Optimal. Leaf size=19 \[ \log (1-x)-2 \log (x+2)-3 \log (x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2074} \[ \log (1-x)-2 \log (x+2)-3 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {align*} \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx &=\int \left (\frac {1}{-1+x}-\frac {2}{2+x}-\frac {3}{3+x}\right ) \, dx\\ &=\log (1-x)-2 \log (2+x)-3 \log (3+x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 1.32 \[ -2 \left (-\frac {1}{2} \log (1-x)+\log (x+2)+\frac {3}{2} \log (x+3)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 17, normalized size = 0.89 \[ -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 20, normalized size = 1.05 \[ -3 \, \log \left ({\left | x + 3 \right |}\right ) - 2 \, \log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 18, normalized size = 0.95 \[ \ln \left (x -1\right )-2 \ln \left (x +2\right )-3 \ln \left (x +3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.03, size = 17, normalized size = 0.89 \[ -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.12, size = 17, normalized size = 0.89 \[ \ln \left (x-1\right )-2\,\ln \left (x+2\right )-3\,\ln \left (x+3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 17, normalized size = 0.89 \[ \log {\left (x - 1 \right )} - 2 \log {\left (x + 2 \right )} - 3 \log {\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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