Optimal. Leaf size=11 \[ \left (x^{2/3}-1\right )^{3/2} \]
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Rubi [A] time = 0.002669, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {261} \[ \left (x^{2/3}-1\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{\sqrt{-1+x^{2/3}}}{\sqrt [3]{x}} \, dx &=\left (-1+x^{2/3}\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0031451, size = 11, normalized size = 1. \[ \left (x^{2/3}-1\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 8, normalized size = 0.7 \begin{align*} \left ( -1+{x}^{{\frac{2}{3}}} \right ) ^{{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.987371, size = 9, normalized size = 0.82 \begin{align*}{\left (x^{\frac{2}{3}} - 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 6.30563, size = 28, normalized size = 2.55 \begin{align*}{\left (x^{\frac{2}{3}} - 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.201983, size = 24, normalized size = 2.18 \begin{align*} x^{\frac{2}{3}} \sqrt{x^{\frac{2}{3}} - 1} - \sqrt{x^{\frac{2}{3}} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19553, size = 9, normalized size = 0.82 \begin{align*}{\left (x^{\frac{2}{3}} - 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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