Optimal. Leaf size=16 \[ \frac {4}{2-x}+\log (2-x) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.75 \[ \log (x-2)-\frac {4}{x-2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 16, normalized size = 1.00 \[ \frac {{\left (x - 2\right )} \log \left (x - 2\right ) - 4}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 13, normalized size = 0.81 \[ -\frac {4}{x - 2} + \log \left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \ln \left (x -2\right )-\frac {4}{x -2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 12, normalized size = 0.75 \[ -\frac {4}{x - 2} + \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 12, normalized size = 0.75 \[ \ln \left (x-2\right )-\frac {4}{x-2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.50 \[ \log {\left (x - 2 \right )} - \frac {4}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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