Optimal. Leaf size=14 \[ \frac {3}{2} \log \left (1-x^{2/3}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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 260
Rule 1593
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*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {3}{2} \log \left (1-x^{2/3}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 8, normalized size = 0.57 \[ \frac {3}{2} \, \log \left (x^{\frac {2}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 18, normalized size = 1.29 \[ \frac {3}{2} \, \log \left (x^{\frac {1}{3}} + 1\right ) + \frac {3}{2} \, \log \left ({\left | x^{\frac {1}{3}} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 50, normalized size = 3.57 \[ \frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2}+\ln \left (x^{\frac {1}{3}}-1\right )+\ln \left (x^{\frac {1}{3}}+1\right )-\frac {\ln \left (x^{\frac {2}{3}}-x^{\frac {1}{3}}+1\right )}{2}-\frac {\ln \left (x^{\frac {2}{3}}+x^{\frac {1}{3}}+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 17, normalized size = 1.21 \[ \frac {3}{2} \, \log \left (x^{\frac {1}{3}} + 1\right ) + \frac {3}{2} \, \log \left (x^{\frac {1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 8, normalized size = 0.57 \[ \frac {3\,\ln \left (x^{2/3}-1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 22, normalized size = 1.57 \[ \frac {3 \log {\left (\sqrt [3]{x} - 1 \right )}}{2} + \frac {3 \log {\left (\sqrt [3]{x} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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