Optimal. Leaf size=20 \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
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Rubi [A] time = 0.0091215, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {1593, 266, 43} \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{1}{-\sqrt [3]{x}+x^{2/3}} \, dx &=\int \frac{1}{\left (-1+\sqrt [3]{x}\right ) \sqrt [3]{x}} \, dx\\ &=3 \operatorname{Subst}\left (\int \frac{x}{-1+x} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \operatorname{Subst}\left (\int \left (1+\frac{1}{-1+x}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right )\\ \end{align*}
Mathematica [A] time = 0.006239, size = 18, normalized size = 0.9 \[ 3 \left (\sqrt [3]{x}+\log \left (1-\sqrt [3]{x}\right )\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 15, normalized size = 0.8 \begin{align*} 3\,\sqrt [3]{x}+3\,\ln \left ( \sqrt [3]{x}-1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.27376, size = 19, normalized size = 0.95 \begin{align*} 3 \, x^{\frac{1}{3}} + 3 \, \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 = 1.28871, size = 43, normalized size = 2.15 \begin{align*} 3 \, x^{\frac{1}{3}} + 3 \, \log \left (x^{\frac{1}{3}} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.137258, size = 15, normalized size = 0.75 \begin{align*} 3 \sqrt [3]{x} + 3 \log{\left (\sqrt [3]{x} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10568, size = 20, normalized size = 1. \begin{align*} 3 \, x^{\frac{1}{3}} + 3 \, \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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