Optimal. Leaf size=110 \[ -\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{a^5 A}{14 x^{14}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac{1}{4} b^5 B x^4 \]
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Rubi [A] time = 0.0677994, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ -\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{a^5 A}{14 x^{14}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac{1}{4} b^5 B x^4 \]
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*}
Mathematica [A] time = 0.0412247, size = 110, normalized size = 1. \[ -\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{a^5 A}{14 x^{14}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac{1}{4} b^5 B x^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 102, normalized size = 0.9 \begin{align*}{\frac{{b}^{5}B{x}^{4}}{4}}+{b}^{5}Ax+5\,a{b}^{4}Bx-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{11\,{x}^{11}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{2\,{x}^{2}}}-{\frac{A{a}^{5}}{14\,{x}^{14}}}-2\,{\frac{{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{{x}^{5}}}-{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{8\,{x}^{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.39243, size = 161, normalized size = 1.46 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4132, size = 277, normalized size = 2.52 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 27.6844, size = 122, normalized size = 1.11 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22931, size = 166, normalized size = 1.51 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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