Optimal. Leaf size=13 \[ \frac {1}{4} \left (x^6+1\right )^{2/3} \]
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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 = {261} \begin {gather*} \frac {1}{4} \left (x^6+1\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
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 = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (x^6+1\right )^{2/3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [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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fricas [A] time = 0.47, 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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giac [A] time = 0.34, 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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maple [A] time = 0.05, 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 | \(\frac {\left (x^{6}+1\right )^{\frac {2}{3}}}{4}\) | \(10\) |
meijerg | \(\frac {\hypergeom \left (\left [\frac {1}{3}, 1\right ], \relax [2], -x^{6}\right ) x^{6}}{6}\) | \(17\) |
gosper | \(\frac {\left (x^{2}+1\right ) \left (x^{4}-x^{2}+1\right )}{4 \left (x^{6}+1\right )^{\frac {1}{3}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, 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 = 0.08, 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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sympy [A] time = 0.22, 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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