Optimal. Leaf size=281 \[ -\frac {b^2 i^2 (c+d x)^5 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{5 g^6 (a+b x)^5 (b c-a d)^3}-\frac {d^2 i^2 (c+d x)^3 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{3 g^6 (a+b x)^3 (b c-a d)^3}+\frac {b d i^2 (c+d x)^4 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{2 g^6 (a+b x)^4 (b c-a d)^3}-\frac {b^2 B i^2 (c+d x)^5}{25 g^6 (a+b x)^5 (b c-a d)^3}-\frac {B d^2 i^2 (c+d x)^3}{9 g^6 (a+b x)^3 (b c-a d)^3}+\frac {b B d i^2 (c+d x)^4}{8 g^6 (a+b x)^4 (b c-a d)^3} \]
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Rubi [A] time = 0.68, antiderivative size = 359, normalized size of antiderivative = 1.28, number of steps used = 14, number of rules used = 4, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2528, 2525, 12, 44} \[ -\frac {d^2 i^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{3 b^3 g^6 (a+b x)^3}-\frac {d i^2 (b c-a d) \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{2 b^3 g^6 (a+b x)^4}-\frac {i^2 (b c-a d)^2 \left (B \log \left (\frac {e (a+b x)}{c+d x}\right )+A\right )}{5 b^3 g^6 (a+b x)^5}-\frac {B d^4 i^2}{30 b^3 g^6 (a+b x) (b c-a d)^2}+\frac {B d^3 i^2}{60 b^3 g^6 (a+b x)^2 (b c-a d)}-\frac {B d^5 i^2 \log (a+b x)}{30 b^3 g^6 (b c-a d)^3}+\frac {B d^5 i^2 \log (c+d x)}{30 b^3 g^6 (b c-a d)^3}-\frac {3 B d i^2 (b c-a d)}{40 b^3 g^6 (a+b x)^4}-\frac {B i^2 (b c-a d)^2}{25 b^3 g^6 (a+b x)^5}-\frac {B d^2 i^2}{90 b^3 g^6 (a+b x)^3} \]
Antiderivative was successfully verified.
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Rule 12
Rule 44
Rule 2525
Rule 2528
Rubi steps
\begin {align*} \int \frac {(19 c+19 d x)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{(a g+b g x)^6} \, dx &=\int \left (\frac {361 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^2 g^6 (a+b x)^6}+\frac {722 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^2 g^6 (a+b x)^5}+\frac {361 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{b^2 g^6 (a+b x)^4}\right ) \, dx\\ &=\frac {\left (361 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 {(722 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 (361 (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}{b^2 g^6}\\ &=-\frac {361 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^3 g^6 (a+b x)^5}-\frac {361 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^3 g^6 (a+b x)^4}-\frac {361 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 b^3 g^6 (a+b x)^3}+\frac {\left (361 B d^2\right ) \int \frac {b c-a d}{(a+b x)^4 (c+d x)} \, dx}{3 b^3 g^6}+\frac {(361 B d (b c-a d)) \int \frac {b c-a d}{(a+b x)^5 (c+d x)} \, dx}{2 b^3 g^6}+\frac {\left (361 B (b c-a d)^2\right ) \int \frac {b c-a d}{(a+b x)^6 (c+d x)} \, dx}{5 b^3 g^6}\\ &=-\frac {361 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^3 g^6 (a+b x)^5}-\frac {361 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^3 g^6 (a+b x)^4}-\frac {361 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 b^3 g^6 (a+b x)^3}+\frac {\left (361 B 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 (361 B d (b c-a d)^2\right ) \int \frac {1}{(a+b x)^5 (c+d x)} \, dx}{2 b^3 g^6}+\frac {\left (361 B (b c-a d)^3\right ) \int \frac {1}{(a+b x)^6 (c+d x)} \, dx}{5 b^3 g^6}\\ &=-\frac {361 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^3 g^6 (a+b x)^5}-\frac {361 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^3 g^6 (a+b x)^4}-\frac {361 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 b^3 g^6 (a+b x)^3}+\frac {\left (361 B 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 (361 B 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}{2 b^3 g^6}+\frac {\left (361 B (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}{5 b^3 g^6}\\ &=-\frac {361 B (b c-a d)^2}{25 b^3 g^6 (a+b x)^5}-\frac {1083 B d (b c-a d)}{40 b^3 g^6 (a+b x)^4}-\frac {361 B d^2}{90 b^3 g^6 (a+b x)^3}+\frac {361 B d^3}{60 b^3 (b c-a d) g^6 (a+b x)^2}-\frac {361 B d^4}{30 b^3 (b c-a d)^2 g^6 (a+b x)}-\frac {361 B d^5 \log (a+b x)}{30 b^3 (b c-a d)^3 g^6}-\frac {361 (b c-a d)^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{5 b^3 g^6 (a+b x)^5}-\frac {361 d (b c-a d) \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{2 b^3 g^6 (a+b x)^4}-\frac {361 d^2 \left (A+B \log \left (\frac {e (a+b x)}{c+d x}\right )\right )}{3 b^3 g^6 (a+b x)^3}+\frac {361 B d^5 \log (c+d x)}{30 b^3 (b c-a d)^3 g^6}\\ \end {align*}
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Mathematica [A] time = 0.86, size = 344, normalized size = 1.22 \[ \frac {i^2 \left (-\frac {360 a^2 A d^2}{(a+b x)^5}-\frac {60 B \left (a^2 d^2+a b d (3 c+5 d x)+b^2 \left (6 c^2+15 c d x+10 d^2 x^2\right )\right ) \log \left (\frac {e (a+b x)}{c+d x}\right )}{(a+b x)^5}-\frac {72 a^2 B d^2}{(a+b x)^5}-\frac {360 A b^2 c^2}{(a+b x)^5}-\frac {900 A b c d}{(a+b x)^4}+\frac {720 a A b c d}{(a+b x)^5}-\frac {600 A d^2}{(a+b x)^3}+\frac {900 a A d^2}{(a+b x)^4}-\frac {72 b^2 B c^2}{(a+b x)^5}-\frac {60 B d^5 \log (a+b x)}{(b c-a d)^3}+\frac {60 B d^5 \log (c+d x)}{(b c-a d)^3}-\frac {60 B d^4}{(a+b x) (b c-a d)^2}+\frac {30 B d^3}{(a+b x)^2 (b c-a d)}-\frac {135 b B c d}{(a+b x)^4}+\frac {144 a b B c d}{(a+b x)^5}-\frac {20 B d^2}{(a+b x)^3}+\frac {135 a B d^2}{(a+b x)^4}\right )}{1800 b^3 g^6} \]
Antiderivative was successfully verified.
