Optimal. Leaf size=12 \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
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Rubi [A] time = 0.0027598, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {260} \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin{align*} \int \frac{1}{\left (1+x^{2/3}\right ) \sqrt [3]{x}} \, dx &=\frac{3}{2} \log \left (1+x^{2/3}\right )\\ \end{align*}
Mathematica [A] time = 0.0013949, size = 12, normalized size = 1. \[ \frac{3}{2} \log \left (x^{2/3}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.8 \begin{align*}{\frac{3}{2}\ln \left ( 1+{x}^{{\frac{2}{3}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97963, size = 11, normalized size = 0.92 \begin{align*} \frac{3}{2} \, \log \left (x^{\frac{2}{3}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45701, size = 30, normalized size = 2.5 \begin{align*} \frac{3}{2} \, \log \left (x^{\frac{2}{3}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.163284, size = 10, normalized size = 0.83 \begin{align*} \frac{3 \log{\left (x^{\frac{2}{3}} + 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11974, size = 11, normalized size = 0.92 \begin{align*} \frac{3}{2} \, \log \left (x^{\frac{2}{3}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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