Optimal. Leaf size=36 \[ \frac{9}{2} a^2 b x^{2/3}+a^3 x+9 a b^2 \sqrt [3]{x}+b^3 \log (x) \]
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Rubi [A] time = 0.019956, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {190, 43} \[ \frac{9}{2} a^2 b x^{2/3}+a^3 x+9 a b^2 \sqrt [3]{x}+b^3 \log (x) \]
Antiderivative was successfully verified.
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Rule 190
Rule 43
Rubi steps
\begin{align*} \int \left (a+\frac{b}{\sqrt [3]{x}}\right )^3 \, dx &=-\left (3 \operatorname{Subst}\left (\int \frac{(a+b x)^3}{x^4} \, dx,x,\frac{1}{\sqrt [3]{x}}\right )\right )\\ &=-\left (3 \operatorname{Subst}\left (\int \left (\frac{a^3}{x^4}+\frac{3 a^2 b}{x^3}+\frac{3 a b^2}{x^2}+\frac{b^3}{x}\right ) \, dx,x,\frac{1}{\sqrt [3]{x}}\right )\right )\\ &=9 a b^2 \sqrt [3]{x}+\frac{9}{2} a^2 b x^{2/3}+a^3 x+b^3 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0146624, size = 36, normalized size = 1. \[ \frac{9}{2} a^2 b x^{2/3}+a^3 x+9 a b^2 \sqrt [3]{x}+b^3 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 31, normalized size = 0.9 \begin{align*} 9\,a{b}^{2}\sqrt [3]{x}+{\frac{9\,b{a}^{2}}{2}{x}^{{\frac{2}{3}}}}+{a}^{3}x+{b}^{3}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0091, size = 41, normalized size = 1.14 \begin{align*} a^{3} x + b^{3} \log \left (x\right ) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50694, size = 89, normalized size = 2.47 \begin{align*} a^{3} x + 3 \, b^{3} \log \left (x^{\frac{1}{3}}\right ) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.290192, size = 36, normalized size = 1. \begin{align*} a^{3} x + \frac{9 a^{2} b x^{\frac{2}{3}}}{2} + 9 a b^{2} \sqrt [3]{x} + b^{3} \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16701, size = 42, normalized size = 1.17 \begin{align*} a^{3} x + b^{3} \log \left ({\left | x \right |}\right ) + \frac{9}{2} \, a^{2} b x^{\frac{2}{3}} + 9 \, a b^{2} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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