Optimal. Leaf size=18 \[ -\frac{1}{x}+3 \log (2-x)+2 \log (x) \]
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Rubi [A] time = 0.0143458, antiderivative size = 18, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0040948, size = 18, normalized size = 1. \[ -\frac{1}{x}+3 \log (2-x)+2 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 17, normalized size = 0.9 \begin{align*} -{x}^{-1}+2\,\ln \left ( x \right ) +3\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.938333, size = 22, normalized size = 1.22 \begin{align*} -\frac{1}{x} + 3 \, \log \left (x - 2\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5578, size = 50, normalized size = 2.78 \begin{align*} \frac{3 \, x \log \left (x - 2\right ) + 2 \, x \log \left (x\right ) - 1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.103647, size = 14, normalized size = 0.78 \begin{align*} 2 \log{\left (x \right )} + 3 \log{\left (x - 2 \right )} - \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06285, size = 24, normalized size = 1.33 \begin{align*} -\frac{1}{x} + 3 \, \log \left ({\left | x - 2 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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