Optimal. Leaf size=36 \[ a^2 b x^3+a^3 \log (x)+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]
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Rubi [A] time = 0.0192102, antiderivative size = 36, 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} \[ a^2 b x^3+a^3 \log (x)+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^3}{x} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (3 a^2 b+\frac{a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx,x,x^3\right )\\ &=a^2 b x^3+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9}+a^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0037551, size = 36, normalized size = 1. \[ a^2 b x^3+a^3 \log (x)+\frac{1}{2} a b^2 x^6+\frac{b^3 x^9}{9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 33, normalized size = 0.9 \begin{align*}{a}^{2}b{x}^{3}+{\frac{a{b}^{2}{x}^{6}}{2}}+{\frac{{b}^{3}{x}^{9}}{9}}+{a}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959988, size = 47, normalized size = 1.31 \begin{align*} \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + \frac{1}{3} \, a^{3} \log \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71889, size = 73, normalized size = 2.03 \begin{align*} \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.350327, size = 32, normalized size = 0.89 \begin{align*} a^{3} \log{\left (x \right )} + a^{2} b x^{3} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12505, size = 45, normalized size = 1.25 \begin{align*} \frac{1}{9} \, b^{3} x^{9} + \frac{1}{2} \, a b^{2} x^{6} + a^{2} b x^{3} + a^{3} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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