Integrand size = 346, antiderivative size = 29 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+\left (x+\log \left (1+\log \left ((2-x)^2\right )\right )\right )^2} \]
Time = 0.25 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \]
Integrate[(E^E^x*(-10 + 5*x - 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x ^4) + (-10 + 5*x + 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x^4))*Log[4 - 4*x + x^2] + (-4*x + E^x*(-4*x^2 + 2*x^3) + E^x*(-4*x^2 + 2*x^3)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + E^x*(-2*x + x^2) + (- 2 + x + E^x*(-2*x + x^2))*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]]^ 2))/((5 - 2*x + x^2 + 2*x*Log[1 + Log[4 - 4*x + x^2]] + Log[1 + Log[4 - 4* x + x^2]]^2)*(-10 + 9*x - 4*x^2 + x^3 + (-10 + 9*x - 4*x^2 + x^3)*Log[4 - 4*x + x^2] + (-4*x + 2*x^2 + (-4*x + 2*x^2)*Log[4 - 4*x + x^2])*Log[1 + Lo g[4 - 4*x + x^2]] + (-2 + x + (-2 + x)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]]^2)),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \frac {e^{e^x} \left (-x^3-2 x^2+\left (e^x \left (x^2-2 x\right )+\left (e^x \left (x^2-2 x\right )+x-2\right ) \log \left (x^2-4 x+4\right )+x-2\right ) \log ^2\left (\log \left (x^2-4 x+4\right )+1\right )+\left (e^x \left (2 x^3-4 x^2\right )+e^x \left (2 x^3-4 x^2\right ) \log \left (x^2-4 x+4\right )-4 x\right ) \log \left (\log \left (x^2-4 x+4\right )+1\right )+e^x \left (x^4-4 x^3+9 x^2-10 x\right )+\left (-x^3+2 x^2+e^x \left (x^4-4 x^3+9 x^2-10 x\right )+5 x-10\right ) \log \left (x^2-4 x+4\right )+5 x-10\right )}{\left (x^2+\log ^2\left (\log \left (x^2-4 x+4\right )+1\right )+2 x \log \left (\log \left (x^2-4 x+4\right )+1\right )-2 x+5\right ) \left (x^3-4 x^2+\left ((x-2) \log \left (x^2-4 x+4\right )+x-2\right ) \log ^2\left (\log \left (x^2-4 x+4\right )+1\right )+\left (2 x^2+\left (2 x^2-4 x\right ) \log \left (x^2-4 x+4\right )-4 x\right ) \log \left (\log \left (x^2-4 x+4\right )+1\right )+\left (x^3-4 x^2+9 x-10\right ) \log \left (x^2-4 x+4\right )+9 x-10\right )} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {e^{e^x} \left (x^3+2 x^2-\left (e^x \left (x^2-2 x\right )+\left (e^x \left (x^2-2 x\right )+x-2\right ) \log \left (x^2-4 x+4\right )+x-2\right ) \log ^2\left (\log \left (x^2-4 x+4\right )+1\right )-\left (e^x \left (2 x^3-4 x^2\right )+e^x \left (2 x^3-4 x^2\right ) \log \left (x^2-4 x+4\right )-4 x\right ) \log \left (\log \left (x^2-4 x+4\right )+1\right )-e^x \left (x^4-4 x^3+9 x^2-10 x\right )-\left (-x^3+2 x^2+e^x \left (x^4-4 x^3+9 x^2-10 x\right )+5 x-10\right ) \log \left (x^2-4 x+4\right )-5 x+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right ) \left (x^2+\log ^2\left (\log \left (x^2-4 x+4\right )+1\right )+2 x \log \left (\log \left (x^2-4 x+4\right )+1\right )-2 x+5\right )}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} \log \left ((x-2)^2\right ) x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {2 e^{e^x} \log \left ((x-2)^2\right ) x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right ) x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right ) x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {4 e^{e^x} \log \left (\log \left ((x-2)^2\right )+1\right ) x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right ) x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x} \log \left ((x-2)^2\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2+2 \log \left (\log \left ((x-2)^2\right )+1\right ) x-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
\(\Big \downarrow \) 7239 |
