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 = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, 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 = {260, 212}
\begin {gather*} \frac {x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \end {gather*}
Antiderivative was successfully verified.
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Rule 212
Rule 260
Rubi steps
\begin {align*} \int \frac {1}{1-4 \sqrt [3]{x^6}} \, dx &=\frac {x \text {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*}
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Mathematica [A]
time = 10.01, size = 22, normalized size = 1.00 \begin {gather*} \frac {x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.25, size = 17, normalized size = 0.77
method | result | size |
meijerg | \(\frac {x \arctanh \left (2 \left (x^{6}\right )^{\frac {1}{6}}\right )}{2 \left (x^{6}\right )^{\frac {1}{6}}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 17, normalized size = 0.77 \begin {gather*} \frac {1}{4} \, \log \left (2 \, x + 1\right ) - \frac {1}{4} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.77 \begin {gather*} \frac {1}{4} \, \log \left (2 \, x + 1\right ) - \frac {1}{4} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.68 \begin {gather*} - \frac {\log {\left (x - \frac {1}{2} \right )}}{4} + \frac {\log {\left (x + \frac {1}{2} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.37, size = 15, normalized size = 0.68 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} -\int \frac {1}{4\,{\left (x^6\right )}^{1/3}-1} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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