Optimal. Leaf size=17 \[ \frac {1}{2} \log (2-x)-\frac {\log (x)}{2} \]
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Rubi [A] time = 0.00, antiderivative size = 17, 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 = {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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{2} \log (2-x)-\frac {\log (x)}{2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 11, normalized size = 0.65 \[ \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, \log \left ({\left | x - 2 \right |}\right ) - \frac {1}{2} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 0.71 \[ -\frac {\ln \relax (x )}{2}+\frac {\ln \left (x -2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 11, normalized size = 0.65 \[ \frac {1}{2} \, \log \left (x - 2\right ) - \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 6, normalized size = 0.35 \[ -\mathrm {atanh}\left (x-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.59 \[ - \frac {\log {\relax (x )}}{2} + \frac {\log {\left (x - 2 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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