Optimal. Leaf size=112 \[ \frac{5}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{2} a^4 x^2 (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{14} b^4 x^{14} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{17} b^5 B x^{17} \]
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Rubi [A] time = 0.060787, antiderivative size = 112, 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} \[ \frac{5}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{2} a^4 x^2 (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{14} b^4 x^{14} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{17} b^5 B x^{17} \]
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^2} \, dx &=\int \left (\frac{a^5 A}{x^2}+a^4 (5 A b+a B) x+5 a^3 b (2 A b+a B) x^4+10 a^2 b^2 (A b+a B) x^7+5 a b^3 (A b+2 a B) x^{10}+b^4 (A b+5 a B) x^{13}+b^5 B x^{16}\right ) \, dx\\ &=-\frac{a^5 A}{x}+\frac{1}{2} a^4 (5 A b+a B) x^2+a^3 b (2 A b+a B) x^5+\frac{5}{4} a^2 b^2 (A b+a B) x^8+\frac{5}{11} a b^3 (A b+2 a B) x^{11}+\frac{1}{14} b^4 (A b+5 a B) x^{14}+\frac{1}{17} b^5 B x^{17}\\ \end{align*}
Mathematica [A] time = 0.0332409, size = 112, normalized size = 1. \[ \frac{5}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{2} a^4 x^2 (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{14} b^4 x^{14} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{17} b^5 B x^{17} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 125, normalized size = 1.1 \begin{align*}{\frac{{b}^{5}B{x}^{17}}{17}}+{\frac{A{x}^{14}{b}^{5}}{14}}+{\frac{5\,B{x}^{14}a{b}^{4}}{14}}+{\frac{5\,A{x}^{11}a{b}^{4}}{11}}+{\frac{10\,B{x}^{11}{a}^{2}{b}^{3}}{11}}+{\frac{5\,A{x}^{8}{a}^{2}{b}^{3}}{4}}+{\frac{5\,B{x}^{8}{a}^{3}{b}^{2}}{4}}+2\,A{x}^{5}{a}^{3}{b}^{2}+B{x}^{5}{a}^{4}b+{\frac{5\,A{x}^{2}{a}^{4}b}{2}}+{\frac{B{x}^{2}{a}^{5}}{2}}-{\frac{A{a}^{5}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.25233, size = 159, normalized size = 1.42 \begin{align*} \frac{1}{17} \, B b^{5} x^{17} + \frac{1}{14} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{14} + \frac{5}{11} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{11} + \frac{5}{4} \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{8} +{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{5} - \frac{A a^{5}}{x} + \frac{1}{2} \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43568, size = 281, normalized size = 2.51 \begin{align*} \frac{308 \, B b^{5} x^{18} + 374 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{15} + 2380 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{12} + 6545 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{9} + 5236 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{6} - 5236 \, A a^{5} + 2618 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{3}}{5236 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.37606, size = 129, normalized size = 1.15 \begin{align*} - \frac{A a^{5}}{x} + \frac{B b^{5} x^{17}}{17} + x^{14} \left (\frac{A b^{5}}{14} + \frac{5 B a b^{4}}{14}\right ) + x^{11} \left (\frac{5 A a b^{4}}{11} + \frac{10 B a^{2} b^{3}}{11}\right ) + x^{8} \left (\frac{5 A a^{2} b^{3}}{4} + \frac{5 B a^{3} b^{2}}{4}\right ) + x^{5} \left (2 A a^{3} b^{2} + B a^{4} b\right ) + x^{2} \left (\frac{5 A a^{4} b}{2} + \frac{B a^{5}}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12063, size = 167, normalized size = 1.49 \begin{align*} \frac{1}{17} \, B b^{5} x^{17} + \frac{5}{14} \, B a b^{4} x^{14} + \frac{1}{14} \, A b^{5} x^{14} + \frac{10}{11} \, B a^{2} b^{3} x^{11} + \frac{5}{11} \, A a b^{4} x^{11} + \frac{5}{4} \, B a^{3} b^{2} x^{8} + \frac{5}{4} \, A a^{2} b^{3} x^{8} + B a^{4} b x^{5} + 2 \, A a^{3} b^{2} x^{5} + \frac{1}{2} \, B a^{5} x^{2} + \frac{5}{2} \, A a^{4} b x^{2} - \frac{A a^{5}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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