Optimal. Leaf size=17 \[ \frac{1}{2} \log (2-x)-\frac{\log (x)}{2} \]
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Rubi [A] time = 0.0020595, antiderivative size = 17, 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 = {615} \[ \frac{1}{2} \log (2-x)-\frac{\log (x)}{2} \]
Antiderivative was successfully verified.
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Rule 615
Rubi steps
\begin{align*} \int \frac{1}{-2 x+x^2} \, dx &=\frac{1}{2} \log (2-x)-\frac{\log (x)}{2}\\ \end{align*}
Mathematica [A] time = 0.0017699, size = 17, normalized size = 1. \[ \frac{1}{2} \log (2-x)-\frac{\log (x)}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 12, normalized size = 0.7 \begin{align*} -{\frac{\ln \left ( x \right ) }{2}}+{\frac{\ln \left ( -2+x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.92438, size = 15, normalized size = 0.88 \begin{align*} \frac{1}{2} \, \log \left (x - 2\right ) - \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86167, size = 39, normalized size = 2.29 \begin{align*} \frac{1}{2} \, \log \left (x - 2\right ) - \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087404, size = 10, normalized size = 0.59 \begin{align*} - \frac{\log{\left (x \right )}}{2} + \frac{\log{\left (x - 2 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05437, size = 18, normalized size = 1.06 \begin{align*} \frac{1}{2} \, \log \left ({\left | x - 2 \right |}\right ) - \frac{1}{2} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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