Integrand size = 32, antiderivative size = 23 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=\log \left (\frac {e^{-x} x^2}{1-(-20+2 x)^2}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1608, 1642} \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=-x-\log (19-2 x)-\log (21-2 x)+2 \log (x) \]
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Rule 1608
Rule 1642
Rubi steps \begin{align*} \text {integral}& = \int \frac {798-479 x+80 x^2-4 x^3}{x \left (399-80 x+4 x^2\right )} \, dx \\ & = \int \left (-1+\frac {2}{x}-\frac {2}{-21+2 x}-\frac {2}{-19+2 x}\right ) \, dx \\ & = -x-\log (19-2 x)-\log (21-2 x)+2 \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=-x+2 \log (x)-\log \left (399-80 x+4 x^2\right ) \]
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Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
method | result | size |
parallelrisch | \(-x +2 \ln \left (x \right )-\ln \left (x -\frac {21}{2}\right )-\ln \left (x -\frac {19}{2}\right )\) | \(21\) |
risch | \(-x +2 \ln \left (x \right )-\ln \left (4 x^{2}-80 x +399\right )\) | \(22\) |
default | \(-x +2 \ln \left (x \right )-\ln \left (2 x -19\right )-\ln \left (2 x -21\right )\) | \(25\) |
norman | \(-x +2 \ln \left (x \right )-\ln \left (2 x -19\right )-\ln \left (2 x -21\right )\) | \(25\) |
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Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=-x - \log \left (4 \, x^{2} - 80 \, x + 399\right ) + 2 \, \log \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.74 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=- x + 2 \log {\left (x \right )} - \log {\left (4 x^{2} - 80 x + 399 \right )} \]
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Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=-x - \log \left (2 \, x - 19\right ) - \log \left (2 \, x - 21\right ) + 2 \, \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=-x - \log \left ({\left | 2 \, x - 19 \right |}\right ) - \log \left ({\left | 2 \, x - 21 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.09 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {798-479 x+80 x^2-4 x^3}{399 x-80 x^2+4 x^3} \, dx=2\,\ln \left (x\right )-\ln \left (x^2-20\,x+\frac {399}{4}\right )-x \]
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