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fricas [B] time = 1.12, size = 807, normalized size = 2.87 \[ -\frac {60 \, {\left (B b^{5} c d^{4} - B a b^{4} d^{5}\right )} i^{2} x^{4} - 30 \, {\left (B b^{5} c^{2} d^{3} - 10 \, B a b^{4} c d^{4} + 9 \, B a^{2} b^{3} d^{5}\right )} i^{2} x^{3} + 10 \, {\left (2 \, {\left (30 \, A + B\right )} b^{5} c^{3} d^{2} - 15 \, {\left (12 \, A + B\right )} a b^{4} c^{2} d^{3} + 60 \, {\left (3 \, A + B\right )} a^{2} b^{3} c d^{4} - {\left (60 \, A + 47 \, B\right )} a^{3} b^{2} d^{5}\right )} i^{2} x^{2} + 5 \, {\left (9 \, {\left (20 \, A + 3 \, B\right )} b^{5} c^{4} d - 20 \, {\left (24 \, A + 5 \, B\right )} a b^{4} c^{3} d^{2} + 120 \, {\left (3 \, A + B\right )} a^{2} b^{3} c^{2} d^{3} - {\left (60 \, A + 47 \, B\right )} a^{4} b d^{5}\right )} i^{2} x + {\left (72 \, {\left (5 \, A + B\right )} b^{5} c^{5} - 225 \, {\left (4 \, A + B\right )} a b^{4} c^{4} d + 200 \, {\left (3 \, A + B\right )} a^{2} b^{3} c^{3} d^{2} - {\left (60 \, A + 47 \, B\right )} a^{5} d^{5}\right )} i^{2} + 60 \, {\left (B b^{5} d^{5} i^{2} x^{5} + 5 \, B a b^{4} d^{5} i^{2} x^{4} + 10 \, B a^{2} b^{3} d^{5} i^{2} x^{3} + 10 \, {\left (B b^{5} c^{3} d^{2} - 3 \, B a b^{4} c^{2} d^{3} + 3 \, B a^{2} b^{3} c d^{4}\right )} i^{2} x^{2} + 5 \, {\left (3 \, B b^{5} c^{4} d - 8 \, B a b^{4} c^{3} d^{2} + 6 \, B a^{2} b^{3} c^{2} d^{3}\right )} i^{2} x + {\left (6 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2}\right )} i^{2}\right )} \log \left (\frac {b e x + a e}{d x + c}\right )}{1800 \, {\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 )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.51, size = 382, normalized size = 1.36 \[ \frac {{\left (360 \, B b^{2} e^{6} \log \left (\frac {b x e + a e}{d x + c}\right ) - \frac {900 \, {\left (b x e + a e\right )} B b d e^{5} \log \left (\frac {b x e + a e}{d x + c}\right )}{d x + c} + \frac {600 \, {\left (b x e + a e\right )}^{2} B d^{2} e^{4} \log \left (\frac {b x e + a e}{d x + c}\right )}{{\left (d x + c\right )}^{2}} + 360 \, A b^{2} e^{6} + 72 \, B b^{2} e^{6} - \frac {900 \, {\left (b x e + a e\right )} A b d e^{5}}{d x + c} - \frac {225 \, {\left (b x e + a e\right )} B b d e^{5}}{d x + c} + \frac {600 \, {\left (b x e + a e\right )}^{2} A d^{2} e^{4}}{{\left (d x + c\right )}^{2}} + \frac {200 \, {\left (b x e + a e\right )}^{2} B d^{2} e^{4}}{{\left (d x + c\right )}^{2}}\right )} {\left (\frac {b c}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}} - \frac {a d}{{\left (b c e - a d e\right )} {\left (b c - a d\right )}}\right )}}{1800 \, {\left (\frac {{\left (b x e + a e\right )}^{5} b^{2} c^{2} g^{6}}{{\left (d x + c\right )}^{5}} - \frac {2 \, {\left (b x e + a e\right )}^{5} a b c d g^{6}}{{\left (d x + c\right )}^{5}} + \frac {{\left (b x e + a e\right )}^{5} a^{2} d^{2} g^{6}}{{\left (d x + c\right )}^{5}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 