Optimal. Leaf size=13 \[ \frac {1}{9} \left (x^6-1\right )^{3/2} \]
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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}{9} \left (x^6-1\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^5 \sqrt {-1+x^6} \, dx &=\frac {1}{9} \left (-1+x^6\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{9} \left (x^6-1\right )^{3/2} \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}{9} \left (x^6-1\right )^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 30, normalized size = 2.31 \begin {gather*} \frac {\left (-1+x \right ) \left (1+x \right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right ) \sqrt {x^{6}-1}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{9} \, {\left (x^{6} - 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (x^6-1\right )}^{3/2}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.27, size = 22, normalized size = 1.69 \begin {gather*} \frac {x^{6} \sqrt {x^{6} - 1}}{9} - \frac {\sqrt {x^{6} - 1}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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