Optimal. Leaf size=13 \[ \frac {1}{8 \left (1-x^2\right )^4} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {1}{8 \left (1-x^2\right )^4} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} \frac {1}{8 \left (x^2-1\right )^4} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\left (1-x^2\right )^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.35, size = 24, normalized size = 1.85 \begin {gather*} \frac {1}{8 \, {\left (x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8 \, {\left (x^{2} - 1\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} \frac {1}{8 \left (x^{2}-1\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8 \, {\left (x^{2} - 1\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{8\,{\left (x^2-1\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 22, normalized size = 1.69 \begin {gather*} \frac {1}{8 x^{8} - 32 x^{6} + 48 x^{4} - 32 x^{2} + 8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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