Optimal. Leaf size=30 \[ x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x) \]
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Rubi [A] time = 0.0576631, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.034, Rules used = {1612} \[ x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x) \]
Antiderivative was successfully verified.
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Rule 1612
Rubi steps
\begin{align*} \int \frac{1+2 x+3 x^2+x^3}{(-3+x) (-2+x) (-1+x)} \, dx &=\int \left (1+\frac{61}{2 (-3+x)}-\frac{25}{-2+x}+\frac{7}{2 (-1+x)}\right ) \, dx\\ &=x+\frac{7}{2} \log (1-x)-25 \log (2-x)+\frac{61}{2} \log (3-x)\\ \end{align*}
Mathematica [A] time = 0.011634, size = 24, normalized size = 0.8 \[ x+\frac{61}{2} \log (x-3)-25 \log (x-2)+\frac{7}{2} \log (x-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 21, normalized size = 0.7 \begin{align*} x+{\frac{7\,\ln \left ( x-1 \right ) }{2}}+{\frac{61\,\ln \left ( -3+x \right ) }{2}}-25\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967553, size = 27, normalized size = 0.9 \begin{align*} x + \frac{7}{2} \, \log \left (x - 1\right ) - 25 \, \log \left (x - 2\right ) + \frac{61}{2} \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5394, size = 73, normalized size = 2.43 \begin{align*} x + \frac{7}{2} \, \log \left (x - 1\right ) - 25 \, \log \left (x - 2\right ) + \frac{61}{2} \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.13527, size = 24, normalized size = 0.8 \begin{align*} x + \frac{61 \log{\left (x - 3 \right )}}{2} - 25 \log{\left (x - 2 \right )} + \frac{7 \log{\left (x - 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12603, size = 31, normalized size = 1.03 \begin{align*} x + \frac{7}{2} \, \log \left ({\left | x - 1 \right |}\right ) - 25 \, \log \left ({\left | x - 2 \right |}\right ) + \frac{61}{2} \, \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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