac {\left (5329 B^2 d^6\right ) \int \frac {\log (a+b x)}{c+d x} \, dx}{b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^6\right ) \int \frac {\log (c+d x)}{c+d x} \, dx}{b^3 (b c-a d)^3 g^6}\\ &=-\frac {10658 B^2 (b c-a d)^2}{125 b^3 g^6 (a+b x)^5}-\frac {37303 B^2 d (b c-a d)}{400 b^3 g^6 (a+b x)^4}+\frac {229147 B^2 d^2}{2700 b^3 g^6 (a+b x)^3}-\frac {69277 B^2 d^3}{1800 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {250463 B^2 d^4}{900 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {250463 B^2 d^5 \log (a+b x)}{900 b^3 (b c-a d)^3 g^6}-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {250463 B^2 d^5 \log (c+d x)}{900 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{15 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{3 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{3 b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,a+b x\right )}{b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,c+d x\right )}{b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{5 b^2 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{3 b^2 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\right ) \int \frac {\log \left (\frac {b (c+d x)}{b c-a d}\right )}{a+b x} \, dx}{b^2 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{3 b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^6\right ) \int \frac {\log \left (\frac {d (a+b x)}{-b c+a d}\right )}{c+d x} \, dx}{b^3 (b c-a d)^3 g^6}\\ &=-\frac {10658 B^2 (b c-a d)^2}{125 b^3 g^6 (a+b x)^5}-\frac {37303 B^2 d (b c-a d)}{400 b^3 g^6 (a+b x)^4}+\frac {229147 B^2 d^2}{2700 b^3 g^6 (a+b x)^3}-\frac {69277 B^2 d^3}{1800 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {250463 B^2 d^4}{900 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {250463 B^2 d^5 \log (a+b x)}{900 b^3 (b c-a d)^3 g^6}+\frac {5329 B^2 d^5 \log ^2(a+b x)}{30 b^3 (b c-a d)^3 g^6}-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {250463 B^2 d^5 \log (c+d x)}{900 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {5329 B^2 d^5 \log ^2(c+d x)}{30 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{15 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{5 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{3 b^3 (b c-a d)^3 g^6}+\frac {\left (10658 B^2 d^5\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 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {d x}{b c-a d}\right )}{x} \, dx,x,a+b x\right )}{b^3 (b c-a d)^3 g^6}-\frac {\left (5329 B^2 d^5\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 (b c-a d)^3 g^6}\\ &=-\frac {10658 B^2 (b c-a d)^2}{125 b^3 g^6 (a+b x)^5}-\frac {37303 B^2 d (b c-a d)}{400 b^3 g^6 (a+b x)^4}+\frac {229147 B^2 d^2}{2700 b^3 g^6 (a+b x)^3}-\frac {69277 B^2 d^3}{1800 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {250463 B^2 d^4}{900 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {250463 B^2 d^5 \log (a+b x)}{900 b^3 (b c-a d)^3 g^6}+\frac {5329 B^2 d^5 \log ^2(a+b x)}{30 b^3 (b c-a d)^3 g^6}-\frac {10658 B (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{25 b^3 g^6 (a+b x)^5}-\frac {15987 B d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{20 b^3 g^6 (a+b x)^4}-\frac {5329 B d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{45 b^3 g^6 (a+b x)^3}+\frac {5329 B d^3 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{30 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {5329 B d^4 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {5329 B d^5 \log (a+b x) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{5 b^3 g^6 (a+b x)^5}-\frac {5329 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{2 b^3 g^6 (a+b x)^4}-\frac {5329 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )^2}{3 b^3 g^6 (a+b x)^3}+\frac {250463 B^2 d^5 \log (c+d x)}{900 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log \left (-\frac {d (a+b x)}{b c-a d}\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {5329 B d^5 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right ) \log (c+d x)}{15 b^3 (b c-a d)^3 g^6}+\frac {5329 B^2 d^5 \log ^2(c+d x)}{30 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \log (a+b x) \log \left (\frac {b (c+d x)}{b c-a d}\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \text {Li}_2\left (-\frac {d (a+b x)}{b c-a d}\right )}{15 b^3 (b c-a d)^3 g^6}-\frac {5329 B^2 d^5 \text {Li}_2\left (\frac {b (c+d x)}{b c-a d}\right )}{15 b^3 (b c-a d)^3 g^6}\\ \end {align*}
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Mathematica [C] Result contains higher order function than in optimal. Order 4 vs. order 3 in
optimal.
time = 2.48, size = 2220, normalized size = 4.79 \begin {gather*} \text {Result too large to show} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1081\) vs.
