Optimal. Leaf size=50 \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
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Rubi [A] time = 0.0266763, antiderivative size = 50, 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} \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
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^3} \, dx &=\int \left (a (2 A b+a B)+\frac{a^2 A}{x^3}+b (A b+2 a B) x^3+b^2 B x^6\right ) \, dx\\ &=-\frac{a^2 A}{2 x^2}+a (2 A b+a B) x+\frac{1}{4} b (A b+2 a B) x^4+\frac{1}{7} b^2 B x^7\\ \end{align*}
Mathematica [A] time = 0.0142723, size = 50, normalized size = 1. \[ -\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 49, normalized size = 1. \begin{align*}{\frac{{b}^{2}B{x}^{7}}{7}}+{\frac{A{x}^{4}{b}^{2}}{4}}+{\frac{B{x}^{4}ab}{2}}+2\,abAx+{a}^{2}Bx-{\frac{A{a}^{2}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15342, size = 65, normalized size = 1.3 \begin{align*} \frac{1}{7} \, B b^{2} x^{7} + \frac{1}{4} \,{\left (2 \, B a b + A b^{2}\right )} x^{4} +{\left (B a^{2} + 2 \, A a b\right )} x - \frac{A a^{2}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38677, size = 119, normalized size = 2.38 \begin{align*} \frac{4 \, B b^{2} x^{9} + 7 \,{\left (2 \, B a b + A b^{2}\right )} x^{6} + 28 \,{\left (B a^{2} + 2 \, A a b\right )} x^{3} - 14 \, A a^{2}}{28 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.284578, size = 49, normalized size = 0.98 \begin{align*} - \frac{A a^{2}}{2 x^{2}} + \frac{B b^{2} x^{7}}{7} + x^{4} \left (\frac{A b^{2}}{4} + \frac{B a b}{2}\right ) + x \left (2 A a b + B a^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2148, size = 65, normalized size = 1.3 \begin{align*} \frac{1}{7} \, B b^{2} x^{7} + \frac{1}{2} \, B a b x^{4} + \frac{1}{4} \, A b^{2} x^{4} + B a^{2} x + 2 \, A a b x - \frac{A a^{2}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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