\(\int \frac {e^{-e^x} (-32 x^2+8 x^4+8 x^5+(-16 x^2+4 x^5) \log (5)+e^x (8 x^5+8 x^6+4 x^6 \log (5))+(64 x+64 x^2+32 x^2 \log (5)+e^x (-32 x^2-32 x^3-16 x^3 \log (5))) \log (-2-2 x-x \log (5)))}{2 x^6+2 x^7+x^7 \log (5)+(-16 x^3-16 x^4-8 x^4 \log (5)) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx\) [2804]

Optimal result

Integrand size = 183, antiderivative size = 34 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=\frac {e^{-e^x} x}{-\frac {x^2}{4}+\frac {\log (-2+x-x (3+\log (5)))}{x}} \] Output:

x/exp(exp(x))/(ln(x-x*(ln(5)+3)-2)/x-1/4*x^2)
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.08 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.94 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=\frac {4 e^{-e^x} x^2}{-x^3+4 \log (-2-x (2+\log (5)))} \] Input:

Integrate[(-32*x^2 + 8*x^4 + 8*x^5 + (-16*x^2 + 4*x^5)*Log[5] + E^x*(8*x^5 
 + 8*x^6 + 4*x^6*Log[5]) + (64*x + 64*x^2 + 32*x^2*Log[5] + E^x*(-32*x^2 - 
 32*x^3 - 16*x^3*Log[5]))*Log[-2 - 2*x - x*Log[5]])/(E^E^x*(2*x^6 + 2*x^7 
+ x^7*Log[5] + (-16*x^3 - 16*x^4 - 8*x^4*Log[5])*Log[-2 - 2*x - x*Log[5]] 
+ (32 + 32*x + 16*x*Log[5])*Log[-2 - 2*x - x*Log[5]]^2)),x]
 

Output:

(4*x^2)/(E^E^x*(-x^3 + 4*Log[-2 - x*(2 + Log[5])]))
 

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.

\(\displaystyle \int \frac {e^{-e^x} \left (8 x^5+8 x^4-32 x^2+e^x \left (8 x^6+4 x^6 \log (5)+8 x^5\right )+\left (4 x^5-16 x^2\right ) \log (5)+\left (64 x^2+32 x^2 \log (5)+e^x \left (-32 x^3-16 x^3 \log (5)-32 x^2\right )+64 x\right ) \log (-2 x+x (-\log (5))-2)\right )}{2 x^7+x^7 \log (5)+2 x^6+\left (-16 x^4-8 x^4 \log (5)-16 x^3\right ) \log (-2 x+x (-\log (5))-2)+(32 x+16 x \log (5)+32) \log ^2(-2 x+x (-\log (5))-2)} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^{-e^x} \left (8 x^5+8 x^4-32 x^2+e^x \left (8 x^6+4 x^6 \log (5)+8 x^5\right )+\left (4 x^5-16 x^2\right ) \log (5)+\left (64 x^2+32 x^2 \log (5)+e^x \left (-32 x^3-16 x^3 \log (5)-32 x^2\right )+64 x\right ) \log (-2 x+x (-\log (5))-2)\right )}{x^7 (2+\log (5))+2 x^6+\left (-16 x^4-8 x^4 \log (5)-16 x^3\right ) \log (-2 x+x (-\log (5))-2)+(32 x+16 x \log (5)+32) \log ^2(-2 x+x (-\log (5))-2)}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 e^{-e^x} x \left (e^x x^5 (2+\log (5))+x^4 \left (2 e^x+2+\log (5)\right )+2 x^3-4 x (2+\log (5))-4 \left (e^x x-2\right ) (x (2+\log (5))+2) \log (-(x (2+\log (5)))-2)\right )}{(x (2+\log (5))+2) \left (x^3-4 \log (-(x (2+\log (5)))-2)\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 4 \int \frac {e^{-e^x} x \left (e^x (2+\log (5)) x^5+\left (2+2 e^x+\log (5)\right ) x^4+2 x^3-4 (2+\log (5)) x+4 \left (2-e^x x\right ) ((2+\log (5)) x+2) \log (-((2+\log (5)) x)-2)\right )}{((2+\log (5)) x+2) \left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 4 \int \left (\frac {2 e^{-e^x} \left (1+\frac {\log (5)}{2}\right ) x^5}{((2+\log (5)) x+2) \left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}+\frac {2 e^{-e^x} x^4}{((2+\log (5)) x+2) \left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}+\frac {e^{x-e^x} x^2}{x^3-4 \log (-((2+\log (5)) x)-2)}+\frac {4 e^{-e^x} (-2-\log (5)) x^2}{((2+\log (5)) x+2) \left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}+\frac {8 e^{-e^x} \log (-((2+\log (5)) x)-2) x}{\left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 4 \left (\frac {8 \int \frac {e^{-e^x}}{\left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}dx}{2+\log (5)}-4 \int \frac {e^{-e^x} x}{\left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}dx-\frac {16 \int \frac {e^{-e^x}}{((2+\log (5)) x+2) \left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}dx}{2+\log (5)}-2 \int \frac {e^{-e^x} x}{x^3-4 \log (-((2+\log (5)) x)-2)}dx+3 \int \frac {e^{-e^x} x^4}{\left (x^3-4 \log (-((2+\log (5)) x)-2)\right )^2}dx+\int \frac {e^{x-e^x} x^2}{x^3-4 \log (-((2+\log (5)) x)-2)}dx\right )\)

