Integrand size = 24, antiderivative size = 19 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=\log (1-x)-2 \log (2+x)-3 \log (3+x) \]
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Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2099} \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=\log (1-x)-2 \log (x+2)-3 \log (x+3) \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{-1+x}-\frac {2}{2+x}-\frac {3}{3+x}\right ) \, dx \\ & = \log (1-x)-2 \log (2+x)-3 \log (3+x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=-2 \left (-\frac {1}{2} \log (1-x)+\log (2+x)+\frac {3}{2} \log (3+x)\right ) \]
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Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95
method | result | size |
default | \(-2 \ln \left (x +2\right )-3 \ln \left (3+x \right )+\ln \left (x -1\right )\) | \(18\) |
norman | \(-2 \ln \left (x +2\right )-3 \ln \left (3+x \right )+\ln \left (x -1\right )\) | \(18\) |
risch | \(-2 \ln \left (x +2\right )-3 \ln \left (3+x \right )+\ln \left (x -1\right )\) | \(18\) |
parallelrisch | \(-2 \ln \left (x +2\right )-3 \ln \left (3+x \right )+\ln \left (x -1\right )\) | \(18\) |
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none
Time = 0.34 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=-3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
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Time = 0.07 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=\log {\left (x - 1 \right )} - 2 \log {\left (x + 2 \right )} - 3 \log {\left (x + 3 \right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=-3 \, \log \left (x + 3\right ) - 2 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=-3 \, \log \left ({\left | x + 3 \right |}\right ) - 2 \, \log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) \]
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Time = 9.62 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {18-2 x-4 x^2}{-6+x+4 x^2+x^3} \, dx=\ln \left (x-1\right )-2\,\ln \left (x+2\right )-3\,\ln \left (x+3\right ) \]
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