Optimal. Leaf size=13 \[ \frac {1}{4} \left (-1+x^6\right )^{2/3} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267}
\begin {gather*} \frac {1}{4} \left (x^6-1\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^5}{\sqrt [3]{-1+x^6}} \, dx &=\frac {1}{4} \left (-1+x^6\right )^{2/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (-1+x^6\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}}}{4}\) | \(10\) |
default | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}}}{4}\) | \(10\) |
trager | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}}}{4}\) | \(10\) |
risch | \(\frac {\left (x^{6}-1\right )^{\frac {2}{3}}}{4}\) | \(10\) |
gosper | \(\frac {\left (-1+x \right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right )}{4 \left (x^{6}-1\right )^{\frac {1}{3}}}\) | \(30\) |
meijerg | \(\frac {\left (-\mathrm {signum}\left (x^{6}-1\right )\right )^{\frac {1}{3}} x^{6} \hypergeom \left (\left [\frac {1}{3}, 1\right ], \left [2\right ], x^{6}\right )}{6 \mathrm {signum}\left (x^{6}-1\right )^{\frac {1}{3}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{6} - 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{6} - 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 8, normalized size = 0.62 \begin {gather*} \frac {\left (x^{6} - 1\right )^{\frac {2}{3}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.37, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{6} - 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.23, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (x^6-1\right )}^{2/3}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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