1262, normalized size = 4.49 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 3.04, size = 3029, normalized size = 10.78 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.99, size = 941, normalized size = 3.35 \[ \frac {B\,d^5\,i^2\,\mathrm {atanh}\left (\frac {30\,a^3\,b^3\,d^3\,g^6-30\,a^2\,b^4\,c\,d^2\,g^6-30\,a\,b^5\,c^2\,d\,g^6+30\,b^6\,c^3\,g^6}{30\,b^3\,g^6\,{\left (a\,d-b\,c\right )}^3}+\frac {2\,b\,d\,x\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}{{\left (a\,d-b\,c\right )}^3}\right )}{15\,b^3\,g^6\,{\left (a\,d-b\,c\right )}^3}-\frac {\ln \left (\frac {e\,\left (a+b\,x\right )}{c+d\,x}\right )\,\left (a\,\left (\frac {B\,a\,d^2\,i^2}{30\,b^4\,g^6}+\frac {B\,c\,d\,i^2}{10\,b^3\,g^6}\right )+x\,\left (b\,\left (\frac {B\,a\,d^2\,i^2}{30\,b^4\,g^6}+\frac {B\,c\,d\,i^2}{10\,b^3\,g^6}\right )+\frac {2\,B\,a\,d^2\,i^2}{15\,b^3\,g^6}+\frac {2\,B\,c\,d\,i^2}{5\,b^2\,g^6}\right )+\frac {B\,c^2\,i^2}{5\,b^2\,g^6}+\frac {B\,d^2\,i^2\,x^2}{3\,b^2\,g^6}\right )}{5\,a^4\,x+\frac {a^5}{b}+b^4\,x^5+10\,a^3\,b\,x^2+5\,a\,b^3\,x^4+10\,a^2\,b^2\,x^3}-\frac {\frac {60\,A\,a^4\,d^4\,i^2+360\,A\,b^4\,c^4\,i^2+47\,B\,a^4\,d^4\,i^2+72\,B\,b^4\,c^4\,i^2+60\,A\,a^2\,b^2\,c^2\,d^2\,i^2+47\,B\,a^2\,b^2\,c^2\,d^2\,i^2-540\,A\,a\,b^3\,c^3\,d\,i^2+60\,A\,a^3\,b\,c\,d^3\,i^2-153\,B\,a\,b^3\,c^3\,d\,i^2+47\,B\,a^3\,b\,c\,d^3\,i^2}{60\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}+\frac {x^2\,\left (60\,A\,a^2\,b^2\,d^4\,i^2+47\,B\,a^2\,b^2\,d^4\,i^2+60\,A\,b^4\,c^2\,d^2\,i^2+2\,B\,b^4\,c^2\,d^2\,i^2-120\,A\,a\,b^3\,c\,d^3\,i^2-13\,B\,a\,b^3\,c\,d^3\,i^2\right )}{6\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}+\frac {x\,\left (60\,A\,a^3\,b\,d^4\,i^2+47\,B\,a^3\,b\,d^4\,i^2+180\,A\,b^4\,c^3\,d\,i^2+27\,B\,b^4\,c^3\,d\,i^2-300\,A\,a\,b^3\,c^2\,d^2\,i^2+60\,A\,a^2\,b^2\,c\,d^3\,i^2-73\,B\,a\,b^3\,c^2\,d^2\,i^2+47\,B\,a^2\,b^2\,c\,d^3\,i^2\right )}{12\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}+\frac {d\,x^3\,\left (9\,B\,a\,b^3\,d^3\,i^2-B\,b^4\,c\,d^2\,i^2\right )}{2\,\left (a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right )}+\frac {B\,b^4\,d^4\,i^2\,x^4}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{30\,a^5\,b^3\,g^6+150\,a^4\,b^4\,g^6\,x+300\,a^3\,b^5\,g^6\,x^2+300\,a^2\,b^6\,g^6\,x^3+150\,a\,b^7\,g^6\,x^4+30\,b^8\,g^6\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 92.23, size = 1300, normalized size = 4.63 \[ - \frac {B d^{5} i^{2} \log {\left (x + \frac {- \frac {B a^{4} d^{9} i^{2}}{\left (a d - b c\right )^{3}} + \frac {4 B a^{3} b c d^{8} i^{2}}{\left (a d - b c\right )^{3}} - \frac {6 B a^{2} b^{2} c^{2} d^{7} i^{2}}{\left (a d - b c\right )^{3}} + \frac {4 B a b^{3} c^{3} d^{6} i^{2}}{\left (a