Optimal. Leaf size=31 \[ \frac{1}{2} x^2 (a B+A b)-\frac{a A}{x}+\frac{1}{5} b B x^5 \]
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Rubi [A] time = 0.0153374, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {448} \[ \frac{1}{2} x^2 (a B+A b)-\frac{a A}{x}+\frac{1}{5} b B x^5 \]
Antiderivative was successfully verified.
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Rule 448
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right ) \left (A+B x^3\right )}{x^2} \, dx &=\int \left (\frac{a A}{x^2}+(A b+a B) x+b B x^4\right ) \, dx\\ &=-\frac{a A}{x}+\frac{1}{2} (A b+a B) x^2+\frac{1}{5} b B x^5\\ \end{align*}
Mathematica [A] time = 0.0099321, size = 31, normalized size = 1. \[ \frac{1}{2} x^2 (a B+A b)-\frac{a A}{x}+\frac{1}{5} b B x^5 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 30, normalized size = 1. \begin{align*}{\frac{bB{x}^{5}}{5}}+{\frac{A{x}^{2}b}{2}}+{\frac{B{x}^{2}a}{2}}-{\frac{Aa}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15168, size = 36, normalized size = 1.16 \begin{align*} \frac{1}{5} \, B b x^{5} + \frac{1}{2} \,{\left (B a + A b\right )} x^{2} - \frac{A a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38473, size = 66, normalized size = 2.13 \begin{align*} \frac{2 \, B b x^{6} + 5 \,{\left (B a + A b\right )} x^{3} - 10 \, A a}{10 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.250824, size = 26, normalized size = 0.84 \begin{align*} - \frac{A a}{x} + \frac{B b x^{5}}{5} + x^{2} \left (\frac{A b}{2} + \frac{B a}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20218, size = 39, normalized size = 1.26 \begin{align*} \frac{1}{5} \, B b x^{5} + \frac{1}{2} \, B a x^{2} + \frac{1}{2} \, A b x^{2} - \frac{A a}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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