Integrand size = 115, antiderivative size = 23 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\frac {3 x}{4+\frac {1}{4} \log \left (\frac {2}{(-1+x)^2}\right )-\log (x)} \]
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\[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {12 \left (20-22 x-(-1+x) \log \left (\frac {2}{(-1+x)^2}\right )+4 (-1+x) \log (x)\right )}{(1-x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx \\ & = 12 \int \frac {20-22 x-(-1+x) \log \left (\frac {2}{(-1+x)^2}\right )+4 (-1+x) \log (x)}{(1-x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx \\ & = 12 \int \left (\frac {2 (-2+3 x)}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}+\frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)}\right ) \, dx \\ & = 12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \frac {-2+3 x}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx \\ & = 12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \left (\frac {3}{\left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}+\frac {1}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2}\right ) \, dx \\ & = 12 \int \frac {1}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \, dx+24 \int \frac {1}{(-1+x) \left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx+72 \int \frac {1}{\left (16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\frac {12 x}{16+\log \left (\frac {2}{(-1+x)^2}\right )-4 \log (x)} \]
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Time = 8.43 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17
method | result | size |
parallelrisch | \(-\frac {12 x}{-16+4 \ln \left (x \right )-\ln \left (\frac {2}{x^{2}-2 x +1}\right )}\) | \(27\) |
default | \(-\frac {24 i x}{\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}-2 i \ln \left (2\right )+8 i \ln \left (x \right )+4 i \ln \left (-1+x \right )-32 i}\) | \(81\) |
risch | \(\frac {24 i x}{-\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )+2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}-\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}+2 i \ln \left (2\right )-8 i \ln \left (x \right )-4 i \ln \left (-1+x \right )+32 i}\) | \(83\) |
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Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=-\frac {12 \, x}{4 \, \log \left (x\right ) - \log \left (\frac {2}{x^{2} - 2 \, x + 1}\right ) - 16} \]
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Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\frac {12 x}{- 4 \log {\left (x \right )} + \log {\left (\frac {2}{x^{2} - 2 x + 1} \right )} + 16} \]
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Time = 0.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\frac {12 \, x}{\log \left (2\right ) - 2 \, \log \left (x - 1\right ) - 4 \, \log \left (x\right ) + 16} \]
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Time = 0.40 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\frac {12 \, x}{\log \left (2\right ) - \log \left (x^{2} - 2 \, x + 1\right ) - 4 \, \log \left (x\right ) + 16} \]
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Timed out. \[ \int \frac {-240+264 x+(48-48 x) \log (x)+(-12+12 x) \log \left (\frac {2}{1-2 x+x^2}\right )}{-256+256 x+(-16+16 x) \log ^2(x)+(-32+32 x) \log \left (\frac {2}{1-2 x+x^2}\right )+(-1+x) \log ^2\left (\frac {2}{1-2 x+x^2}\right )+\log (x) \left (128-128 x+(8-8 x) \log \left (\frac {2}{1-2 x+x^2}\right )\right )} \, dx=\int \frac {264\,x-\ln \left (x\right )\,\left (48\,x-48\right )+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (12\,x-12\right )-240}{256\,x-\ln \left (x\right )\,\left (128\,x+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (8\,x-8\right )-128\right )+\ln \left (\frac {2}{x^2-2\,x+1}\right )\,\left (32\,x-32\right )+{\ln \left (\frac {2}{x^2-2\,x+1}\right )}^2\,\left (x-1\right )+{\ln \left (x\right )}^2\,\left (16\,x-16\right )-256} \,d x \]
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