Optimal. Leaf size=53 \[ -\frac{a^2 A}{x}+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
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Rubi [A] time = 0.0282968, antiderivative size = 53, 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} \[ -\frac{a^2 A}{x}+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2 \left (A+B x^3\right )}{x^2} \, dx &=\int \left (\frac{a^2 A}{x^2}+a (2 A b+a B) x+b (A b+2 a B) x^4+b^2 B x^7\right ) \, dx\\ &=-\frac{a^2 A}{x}+\frac{1}{2} a (2 A b+a B) x^2+\frac{1}{5} b (A b+2 a B) x^5+\frac{1}{8} b^2 B x^8\\ \end{align*}
Mathematica [A] time = 0.0164872, size = 53, normalized size = 1. \[ -\frac{a^2 A}{x}+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{8} b^2 B x^8 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 53, normalized size = 1. \begin{align*}{\frac{{b}^{2}B{x}^{8}}{8}}+{\frac{A{x}^{5}{b}^{2}}{5}}+{\frac{2\,B{x}^{5}ab}{5}}+A{x}^{2}ab+{\frac{B{x}^{2}{a}^{2}}{2}}-{\frac{A{a}^{2}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.20415, size = 69, normalized size = 1.3 \begin{align*} \frac{1}{8} \, B b^{2} x^{8} + \frac{1}{5} \,{\left (2 \, B a b + A b^{2}\right )} x^{5} + \frac{1}{2} \,{\left (B a^{2} + 2 \, A a b\right )} x^{2} - \frac{A a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42236, size = 116, normalized size = 2.19 \begin{align*} \frac{5 \, B b^{2} x^{9} + 8 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 20 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 40 \, A a^{2}}{40 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.280175, size = 49, normalized size = 0.92 \begin{align*} - \frac{A a^{2}}{x} + \frac{B b^{2} x^{8}}{8} + x^{5} \left (\frac{A b^{2}}{5} + \frac{2 B a b}{5}\right ) + x^{2} \left (A a b + \frac{B a^{2}}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10672, size = 70, normalized size = 1.32 \begin{align*} \frac{1}{8} \, B b^{2} x^{8} + \frac{2}{5} \, B a b x^{5} + \frac{1}{5} \, A b^{2} x^{5} + \frac{1}{2} \, B a^{2} x^{2} + A a b x^{2} - \frac{A a^{2}}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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