Optimal. Leaf size=21 \[ 2 \log (1-x)-\log (2-x)+\log (x+1) \]
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Rubi [A] time = 0.0298171, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038, Rules used = {2074} \[ 2 \log (1-x)-\log (2-x)+\log (x+1) \]
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin{align*} \int \frac{-1-5 x+2 x^2}{2-x-2 x^2+x^3} \, dx &=\int \left (\frac{1}{2-x}+\frac{2}{-1+x}+\frac{1}{1+x}\right ) \, dx\\ &=2 \log (1-x)-\log (2-x)+\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0068186, size = 21, normalized size = 1. \[ 2 \log (1-x)-\log (2-x)+\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 18, normalized size = 0.9 \begin{align*} 2\,\ln \left ( x-1 \right ) +\ln \left ( 1+x \right ) -\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992899, size = 23, normalized size = 1.1 \begin{align*} \log \left (x + 1\right ) + 2 \, \log \left (x - 1\right ) - \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57002, size = 54, normalized size = 2.57 \begin{align*} \log \left (x + 1\right ) + 2 \, \log \left (x - 1\right ) - \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.117912, size = 15, normalized size = 0.71 \begin{align*} - \log{\left (x - 2 \right )} + 2 \log{\left (x - 1 \right )} + \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.31567, size = 27, normalized size = 1.29 \begin{align*} \log \left ({\left | x + 1 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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