Optimal. Leaf size=25 \[ 4 \log (1-x)-14 \log (2-x)+11 \log (3-x) \]
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Rubi [A] time = 0.0545906, antiderivative size = 25, 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 = {1612} \[ 4 \log (1-x)-14 \log (2-x)+11 \log (3-x) \]
Antiderivative was successfully verified.
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Rule 1612
Rubi steps
\begin{align*} \int \frac{4+3 x+x^2}{(-3+x) (-2+x) (-1+x)} \, dx &=\int \left (\frac{11}{-3+x}-\frac{14}{-2+x}+\frac{4}{-1+x}\right ) \, dx\\ &=4 \log (1-x)-14 \log (2-x)+11 \log (3-x)\\ \end{align*}
Mathematica [A] time = 0.0082174, size = 19, normalized size = 0.76 \[ 11 \log (x-3)-14 \log (x-2)+4 \log (x-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 20, normalized size = 0.8 \begin{align*} 4\,\ln \left ( x-1 \right ) +11\,\ln \left ( -3+x \right ) -14\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16459, size = 26, normalized size = 1.04 \begin{align*} 4 \, \log \left (x - 1\right ) - 14 \, \log \left (x - 2\right ) + 11 \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51765, size = 62, normalized size = 2.48 \begin{align*} 4 \, \log \left (x - 1\right ) - 14 \, \log \left (x - 2\right ) + 11 \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.132669, size = 19, normalized size = 0.76 \begin{align*} 11 \log{\left (x - 3 \right )} - 14 \log{\left (x - 2 \right )} + 4 \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13396, size = 30, normalized size = 1.2 \begin{align*} 4 \, \log \left ({\left | x - 1 \right |}\right ) - 14 \, \log \left ({\left | x - 2 \right |}\right ) + 11 \, \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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