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 = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.02, size = 39, normalized size = 1.00 \[ \frac {1}{8} \log (1-x)-\frac {1}{5} \log (2-x)+\frac {1}{12} \log (3-x)-\frac {1}{120} \log (x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 25, normalized size = 0.64 \[ -\frac {1}{120} \, \log \left (x + 3\right ) + \frac {1}{8} \, \log \left (x - 1\right ) - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{12} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 29, normalized size = 0.74 \[ -\frac {1}{120} \, \log \left ({\left | x + 3 \right |}\right ) + \frac {1}{8} \, \log \left ({\left | x - 1 \right |}\right ) - \frac {1}{5} \, \log \left ({\left | x - 2 \right |}\right ) + \frac {1}{12} \, \log \left ({\left | x - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 26, normalized size = 0.67 \[ \frac {\ln \left (x -3\right )}{12}-\frac {\ln \left (x -2\right )}{5}+\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x +3\right )}{120} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 25, normalized size = 0.64 \[ -\frac {1}{120} \, \log \left (x + 3\right ) + \frac {1}{8} \, \log \left (x - 1\right ) - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{12} \, \log \left (x - 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 25, normalized size = 0.64 \[ \frac {\ln \left (x-1\right )}{8}-\frac {\ln \left (x-2\right )}{5}+\frac {\ln \left (x-3\right )}{12}-\frac {\ln \left (x+3\right )}{120} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 26, normalized size = 0.67 \[ \frac {\log {\left (x - 3 \right )}}{12} - \frac {\log {\left (x - 2 \right )}}{5} + \frac {\log {\left (x - 1 \right )}}{8} - \frac {\log {\left (x + 3 \right )}}{120} \]
Verification of antiderivative is not currently implemented for this CAS.
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