Optimal. Leaf size=20 \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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 43
Rule 266
Rule 1593
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*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.90 \[ 3 \left (\sqrt [3]{x}+\log \left (1-\sqrt [3]{x}\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 14, normalized size = 0.70 \[ 3 \, x^{\frac {1}{3}} + 3 \, \log \left (x^{\frac {1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.43, size = 15, normalized size = 0.75 \[ 3 \, x^{\frac {1}{3}} + 3 \, \log \left ({\left | x^{\frac {1}{3}} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.75 \[ 3 \ln \left (x^{\frac {1}{3}}-1\right )+3 x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 14, normalized size = 0.70 \[ 3 \, x^{\frac {1}{3}} + 3 \, \log \left (x^{\frac {1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 14, normalized size = 0.70 \[ 3\,\ln \left (x^{1/3}-1\right )+3\,x^{1/3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 15, normalized size = 0.75 \[ 3 \sqrt [3]{x} + 3 \log {\left (\sqrt [3]{x} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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