Optimal. Leaf size=16 \[ 3 \sqrt [3]{x}-3 \tan ^{-1}\left (\sqrt [3]{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {243, 321, 203} \[ 3 \sqrt [3]{x}-3 \tan ^{-1}\left (\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
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Rule 203
Rule 243
Rule 321
Rubi steps
\begin {align*} \int \frac {1}{1+x^{2/3}} \, dx &=3 \operatorname {Subst}\left (\int \frac {x^2}{1+x^2} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \sqrt [3]{x}-3 \operatorname {Subst}\left (\int \frac {1}{1+x^2} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \sqrt [3]{x}-3 \tan ^{-1}\left (\sqrt [3]{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ 3 \sqrt [3]{x}-3 \tan ^{-1}\left (\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 12, normalized size = 0.75 \[ 3 \, x^{\frac {1}{3}} - 3 \, \arctan \left (x^{\frac {1}{3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 12, normalized size = 0.75 \[ 3 \, x^{\frac {1}{3}} - 3 \, \arctan \left (x^{\frac {1}{3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.04, size = 41, normalized size = 2.56 \[ \arctan \relax (x )-2 \arctan \left (x^{\frac {1}{3}}\right )-\arctan \left (2 x^{\frac {1}{3}}-\sqrt {3}\right )-\arctan \left (2 x^{\frac {1}{3}}+\sqrt {3}\right )+3 x^{\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.20, size = 12, normalized size = 0.75 \[ 3 \, x^{\frac {1}{3}} - 3 \, \arctan \left (x^{\frac {1}{3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 12, normalized size = 0.75 \[ 3\,x^{1/3}-3\,\mathrm {atan}\left (x^{1/3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 14, normalized size = 0.88 \[ 3 \sqrt [3]{x} - 3 \operatorname {atan}{\left (\sqrt [3]{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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