Optimal. Leaf size=17 \[ \frac {x \tan ^{-1}\left (\sqrt [3]{x^3}\right )}{\sqrt [3]{x^3}} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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 = {254, 203} \[ \frac {x \tan ^{-1}\left (\sqrt [3]{x^3}\right )}{\sqrt [3]{x^3}} \]
Antiderivative was successfully verified.
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Rule 203
Rule 254
Rubi steps
\begin {align*} \int \frac {1}{1+\left (x^3\right )^{2/3}} \, dx &=\frac {x \operatorname {Subst}\left (\int \frac {1}{1+x^2} \, dx,x,\sqrt [3]{x^3}\right )}{\sqrt [3]{x^3}}\\ &=\frac {x \tan ^{-1}\left (\sqrt [3]{x^3}\right )}{\sqrt [3]{x^3}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \frac {x \tan ^{-1}\left (\sqrt [3]{x^3}\right )}{\sqrt [3]{x^3}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 6, normalized size = 0.35 \[ \arctan \left ({\left (x^{3}\right )}^{\frac {1}{3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 2, normalized size = 0.12 \[ \arctan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 14, normalized size = 0.82 \[ \frac {x \arctan \left (\left (x^{3}\right )^{\frac {1}{3}}\right )}{\left (x^{3}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.17, size = 2, normalized size = 0.12 \[ \arctan \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{{\left (x^3\right )}^{2/3}+1} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 2, normalized size = 0.12 \[ \operatorname {atan}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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