Optimal. Leaf size=13 \[ \frac{4}{\sqrt [8]{1-x^2}} \]
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Rubi [A] time = 0.0024579, 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} \[ \frac{4}{\sqrt [8]{1-x^2}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (1-x^2\right )^{9/8}} \, dx &=\frac{4}{\sqrt [8]{1-x^2}}\\ \end{align*}
Mathematica [A] time = 0.0021493, size = 13, normalized size = 1. \[ \frac{4}{\sqrt [8]{1-x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 18, normalized size = 1.4 \begin{align*} -4\,{ \left ( -1+x \right ) \left ( 1+x \right ) \left ( -{x}^{2}+1 \right ) ^{-{\frac{9}{8}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957097, size = 15, normalized size = 1.15 \begin{align*} \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52099, size = 42, normalized size = 3.23 \begin{align*} -\frac{4 \,{\left (-x^{2} + 1\right )}^{\frac{7}{8}}}{x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.07254, size = 8, normalized size = 0.62 \begin{align*} \frac{4}{\sqrt [8]{1 - x^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08615, size = 15, normalized size = 1.15 \begin{align*} \frac{4}{{\left (-x^{2} + 1\right )}^{\frac{1}{8}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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