Input:

Int[(-32*x^2 + 8*x^4 + 8*x^5 + (-16*x^2 + 4*x^5)*Log[5] + E^x*(8*x^5 + 8*x 
^6 + 4*x^6*Log[5]) + (64*x + 64*x^2 + 32*x^2*Log[5] + E^x*(-32*x^2 - 32*x^ 
3 - 16*x^3*Log[5]))*Log[-2 - 2*x - x*Log[5]])/(E^E^x*(2*x^6 + 2*x^7 + x^7* 
Log[5] + (-16*x^3 - 16*x^4 - 8*x^4*Log[5])*Log[-2 - 2*x - x*Log[5]] + (32 
+ 32*x + 16*x*Log[5])*Log[-2 - 2*x - x*Log[5]]^2)),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 157.44 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.88

method	result	size
parallelrisch	\(-\frac {4 x^{2} {\mathrm e}^{-{\mathrm e}^{x}}}{x^{3}-4 \ln \left (-x \ln \left (5\right )-2 x -2\right )}\)	\(30\)

Input:

int((((-16*x^3*ln(5)-32*x^3-32*x^2)*exp(x)+32*x^2*ln(5)+64*x^2+64*x)*ln(-x 
*ln(5)-2*x-2)+(4*x^6*ln(5)+8*x^6+8*x^5)*exp(x)+(4*x^5-16*x^2)*ln(5)+8*x^5+ 
8*x^4-32*x^2)/((16*x*ln(5)+32*x+32)*ln(-x*ln(5)-2*x-2)^2+(-8*x^4*ln(5)-16* 
x^4-16*x^3)*ln(-x*ln(5)-2*x-2)+x^7*ln(5)+2*x^7+2*x^6)/exp(exp(x)),x,method 
=_RETURNVERBOSE)
 

Output:

-4*x^2/(x^3-4*ln(-x*ln(5)-2*x-2))/exp(exp(x))
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=-\frac {4 \, x^{2} e^{\left (-e^{x}\right )}}{x^{3} - 4 \, \log \left (-x \log \left (5\right ) - 2 \, x - 2\right )} \] Input:

integrate((((-16*x^3*log(5)-32*x^3-32*x^2)*exp(x)+32*x^2*log(5)+64*x^2+64* 
x)*log(-x*log(5)-2*x-2)+(4*x^6*log(5)+8*x^6+8*x^5)*exp(x)+(4*x^5-16*x^2)*l 
og(5)+8*x^5+8*x^4-32*x^2)/((16*x*log(5)+32*x+32)*log(-x*log(5)-2*x-2)^2+(- 
8*x^4*log(5)-16*x^4-16*x^3)*log(-x*log(5)-2*x-2)+x^7*log(5)+2*x^7+2*x^6)/e 
xp(exp(x)),x, algorithm="fricas")
 

Output:

-4*x^2*e^(-e^x)/(x^3 - 4*log(-x*log(5) - 2*x - 2))
 

Sympy [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=- \frac {4 x^{2} e^{- e^{x}}}{x^{3} - 4 \log {\left (- 2 x - x \log {\left (5 \right )} - 2 \right )}} \] Input:

integrate((((-16*x**3*ln(5)-32*x**3-32*x**2)*exp(x)+32*x**2*ln(5)+64*x**2+ 
64*x)*ln(-x*ln(5)-2*x-2)+(4*x**6*ln(5)+8*x**6+8*x**5)*exp(x)+(4*x**5-16*x* 
*2)*ln(5)+8*x**5+8*x**4-32*x**2)/((16*x*ln(5)+32*x+32)*ln(-x*ln(5)-2*x-2)* 
*2+(-8*x**4*ln(5)-16*x**4-16*x**3)*ln(-x*ln(5)-2*x-2)+x**7*ln(5)+2*x**7+2* 
x**6)/exp(exp(x)),x)
 

Output:

-4*x**2*exp(-exp(x))/(x**3 - 4*log(-2*x - x*log(5) - 2))
 

