Optimal. Leaf size=15 \[ \frac{1}{2 \sqrt{1-x^4}} \]
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Rubi [A] time = 0.0036682, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{1}{2 \sqrt{1-x^4}} \]
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 = 0.0022778, size = 15, normalized size = 1. \[ \frac{1}{2 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 23, normalized size = 1.5 \begin{align*} -{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) }{2} \left ( -{x}^{4}+1 \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03397, size = 15, normalized size = 1. \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 = 1.5437, size = 42, normalized size = 2.8 \begin{align*} -\frac{\sqrt{-x^{4} + 1}}{2 \,{\left (x^{4} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.418224, size = 10, normalized size = 0.67 \begin{align*} \frac{1}{2 \sqrt{1 - x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11264, size = 15, normalized size = 1. \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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