Optimal. Leaf size=14 \[ \frac{3}{2} \log \left (1-x^{2/3}\right ) \]
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Rubi [A] time = 0.00433, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {1593, 260} \[ \frac{3}{2} \log \left (1-x^{2/3}\right ) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 260
Rubi steps
\begin{align*} \int \frac{1}{-\sqrt [3]{x}+x} \, dx &=\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 = 0.0018832, size = 14, normalized size = 1. \[ \frac{3}{2} \log \left (1-x^{2/3}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.011, size = 50, normalized size = 3.6 \begin{align*}{\frac{\ln \left ( -1+x \right ) }{2}}+{\frac{\ln \left ( 1+x \right ) }{2}}+\ln \left ( -1+\sqrt [3]{x} \right ) -{\frac{1}{2}\ln \left ({x}^{{\frac{2}{3}}}+\sqrt [3]{x}+1 \right ) }+\ln \left ( \sqrt [3]{x}+1 \right ) -{\frac{1}{2}\ln \left ({x}^{{\frac{2}{3}}}-\sqrt [3]{x}+1 \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.927172, size = 23, normalized size = 1.64 \begin{align*} \frac{3}{2} \, \log \left (x^{\frac{1}{3}} + 1\right ) + \frac{3}{2} \, \log \left (x^{\frac{1}{3}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90974, size = 30, normalized size = 2.14 \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 [B] time = 0.178474, size = 22, normalized size = 1.57 \begin{align*} \frac{3 \log{\left (\sqrt [3]{x} - 1 \right )}}{2} + \frac{3 \log{\left (\sqrt [3]{x} + 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05442, size = 24, normalized size = 1.71 \begin{align*} \frac{3}{2} \, \log \left (x^{\frac{1}{3}} + 1\right ) + \frac{3}{2} \, \log \left ({\left | x^{\frac{1}{3}} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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