Maxima [A] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.88 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=-\frac {4 \, x^{2}}{x^{3} e^{\left (e^{x}\right )} - 4 \, e^{\left (e^{x}\right )} \log \left (-x {\left (\log \left (5\right ) + 2\right )} - 2\right )} \] Input:

integrate((((-16*x^3*log(5)-32*x^3-32*x^2)*exp(x)+32*x^2*log(5)+64*x^2+64* 
x)*log(-x*log(5)-2*x-2)+(4*x^6*log(5)+8*x^6+8*x^5)*exp(x)+(4*x^5-16*x^2)*l 
og(5)+8*x^5+8*x^4-32*x^2)/((16*x*log(5)+32*x+32)*log(-x*log(5)-2*x-2)^2+(- 
8*x^4*log(5)-16*x^4-16*x^3)*log(-x*log(5)-2*x-2)+x^7*log(5)+2*x^7+2*x^6)/e 
xp(exp(x)),x, algorithm="maxima")
 

Output:

-4*x^2/(x^3*e^(e^x) - 4*e^(e^x)*log(-x*(log(5) + 2) - 2))
 

Giac [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=-\frac {4 \, x^{2} e^{\left (-e^{x}\right )}}{x^{3} - 4 \, \log \left (-x \log \left (5\right ) - 2 \, x - 2\right )} \] Input:

integrate((((-16*x^3*log(5)-32*x^3-32*x^2)*exp(x)+32*x^2*log(5)+64*x^2+64* 
x)*log(-x*log(5)-2*x-2)+(4*x^6*log(5)+8*x^6+8*x^5)*exp(x)+(4*x^5-16*x^2)*l 
og(5)+8*x^5+8*x^4-32*x^2)/((16*x*log(5)+32*x+32)*log(-x*log(5)-2*x-2)^2+(- 
8*x^4*log(5)-16*x^4-16*x^3)*log(-x*log(5)-2*x-2)+x^7*log(5)+2*x^7+2*x^6)/e 
xp(exp(x)),x, algorithm="giac")
 

Output:

-4*x^2*e^(-e^x)/(x^3 - 4*log(-x*log(5) - 2*x - 2))
 

Mupad [B] (verification not implemented)

Time = 4.59 (sec) , antiderivative size = 254, normalized size of antiderivative = 7.47 \[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=\frac {\frac {4\,x^2\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,\left (2\,x^3\,{\mathrm {e}}^x-4\,\ln \left (5\right )+2\,x^4\,{\mathrm {e}}^x+x^3\,\ln \left (5\right )+2\,x^2+2\,x^3+x^4\,{\mathrm {e}}^x\,\ln \left (5\right )-8\right )}{3\,x^3\,\ln \left (5\right )-4\,\ln \left (5\right )+6\,x^2+6\,x^3-8}-\frac {16\,x\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,\ln \left (-2\,x-x\,\ln \left (5\right )-2\right )\,\left (x\,{\mathrm {e}}^x-2\right )\,\left (2\,x+x\,\ln \left (5\right )+2\right )}{3\,x^3\,\ln \left (5\right )-4\,\ln \left (5\right )+6\,x^2+6\,x^3-8}}{4\,\ln \left (-2\,x-x\,\ln \left (5\right )-2\right )-x^3}-\frac {{\mathrm {e}}^{-{\mathrm {e}}^x}\,\left (\frac {16\,x}{\ln \left (125\right )+6}-\frac {8\,x^2\,{\mathrm {e}}^x}{\ln \left (125\right )+6}+\frac {x^2\,\left (8\,\ln \left (5\right )+16\right )}{\ln \left (125\right )+6}-\frac {x^3\,{\mathrm {e}}^x\,\left (\ln \left (625\right )+8\right )}{\ln \left (125\right )+6}\right )}{x^3+\frac {6\,x^2}{\ln \left (125\right )+6}-\frac {\ln \left (625\right )+8}{\ln \left (125\right )+6}} \] Input:

int((exp(-exp(x))*(log(- 2*x - x*log(5) - 2)*(64*x + 32*x^2*log(5) - exp(x 
)*(16*x^3*log(5) + 32*x^2 + 32*x^3) + 64*x^2) - log(5)*(16*x^2 - 4*x^5) + 
exp(x)*(4*x^6*log(5) + 8*x^5 + 8*x^6) - 32*x^2 + 8*x^4 + 8*x^5))/(log(- 2* 
x - x*log(5) - 2)^2*(32*x + 16*x*log(5) + 32) + x^7*log(5) - log(- 2*x - x 
*log(5) - 2)*(8*x^4*log(5) + 16*x^3 + 16*x^4) + 2*x^6 + 2*x^7),x)
 

Output:

((4*x^2*exp(-exp(x))*(2*x^3*exp(x) - 4*log(5) + 2*x^4*exp(x) + x^3*log(5) 
+ 2*x^2 + 2*x^3 + x^4*exp(x)*log(5) - 8))/(3*x^3*log(5) - 4*log(5) + 6*x^2 
 + 6*x^3 - 8) - (16*x*exp(-exp(x))*log(- 2*x - x*log(5) - 2)*(x*exp(x) - 2 
)*(2*x + x*log(5) + 2))/(3*x^3*log(5) - 4*log(5) + 6*x^2 + 6*x^3 - 8))/(4* 
log(- 2*x - x*log(5) - 2) - x^3) - (exp(-exp(x))*((16*x)/(log(125) + 6) - 
(8*x^2*exp(x))/(log(125) + 6) + (x^2*(8*log(5) + 16))/(log(125) + 6) - (x^ 
3*exp(x)*(log(625) + 8))/(log(125) + 6)))/((6*x^2)/(log(125) + 6) - (log(6 
25) + 8)/(log(125) + 6) + x^3)
 

Reduce [F]

\[ \int \frac {e^{-e^x} \left (-32 x^2+8 x^4+8 x^5+\left (-16 x^2+4 x^5\right ) \log (5)+e^x \left (8 x^5+8 x^6+4 x^6 \log (5)\right )+\left (64 x+64 x^2+32 x^2 \log (5)+e^x \left (-32 x^2-32 x^3-16 x^3 \log (5)\right )\right ) \log (-2-2 x-x \log (5))\right )}{2 x^6+2 x^7+x^7 \log (5)+\left (-16 x^3-16 x^4-8 x^4 \log (5)\right ) \log (-2-2 x-x \log (5))+(32+32 x+16 x \log (5)) \log ^2(-2-2 x-x \log (5))} \, dx=\text {too large to display} \] Input:

int((((-16*x^3*log(5)-32*x^3-32*x^2)*exp(x)+32*x^2*log(5)+64*x^2+64*x)*log 
(-x*log(5)-2*x-2)+(4*x^6*log(5)+8*x^6+8*x^5)*exp(x)+(4*x^5-16*x^2)*log(5)+ 
8*x^5+8*x^4-32*x^2)/((16*x*log(5)+32*x+32)*log(-x*log(5)-2*x-2)^2+(-8*x^4* 
log(5)-16*x^4-16*x^3)*log(-x*log(5)-2*x-2)+x^7*log(5)+2*x^7+2*x^6)/exp(exp 
(x)),x)
 

Output:

4*(int(x**5/(16*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*log(5)*x + 32*e**( 
e**x)*log( - log(5)*x - 2*x - 2)**2*x + 32*e**(e**x)*log( - log(5)*x - 2*x 
 - 2)**2 - 8*e**(e**x)*log( - log(5)*x - 2*x - 2)*log(5)*x**4 - 16*e**(e** 
x)*log( - log(5)*x - 2*x - 2)*x**4 - 16*e**(e**x)*log( - log(5)*x - 2*x - 
2)*x**3 + e**(e**x)*log(5)*x**7 + 2*e**(e**x)*x**7 + 2*e**(e**x)*x**6),x)* 
log(5) + 2*int(x**5/(16*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*log(5)*x + 
 32*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*x + 32*e**(e**x)*log( - log(5) 
*x - 2*x - 2)**2 - 8*e**(e**x)*log( - log(5)*x - 2*x - 2)*log(5)*x**4 - 16 
*e**(e**x)*log( - log(5)*x - 2*x - 2)*x**4 - 16*e**(e**x)*log( - log(5)*x 
- 2*x - 2)*x**3 + e**(e**x)*log(5)*x**7 + 2*e**(e**x)*x**7 + 2*e**(e**x)*x 
**6),x) + 2*int(x**4/(16*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*log(5)*x 
+ 32*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*x + 32*e**(e**x)*log( - log(5 
)*x - 2*x - 2)**2 - 8*e**(e**x)*log( - log(5)*x - 2*x - 2)*log(5)*x**4 - 1 
6*e**(e**x)*log( - log(5)*x - 2*x - 2)*x**4 - 16*e**(e**x)*log( - log(5)*x 
 - 2*x - 2)*x**3 + e**(e**x)*log(5)*x**7 + 2*e**(e**x)*x**7 + 2*e**(e**x)* 
x**6),x) - 4*int(x**2/(16*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*log(5)*x 
 + 32*e**(e**x)*log( - log(5)*x - 2*x - 2)**2*x + 32*e**(e**x)*log( - log( 
5)*x - 2*x - 2)**2 - 8*e**(e**x)*log( - log(5)*x - 2*x - 2)*log(5)*x**4 - 
16*e**(e**x)*log( - log(5)*x - 2*x - 2)*x**4 - 16*e**(e**x)*log( - log(5)* 
x - 2*x - 2)*x**3 + e**(e**x)*log(5)*x**7 + 2*e**(e**x)*x**7 + 2*e**(e*...