\(2(445)=890\).
time = 0.92, size = 1082, normalized size = 2.34 Too large to display
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. 10862 vs.
\(2 (424) = 848\).
time = 1.64, size = 10862, normalized size = 23.46 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1264 vs.
\(2 (424) = 848\).
time = 0.45, size = 1264, normalized size = 2.73 \begin {gather*} \frac {432 \, {\left (25 \, A^{2} + 10 \, A B + 2 \, B^{2}\right )} b^{5} c^{5} - 3375 \, {\left (8 \, A^{2} + 4 \, A B + B^{2}\right )} a b^{4} c^{4} d + 2000 \, {\left (9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right )} a^{2} b^{3} c^{3} d^{2} - {\left (1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right )} a^{5} d^{5} + 60 \, {\left ({\left (60 \, A B + 47 \, B^{2}\right )} b^{5} c d^{4} - {\left (60 \, A B + 47 \, B^{2}\right )} a b^{4} d^{5}\right )} x^{4} - 30 \, {\left ({\left (60 \, A B - 13 \, B^{2}\right )} b^{5} c^{2} d^{3} - 50 \, {\left (12 \, A B + 7 \, B^{2}\right )} a b^{4} c d^{4} + 3 \, {\left (180 \, A B + 121 \, B^{2}\right )} a^{2} b^{3} d^{5}\right )} x^{3} + 10 \, {\left (2 \, {\left (900 \, A^{2} + 60 \, A B - 43 \, B^{2}\right )} b^{5} c^{3} d^{2} - 75 \, {\left (72 \, A^{2} + 12 \, A B - 5 \, B^{2}\right )} a b^{4} c^{2} d^{3} + 600 \, {\left (9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right )} a^{2} b^{3} c d^{4} - {\left (1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right )} a^{3} b^{2} d^{5}\right )} x^{2} + 1800 \, {\left (B^{2} b^{5} d^{5} x^{5} + 5 \, B^{2} a b^{4} d^{5} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} x^{3} + 6 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 10 \, B^{2} a^{2} b^{3} c^{3} d^{2} + 10 \, {\left (B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3} + 3 \, B^{2} a^{2} b^{3} c d^{4}\right )} x^{2} + 5 \, {\left (3 \, B^{2} b^{5} c^{4} d - 8 \, B^{2} a b^{4} c^{3} d^{2} + 6 \, B^{2} a^{2} b^{3} c^{2} d^{3}\right )} x\right )} \log \left (\frac {{\left (b x + a\right )} e}{d x + c}\right )^{2} + 5 \, {\left (27 \, {\left (200 \, A^{2} + 60 \, A B + 7 \, B^{2}\right )} b^{5} c^{4} d - 100 \, {\left (144 \, A^{2} + 60 \, A B + 11 \, B^{2}\right )} a b^{4} c^{3} d^{2} + 1200 \, {\left (9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right )} a^{2} b^{3} c^{2} d^{3} - {\left (1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right )} a^{4} b d^{5}\right )} x + 60 \, {\left ({\left (60 \, A B + 47 \, B^{2}\right )} b^{5} d^{5} x^{5} + 72 \, {\left (5 \, A B + B^{2}\right )} b^{5} c^{5} - 225 \, {\left (4 \, A B + B^{2}\right )} a b^{4} c^{4} d + 200 \, {\left (3 \, A B + B^{2}\right )} a^{2} b^{3} c^{3} d^{2} + 5 \, {\left (12 \, B^{2} b^{5} c d^{4} + 5 \, {\left (12 \, A B + 7 \, B^{2}\right )} a b^{4} d^{5}\right )} x^{4} - 10 \, {\left (3 \, B^{2} b^{5} c^{2} d^{3} - 30 \, B^{2} a b^{4} c d^{4} - 20 \, {\left (3 \, A B + B^{2}\right )} a^{2} b^{3} d^{5}\right )} x^{3} + 10 \, {\left (2 \, {\left (30 \, A B + B^{2}\right )} b^{5} c^{3} d^{2} - 15 \, {\left (12 \, A B + B^{2}\right )} a b^{4} c^{2} d^{3} + 60 \, {\left (3 \, A B + B^{2}\right )} a^{2} b^{3} c d^{4}\right )} x^{2} + 5 \, {\left (9 \, {\left (20 \, A B + 3 \, B^{2}\right )} b^{5} c^{4} d - 20 \, {\left (24 \, A