Optimal. Leaf size=36 \[ 9 a^2 b \sqrt [3]{x}+a^3 \log (x)+\frac{9}{2} a b^2 x^{2/3}+b^3 x \]
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Rubi [A] time = 0.0167985, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {266, 43} \[ 9 a^2 b \sqrt [3]{x}+a^3 \log (x)+\frac{9}{2} a b^2 x^{2/3}+b^3 x \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt [3]{x}\right )^3}{x} \, dx &=3 \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x} \, dx,x,\sqrt [3]{x}\right )\\ &=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,\sqrt [3]{x}\right )\\ &=9 a^2 b \sqrt [3]{x}+\frac{9}{2} a b^2 x^{2/3}+b^3 x+a^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0128372, size = 36, normalized size = 1. \[ 9 a^2 b \sqrt [3]{x}+a^3 \log (x)+\frac{9}{2} a b^2 x^{2/3}+b^3 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 31, normalized size = 0.9 \begin{align*} 9\,{a}^{2}b\sqrt [3]{x}+{\frac{9\,{b}^{2}a}{2}{x}^{{\frac{2}{3}}}}+{b}^{3}x+{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 = 0.990877, size = 41, normalized size = 1.14 \begin{align*} b^{3} x + a^{3} \log \left (x\right ) + \frac{9}{2} \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.53227, size = 89, normalized size = 2.47 \begin{align*} b^{3} x + 3 \, a^{3} \log \left (x^{\frac{1}{3}}\right ) + \frac{9}{2} \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.29268, size = 36, normalized size = 1. \begin{align*} a^{3} \log{\left (x \right )} + 9 a^{2} b \sqrt [3]{x} + \frac{9 a b^{2} x^{\frac{2}{3}}}{2} + b^{3} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12399, size = 42, normalized size = 1.17 \begin{align*} b^{3} x + a^{3} \log \left ({\left | x \right |}\right ) + \frac{9}{2} \, a b^{2} x^{\frac{2}{3}} + 9 \, a^{2} b x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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