Integrand size = 57, antiderivative size = 27 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=1-\frac {x}{x-x^2}+\frac {1}{3} \log ^2(\log (-4+2 x)) \]
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Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6820, 6818} \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {1}{x-1}+\frac {1}{3} \log ^2(\log (2 x-4)) \]
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Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1}{(-1+x)^2}+\frac {2 \log (\log (-4+2 x))}{3 (-2+x) \log (-4+2 x)}\right ) \, dx \\ & = \frac {1}{-1+x}+\frac {2}{3} \int \frac {\log (\log (-4+2 x))}{(-2+x) \log (-4+2 x)} \, dx \\ & = \frac {1}{-1+x}+\frac {1}{3} \log ^2(\log (-4+2 x)) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {1}{-1+x}+\frac {1}{3} \log ^2(\log (2 (-2+x))) \]
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Time = 0.85 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.67
method | result | size |
risch | \(\frac {\ln \left (\ln \left (2 x -4\right )\right )^{2}}{3}+\frac {1}{-1+x}\) | \(18\) |
parts | \(\frac {\ln \left (\ln \left (2 x -4\right )\right )^{2}}{3}+\frac {1}{-1+x}\) | \(18\) |
default | \(\frac {1}{-1+x}+\frac {\ln \left (\ln \left (2\right )+\ln \left (-2+x \right )\right )^{2}}{3}\) | \(19\) |
parallelrisch | \(\frac {12+5 x \ln \left (\ln \left (2 x -4\right )\right )^{2}-5 \ln \left (\ln \left (2 x -4\right )\right )^{2}+3 x}{15 x -15}\) | \(36\) |
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none
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.81 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {{\left (x - 1\right )} \log \left (\log \left (2 \, x - 4\right )\right )^{2} + 3}{3 \, {\left (x - 1\right )}} \]
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Time = 0.12 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.56 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {\log {\left (\log {\left (2 x - 4 \right )} \right )}^{2}}{3} + \frac {1}{x - 1} \]
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none
Time = 0.35 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.67 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {1}{3} \, \log \left (\log \left (2\right ) + \log \left (x - 2\right )\right )^{2} + \frac {1}{x - 1} \]
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Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {1}{3} \, \log \left (\log \left (2 \, x - 4\right )\right )^{2} + \frac {1}{x - 1} \]
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Time = 9.68 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.63 \[ \int \frac {(6-3 x) \log (-4+2 x)+\left (2-4 x+2 x^2\right ) \log (\log (-4+2 x))}{\left (-6+15 x-12 x^2+3 x^3\right ) \log (-4+2 x)} \, dx=\frac {1}{x-1}+\frac {{\ln \left (\ln \left (2\,x-4\right )\right )}^2}{3} \]
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