Optimal. Leaf size=26 \[ a^2 \log (x)+\frac{2}{3} a b x^3+\frac{b^2 x^6}{6} \]
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Rubi [A] time = 0.0120073, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ a^2 \log (x)+\frac{2}{3} a b x^3+\frac{b^2 x^6}{6} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^2}{x} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (2 a b+\frac{a^2}{x}+b^2 x\right ) \, dx,x,x^3\right )\\ &=\frac{2}{3} a b x^3+\frac{b^2 x^6}{6}+a^2 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0007127, size = 26, normalized size = 1. \[ a^2 \log (x)+\frac{2}{3} a b x^3+\frac{b^2 x^6}{6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.9 \begin{align*}{\frac{2\,{x}^{3}ab}{3}}+{\frac{{b}^{2}{x}^{6}}{6}}+{a}^{2}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965412, size = 34, normalized size = 1.31 \begin{align*} \frac{1}{6} \, b^{2} x^{6} + \frac{2}{3} \, a b x^{3} + \frac{1}{3} \, a^{2} \log \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6821, size = 54, normalized size = 2.08 \begin{align*} \frac{1}{6} \, b^{2} x^{6} + \frac{2}{3} \, a b x^{3} + a^{2} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.330352, size = 24, normalized size = 0.92 \begin{align*} a^{2} \log{\left (x \right )} + \frac{2 a b x^{3}}{3} + \frac{b^{2} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13771, size = 31, normalized size = 1.19 \begin{align*} \frac{1}{6} \, b^{2} x^{6} + \frac{2}{3} \, a b x^{3} + a^{2} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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