Optimal. Leaf size=16 \[ \frac{4}{2-x}+\log (2-x) \]
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Rubi [A] time = 0.0052333, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {27, 43} \[ \frac{4}{2-x}+\log (2-x) \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin{align*} \int \frac{2+x}{4-4 x+x^2} \, dx &=\int \frac{2+x}{(-2+x)^2} \, dx\\ &=\int \left (\frac{4}{(-2+x)^2}+\frac{1}{-2+x}\right ) \, dx\\ &=\frac{4}{2-x}+\log (2-x)\\ \end{align*}
Mathematica [A] time = 0.002953, size = 12, normalized size = 0.75 \[ \log (x-2)-\frac{4}{x-2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -4\, \left ( -2+x \right ) ^{-1}+\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961557, size = 16, normalized size = 1. \begin{align*} -\frac{4}{x - 2} + \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.14659, size = 46, normalized size = 2.88 \begin{align*} \frac{{\left (x - 2\right )} \log \left (x - 2\right ) - 4}{x - 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.075429, size = 8, normalized size = 0.5 \begin{align*} \log{\left (x - 2 \right )} - \frac{4}{x - 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07706, size = 18, normalized size = 1.12 \begin{align*} -\frac{4}{x - 2} + \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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