Optimal. Leaf size=13 \[ \frac {2}{15} \left (x^6-1\right )^{5/4} \]
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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 = {261} \begin {gather*} \frac {2}{15} \left (x^6-1\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^5 \sqrt [4]{-1+x^6} \, dx &=\frac {2}{15} \left (-1+x^6\right )^{5/4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{15} \left (x^6-1\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{15} \left (-1+x^6\right )^{5/4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{15} \, {\left (x^{6} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.38, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{15} \, {\left (x^{6} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {2 \left (x^{6}-1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
default | \(\frac {2 \left (x^{6}-1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
risch | \(\frac {2 \left (x^{6}-1\right )^{\frac {5}{4}}}{15}\) | \(10\) |
trager | \(\left (\frac {2 x^{6}}{15}-\frac {2}{15}\right ) \left (x^{6}-1\right )^{\frac {1}{4}}\) | \(16\) |
gosper | \(\frac {2 \left (-1+x \right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right ) \left (x^{6}-1\right )^{\frac {1}{4}}}{15}\) | \(30\) |
meijerg | \(\frac {\mathrm {signum}\left (x^{6}-1\right )^{\frac {1}{4}} \hypergeom \left (\left [-\frac {1}{4}, 1\right ], \relax [2], x^{6}\right ) x^{6}}{6 \left (-\mathrm {signum}\left (x^{6}-1\right )\right )^{\frac {1}{4}}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{15} \, {\left (x^{6} - 1\right )}^{\frac {5}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 9, normalized size = 0.69 \begin {gather*} \frac {2\,{\left (x^6-1\right )}^{5/4}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.42, size = 26, normalized size = 2.00 \begin {gather*} \frac {2 x^{6} \sqrt [4]{x^{6} - 1}}{15} - \frac {2 \sqrt [4]{x^{6} - 1}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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