Optimal. Leaf size=110 \[ -\frac {a^5 A}{14 x^{14}}-\frac {a^4 (a B+5 A b)}{11 x^{11}}-\frac {5 a^3 b (a B+2 A b)}{8 x^8}-\frac {2 a^2 b^2 (a B+A b)}{x^5}+b^4 x (5 a B+A b)-\frac {5 a b^3 (2 a B+A b)}{2 x^2}+\frac {1}{4} b^5 B x^4 \]
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Rubi [A] time = 0.07, antiderivative size = 110, 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 {2 a^2 b^2 (a B+A b)}{x^5}-\frac {a^4 (a B+5 A b)}{11 x^{11}}-\frac {5 a^3 b (a B+2 A b)}{8 x^8}-\frac {a^5 A}{14 x^{14}}-\frac {5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac {1}{4} b^5 B x^4 \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^{15}} \, dx &=\int \left (b^4 (A b+5 a B)+\frac {a^5 A}{x^{15}}+\frac {a^4 (5 A b+a B)}{x^{12}}+\frac {5 a^3 b (2 A b+a B)}{x^9}+\frac {10 a^2 b^2 (A b+a B)}{x^6}+\frac {5 a b^3 (A b+2 a B)}{x^3}+b^5 B x^3\right ) \, dx\\ &=-\frac {a^5 A}{14 x^{14}}-\frac {a^4 (5 A b+a B)}{11 x^{11}}-\frac {5 a^3 b (2 A b+a B)}{8 x^8}-\frac {2 a^2 b^2 (A b+a B)}{x^5}-\frac {5 a b^3 (A b+2 a B)}{2 x^2}+b^4 (A b+5 a B) x+\frac {1}{4} b^5 B x^4\\ \end {align*}
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Mathematica [A] time = 0.07, size = 110, normalized size = 1.00 \begin {gather*} -\frac {a^5 A}{14 x^{14}}-\frac {a^4 (a B+5 A b)}{11 x^{11}}-\frac {5 a^3 b (a B+2 A b)}{8 x^8}-\frac {2 a^2 b^2 (a B+A b)}{x^5}+b^4 x (5 a B+A b)-\frac {5 a b^3 (2 a B+A b)}{2 x^2}+\frac {1}{4} b^5 B x^4 \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^{15}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.56, size = 121, normalized size = 1.10 \begin {gather*} \frac {154 \, B b^{5} x^{18} + 616 \, {\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} - 1540 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} - 1232 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} - 385 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 44 \, A a^{5} - 56 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{616 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 123, normalized size = 1.12 \begin {gather*} \frac {1}{4} \, B b^{5} x^{4} + 5 \, B a b^{4} x + A b^{5} x - \frac {3080 \, B a^{2} b^{3} x^{12} + 1540 \, A a b^{4} x^{12} + 1232 \, B a^{3} b^{2} x^{9} + 1232 \, A a^{2} b^{3} x^{9} + 385 \, B a^{4} b x^{6} + 770 \, A a^{3} b^{2} x^{6} + 56 \, B a^{5} x^{3} + 280 \, A a^{4} b x^{3} + 44 \, A a^{5}}{616 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 102, normalized size = 0.93 \begin {gather*} \frac {B \,b^{5} x^{4}}{4}+A \,b^{5} x +5 B a \,b^{4} x -\frac {5 \left (A b +2 B a \right ) a \,b^{3}}{2 x^{2}}-\frac {2 \left (A b +B a \right ) a^{2} b^{2}}{x^{5}}-\frac {5 \left (2 A b +B a \right ) a^{3} b}{8 x^{8}}-\frac {\left (5 A b +B a \right ) a^{4}}{11 x^{11}}-\frac {A \,a^{5}}{14 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 119, normalized size = 1.08 \begin {gather*} \frac {1}{4} \, B b^{5} x^{4} + {\left (5 \, B a b^{4} + A b^{5}\right )} x - \frac {1540 \, {\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 1232 \, {\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 385 \, {\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} + 44 \, A a^{5} + 56 \, {\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{616 \, x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.39, size = 120, normalized size = 1.09 \begin {gather*} x\,\left (A\,b^5+5\,B\,a\,b^4\right )-\frac {\frac {A\,a^5}{14}+x^{12}\,\left (5\,B\,a^2\,b^3+\frac {5\,A\,a\,b^4}{2}\right )+x^6\,\left (\frac {5\,B\,a^4\,b}{8}+\frac {5\,A\,a^3\,b^2}{4}\right )+x^3\,\left (\frac {B\,a^5}{11}+\frac {5\,A\,b\,a^4}{11}\right )+x^9\,\left (2\,B\,a^3\,b^2+2\,A\,a^2\,b^3\right )}{x^{14}}+\frac {B\,b^5\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 22.98, size = 129, normalized size = 1.17 \begin {gather*} \frac {B b^{5} x^{4}}{4} + x \left (A b^{5} + 5 B a b^{4}\right ) + \frac {- 44 A a^{5} + x^{12} \left (- 1540 A a b^{4} - 3080 B a^{2} b^{3}\right ) + x^{9} \left (- 1232 A a^{2} b^{3} - 1232 B a^{3} b^{2}\right ) + x^{6} \left (- 770 A a^{3} b^{2} - 385 B a^{4} b\right ) + x^{3} \left (- 280 A a^{4} b - 56 B a^{5}\right )}{616 x^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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