Integrand size = 38, antiderivative size = 28 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=\log \left (\frac {e^x \left (-1+\frac {80}{3+\frac {x}{25}}\right )}{(5-x) x}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2099} \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x-\log (5-x)+\log (1925-x)-\log (x)-\log (x+75) \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (1+\frac {1}{-75-x}+\frac {1}{5-x}+\frac {1}{-1925+x}-\frac {1}{x}\right ) \, dx \\ & = x-\log (5-x)+\log (1925-x)-\log (x)-\log (75+x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x+\log (1925-x)-\log (x)-\log \left (375-70 x-x^2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79
method | result | size |
risch | \(x +\ln \left (x -1925\right )-\ln \left (x^{3}+70 x^{2}-375 x \right )\) | \(22\) |
default | \(x -\ln \left (x \right )-\ln \left (x +75\right )-\ln \left (-5+x \right )+\ln \left (x -1925\right )\) | \(23\) |
norman | \(x -\ln \left (x \right )-\ln \left (x +75\right )-\ln \left (-5+x \right )+\ln \left (x -1925\right )\) | \(23\) |
parallelrisch | \(x -\ln \left (x \right )-\ln \left (x +75\right )-\ln \left (-5+x \right )+\ln \left (x -1925\right )\) | \(23\) |
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Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x - \log \left (x^{3} + 70 \, x^{2} - 375 \, x\right ) + \log \left (x - 1925\right ) \]
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Time = 0.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x + \log {\left (x - 1925 \right )} - \log {\left (x^{3} + 70 x^{2} - 375 x \right )} \]
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Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x - \log \left (x + 75\right ) - \log \left (x - 5\right ) + \log \left (x - 1925\right ) - \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.93 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x - \log \left ({\left | x + 75 \right |}\right ) - \log \left ({\left | x - 5 \right |}\right ) + \log \left ({\left | x - 1925 \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
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Time = 7.47 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.68 \[ \int \frac {-721875+991375 x-129420 x^2-1857 x^3+x^4}{721875 x-135125 x^2-1855 x^3+x^4} \, dx=x+\ln \left (x-1925\right )-\ln \left (x\,\left (x^2+70\,x-375\right )\right ) \]
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