Optimal. Leaf size=19 \[ \log (1-x)-2 \log (x+2)-3 \log (x+3) \]
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Rubi [A] time = 0.0267347, antiderivative size = 19, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0066508, 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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Maple [A] time = 0.007, size = 18, normalized size = 1. \begin{align*} -2\,\ln \left ( 2+x \right ) -3\,\ln \left ( 3+x \right ) +\ln \left ( -1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929736, size = 23, normalized size = 1.21 \begin{align*} -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.78051, size = 58, normalized size = 3.05 \begin{align*} -3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.115153, size = 17, normalized size = 0.89 \begin{align*} \log{\left (x - 1 \right )} - 2 \log{\left (x + 2 \right )} - 3 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05505, size = 27, normalized size = 1.42 \begin{align*} -3 \, \log \left ({\left | x + 3 \right |}\right ) - 2 \, \log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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