Integrand size = 346, antiderivative size = 29 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+\left (x+\log \left (1+\log \left ((2-x)^2\right )\right )\right )^2} \]
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\[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{e^x} \left (10-5 x+10 e^x x+2 x^2-9 e^x x^2+x^3+4 e^x x^3-e^x x^4-2 x \left (-2+e^x (-2+x) x\right ) \log \left (1+\log \left ((-2+x)^2\right )\right )-(-2+x) \left (1+e^x x\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )-(-2+x) \log \left ((-2+x)^2\right ) \left (5-x^2+e^x x \left (5-2 x+x^2\right )+2 e^x x^2 \log \left (1+\log \left ((-2+x)^2\right )\right )+\left (1+e^x x\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )\right )}{(2-x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx \\ & = \int \left (-\frac {10 e^{e^x}}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {5 e^{e^x} x}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {2 e^{e^x} x^2}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {e^{e^x} x^3}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {5 e^{e^x} \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {e^{e^x} x^2 \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {4 e^{e^x} x \log \left (1+\log \left ((-2+x)^2\right )\right )}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x} \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x} \log \left ((-2+x)^2\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x+x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )}\right ) \, dx \\ & = -\left (2 \int \frac {e^{e^x} x^2}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx\right )-4 \int \frac {e^{e^x} x \log \left (1+\log \left ((-2+x)^2\right )\right )}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+5 \int \frac {e^{e^x} x}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+5 \int \frac {e^{e^x} \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-10 \int \frac {e^{e^x}}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-\int \frac {e^{e^x} x^3}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-\int \frac {e^{e^x} x^2 \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x} \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x} \log \left ((-2+x)^2\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x+x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \]
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\[\int \frac {\left (\left (\left (\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x} \ln \left (x^{2}-4 x +4\right )+\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}+2 x^{2}+5 x -10\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}-2 x^{2}+5 x -10\right ) {\mathrm e}^{-\ln \left ({\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+2 x \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+x^{2}-2 x +5\right )+{\mathrm e}^{x}}}{\left (\left (-2+x \right ) \ln \left (x^{2}-4 x +4\right )+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{2}-4 x \right ) \ln \left (x^{2}-4 x +4\right )+2 x^{2}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (x^{3}-4 x^{2}+9 x -10\right ) \ln \left (x^{2}-4 x +4\right )+x^{3}-4 x^{2}+9 x -10}d x\]
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Time = 0.25 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=x e^{\left (e^{x} - \log \left (x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5\right )\right )} \]
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Time = 0.59 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{e^{x}}}{x^{2} + 2 x \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )} - 2 x + \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )}^{2} + 5} \]
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Time = 0.38 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (2 \, \log \left (x - 2\right ) + 1\right ) + \log \left (2 \, \log \left (x - 2\right ) + 1\right )^{2} - 2 \, x + 5} \]
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Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (27) = 54\).
Time = 3.02 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.66 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {2 \, x e^{\left (x + e^{x}\right )}}{x^{2} e^{x} + 2 \, x e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x e^{x} + 5 \, e^{x}} + \frac {2 \, x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5} \]
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Time = 11.41 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )}^2+x^2+x\,\left (2\,\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )-2\right )+5} \]
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