Integrand size = 17, antiderivative size = 15 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=\log \left (\frac {(1-2 x)^2}{e^3 x^8}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {645} \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2 \log (1-2 x)-8 \log (x) \]
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Rule 645
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {8}{x}+\frac {4}{-1+2 x}\right ) \, dx \\ & = 2 \log (1-2 x)-8 \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2 \log (1-2 x)-8 \log (x) \]
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Time = 0.18 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80
method | result | size |
parallelrisch | \(-8 \ln \left (x \right )+2 \ln \left (x -\frac {1}{2}\right )\) | \(12\) |
default | \(2 \ln \left (-1+2 x \right )-8 \ln \left (x \right )\) | \(14\) |
norman | \(2 \ln \left (-1+2 x \right )-8 \ln \left (x \right )\) | \(14\) |
risch | \(2 \ln \left (-1+2 x \right )-8 \ln \left (x \right )\) | \(14\) |
meijerg | \(-8 \ln \left (x \right )-8 \ln \left (2\right )-8 i \pi +2 \ln \left (1-2 x \right )\) | \(22\) |
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none
Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2 \, \log \left (2 \, x - 1\right ) - 8 \, \log \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=- 8 \log {\left (x \right )} + 2 \log {\left (x - \frac {1}{2} \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2 \, \log \left (2 \, x - 1\right ) - 8 \, \log \left (x\right ) \]
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none
Time = 0.30 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2 \, \log \left ({\left | 2 \, x - 1 \right |}\right ) - 8 \, \log \left ({\left | x \right |}\right ) \]
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Time = 13.44 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \frac {8-12 x}{-x+2 x^2} \, dx=2\,\ln \left (x-\frac {1}{2}\right )-8\,\ln \left (x\right ) \]
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