Optimal. Leaf size=12 \[ \frac{3}{4} \log \left (x^{4/3}+1\right ) \]
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Rubi [A] time = 0.0034391, antiderivative size = 12, normalized size of antiderivative = 1., 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 1593
Rule 260
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*}
Mathematica [A] time = 0.0017443, size = 12, normalized size = 1. \[ \frac{3}{4} \log \left (x^{4/3}+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.8 \begin{align*}{\frac{3}{4}\ln \left ( 1+{x}^{{\frac{4}{3}}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.41533, size = 11, normalized size = 0.92 \begin{align*} \frac{3}{4} \, \log \left (x^{\frac{4}{3}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.1519, size = 30, normalized size = 2.5 \begin{align*} \frac{3}{4} \, \log \left (x^{\frac{4}{3}} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.217919, size = 10, normalized size = 0.83 \begin{align*} \frac{3 \log{\left (x^{\frac{4}{3}} + 1 \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.05467, size = 43, normalized size = 3.58 \begin{align*} \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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