Optimal. Leaf size=13 \[ -\frac{1}{2 \sqrt{x^4+1}} \]
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Rubi [A] time = 0.0026001, 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} \[ -\frac{1}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (1+x^4\right )^{3/2}} \, dx &=-\frac{1}{2 \sqrt{1+x^4}}\\ \end{align*}
Mathematica [A] time = 0.0020503, size = 13, normalized size = 1. \[ -\frac{1}{2 \sqrt{x^4+1}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 10, normalized size = 0.8 \begin{align*} -{\frac{1}{2}{\frac{1}{\sqrt{{x}^{4}+1}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.997663, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{2 \, \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42802, size = 27, normalized size = 2.08 \begin{align*} -\frac{1}{2 \, \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.46822, size = 12, normalized size = 0.92 \begin{align*} - \frac{1}{2 \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17582, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{2 \, \sqrt{x^{4} + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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