Optimal. Leaf size=39 \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
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Rubi [A] time = 0.0199904, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {2058} \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
Antiderivative was successfully verified.
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Rule 2058
Rubi steps
\begin{align*} \int \frac{1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx &=\int \left (\frac{1}{12 (-3+x)}-\frac{1}{5 (-2+x)}+\frac{1}{8 (-1+x)}-\frac{1}{120 (3+x)}\right ) \, dx\\ &=\frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0062116, size = 39, normalized size = 1. \[ \frac{1}{8} \log (1-x)-\frac{1}{5} \log (2-x)+\frac{1}{12} \log (3-x)-\frac{1}{120} \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 26, normalized size = 0.7 \begin{align*}{\frac{\ln \left ( x-1 \right ) }{8}}+{\frac{\ln \left ( -3+x \right ) }{12}}-{\frac{\ln \left ( 3+x \right ) }{120}}-{\frac{\ln \left ( -2+x \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974703, size = 34, normalized size = 0.87 \begin{align*} -\frac{1}{120} \, \log \left (x + 3\right ) + \frac{1}{8} \, \log \left (x - 1\right ) - \frac{1}{5} \, \log \left (x - 2\right ) + \frac{1}{12} \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26296, size = 96, normalized size = 2.46 \begin{align*} -\frac{1}{120} \, \log \left (x + 3\right ) + \frac{1}{8} \, \log \left (x - 1\right ) - \frac{1}{5} \, \log \left (x - 2\right ) + \frac{1}{12} \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.210924, size = 26, normalized size = 0.67 \begin{align*} \frac{\log{\left (x - 3 \right )}}{12} - \frac{\log{\left (x - 2 \right )}}{5} + \frac{\log{\left (x - 1 \right )}}{8} - \frac{\log{\left (x + 3 \right )}}{120} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1608, size = 39, normalized size = 1. \begin{align*} -\frac{1}{120} \, \log \left ({\left | x + 3 \right |}\right ) + \frac{1}{8} \, \log \left ({\left | x - 1 \right |}\right ) - \frac{1}{5} \, \log \left ({\left | x - 2 \right |}\right ) + \frac{1}{12} \, \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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