Optimal. Leaf size=12 \[ \frac {3}{4} \log \left (x^{4/3}+1\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {1593, 260} \[ \frac {3}{4} \log \left (x^{4/3}+1\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{\frac {1}{\sqrt [3]{x}}+x} \, dx &=\int \frac {\sqrt [3]{x}}{1+x^{4/3}} \, dx\\ &=\frac {3}{4} \log \left (1+x^{4/3}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {3}{4} \log \left (x^{4/3}+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 8, normalized size = 0.67 \[ \frac {3}{4} \, \log \left (x^{\frac {4}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 32, normalized size = 2.67 \[ \frac {3}{4} \, \log \left (\sqrt {2} x^{\frac {1}{3}} + x^{\frac {2}{3}} + 1\right ) + \frac {3}{4} \, \log \left (-\sqrt {2} x^{\frac {1}{3}} + x^{\frac {2}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 9, normalized size = 0.75 \[ \frac {3 \ln \left (x^{\frac {4}{3}}+1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.89, size = 8, normalized size = 0.67 \[ \frac {3}{4} \, \log \left (x^{\frac {4}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 8, normalized size = 0.67 \[ \frac {3\,\ln \left (x^{4/3}+1\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 10, normalized size = 0.83 \[ \frac {3 \log {\left (x^{\frac {4}{3}} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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