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 = 0.01, 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 = {254, 203} \begin {gather*} \frac {x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \end {gather*}
Antiderivative was successfully verified.
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Rule 203
Rule 254
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*}
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Mathematica [A] time = 0.02, size = 22, normalized size = 1.00 \begin {gather*} \frac {x \tan ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 44.78, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{1+4 \sqrt [3]{x^6}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.88, size = 6, normalized size = 0.27 \begin {gather*} \frac {1}{2} \, \arctan \left (2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 6, normalized size = 0.27 \begin {gather*} \frac {1}{2} \, \arctan \left (2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.33, size = 17, normalized size = 0.77 \begin {gather*} \frac {x \arctan \left (2 \left (x^{6}\right )^{\frac {1}{6}}\right )}{2 \left (x^{6}\right )^{\frac {1}{6}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 6, normalized size = 0.27 \begin {gather*} \frac {1}{2} \, \arctan \left (2 \, x\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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sympy [A] time = 0.13, size = 5, normalized size = 0.23 \begin {gather*} \frac {\operatorname {atan}{\left (2 x \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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