d - b c\right )^{3}} + B a d^{6} i^{2} - \frac {B b^{4} c^{4} d^{5} i^{2}}{\left (a d - b c\right )^{3}} + B b c d^{5} i^{2}}{2 B b d^{6} i^{2}} \right )}}{30 b^{3} g^{6} \left (a d - b c\right )^{3}} + \frac {B d^{5} i^{2} \log {\left (x + \frac {\frac {B a^{4} d^{9} i^{2}}{\left (a d - b c\right )^{3}} - \frac {4 B a^{3} b c d^{8} i^{2}}{\left (a d - b c\right )^{3}} + \frac {6 B a^{2} b^{2} c^{2} d^{7} i^{2}}{\left (a d - b c\right )^{3}} - \frac {4 B a b^{3} c^{3} d^{6} i^{2}}{\left (a d - b c\right )^{3}} + B a d^{6} i^{2} + \frac {B b^{4} c^{4} d^{5} i^{2}}{\left (a d - b c\right )^{3}} + B b c d^{5} i^{2}}{2 B b d^{6} i^{2}} \right )}}{30 b^{3} g^{6} \left (a d - b c\right )^{3}} + \frac {- 60 A a^{4} d^{4} i^{2} - 60 A a^{3} b c d^{3} i^{2} - 60 A a^{2} b^{2} c^{2} d^{2} i^{2} + 540 A a b^{3} c^{3} d i^{2} - 360 A b^{4} c^{4} i^{2} - 47 B a^{4} d^{4} i^{2} - 47 B a^{3} b c d^{3} i^{2} - 47 B a^{2} b^{2} c^{2} d^{2} i^{2} + 153 B a b^{3} c^{3} d i^{2} - 72 B b^{4} c^{4} i^{2} - 60 B b^{4} d^{4} i^{2} x^{4} + x^{3} \left (- 270 B a b^{3} d^{4} i^{2} + 30 B b^{4} c d^{3} i^{2}\right ) + x^{2} \left (- 600 A a^{2} b^{2} d^{4} i^{2} + 1200 A a b^{3} c d^{3} i^{2} - 600 A b^{4} c^{2} d^{2} i^{2} - 470 B a^{2} b^{2} d^{4} i^{2} + 130 B a b^{3} c d^{3} i^{2} - 20 B b^{4} c^{2} d^{2} i^{2}\right ) + x \left (- 300 A a^{3} b d^{4} i^{2} - 300 A a^{2} b^{2} c d^{3} i^{2} + 1500 A a b^{3} c^{2} d^{2} i^{2} - 900 A b^{4} c^{3} d i^{2} - 235 B a^{3} b d^{4} i^{2} - 235 B a^{2} b^{2} c d^{3} i^{2} + 365 B a b^{3} c^{2} d^{2} i^{2} - 135 B b^{4} c^{3} d i^{2}\right )}{1800 a^{7} b^{3} d^{2} g^{6} - 3600 a^{6} b^{4} c d g^{6} + 1800 a^{5} b^{5} c^{2} g^{6} + x^{5} \left (1800 a^{2} b^{8} d^{2} g^{6} - 3600 a b^{9} c d g^{6} + 1800 b^{10} c^{2} g^{6}\right ) + x^{4} \left (9000 a^{3} b^{7} d^{2} g^{6} - 18000 a^{2} b^{8} c d g^{6} + 9000 a b^{9} c^{2} g^{6}\right ) + x^{3} \left (18000 a^{4} b^{6} d^{2} g^{6} - 36000 a^{3} b^{7} c d g^{6} + 18000 a^{2} b^{8} c^{2} g^{6}\right ) + x^{2} \left (18000 a^{5} b^{5} d^{2} g^{6} - 36000 a^{4} b^{6} c d g^{6} + 18000 a^{3} b^{7} c^{2} g^{6}\right ) + x \left (9000 a^{6} b^{4} d^{2} g^{6} - 18000 a^{5} b^{5} c d g^{6} + 9000 a^{4} b^{6} c^{2} g^{6}\right )} + \frac {\left (- B a^{2} d^{2} i^{2} - 3 B a b c d i^{2} - 5 B a b d^{2} i^{2} x - 6 B b^{2} c^{2} i^{2} - 15 B b^{2} c d i^{2} x - 10 B b^{2} d^{2} i^{2} x^{2}\right ) \log {\left (\frac {e \left (a + b x\right )}{c + d x} \right )}}{30 a^{5} b^{3} g^{6} + 150 a^{4} b^{4} g^{6} x + 300 a^{3} b^{5} g^{6} x^{2} + 300 a^{2} b^{6} g^{6} x^{3} + 150 a b^{7} g^{6} x^{4} + 30 b^{8} g^{6} x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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