Optimal. Leaf size=19 \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
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Rubi [A] time = 0.0050783, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {14} \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \left (a+b \sqrt [3]{x}\right ) x \, dx &=\int \left (a x+b x^{4/3}\right ) \, dx\\ &=\frac{a x^2}{2}+\frac{3}{7} b x^{7/3}\\ \end{align*}
Mathematica [A] time = 0.0056669, size = 19, normalized size = 1. \[ \frac{a x^2}{2}+\frac{3}{7} b x^{7/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.7 \begin{align*}{\frac{a{x}^{2}}{2}}+{\frac{3\,b}{7}{x}^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.967424, size = 132, normalized size = 6.95 \begin{align*} \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{7}}{7 \, b^{6}} - \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{6} a}{2 \, b^{6}} + \frac{6 \,{\left (b x^{\frac{1}{3}} + a\right )}^{5} a^{2}}{b^{6}} - \frac{15 \,{\left (b x^{\frac{1}{3}} + a\right )}^{4} a^{3}}{2 \, b^{6}} + \frac{5 \,{\left (b x^{\frac{1}{3}} + a\right )}^{3} a^{4}}{b^{6}} - \frac{3 \,{\left (b x^{\frac{1}{3}} + a\right )}^{2} a^{5}}{2 \, b^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42369, size = 36, normalized size = 1.89 \begin{align*} \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.28521, size = 15, normalized size = 0.79 \begin{align*} \frac{a x^{2}}{2} + \frac{3 b x^{\frac{7}{3}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12125, size = 18, normalized size = 0.95 \begin{align*} \frac{3}{7} \, b x^{\frac{7}{3}} + \frac{1}{2} \, a x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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