Integrand size = 241, antiderivative size = 27 \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=e^{2 \left (-e^3+x+\log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )^2} \]
Time = 0.34 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00 \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=e^{2 \left (\left (e^3-x\right )^2+\log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )\right )} \left (-2+x^2+\log \left (2-e^x\right )\right )^{-4 e^3+4 x} \]
Integrate[(E^(2*E^6 - 4*E^3*x + 2*x^2 + 2*(-2*E^3 + 2*x)*Log[-2 + x^2 + Lo g[2 - E^x]] + 2*Log[-2 + x^2 + Log[2 - E^x]]^2)*(16*x - 16*x^2 - 8*x^3 + E ^3*(-16 + 16*x + 8*x^2) + E^x*(-4*x + 8*x^2 + 4*x^3 + E^3*(4 - 8*x - 4*x^2 )) + (8*E^3 - 8*x + E^x*(-4*E^3 + 4*x))*Log[2 - E^x] + (16 - 16*x - 8*x^2 + E^x*(-4 + 8*x + 4*x^2) + (-8 + 4*E^x)*Log[2 - E^x])*Log[-2 + x^2 + Log[2 - E^x]]))/(4 - 2*x^2 + E^x*(-2 + x^2) + (-2 + E^x)*Log[2 - E^x]),x]
E^(2*((E^3 - x)^2 + Log[-2 + x^2 + Log[2 - E^x]]^2))*(-2 + x^2 + Log[2 - E ^x])^(-4*E^3 + 4*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.
| \(\displaystyle \int \frac {\left (-8 x^3-16 x^2+e^3 \left (8 x^2+16 x-16\right )+\left (-8 x^2+e^x \left (4 x^2+8 x-4\right )-16 x+\left (4 e^x-8\right ) \log \left (2-e^x\right )+16\right ) \log \left (x^2+\log \left (2-e^x\right )-2\right )+e^x \left (4 x^3+8 x^2+e^3 \left (-4 x^2-8 x+4\right )-4 x\right )+16 x+\left (-8 x+e^x \left (4 x-4 e^3\right )+8 e^3\right ) \log \left (2-e^x\right )\right ) \exp \left (2 x^2+2 \log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+2 \left (2 x-2 e^3\right ) \log \left (x^2+\log \left (2-e^x\right )-2\right )-4 e^3 x+2 e^6\right )}{-2 x^2+e^x \left (x^2-2\right )+\left (e^x-2\right ) \log \left (2-e^x\right )+4} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1} \left (2 \left (x^2+2 x-2\right )-e^x \left (x^2+2 x-1\right )-\left (e^x-2\right ) \log \left (2-e^x\right )\right ) \left (\log \left (x^2+\log \left (2-e^x\right )-2\right )+x-e^3\right ) \exp \left (2 \left (\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+\left (e^3-x\right )^2\right )\right )}{2-e^x}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )\right )\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1} \left (e^x \left (-x^2-2 x+1\right )-2 \left (-x^2-2 x+2\right )+\left (2-e^x\right ) \log \left (2-e^x\right )\right ) \left (-x-\log \left (x^2+\log \left (2-e^x\right )-2\right )+e^3\right )}{2-e^x}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )\right )\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1} \left (e^x \left (-x^2-2 x+1\right )-2 \left (-x^2-2 x+2\right )+\left (2-e^x\right ) \log \left (2-e^x\right )\right ) \left (-x-\log \left (x^2+\log \left (2-e^x\right )-2\right )+e^3\right )}{2-e^x}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\frac {2 \exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )\right )\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1} \left (-x-\log \left (x^2+\log \left (2-e^x\right )-2\right )+e^3\right )}{-2+e^x}-\exp \left (2 \left (\left (e^3-x\right )^2+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )\right )\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1} \left (x^2+2 x+\log \left (2-e^x\right )-1\right ) \left (x+\log \left (x^2+\log \left (2-e^x\right )-2\right )-e^3\right )\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (\exp \left (2 \left (x^2-2 e^3 x+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+e^6\right )\right ) \left (-x^2-2 x-\log \left (2-e^x\right )+1\right ) \left (x+\log \left (x^2+\log \left (2-e^x\right )-2\right )-e^3\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1}+\frac {2 \exp \left (2 \left (x^2-2 e^3 x+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+e^6\right )\right ) \left (x+\log \left (x^2+\log \left (2-e^x\right )-2\right )-e^3\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1}}{2-e^x}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -4 \int \left (\exp \left (2 \left (x^2-2 e^3 x+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+e^6\right )\right ) \left (-x^2-2 x-\log \left (2-e^x\right )+1\right ) \left (x+\log \left (x^2+\log \left (2-e^x\right )-2\right )-e^3\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1}+\frac {2 \exp \left (2 \left (x^2-2 e^3 x+\log ^2\left (x^2+\log \left (2-e^x\right )-2\right )+e^6\right )\right ) \left (x+\log \left (x^2+\log \left (2-e^x\right )-2\right )-e^3\right ) \left (x^2+\log \left (2-e^x\right )-2\right )^{4 x-4 e^3-1}}{2-e^x}\right )dx\) |
Int[(E^(2*E^6 - 4*E^3*x + 2*x^2 + 2*(-2*E^3 + 2*x)*Log[-2 + x^2 + Log[2 - E^x]] + 2*Log[-2 + x^2 + Log[2 - E^x]]^2)*(16*x - 16*x^2 - 8*x^3 + E^3*(-1 6 + 16*x + 8*x^2) + E^x*(-4*x + 8*x^2 + 4*x^3 + E^3*(4 - 8*x - 4*x^2)) + ( 8*E^3 - 8*x + E^x*(-4*E^3 + 4*x))*Log[2 - E^x] + (16 - 16*x - 8*x^2 + E^x* (-4 + 8*x + 4*x^2) + (-8 + 4*E^x)*Log[2 - E^x])*Log[-2 + x^2 + Log[2 - E^x ]]))/(4 - 2*x^2 + E^x*(-2 + x^2) + (-2 + E^x)*Log[2 - E^x]),x]
3.12.24.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(24)=48\).
