Optimal. Leaf size=109 \[ -\frac {a^5 A}{11 x^{11}}-\frac {a^4 (a B+5 A b)}{8 x^8}-\frac {a^3 b (a B+2 A b)}{x^5}-\frac {5 a^2 b^2 (a B+A b)}{x^2}+\frac {1}{4} b^4 x^4 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac {1}{7} b^5 B x^7 \]
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Rubi [A] time = 0.06, antiderivative size = 109, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {448} \begin {gather*} -\frac {5 a^2 b^2 (a B+A b)}{x^2}-\frac {a^3 b (a B+2 A b)}{x^5}-\frac {a^4 (a B+5 A b)}{8 x^8}-\frac {a^5 A}{11 x^{11}}+\frac {1}{4} b^4 x^4 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac {1}{7} b^5 B x^7 \end {gather*}
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{12}} \, dx &=\int \left (5 a b^3 (A b+2 a B)+\frac {a^5 A}{x^{12}}+\frac {a^4 (5 A b+a B)}{x^9}+\frac {5 a^3 b (2 A b+a B)}{x^6}+\frac {10 a^2 b^2 (A b+a B)}{x^3}+b^4 (A b+5 a B) x^3+b^5 B x^6\right ) \, dx\\ &=-\frac {a^5 A}{11 x^{11}}-\frac {a^4 (5 A b+a B)}{8 x^8}-\frac {a^3 b (2 A b+a B)}{x^5}-\frac {5 a^2 b^2 (A b+a B)}{x^2}+5 a b^3 (A b+2 a B) x+\frac {1}{4} b^4 (A b+5 a B) x^4+\frac {1}{7} b^5 B x^7\\ \end {align*}
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Mathematica [A] time = 0.04, size = 109, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{11 x^{11}}-\frac {a^4 (a B+5 A b)}{8 x^8}-\frac {a^3 b (a B+2 A b)}{x^5}-\frac {5 a^2 b^2 (a B+A b)}{x^2}+\frac {1}{4} b^4 x^4 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac {1}{7} b^5 B x^7 \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b x^3\right )^5 \left (A+B x^3\right )}{x^{12}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.79, size = 121, normalized size = 1.11 \begin {gather*} \frac {88 \, B b^{5} x^{18} + 154 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 3080 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 3080 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 616 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 56 \, A a^{5} - 77 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{616 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 124, normalized size = 1.14 \begin {gather*} \frac {1}{7} \, B b^{5} x^{7} + \frac {5}{4} \, B a b^{4} x^{4} + \frac {1}{4} \, A b^{5} x^{4} + 10 \, B a^{2} b^{3} x + 5 \, A a b^{4} x - \frac {440 \, B a^{3} b^{2} x^{9} + 440 \, A a^{2} b^{3} x^{9} + 88 \, B a^{4} b x^{6} + 176 \, A a^{3} b^{2} x^{6} + 11 \, B a^{5} x^{3} + 55 \, A a^{4} b x^{3} + 8 \, A a^{5}}{88 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 108, normalized size = 0.99 \begin {gather*} \frac {B \,b^{5} x^{7}}{7}+\frac {A \,b^{5} x^{4}}{4}+\frac {5 B a \,b^{4} x^{4}}{4}+5 A a \,b^{4} x +10 B \,a^{2} b^{3} x -\frac {5 \left (A b +B a \right ) a^{2} b^{2}}{x^{2}}-\frac {\left (2 A b +B a \right ) a^{3} b}{x^{5}}-\frac {\left (5 A b +B a \right ) a^{4}}{8 x^{8}}-\frac {A \,a^{5}}{11 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 120, normalized size = 1.10 \begin {gather*} \frac {1}{7} \, B b^{5} x^{7} + \frac {1}{4} \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{4} + 5 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x - \frac {440 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 88 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 8 \, A a^{5} + 11 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{88 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 116, normalized size = 1.06 \begin {gather*} x^4\,\left (\frac {A\,b^5}{4}+\frac {5\,B\,a\,b^4}{4}\right )-\frac {\frac {A\,a^5}{11}+x^6\,\left (B\,a^4\,b+2\,A\,a^3\,b^2\right )+x^3\,\left (\frac {B\,a^5}{8}+\frac {5\,A\,b\,a^4}{8}\right )+x^9\,\left (5\,B\,a^3\,b^2+5\,A\,a^2\,b^3\right )}{x^{11}}+\frac {B\,b^5\,x^7}{7}+5\,a\,b^3\,x\,\left (A\,b+2\,B\,a\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.73, size = 131, normalized size = 1.20 \begin {gather*} \frac {B b^{5} x^{7}}{7} + x^{4} \left (\frac {A b^{5}}{4} + \frac {5 B a b^{4}}{4}\right ) + x \left (5 A a b^{4} + 10 B a^{2} b^{3}\right ) + \frac {- 8 A a^{5} + x^{9} \left (- 440 A a^{2} b^{3} - 440 B a^{3} b^{2}\right ) + x^{6} \left (- 176 A a^{3} b^{2} - 88 B a^{4} b\right ) + x^{3} \left (- 55 A a^{4} b - 11 B a^{5}\right )}{88 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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