\(\displaystyle \int \frac {e^{e^x} \left (-e^x x^4+4 e^x x^3+x^3-9 e^x x^2+2 x^2-(x-2) \log \left ((x-2)^2\right ) \left (-x^2+e^x \left (x^2-2 x+5\right ) x+2 e^x x^2 \log \left (\log \left ((x-2)^2\right )+1\right )+\left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )+5\right )+10 e^x x-5 x-(x-2) \left (e^x x+1\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )-2 \left (e^x (x-2) x-2\right ) x \log \left (\log \left ((x-2)^2\right )+1\right )+10\right )}{(2-x) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (-\frac {e^{e^x} x^2 \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {2 e^{e^x} x^2}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{x+e^x} x}{x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5}-\frac {4 e^{e^x} x \log \left (\log \left ((x-2)^2\right )+1\right )}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} x}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {e^{e^x} \log \left ((x-2)^2\right ) \log ^2\left (\log \left ((x-2)^2\right )+1\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}+\frac {5 e^{e^x} \log \left ((x-2)^2\right )}{\left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {10 e^{e^x}}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}-\frac {e^{e^x} x^3}{(x-2) \left (\log \left ((x-2)^2\right )+1\right ) \left (x^2-2 x+\log ^2\left (\log \left ((x-2)^2\right )+1\right )+2 x \log \left (\log \left ((x-2)^2\right )+1\right )+5\right )^2}\right )dx\) |
Int[(E^E^x*(-10 + 5*x - 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x^4) + (-10 + 5*x + 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x^4))*Log[4 - 4*x + x^2] + (-4*x + E^x*(-4*x^2 + 2*x^3) + E^x*(-4*x^2 + 2*x^3)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + E^x*(-2*x + x^2) + (-2 + x + E^x*(-2*x + x^2))*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]]^2))/(( 5 - 2*x + x^2 + 2*x*Log[1 + Log[4 - 4*x + x^2]] + Log[1 + Log[4 - 4*x + x^ 2]]^2)*(-10 + 9*x - 4*x^2 + x^3 + (-10 + 9*x - 4*x^2 + x^3)*Log[4 - 4*x + x^2] + (-4*x + 2*x^2 + (-4*x + 2*x^2)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + (-2 + x)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]]^2)),x]
3.14.8.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
\[\int \frac {\left (\left (\left (\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x} \ln \left (x^{2}-4 x +4\right )+\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}+2 x^{2}+5 x -10\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}-2 x^{2}+5 x -10\right ) {\mathrm e}^{-\ln \left ({\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+2 x \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+x^{2}-2 x +5\right )+{\mathrm e}^{x}}}{\left (\left (-2+x \right ) \ln \left (x^{2}-4 x +4\right )+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{2}-4 x \right ) \ln \left (x^{2}-4 x +4\right )+2 x^{2}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (x^{3}-4 x^{2}+9 x -10\right ) \ln \left (x^{2}-4 x +4\right )+x^{3}-4 x^{2}+9 x -10}d x\]
int(((((x^2-2*x)*exp(x)+x-2)*ln(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*ln(ln(x^2 -4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*ln(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x) *ln(ln(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+5*x-10)*ln(x ^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-ln(ln(ln(x^ 2-4*x+4)+1)^2+2*x*ln(ln(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((-2+x)*ln(x^2-4 *x+4)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^2-4*x)*ln(x^2-4*x+4)+2*x^2-4*x)*ln( ln(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*ln(x^2-4*x+4)+x^3-4*x^2+9*x-10),x)
int(((((x^2-2*x)*exp(x)+x-2)*ln(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*ln(ln(x^2 -4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*ln(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x) *ln(ln(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+5*x-10)*ln(x ^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-ln(ln(ln(x^ 2-4*x+4)+1)^2+2*x*ln(ln(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((-2+x)*ln(x^2-4 *x+4)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^2-4*x)*ln(x^2-4*x+4)+2*x^2-4*x)*ln( ln(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*ln(x^2-4*x+4)+x^3-4*x^2+9*x-10),x)
Time = 0.25 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=x e^{\left (e^{x} - \log \left (x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5\right )\right )} \]
integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*lo g(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*e xp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+ 5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp (-log(log(log(x^2-4*x+4)+1)^2+2*x*log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x)) /(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log(x^2 -4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4) +x^3-4*x^2+9*x-10),x, algorithm=\
x*e^(e^x - log(x^2 + 2*x*log(log(x^2 - 4*x + 4) + 1) + log(log(x^2 - 4*x + 4) + 1)^2 - 2*x + 5))
Time = 0.59 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{e^{x}}}{x^{2} + 2 x \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )} - 2 x + \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )}^{2} + 5} \]
integrate(((((x**2-2*x)*exp(x)+x-2)*ln(x**2-4*x+4)+(x**2-2*x)*exp(x)+x-2)* ln(ln(x**2-4*x+4)+1)**2+((2*x**3-4*x**2)*exp(x)*ln(x**2-4*x+4)+(2*x**3-4*x **2)*exp(x)-4*x)*ln(ln(x**2-4*x+4)+1)+((x**4-4*x**3+9*x**2-10*x)*exp(x)-x* *3+2*x**2+5*x-10)*ln(x**2-4*x+4)+(x**4-4*x**3+9*x**2-10*x)*exp(x)-x**3-2*x **2+5*x-10)*exp(-ln(ln(ln(x**2-4*x+4)+1)**2+2*x*ln(ln(x**2-4*x+4)+1)+x**2- 2*x+5)+exp(x))/(((-2+x)*ln(x**2-4*x+4)+x-2)*ln(ln(x**2-4*x+4)+1)**2+((2*x* *2-4*x)*ln(x**2-4*x+4)+2*x**2-4*x)*ln(ln(x**2-4*x+4)+1)+(x**3-4*x**2+9*x-1 0)*ln(x**2-4*x+4)+x**3-4*x**2+9*x-10),x)
x*exp(exp(x))/(x**2 + 2*x*log(log(x**2 - 4*x + 4) + 1) - 2*x + log(log(x** 2 - 4*x + 4) + 1)**2 + 5)
Time = 0.38 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (2 \, \log \left (x - 2\right ) + 1\right ) + \log \left (2 \, \log \left (x - 2\right ) + 1\right )^{2} - 2 \, x + 5} \]
integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*lo g(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*e xp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+ 5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp (-log(log(log(x^2-4*x+4)+1)^2+2*x*log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x)) /(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log(x^2 -4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4) +x^3-4*x^2+9*x-10),x, algorithm=\
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 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {2 \, x e^{\left (x + e^{x}\right )}}{x^{2} e^{x} + 2 \, x e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x e^{x} + 5 \, e^{x}} + \frac {2 \, x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5} \]
integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*lo g(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*e xp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+ 5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp (-log(log(log(x^2-4*x+4)+1)^2+2*x*log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x)) /(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log(x^2 -4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4) +x^3-4*x^2+9*x-10),x, algorithm=\
2*x*e^(x + e^x)/(x^2*e^x + 2*x*e^x*log(log(x^2 - 4*x + 4) + 1) + e^x*log(l og(x^2 - 4*x + 4) + 1)^2 - 2*x*e^x + 5*e^x) + 2*x*e^(e^x)/(x^2 + 2*x*log(l og(x^2 - 4*x + 4) + 1) + log(log(x^2 - 4*x + 4) + 1)^2 - 2*x + 5)
Time = 11.41 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )}^2+x^2+x\,\left (2\,\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )-2\right )+5} \]
int(-(exp(exp(x) - log(2*x*log(log(x^2 - 4*x + 4) + 1) - 2*x + log(log(x^2 - 4*x + 4) + 1)^2 + x^2 + 5))*(exp(x)*(10*x - 9*x^2 + 4*x^3 - x^4) - 5*x + log(x^2 - 4*x + 4)*(exp(x)*(10*x - 9*x^2 + 4*x^3 - x^4) - 5*x - 2*x^2 + x^3 + 10) + log(log(x^2 - 4*x + 4) + 1)*(4*x + exp(x)*(4*x^2 - 2*x^3) + ex p(x)*log(x^2 - 4*x + 4)*(4*x^2 - 2*x^3)) + log(log(x^2 - 4*x + 4) + 1)^2*( exp(x)*(2*x - x^2) - x + log(x^2 - 4*x + 4)*(exp(x)*(2*x - x^2) - x + 2) + 2) + 2*x^2 + x^3 + 10))/(9*x + log(x^2 - 4*x + 4)*(9*x - 4*x^2 + x^3 - 10 ) - log(log(x^2 - 4*x + 4) + 1)*(4*x + log(x^2 - 4*x + 4)*(4*x - 2*x^2) - 2*x^2) + log(log(x^2 - 4*x + 4) + 1)^2*(x + log(x^2 - 4*x + 4)*(x - 2) - 2 ) - 4*x^2 + x^3 - 10),x)