B + 5 \, B^{2}\right )} a b^{4} c^{3} d^{2} + 120 \, {\left (3 \, A B + B^{2}\right )} a^{2} b^{3} c^{2} d^{3}\right )} x\right )} \log \left (\frac {{\left (b x + a\right )} e}{d x + c}\right )}{54000 \, {\left ({\left (b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right )} g^{6} x^{5} + 5 \, {\left (a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right )} g^{6} x^{4} + 10 \, {\left (a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right )} g^{6} x^{3} + 10 \, {\left (a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right )} g^{6} x^{2} + 5 \, {\left (a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right )} g^{6} x + {\left (a^{5} b^{6} c^{3} - 3 \, a^{6} b^{5} c^{2} d + 3 \, a^{7} b^{4} c d^{2} - a^{8} b^{3} d^{3}\right )} g^{6}\right )}} \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 [A]
time = 3.87, size = 709, normalized size = 1.53 \begin {gather*} \frac {{\left (10800 \, B^{2} b^{2} e^{6} \log \left (\frac {b x e + a e}{d x + c}\right )^{2} - \frac {27000 \, {\left (b x e + a e\right )} B^{2} b d e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )^{2}}{d x + c} + \frac {18000 \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{4} \log \left (\frac {b x e + a e}{d x + c}\right )^{2}}{{\left (d x + c\right )}^{2}} + 21600 \, A B b^{2} e^{6} \log \left (\frac {b x e + a e}{d x + c}\right ) + 4320 \, B^{2} b^{2} e^{6} \log \left (\frac {b x e + a e}{d x + c}\right ) - \frac {54000 \, {\left (b x e + a e\right )} A B b d e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} - \frac {13500 \, {\left (b x e + a e\right )} B^{2} b d e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} + \frac {36000 \, {\left (b x e + a e\right )}^{2} A B d^{2} e^{4} \log \left (\frac {b x e + a e}{d x + c}\right )}{{\left (d x + c\right )}^{2}} + \frac {12000 \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{4} \log \left (\frac {b x e + a e}{d x + c}\right )}{{\left (d x + c\right )}^{2}} + 10800 \, A^{2} b^{2} e^{6} + 4320 \, A B b^{2} e^{6} + 864 \, B^{2} b^{2} e^{6} - \frac {27000 \, {\left (b x e + a e\right )} A^{2} b d e^{5}}{d x + c} - \frac {13500 \, {\left (b x e + a e\right )} A B b d e^{5}}{d x + c} - \frac {3375 \, {\left (b x e + a e\right )} B^{2} b d e^{5}}{d x + c} + \frac {18000 \, {\left (b x e + a e\right )}^{2} A^{2} d^{2} e^{4}}{{\left (d x + c\right )}^{2}} + \frac {12000 \, {\left (b x e + a e\right )}^{2} A B d^{2} e^{4}}{{\left (d x + c\right )}^{2}} + \frac {4000 \, {\left (b x e + a e\right )}^{2} B^{2} d^{2} e^{4}}{{\left (d x + c\right )}^{2}}\right )} {\left (\frac {b c}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}} - \frac {a d}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}}\right )}}{54000 \, {\left (\frac {{\left (b x e + a e\right )}^{5} b^{2} c^{2} g^{6}}{{\left (d x + c\right )}^{5}} - \frac {2 \, {\left (b x e + a e\right )}^{5} a b c d g^{6}}{{\left (d x + c\right )}^{5}} + \frac {{\left (b x e + a e\right )}^{5} a^{2} d^{2} g^{6}}{{\left (d x + c\right )}^{5}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 12.77, size = 2500, normalized size = 5.40 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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