Integrand size = 28, antiderivative size = 18 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\log \left (30 \left (\frac {2}{5 (4-x)}+7 x\right )\right ) \]
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Time = 0.02 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2099, 642} \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\log \left (-35 x^2+140 x+2\right )-\log (4-x) \]
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Rule 642
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{4-x}+\frac {70 (-2+x)}{-2-140 x+35 x^2}\right ) \, dx \\ & = -\log (4-x)+70 \int \frac {-2+x}{-2-140 x+35 x^2} \, dx \\ & = -\log (4-x)+\log \left (2+140 x-35 x^2\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=-\log (4-x)+\log \left (2+140 x-35 x^2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94
method | result | size |
parallelrisch | \(-\ln \left (x -4\right )+\ln \left (x^{2}-4 x -\frac {2}{35}\right )\) | \(17\) |
default | \(-\ln \left (x -4\right )+\ln \left (35 x^{2}-140 x -2\right )\) | \(19\) |
norman | \(-\ln \left (x -4\right )+\ln \left (35 x^{2}-140 x -2\right )\) | \(19\) |
risch | \(-\ln \left (x -4\right )+\ln \left (35 x^{2}-140 x -2\right )\) | \(19\) |
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none
Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\log \left (35 \, x^{2} - 140 \, x - 2\right ) - \log \left (x - 4\right ) \]
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Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=- \log {\left (x - 4 \right )} + \log {\left (35 x^{2} - 140 x - 2 \right )} \]
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none
Time = 0.30 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\log \left (35 \, x^{2} - 140 \, x - 2\right ) - \log \left (x - 4\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\log \left ({\left | 35 \, x^{2} - 140 \, x - 2 \right |}\right ) - \log \left ({\left | x - 4 \right |}\right ) \]
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Time = 9.10 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int \frac {562-280 x+35 x^2}{8+558 x-280 x^2+35 x^3} \, dx=\ln \left (x^2-4\,x-\frac {2}{35}\right )-\ln \left (x-4\right ) \]
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