Optimal. Leaf size=12 \[ \frac {1}{2} \log \left (1-x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {260} \[ \frac {1}{2} \log \left (1-x^2\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin {align*} \int \frac {x}{-1+x^2} \, dx &=\frac {1}{2} \log \left (1-x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.83 \[ \frac {1}{2} \log \left (x^2-1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 8, normalized size = 0.67 \[ \frac {1}{2} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 9, normalized size = 0.75 \[ \frac {1}{2} \, \log \left ({\left | x^{2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.17 \[ \frac {\ln \left (x -1\right )}{2}+\frac {\ln \left (x +1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 8, normalized size = 0.67 \[ \frac {1}{2} \, \log \left (x^{2} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 8, normalized size = 0.67 \[ \frac {\ln \left (x^2-1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.58 \[ \frac {\log {\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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