Optimal. Leaf size=12 \[ \frac{1}{2} \log \left (1-x^2\right ) \]
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Rubi [A] time = 0.0018597, antiderivative size = 12, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.001481, size = 10, normalized size = 0.83 \[ \frac{1}{2} \log \left (x^2-1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 1.2 \begin{align*}{\frac{\ln \left ( -1+x \right ) }{2}}+{\frac{\ln \left ( 1+x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.917003, size = 11, normalized size = 0.92 \begin{align*} \frac{1}{2} \, \log \left (x^{2} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.01126, size = 24, normalized size = 2. \begin{align*} \frac{1}{2} \, \log \left (x^{2} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.071522, size = 7, normalized size = 0.58 \begin{align*} \frac{\log{\left (x^{2} - 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05911, size = 12, normalized size = 1. \begin{align*} \frac{1}{2} \, \log \left ({\left | x^{2} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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