Optimal. Leaf size=113 \[ \frac{5}{2} a^2 b^2 x^4 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac{a^5 A}{5 x^5}+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{13} b^5 B x^{13} \]
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Rubi [A] time = 0.062649, antiderivative size = 113, 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} \[ \frac{5}{2} a^2 b^2 x^4 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac{a^5 A}{5 x^5}+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{13} b^5 B x^{13} \]
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^6} \, dx &=\int \left (5 a^3 b (2 A b+a B)+\frac{a^5 A}{x^6}+\frac{a^4 (5 A b+a B)}{x^3}+10 a^2 b^2 (A b+a B) x^3+5 a b^3 (A b+2 a B) x^6+b^4 (A b+5 a B) x^9+b^5 B x^{12}\right ) \, dx\\ &=-\frac{a^5 A}{5 x^5}-\frac{a^4 (5 A b+a B)}{2 x^2}+5 a^3 b (2 A b+a B) x+\frac{5}{2} a^2 b^2 (A b+a B) x^4+\frac{5}{7} a b^3 (A b+2 a B) x^7+\frac{1}{10} b^4 (A b+5 a B) x^{10}+\frac{1}{13} b^5 B x^{13}\\ \end{align*}
Mathematica [A] time = 0.0355137, size = 113, normalized size = 1. \[ \frac{5}{2} a^2 b^2 x^4 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac{a^5 A}{5 x^5}+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{13} b^5 B x^{13} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 119, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{13}}{13}}+{\frac{A{x}^{10}{b}^{5}}{10}}+{\frac{B{x}^{10}a{b}^{4}}{2}}+{\frac{5\,A{x}^{7}a{b}^{4}}{7}}+{\frac{10\,B{x}^{7}{a}^{2}{b}^{3}}{7}}+{\frac{5\,A{x}^{4}{a}^{2}{b}^{3}}{2}}+{\frac{5\,B{x}^{4}{a}^{3}{b}^{2}}{2}}+10\,{a}^{3}{b}^{2}Ax+5\,{a}^{4}bBx-{\frac{A{a}^{5}}{5\,{x}^{5}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00114, size = 162, normalized size = 1.43 \begin{align*} \frac{1}{13} \, B b^{5} x^{13} + \frac{1}{10} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + \frac{5}{7} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{7} + \frac{5}{2} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{4} + 5 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x - \frac{2 \, A a^{5} + 5 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.36795, size = 275, normalized size = 2.43 \begin{align*} \frac{70 \, B b^{5} x^{18} + 91 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 650 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 2275 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 4550 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 182 \, A a^{5} - 455 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{910 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.596036, size = 131, normalized size = 1.16 \begin{align*} \frac{B b^{5} x^{13}}{13} + x^{10} \left (\frac{A b^{5}}{10} + \frac{B a b^{4}}{2}\right ) + x^{7} \left (\frac{5 A a b^{4}}{7} + \frac{10 B a^{2} b^{3}}{7}\right ) + x^{4} \left (\frac{5 A a^{2} b^{3}}{2} + \frac{5 B a^{3} b^{2}}{2}\right ) + x \left (10 A a^{3} b^{2} + 5 B a^{4} b\right ) - \frac{2 A a^{5} + x^{3} \left (25 A a^{4} b + 5 B a^{5}\right )}{10 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20654, size = 167, normalized size = 1.48 \begin{align*} \frac{1}{13} \, B b^{5} x^{13} + \frac{1}{2} \, B a b^{4} x^{10} + \frac{1}{10} \, A b^{5} x^{10} + \frac{10}{7} \, B a^{2} b^{3} x^{7} + \frac{5}{7} \, A a b^{4} x^{7} + \frac{5}{2} \, B a^{3} b^{2} x^{4} + \frac{5}{2} \, A a^{2} b^{3} x^{4} + 5 \, B a^{4} b x + 10 \, A a^{3} b^{2} x - \frac{5 \, B a^{5} x^{3} + 25 \, A a^{4} b x^{3} + 2 \, A a^{5}}{10 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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