\(\int \frac {e^{e^x} (-10+5 x-2 x^2-x^3+e^x (-10 x+9 x^2-4 x^3+x^4)+(-10+5 x+2 x^2-x^3+e^x (-10 x+9 x^2-4 x^3+x^4)) \log (4-4 x+x^2)+(-4 x+e^x (-4 x^2+2 x^3)+e^x (-4 x^2+2 x^3) \log (4-4 x+x^2)) \log (1+\log (4-4 x+x^2))+(-2+x+e^x (-2 x+x^2)+(-2+x+e^x (-2 x+x^2)) \log (4-4 x+x^2)) \log ^2(1+\log (4-4 x+x^2)))}{(5-2 x+x^2+2 x \log (1+\log (4-4 x+x^2))+\log ^2(1+\log (4-4 x+x^2))) (-10+9 x-4 x^2+x^3+(-10+9 x-4 x^2+x^3) \log (4-4 x+x^2)+(-4 x+2 x^2+(-4 x+2 x^2) \log (4-4 x+x^2)) \log (1+\log (4-4 x+x^2))+(-2+x+(-2+x) \log (4-4 x+x^2)) \log ^2(1+\log (4-4 x+x^2)))} \, dx\) [1308]

Optimal result

Integrand size = 346, antiderivative size = 29 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+\left (x+\log \left (1+\log \left ((2-x)^2\right )\right )\right )^2} \] Output:

exp(exp(x)-ln((x+ln(1+ln((2-x)^2)))^2+5-2*x))*x
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.15 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \] Input:

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]
 

Output:

(E^E^x*x)/(5 - 2*x + x^2 + 2*x*Log[1 + Log[(-2 + x)^2]] + Log[1 + Log[(-2 
+ x)^2]]^2)
 

Rubi [F]

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\)

Input:

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]
 

Output:

$Aborted
 

Maple [F]

\[\int \frac {\left (\left (\left (\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x} \ln \left (x^{2}-4 x +4\right )+\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}+2 x^{2}+5 x -10\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}-2 x^{2}+5 x -10\right ) {\mathrm e}^{-\ln \left ({\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+2 x \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+x^{2}-2 x +5\right )+{\mathrm e}^{x}}}{\left (\left (-2+x \right ) \ln \left (x^{2}-4 x +4\right )+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{2}-4 x \right ) \ln \left (x^{2}-4 x +4\right )+2 x^{2}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (x^{3}-4 x^{2}+9 x -10\right ) \ln \left (x^{2}-4 x +4\right )+x^{3}-4 x^{2}+9 x -10}d x\]

Input:

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)
 

Output:

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)
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=x e^{\left (e^{x} - \log \left (x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5\right )\right )} \] Input:

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="fricas")
 

Output:

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))
 

Sympy [A] (verification not implemented)

Time = 0.59 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{e^{x}}}{x^{2} + 2 x \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )} - 2 x + \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )}^{2} + 5} \] Input:

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)
 

Output:

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)
 

Maxima [A] (verification not implemented)

Time = 0.23 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (2 \, \log \left (x - 2\right ) + 1\right ) + \log \left (2 \, \log \left (x - 2\right ) + 1\right )^{2} - 2 \, x + 5} \] Input:

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="maxima")
 

Output:

x*e^(e^x)/(x^2 + 2*x*log(2*log(x - 2) + 1) + log(2*log(x - 2) + 1)^2 - 2*x 
 + 5)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (27) = 54\).

Time = 2.74 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.66 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {2 \, x e^{\left (x + e^{x}\right )}}{x^{2} e^{x} + 2 \, x e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x e^{x} + 5 \, e^{x}} + \frac {2 \, x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5} \] Input:

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="giac")
 

Output:

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)
 

Mupad [B] (verification not implemented)

Time = 4.36 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )}^2+x^2+x\,\left (2\,\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )-2\right )+5} \] Input:

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)
 

Output:

(x*exp(exp(x)))/(log(log(x^2 - 4*x + 4) + 1)^2 + x^2 + x*(2*log(log(x^2 - 
4*x + 4) + 1) - 2) + 5)
 

Reduce [F]

\[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\text {too large to display} \] Input:

int(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*log(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)*exp(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)
 

Output:

 - 10*int(e**(e**x)/(log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)**4*x 
 - 2*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)**4 + 4*log(x**2 - 4* 
x + 4)*log(log(x**2 - 4*x + 4) + 1)**3*x**2 - 8*log(x**2 - 4*x + 4)*log(lo 
g(x**2 - 4*x + 4) + 1)**3*x + 6*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4 
) + 1)**2*x**3 - 16*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)**2*x* 
*2 + 18*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)**2*x - 20*log(x** 
2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)**2 + 4*log(x**2 - 4*x + 4)*log(l 
og(x**2 - 4*x + 4) + 1)*x**4 - 16*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 
 4) + 1)*x**3 + 36*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)*x**2 - 
 40*log(x**2 - 4*x + 4)*log(log(x**2 - 4*x + 4) + 1)*x + log(x**2 - 4*x + 
4)*x**5 - 6*log(x**2 - 4*x + 4)*x**4 + 22*log(x**2 - 4*x + 4)*x**3 - 48*lo 
g(x**2 - 4*x + 4)*x**2 + 65*log(x**2 - 4*x + 4)*x - 50*log(x**2 - 4*x + 4) 
 + log(log(x**2 - 4*x + 4) + 1)**4*x - 2*log(log(x**2 - 4*x + 4) + 1)**4 + 
 4*log(log(x**2 - 4*x + 4) + 1)**3*x**2 - 8*log(log(x**2 - 4*x + 4) + 1)** 
3*x + 6*log(log(x**2 - 4*x + 4) + 1)**2*x**3 - 16*log(log(x**2 - 4*x + 4) 
+ 1)**2*x**2 + 18*log(log(x**2 - 4*x + 4) + 1)**2*x - 20*log(log(x**2 - 4* 
x + 4) + 1)**2 + 4*log(log(x**2 - 4*x + 4) + 1)*x**4 - 16*log(log(x**2 - 4 
*x + 4) + 1)*x**3 + 36*log(log(x**2 - 4*x + 4) + 1)*x**2 - 40*log(log(x**2 
 - 4*x + 4) + 1)*x + x**5 - 6*x**4 + 22*x**3 - 48*x**2 + 65*x - 50),x) + i 
nt((e**(e**x)*log(log(x**2 - 4*x + 4) + 1)**2*x)/(log(x**2 - 4*x + 4)*l...