Time = 0.07 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.15
\[{\left (\ln \left (-{\mathrm e}^{x}+2\right )+x^{2}-2\right )}^{4 x -4 \,{\mathrm e}^{3}} {\mathrm e}^{2 {\ln \left (\ln \left (-{\mathrm e}^{x}+2\right )+x^{2}-2\right )}^{2}+2 \,{\mathrm e}^{6}-4 x \,{\mathrm e}^{3}+2 x^{2}}\]
int((((4*exp(x)-8)*ln(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16)*ln(ln (-exp(x)+2)+x^2-2)+((4*x-4*exp(3))*exp(x)+8*exp(3)-8*x)*ln(-exp(x)+2)+((-4 *x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp(3)-8*x^3-16 *x^2+16*x)*exp(ln(ln(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*ln(ln(-exp(x)+2)+ x^2-2)+exp(3)^2-2*x*exp(3)+x^2)^2/((exp(x)-2)*ln(-exp(x)+2)+(x^2-2)*exp(x) -2*x^2+4),x)
((ln(-exp(x)+2)+x^2-2)^(-2*exp(3)+2*x))^2*exp(2*ln(ln(-exp(x)+2)+x^2-2)^2+ 2*exp(6)-4*x*exp(3)+2*x^2)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00 \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=e^{\left (2 \, x^{2} - 4 \, x e^{3} + 4 \, {\left (x - e^{3}\right )} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) + 2 \, \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right )^{2} + 2 \, e^{6}\right )} \]
integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16 )*log(log(-exp(x)+2)+x^2-2)+((4*x-4*exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp( x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp(3 )-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(l og(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2) +(x^2-2)*exp(x)-2*x^2+4),x, algorithm=\
e^(2*x^2 - 4*x*e^3 + 4*(x - e^3)*log(x^2 + log(-e^x + 2) - 2) + 2*log(x^2 + log(-e^x + 2) - 2)^2 + 2*e^6)
Timed out. \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=\text {Timed out} \]
integrate((((4*exp(x)-8)*ln(-exp(x)+2)+(4*x**2+8*x-4)*exp(x)-8*x**2-16*x+1 6)*ln(ln(-exp(x)+2)+x**2-2)+((4*x-4*exp(3))*exp(x)+8*exp(3)-8*x)*ln(-exp(x )+2)+((-4*x**2-8*x+4)*exp(3)+4*x**3+8*x**2-4*x)*exp(x)+(8*x**2+16*x-16)*ex p(3)-8*x**3-16*x**2+16*x)*exp(ln(ln(-exp(x)+2)+x**2-2)**2+(-2*exp(3)+2*x)* ln(ln(-exp(x)+2)+x**2-2)+exp(3)**2-2*x*exp(3)+x**2)**2/((exp(x)-2)*ln(-exp (x)+2)+(x**2-2)*exp(x)-2*x**2+4),x)
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (24) = 48\).
