Optimal. Leaf size=13 \[ \frac{1}{8 \left (1-x^2\right )^4} \]
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Rubi [A] time = 0.0021836, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{1}{8 \left (1-x^2\right )^4} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (1-x^2\right )^5} \, dx &=\frac{1}{8 \left (1-x^2\right )^4}\\ \end{align*}
Mathematica [A] time = 0.0024871, size = 11, normalized size = 0.85 \[ \frac{1}{8 \left (x^2-1\right )^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{8\, \left ({x}^{2}-1 \right ) ^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.95232, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.923981, size = 53, normalized size = 4.08 \begin{align*} \frac{1}{8 \,{\left (x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.120779, size = 22, normalized size = 1.69 \begin{align*} \frac{1}{8 x^{8} - 32 x^{6} + 48 x^{4} - 32 x^{2} + 8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12121, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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