Integrand size = 35, antiderivative size = 16 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\log \left (\frac {\frac {12}{x}+x}{(25-x)^4}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.19, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {2099, 266} \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\log \left (x^2+12\right )-4 \log (25-x)-\log (x) \]
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Rule 266
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {4}{-25+x}-\frac {1}{x}+\frac {2 x}{12+x^2}\right ) \, dx \\ & = -4 \log (25-x)-\log (x)+2 \int \frac {x}{12+x^2} \, dx \\ & = -4 \log (25-x)-\log (x)+\log \left (12+x^2\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.19 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=-4 \log (25-x)-\log (x)+\log \left (12+x^2\right ) \]
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Time = 0.11 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12
method | result | size |
default | \(-\ln \left (x \right )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
norman | \(-\ln \left (x \right )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
risch | \(-\ln \left (x \right )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
parallelrisch | \(-\ln \left (x \right )-4 \ln \left (x -25\right )+\ln \left (x^{2}+12\right )\) | \(18\) |
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none
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\log \left (x^{2} + 12\right ) - 4 \, \log \left (x - 25\right ) - \log \left (x\right ) \]
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Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=- \log {\left (x \right )} - 4 \log {\left (x - 25 \right )} + \log {\left (x^{2} + 12 \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\log \left (x^{2} + 12\right ) - 4 \, \log \left (x - 25\right ) - \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.19 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\log \left (x^{2} + 12\right ) - 4 \, \log \left ({\left | x - 25 \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
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Time = 16.37 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int \frac {300-60 x-25 x^2-3 x^3}{-300 x+12 x^2-25 x^3+x^4} \, dx=\ln \left (x^2+12\right )-4\,\ln \left (x-25\right )-\ln \left (x\right ) \]
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