Integrand size = 85, antiderivative size = 24 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (-3-\frac {x}{2}+\log \left ((4-x) \left (\frac {75}{x}-x\right )\right )\right ) \]
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Time = 0.15 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6820, 6816} \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (-2 \log \left (x^2-4 x+\frac {300}{x}-75\right )+x+6\right ) \]
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Rule 6816
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {600+300 x-67 x^2-8 x^3+x^4}{x \left (300-75 x-4 x^2+x^3\right ) \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right )} \, dx \\ & = \log \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right ) \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (6+x-2 \log \left (-75+\frac {300}{x}-4 x+x^2\right )\right ) \]
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Time = 1.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.04
method | result | size |
norman | \(\ln \left (x -2 \ln \left (\frac {x^{3}-4 x^{2}-75 x +300}{x}\right )+6\right )\) | \(25\) |
risch | \(\ln \left (-\frac {x}{2}+\ln \left (\frac {x^{3}-4 x^{2}-75 x +300}{x}\right )-3\right )\) | \(25\) |
parallelrisch | \(\ln \left (x -2 \ln \left (\frac {x^{3}-4 x^{2}-75 x +300}{x}\right )+6\right )\) | \(25\) |
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none
Time = 0.23 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (-x + 2 \, \log \left (\frac {x^{3} - 4 \, x^{2} - 75 \, x + 300}{x}\right ) - 6\right ) \]
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Time = 0.23 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log {\left (- \frac {x}{2} + \log {\left (\frac {x^{3} - 4 x^{2} - 75 x + 300}{x} \right )} - 3 \right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (-\frac {1}{2} \, x + \log \left (x^{2} - 75\right ) + \log \left (x - 4\right ) - \log \left (x\right ) - 3\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\log \left (x - 2 \, \log \left (\frac {x^{3} - 4 \, x^{2} - 75 \, x + 300}{x}\right ) + 6\right ) \]
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Time = 9.87 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {-600-300 x+67 x^2+8 x^3-x^4}{-1800 x+150 x^2+99 x^3-2 x^4-x^5+\left (600 x-150 x^2-8 x^3+2 x^4\right ) \log \left (\frac {300-75 x-4 x^2+x^3}{x}\right )} \, dx=\ln \left (\ln \left (-\frac {-x^3+4\,x^2+75\,x-300}{x}\right )-\frac {x}{2}-3\right ) \]
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