Integrand size = 179, antiderivative size = 35 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=-3+\frac {x^2 \log ^2(2)}{\left (-x+\frac {\log (2)}{\log \left (\frac {2}{x+2 \left (-1+x^2\right )}\right )}\right )^2} \]
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\[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=\int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right ) \left (x (1+4 x)-\left (-2+x+2 x^2\right ) \log \left (\frac {2}{-2+x+2 x^2}\right )\right )}{\left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx \\ & = \left (2 \log ^3(2)\right ) \int \frac {x \log \left (\frac {2}{-2+x+2 x^2}\right ) \left (x (1+4 x)-\left (-2+x+2 x^2\right ) \log \left (\frac {2}{-2+x+2 x^2}\right )\right )}{\left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx \\ & = \left (2 \log ^3(2)\right ) \int \left (\frac {\log (2) \left (4 x^3-x \log (2)+x^2 (1-\log (4))+\log (4)\right )}{x \left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}+\frac {-4 x^3-x^2 (1-4 \log (2))+x \log (4)-\log (16)}{x \left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}-\frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )}\right ) \, dx \\ & = \left (2 \log ^3(2)\right ) \int \frac {-4 x^3-x^2 (1-4 \log (2))+x \log (4)-\log (16)}{x \left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx+\left (2 \log ^4(2)\right ) \int \frac {4 x^3-x \log (2)+x^2 (1-\log (4))+\log (4)}{x \left (2-x-2 x^2\right ) \left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx \\ & = -\left (\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx\right )+\left (2 \log ^3(2)\right ) \int \left (\frac {2}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}+\frac {4-x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}-\frac {\log (16)}{2 x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}\right ) \, dx+\left (2 \log ^4(2)\right ) \int \left (-\frac {2}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}+\frac {4-x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}-\frac {\log (4)}{2 x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}\right ) \, dx \\ & = \left (2 \log ^3(2)\right ) \int \frac {4-x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx+\left (4 \log ^3(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx+\left (2 \log ^4(2)\right ) \int \frac {4-x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (4 \log ^4(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^4(2) \log (4)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^3(2) \log (16)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx \\ & = -\left (\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx\right )+\left (2 \log ^3(2)\right ) \int \left (\frac {4}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}-\frac {x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}\right ) \, dx+\left (4 \log ^3(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx+\left (2 \log ^4(2)\right ) \int \left (\frac {4}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}-\frac {x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}\right ) \, dx-\left (4 \log ^4(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^4(2) \log (4)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^3(2) \log (16)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx \\ & = -\left (\left (2 \log ^3(2)\right ) \int \frac {x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx\right )-\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx+\left (4 \log ^3(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx+\left (8 \log ^3(2)\right ) \int \frac {1}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\left (2 \log ^4(2)\right ) \int \frac {x}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (4 \log ^4(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx+\left (8 \log ^4(2)\right ) \int \frac {1}{\left (-2+x+2 x^2\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^4(2) \log (4)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^3(2) \log (16)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx \\ & = -\left (\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx\right )-\left (2 \log ^3(2)\right ) \int \left (\frac {1-\frac {1}{\sqrt {17}}}{\left (1-\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}+\frac {1+\frac {1}{\sqrt {17}}}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}\right ) \, dx+\left (4 \log ^3(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx+\left (8 \log ^3(2)\right ) \int \left (-\frac {4}{\sqrt {17} \left (-1+\sqrt {17}-4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}-\frac {4}{\sqrt {17} \left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2}\right ) \, dx-\left (2 \log ^4(2)\right ) \int \left (\frac {1-\frac {1}{\sqrt {17}}}{\left (1-\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}+\frac {1+\frac {1}{\sqrt {17}}}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}\right ) \, dx-\left (4 \log ^4(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx+\left (8 \log ^4(2)\right ) \int \left (-\frac {4}{\sqrt {17} \left (-1+\sqrt {17}-4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}-\frac {4}{\sqrt {17} \left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3}\right ) \, dx-\left (\log ^4(2) \log (4)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^3(2) \log (16)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx \\ & = -\left (\left (2 \log ^3(2)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )} \, dx\right )+\left (4 \log ^3(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\frac {\left (32 \log ^3(2)\right ) \int \frac {1}{\left (-1+\sqrt {17}-4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx}{\sqrt {17}}-\frac {\left (32 \log ^3(2)\right ) \int \frac {1}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx}{\sqrt {17}}-\frac {1}{17} \left (2 \left (17-\sqrt {17}\right ) \log ^3(2)\right ) \int \frac {1}{\left (1-\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\frac {1}{17} \left (2 \left (17+\sqrt {17}\right ) \log ^3(2)\right ) \int \frac {1}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx-\left (4 \log ^4(2)\right ) \int \frac {1}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\frac {\left (32 \log ^4(2)\right ) \int \frac {1}{\left (-1+\sqrt {17}-4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx}{\sqrt {17}}-\frac {\left (32 \log ^4(2)\right ) \int \frac {1}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx}{\sqrt {17}}-\frac {1}{17} \left (2 \left (17-\sqrt {17}\right ) \log ^4(2)\right ) \int \frac {1}{\left (1-\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\frac {1}{17} \left (2 \left (17+\sqrt {17}\right ) \log ^4(2)\right ) \int \frac {1}{\left (1+\sqrt {17}+4 x\right ) \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^4(2) \log (4)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^3} \, dx-\left (\log ^3(2) \log (16)\right ) \int \frac {1}{x \left (-\log (2)+x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \, dx \\ \end{align*}
Time = 5.07 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.31 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=-\frac {\log ^3(2) \left (\log (2)-2 x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )}{\left (\log (2)-x \log \left (\frac {2}{-2+x+2 x^2}\right )\right )^2} \]
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Time = 2.18 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.34
method | result | size |
risch | \(-\frac {\left (-2 x \ln \left (\frac {2}{2 x^{2}+x -2}\right )+\ln \left (2\right )\right ) \ln \left (2\right )^{3}}{{\left (-x \ln \left (\frac {2}{2 x^{2}+x -2}\right )+\ln \left (2\right )\right )}^{2}}\) | \(47\) |
norman | \(\frac {2 \ln \left (2\right )^{3} x \ln \left (\frac {2}{2 x^{2}+x -2}\right )-\ln \left (2\right )^{4}}{{\left (-x \ln \left (\frac {2}{2 x^{2}+x -2}\right )+\ln \left (2\right )\right )}^{2}}\) | \(50\) |
parallelrisch | \(-\frac {-8 \ln \left (2\right )^{3} x \ln \left (\frac {2}{2 x^{2}+x -2}\right )+4 \ln \left (2\right )^{4}}{4 \left (\ln \left (\frac {2}{2 x^{2}+x -2}\right )^{2} x^{2}-2 \ln \left (\frac {2}{2 x^{2}+x -2}\right ) \ln \left (2\right ) x +\ln \left (2\right )^{2}\right )}\) | \(74\) |
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Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (33) = 66\).
