Optimal. Leaf size=13 \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
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Rubi [A] time = 0.0030519, 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} \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (1+x^4\right )^{4/3}} \, dx &=-\frac{3}{4 \sqrt [3]{1+x^4}}\\ \end{align*}
Mathematica [A] time = 0.0025828, size = 13, normalized size = 1. \[ -\frac{3}{4 \sqrt [3]{x^4+1}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*} -{\frac{3}{4}{\frac{1}{\sqrt [3]{{x}^{4}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.984289, size = 12, normalized size = 0.92 \begin{align*} -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45828, size = 30, normalized size = 2.31 \begin{align*} -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.530659, size = 12, normalized size = 0.92 \begin{align*} - \frac{3}{4 \sqrt [3]{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15047, size = 12, normalized size = 0.92 \begin{align*} -\frac{3}{4 \,{\left (x^{4} + 1\right )}^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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