Optimal. Leaf size=13 \[ \frac {4}{9} \left (x^3-1\right )^{3/4} \]
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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 {4}{9} \left (x^3-1\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x^2}{\sqrt [4]{-1+x^3}} \, dx &=\frac {4}{9} \left (-1+x^3\right )^{3/4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {4}{9} \left (x^3-1\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} \frac {4}{9} \left (x^3-1\right )^{3/4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 9, normalized size = 0.69 \begin {gather*} \frac {4}{9} \, {\left (x^{3} - 1\right )}^{\frac {3}{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 {4}{9} \, {\left (x^{3} - 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 1.46 \begin {gather*} \frac {4 \left (-1+x \right ) \left (x^{2}+x +1\right )}{9 \left (x^{3}-1\right )^{\frac {1}{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 9, normalized size = 0.69 \begin {gather*} \frac {4}{9} \, {\left (x^{3} - 1\right )}^{\frac {3}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 9, normalized size = 0.69 \begin {gather*} \frac {4\,{\left (x^3-1\right )}^{3/4}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 10, normalized size = 0.77 \begin {gather*} \frac {4 \left (x^{3} - 1\right )^{\frac {3}{4}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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