Time = 0.26 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.06 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=\frac {2 \, x \log \left (2\right )^{3} \log \left (\frac {2}{2 \, x^{2} + x - 2}\right ) - \log \left (2\right )^{4}}{x^{2} \log \left (\frac {2}{2 \, x^{2} + x - 2}\right )^{2} - 2 \, x \log \left (2\right ) \log \left (\frac {2}{2 \, x^{2} + x - 2}\right ) + \log \left (2\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (27) = 54\).
Time = 0.17 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.86 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=\frac {2 x \log {\left (2 \right )}^{3} \log {\left (\frac {2}{2 x^{2} + x - 2} \right )} - \log {\left (2 \right )}^{4}}{x^{2} \log {\left (\frac {2}{2 x^{2} + x - 2} \right )}^{2} - 2 x \log {\left (2 \right )} \log {\left (\frac {2}{2 x^{2} + x - 2} \right )} + \log {\left (2 \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (33) = 66\).
Time = 0.38 (sec) , antiderivative size = 91, normalized size of antiderivative = 2.60 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=\frac {2 \, x \log \left (2\right )^{4} - 2 \, x \log \left (2\right )^{3} \log \left (2 \, x^{2} + x - 2\right ) - \log \left (2\right )^{4}}{x^{2} \log \left (2\right )^{2} + x^{2} \log \left (2 \, x^{2} + x - 2\right )^{2} - 2 \, x \log \left (2\right )^{2} + \log \left (2\right )^{2} - 2 \, {\left (x^{2} \log \left (2\right ) - x \log \left (2\right )\right )} \log \left (2 \, x^{2} + x - 2\right )} \]
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Result contains complex when optimal does not.
Time = 0.41 (sec) , antiderivative size = 145, normalized size of antiderivative = 4.14 \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=\frac {-4 i \, \pi x \log \left (2\right )^{3} - 2 \, x \log \left (2\right )^{4} + 2 \, x \log \left (2\right )^{3} \log \left (2 \, x^{2} + x - 2\right ) + \log \left (2\right )^{4}}{4 \, \pi ^{2} x^{2} - 4 i \, \pi x^{2} \log \left (2\right ) - x^{2} \log \left (2\right )^{2} + 4 i \, \pi x^{2} \log \left (2 \, x^{2} + x - 2\right ) + 2 \, x^{2} \log \left (2\right ) \log \left (2 \, x^{2} + x - 2\right ) - x^{2} \log \left (2 \, x^{2} + x - 2\right )^{2} + 4 i \, \pi x \log \left (2\right ) + 2 \, x \log \left (2\right )^{2} - 2 \, x \log \left (2\right ) \log \left (2 \, x^{2} + x - 2\right ) - \log \left (2\right )^{2}} \]
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Timed out. \[ \int \frac {\left (2 x^2+8 x^3\right ) \log ^3(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (4 x-2 x^2-4 x^3\right ) \log ^3(2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )}{\left (2-x-2 x^2\right ) \log ^3(2)+\left (-6 x+3 x^2+6 x^3\right ) \log ^2(2) \log \left (\frac {2}{-2+x+2 x^2}\right )+\left (6 x^2-3 x^3-6 x^4\right ) \log (2) \log ^2\left (\frac {2}{-2+x+2 x^2}\right )+\left (-2 x^3+x^4+2 x^5\right ) \log ^3\left (\frac {2}{-2+x+2 x^2}\right )} \, dx=-\int \frac {\ln \left (\frac {2}{2\,x^2+x-2}\right )\,{\ln \left (2\right )}^3\,\left (8\,x^3+2\,x^2\right )-{\ln \left (\frac {2}{2\,x^2+x-2}\right )}^2\,{\ln \left (2\right )}^3\,\left (4\,x^3+2\,x^2-4\,x\right )}{\left (-2\,x^5-x^4+2\,x^3\right )\,{\ln \left (\frac {2}{2\,x^2+x-2}\right )}^3+\ln \left (2\right )\,\left (6\,x^4+3\,x^3-6\,x^2\right )\,{\ln \left (\frac {2}{2\,x^2+x-2}\right )}^2-{\ln \left (2\right )}^2\,\left (6\,x^3+3\,x^2-6\,x\right )\,\ln \left (\frac {2}{2\,x^2+x-2}\right )+{\ln \left (2\right )}^3\,\left (2\,x^2+x-2\right )} \,d x \]
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