Optimal. Leaf size=13 \[ \frac{4}{9} \left (x^3+2\right )^{3/4} \]
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Rubi [A] time = 0.0026733, antiderivative size = 13, normalized size of antiderivative = 1., 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} \[ \frac{4}{9} \left (x^3+2\right )^{3/4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^2}{\sqrt [4]{2+x^3}} \, dx &=\frac{4}{9} \left (2+x^3\right )^{3/4}\\ \end{align*}
Mathematica [A] time = 0.0024442, size = 13, normalized size = 1. \[ \frac{4}{9} \left (x^3+2\right )^{3/4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 10, normalized size = 0.8 \begin{align*}{\frac{4}{9} \left ({x}^{3}+2 \right ) ^{{\frac{3}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974676, size = 12, normalized size = 0.92 \begin{align*} \frac{4}{9} \,{\left (x^{3} + 2\right )}^{\frac{3}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42635, size = 28, normalized size = 2.15 \begin{align*} \frac{4}{9} \,{\left (x^{3} + 2\right )}^{\frac{3}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.220696, size = 10, normalized size = 0.77 \begin{align*} \frac{4 \left (x^{3} + 2\right )^{\frac{3}{4}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08938, size = 12, normalized size = 0.92 \begin{align*} \frac{4}{9} \,{\left (x^{3} + 2\right )}^{\frac{3}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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