Time = 0.47 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.44 \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=e^{\left (2 \, x^{2} - 4 \, x e^{3} + 4 \, x \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) - 4 \, e^{3} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) + 2 \, \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right )^{2} + 2 \, e^{6}\right )} \]
integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16 )*log(log(-exp(x)+2)+x^2-2)+((4*x-4*exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp( x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp(3 )-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(l og(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2) +(x^2-2)*exp(x)-2*x^2+4),x, algorithm=\
e^(2*x^2 - 4*x*e^3 + 4*x*log(x^2 + log(-e^x + 2) - 2) - 4*e^3*log(x^2 + lo g(-e^x + 2) - 2) + 2*log(x^2 + log(-e^x + 2) - 2)^2 + 2*e^6)
\[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx=\int { \frac {4 \, {\left (2 \, x^{3} + 4 \, x^{2} - 2 \, {\left (x^{2} + 2 \, x - 2\right )} e^{3} - {\left (x^{3} + 2 \, x^{2} - {\left (x^{2} + 2 \, x - 1\right )} e^{3} - x\right )} e^{x} + {\left (2 \, x^{2} - {\left (x^{2} + 2 \, x - 1\right )} e^{x} - {\left (e^{x} - 2\right )} \log \left (-e^{x} + 2\right ) + 4 \, x - 4\right )} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) - {\left ({\left (x - e^{3}\right )} e^{x} - 2 \, x + 2 \, e^{3}\right )} \log \left (-e^{x} + 2\right ) - 4 \, x\right )} e^{\left (2 \, x^{2} - 4 \, x e^{3} + 4 \, {\left (x - e^{3}\right )} \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right ) + 2 \, \log \left (x^{2} + \log \left (-e^{x} + 2\right ) - 2\right )^{2} + 2 \, e^{6}\right )}}{2 \, x^{2} - {\left (x^{2} - 2\right )} e^{x} - {\left (e^{x} - 2\right )} \log \left (-e^{x} + 2\right ) - 4} \,d x } \]
integrate((((4*exp(x)-8)*log(-exp(x)+2)+(4*x^2+8*x-4)*exp(x)-8*x^2-16*x+16 )*log(log(-exp(x)+2)+x^2-2)+((4*x-4*exp(3))*exp(x)+8*exp(3)-8*x)*log(-exp( x)+2)+((-4*x^2-8*x+4)*exp(3)+4*x^3+8*x^2-4*x)*exp(x)+(8*x^2+16*x-16)*exp(3 )-8*x^3-16*x^2+16*x)*exp(log(log(-exp(x)+2)+x^2-2)^2+(-2*exp(3)+2*x)*log(l og(-exp(x)+2)+x^2-2)+exp(3)^2-2*x*exp(3)+x^2)^2/((exp(x)-2)*log(-exp(x)+2) +(x^2-2)*exp(x)-2*x^2+4),x, algorithm=\
integrate(4*(2*x^3 + 4*x^2 - 2*(x^2 + 2*x - 2)*e^3 - (x^3 + 2*x^2 - (x^2 + 2*x - 1)*e^3 - x)*e^x + (2*x^2 - (x^2 + 2*x - 1)*e^x - (e^x - 2)*log(-e^x + 2) + 4*x - 4)*log(x^2 + log(-e^x + 2) - 2) - ((x - e^3)*e^x - 2*x + 2*e ^3)*log(-e^x + 2) - 4*x)*e^(2*x^2 - 4*x*e^3 + 4*(x - e^3)*log(x^2 + log(-e ^x + 2) - 2) + 2*log(x^2 + log(-e^x + 2) - 2)^2 + 2*e^6)/(2*x^2 - (x^2 - 2 )*e^x - (e^x - 2)*log(-e^x + 2) - 4), x)
Time = 8.45 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.11 \[ \int \frac {e^{2 e^6-4 e^3 x+2 x^2+2 \left (-2 e^3+2 x\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )+2 \log ^2\left (-2+x^2+\log \left (2-e^x\right )\right )} \left (16 x-16 x^2-8 x^3+e^3 \left (-16+16 x+8 x^2\right )+e^x \left (-4 x+8 x^2+4 x^3+e^3 \left (4-8 x-4 x^2\right )\right )+\left (8 e^3-8 x+e^x \left (-4 e^3+4 x\right )\right ) \log \left (2-e^x\right )+\left (16-16 x-8 x^2+e^x \left (-4+8 x+4 x^2\right )+\left (-8+4 e^x\right ) \log \left (2-e^x\right )\right ) \log \left (-2+x^2+\log \left (2-e^x\right )\right )\right )}{4-2 x^2+e^x \left (-2+x^2\right )+\left (-2+e^x\right ) \log \left (2-e^x\right )} \, dx={\mathrm {e}}^{2\,{\mathrm {e}}^6}\,{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^{-4\,x\,{\mathrm {e}}^3}\,{\mathrm {e}}^{2\,{\ln \left (\ln \left (2-{\mathrm {e}}^x\right )+x^2-2\right )}^2}\,{\left (\ln \left (2-{\mathrm {e}}^x\right )+x^2-2\right )}^{4\,x-4\,{\mathrm {e}}^3} \]
int((exp(2*exp(6) + 2*log(log(2 - exp(x)) + x^2 - 2)*(2*x - 2*exp(3)) + 2* log(log(2 - exp(x)) + x^2 - 2)^2 - 4*x*exp(3) + 2*x^2)*(16*x - exp(x)*(4*x + exp(3)*(8*x + 4*x^2 - 4) - 8*x^2 - 4*x^3) + log(log(2 - exp(x)) + x^2 - 2)*(log(2 - exp(x))*(4*exp(x) - 8) - 16*x + exp(x)*(8*x + 4*x^2 - 4) - 8* x^2 + 16) + exp(3)*(16*x + 8*x^2 - 16) + log(2 - exp(x))*(8*exp(3) - 8*x + exp(x)*(4*x - 4*exp(3))) - 16*x^2 - 8*x^3))/(exp(x)*(x^2 - 2) + log(2 - e xp(x))*(exp(x) - 2) - 2*x^2 + 4),x)