Optimal. Leaf size=22 \[ \frac{x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
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Rubi [A] time = 0.0047655, 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, 206} \[ \frac{x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
Antiderivative was successfully verified.
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Rule 254
Rule 206
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 \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}}\\ \end{align*}
Mathematica [A] time = 0.0035964, size = 22, normalized size = 1. \[ \frac{x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.197, size = 17, normalized size = 0.8 \begin{align*}{\frac{x}{2}{\it Artanh} \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 = 0.953695, size = 23, normalized size = 1.05 \begin{align*} \frac{1}{4} \, \log \left (2 \, x + 1\right ) - \frac{1}{4} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23169, size = 50, normalized size = 2.27 \begin{align*} \frac{1}{4} \, \log \left (2 \, x + 1\right ) - \frac{1}{4} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.094899, size = 15, normalized size = 0.68 \begin{align*} - \frac{\log{\left (x - \frac{1}{2} \right )}}{4} + \frac{\log{\left (x + \frac{1}{2} \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20585, size = 20, normalized size = 0.91 \begin{align*} \frac{1}{4} \, \log \left ({\left | x + \frac{1}{2} \right |}\right ) - \frac{1}{4} \, \log \left ({\left | x - \frac{1}{2} \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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