Integrand size = 20, antiderivative size = 39 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=\frac {1}{8} \log (1-x)-\frac {1}{5} \log (2-x)+\frac {1}{12} \log (3-x)-\frac {1}{120} \log (3+x) \]
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Time = 0.01 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2083} \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=\frac {1}{8} \log (1-x)-\frac {1}{5} \log (2-x)+\frac {1}{12} \log (3-x)-\frac {1}{120} \log (x+3) \]
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Rule 2083
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.00 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.00 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=\frac {1}{8} \log (1-x)-\frac {1}{5} \log (2-x)+\frac {1}{12} \log (3-x)-\frac {1}{120} \log (3+x) \]
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Time = 0.06 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.67
method | result | size |
default | \(\frac {\ln \left (-3+x \right )}{12}-\frac {\ln \left (3+x \right )}{120}+\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x -2\right )}{5}\) | \(26\) |
norman | \(\frac {\ln \left (-3+x \right )}{12}-\frac {\ln \left (3+x \right )}{120}+\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x -2\right )}{5}\) | \(26\) |
risch | \(\frac {\ln \left (-3+x \right )}{12}-\frac {\ln \left (3+x \right )}{120}+\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x -2\right )}{5}\) | \(26\) |
parallelrisch | \(\frac {\ln \left (-3+x \right )}{12}-\frac {\ln \left (3+x \right )}{120}+\frac {\ln \left (x -1\right )}{8}-\frac {\ln \left (x -2\right )}{5}\) | \(26\) |
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Time = 0.26 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.64 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=-\frac {1}{120} \, \log \left (x + 3\right ) + \frac {1}{8} \, \log \left (x - 1\right ) - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{12} \, \log \left (x - 3\right ) \]
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Time = 0.13 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.67 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=\frac {\log {\left (x - 3 \right )}}{12} - \frac {\log {\left (x - 2 \right )}}{5} + \frac {\log {\left (x - 1 \right )}}{8} - \frac {\log {\left (x + 3 \right )}}{120} \]
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Time = 0.19 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.64 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=-\frac {1}{120} \, \log \left (x + 3\right ) + \frac {1}{8} \, \log \left (x - 1\right ) - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{12} \, \log \left (x - 3\right ) \]
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Time = 0.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.74 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=-\frac {1}{120} \, \log \left ({\left | x + 3 \right |}\right ) + \frac {1}{8} \, \log \left ({\left | x - 1 \right |}\right ) - \frac {1}{5} \, \log \left ({\left | x - 2 \right |}\right ) + \frac {1}{12} \, \log \left ({\left | x - 3 \right |}\right ) \]
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Time = 9.28 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.64 \[ \int \frac {1}{-18+27 x-7 x^2-3 x^3+x^4} \, dx=\frac {\ln \left (x-1\right )}{8}-\frac {\ln \left (x-2\right )}{5}+\frac {\ln \left (x-3\right )}{12}-\frac {\ln \left (x+3\right )}{120} \]
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