Optimal. Leaf size=21 \[ 2 \log (1-x)-\log (2-x)+\log (x+1) \]
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Rubi [A] time = 0.03, antiderivative size = 21, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ 2 \log (1-x)-\log (2-x)+\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 17, normalized size = 0.81 \[ \log \left (x + 1\right ) + 2 \, \log \left (x - 1\right ) - \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 20, normalized size = 0.95 \[ \log \left ({\left | x + 1 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 18, normalized size = 0.86 \[ -\ln \left (x -2\right )+2 \ln \left (x -1\right )+\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 17, normalized size = 0.81 \[ \log \left (x + 1\right ) + 2 \, \log \left (x - 1\right ) - \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 21, normalized size = 1.00 \[ 2\,\ln \left (x-1\right )-2\,\mathrm {atanh}\left (\frac {144}{11\,\left (22\,x-50\right )}+\frac {13}{11}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.71 \[ - \log {\left (x - 2 \right )} + 2 \log {\left (x - 1 \right )} + \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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