Optimal. Leaf size=22 \[ \frac{x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
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Rubi [A] time = 0.0061772, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {254, 203} \[ \frac{x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
Antiderivative was successfully verified.
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Rule 254
Rule 203
Rubi steps
\begin{align*} \int \frac{1}{1+4 \sqrt [3]{x^6}} \, dx &=\frac{x \operatorname{Subst}\left (\int \frac{1}{1+4 x^2} \, dx,x,\sqrt [6]{x^6}\right )}{\sqrt [6]{x^6}}\\ &=\frac{x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}}\\ \end{align*}
Mathematica [A] time = 0.0136633, size = 22, normalized size = 1. \[ \frac{x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.241, size = 17, normalized size = 0.8 \begin{align*}{\frac{x}{2}\arctan \left ( 2\,\sqrt [6]{{x}^{6}} \right ){\frac{1}{\sqrt [6]{{x}^{6}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.43419, size = 8, normalized size = 0.36 \begin{align*} \frac{1}{2} \, \arctan \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32411, size = 23, normalized size = 1.05 \begin{align*} \frac{1}{2} \, \arctan \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095412, size = 5, normalized size = 0.23 \begin{align*} \frac{\operatorname{atan}{\left (2 x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11619, size = 8, normalized size = 0.36 \begin{align*} \frac{1}{2} \, \arctan \left (2 \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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