Optimal. Leaf size=13 \[ \frac{1}{6} \left (x^4+5\right )^{3/2} \]
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Rubi [A] time = 0.0023835, 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} \[ \frac{1}{6} \left (x^4+5\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^3 \sqrt{5+x^4} \, dx &=\frac{1}{6} \left (5+x^4\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0030452, size = 13, normalized size = 1. \[ \frac{1}{6} \left (x^4+5\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{6} \left ({x}^{4}+5 \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.98323, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{6} \,{\left (x^{4} + 5\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43457, size = 28, normalized size = 2.15 \begin{align*} \frac{1}{6} \,{\left (x^{4} + 5\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.277769, size = 24, normalized size = 1.85 \begin{align*} \frac{x^{4} \sqrt{x^{4} + 5}}{6} + \frac{5 \sqrt{x^{4} + 5}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10859, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{6} \,{\left (x^{4} + 5\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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