Optimal. Leaf size=13 \[ \frac{3}{8} \left (x^4+1\right )^{2/3} \]
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Rubi [A] time = 0.0026967, 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} \[ \frac{3}{8} \left (x^4+1\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt [3]{1+x^4}} \, dx &=\frac{3}{8} \left (1+x^4\right )^{2/3}\\ \end{align*}
Mathematica [A] time = 0.0022577, size = 13, normalized size = 1. \[ \frac{3}{8} \left (x^4+1\right )^{2/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*}{\frac{3}{8} \left ({x}^{4}+1 \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961474, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{8} \,{\left (x^{4} + 1\right )}^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44132, size = 28, normalized size = 2.15 \begin{align*} \frac{3}{8} \,{\left (x^{4} + 1\right )}^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.197193, size = 10, normalized size = 0.77 \begin{align*} \frac{3 \left (x^{4} + 1\right )^{\frac{2}{3}}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16229, size = 12, normalized size = 0.92 \begin{align*} \frac{3}{8} \,{\left (x^{4} + 1\right )}^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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