Optimal. Leaf size=18 \[ -\frac {1}{x}+3 \log (2-x)+2 \log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {893} \[ -\frac {1}{x}+3 \log (2-x)+2 \log (x) \]
Antiderivative was successfully verified.
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Rule 893
Rubi steps
\begin {align*} \int \frac {-2-3 x+5 x^2}{(-2+x) x^2} \, dx &=\int \left (\frac {3}{-2+x}+\frac {1}{x^2}+\frac {2}{x}\right ) \, dx\\ &=-\frac {1}{x}+3 \log (2-x)+2 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ -\frac {1}{x}+3 \log (2-x)+2 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 18, normalized size = 1.00 \[ \frac {3 \, x \log \left (x - 2\right ) + 2 \, x \log \relax (x) - 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 18, normalized size = 1.00 \[ -\frac {1}{x} + 3 \, \log \left ({\left | x - 2 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 17, normalized size = 0.94 \[ 2 \ln \relax (x )+3 \ln \left (x -2\right )-\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 16, normalized size = 0.89 \[ -\frac {1}{x} + 3 \, \log \left (x - 2\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 16, normalized size = 0.89 \[ 3\,\ln \left (x-2\right )+2\,\ln \relax (x)-\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 14, normalized size = 0.78 \[ 2 \log {\relax (x )} + 3 \log {\left (x - 2 \right )} - \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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