\(\int \frac {e^{e^{2 x}} (-1+2 e^{2 x} x) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} (512+(1-x) \log (x) \log ^3(\log (x)))}{e^{\frac {2 (256+x \log ^2(\log (x)))}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} (-2 e^{e^{2 x}} \log (x)+2 x \log (x)) \log ^3(\log (x))+(e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)) \log ^3(\log (x))} \, dx\) [827]

Optimal result

Integrand size = 166, antiderivative size = 26 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\frac {x}{-e^{e^{2 x}}+e^{x+\frac {256}{\log ^2(\log (x))}}+x} \] Output:

x/(exp(256/ln(ln(x))^2+x)+x-exp(exp(x)^2))
 

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\frac {x}{-e^{e^{2 x}}+e^{x+\frac {256}{\log ^2(\log (x))}}+x} \] Input:

Integrate[(E^E^(2*x)*(-1 + 2*E^(2*x)*x)*Log[x]*Log[Log[x]]^3 + E^((256 + x 
*Log[Log[x]]^2)/Log[Log[x]]^2)*(512 + (1 - x)*Log[x]*Log[Log[x]]^3))/(E^(( 
2*(256 + x*Log[Log[x]]^2))/Log[Log[x]]^2)*Log[x]*Log[Log[x]]^3 + E^((256 + 
 x*Log[Log[x]]^2)/Log[Log[x]]^2)*(-2*E^E^(2*x)*Log[x] + 2*x*Log[x])*Log[Lo 
g[x]]^3 + (E^(2*E^(2*x))*Log[x] - 2*E^E^(2*x)*x*Log[x] + x^2*Log[x])*Log[L 
og[x]]^3),x]
 

Output:

x/(-E^E^(2*x) + E^(x + 256/Log[Log[x]]^2) + x)
 

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.

\(\displaystyle \int \frac {e^{e^{2 x}} \left (2 e^{2 x} x-1\right ) \log (x) \log ^3(\log (x))+e^{\frac {x \log ^2(\log (x))+256}{\log ^2(\log (x))}} \left ((1-x) \log (x) \log ^3(\log (x))+512\right )}{\left (x^2 \log (x)-2 e^{e^{2 x}} x \log (x)+e^{2 e^{2 x}} \log (x)\right ) \log ^3(\log (x))+e^{\frac {2 \left (x \log ^2(\log (x))+256\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {x \log ^2(\log (x))+256}{\log ^2(\log (x))}} \left (2 x \log (x)-2 e^{e^{2 x}} \log (x)\right ) \log ^3(\log (x))} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {512 e^{x+\frac {256}{\log ^2(\log (x))}}+\left (-e^{e^{2 x}}+2 e^{2 x+e^{2 x}} x+(x-1) \left (-e^{x+\frac {256}{\log ^2(\log (x))}}\right )\right ) \log (x) \log ^3(\log (x))}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2 \log (x) \log ^3(\log (x))}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {x^2 \log (x) \log ^3(\log (x))+512 e^{e^{2 x}}-512 x-e^{e^{2 x}} x \log (x) \log ^3(\log (x))+2 e^{2 x+e^{2 x}} x \log (x) \log ^3(\log (x))-x \log (x) \log ^3(\log (x))}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2 \log (x) \log ^3(\log (x))}+\frac {x \log (x) \log ^3(\log (x))-\log (x) \log ^3(\log (x))-512}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right ) \log (x) \log ^3(\log (x))}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \int \frac {x^2}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2}dx-\int \frac {1}{-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}}dx-\int \frac {x}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2}dx-\int \frac {e^{e^{2 x}} x}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2}dx+\int \frac {x}{-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}}dx+2 \int \frac {e^{2 x+e^{2 x}} x}{\left (x-e^{e^{2 x}}+e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2}dx+512 \int \frac {e^{e^{2 x}}}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2 \log (x) \log ^3(\log (x))}dx-512 \int \frac {1}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right ) \log (x) \log ^3(\log (x))}dx-512 \int \frac {x}{\left (-x+e^{e^{2 x}}-e^{x+\frac {256}{\log ^2(\log (x))}}\right )^2 \log (x) \log ^3(\log (x))}dx\)

Input:

Int[(E^E^(2*x)*(-1 + 2*E^(2*x)*x)*Log[x]*Log[Log[x]]^3 + E^((256 + x*Log[L 
og[x]]^2)/Log[Log[x]]^2)*(512 + (1 - x)*Log[x]*Log[Log[x]]^3))/(E^((2*(256 
 + x*Log[Log[x]]^2))/Log[Log[x]]^2)*Log[x]*Log[Log[x]]^3 + E^((256 + x*Log 
[Log[x]]^2)/Log[Log[x]]^2)*(-2*E^E^(2*x)*Log[x] + 2*x*Log[x])*Log[Log[x]]^ 
3 + (E^(2*E^(2*x))*Log[x] - 2*E^E^(2*x)*x*Log[x] + x^2*Log[x])*Log[Log[x]] 
^3),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15

\[\frac {x}{x +{\mathrm e}^{\frac {x \ln \left (\ln \left (x \right )\right )^{2}+256}{\ln \left (\ln \left (x \right )\right )^{2}}}-{\mathrm e}^{{\mathrm e}^{2 x}}}\]

Input:

int((((1-x)*ln(x)*ln(ln(x))^3+512)*exp((x*ln(ln(x))^2+256)/ln(ln(x))^2)+(2 
*x*exp(x)^2-1)*ln(x)*exp(exp(x)^2)*ln(ln(x))^3)/(ln(x)*ln(ln(x))^3*exp((x* 
ln(ln(x))^2+256)/ln(ln(x))^2)^2+(-2*ln(x)*exp(exp(x)^2)+2*x*ln(x))*ln(ln(x 
))^3*exp((x*ln(ln(x))^2+256)/ln(ln(x))^2)+(ln(x)*exp(exp(x)^2)^2-2*x*ln(x) 
*exp(exp(x)^2)+x^2*ln(x))*ln(ln(x))^3),x)
 

Output:

x/(x+exp((x*ln(ln(x))^2+256)/ln(ln(x))^2)-exp(exp(2*x)))
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\frac {x}{x + e^{\left (\frac {x \log \left (\log \left (x\right )\right )^{2} + 256}{\log \left (\log \left (x\right )\right )^{2}}\right )} - e^{\left (e^{\left (2 \, x\right )}\right )}} \] Input:

integrate((((1-x)*log(x)*log(log(x))^3+512)*exp((x*log(log(x))^2+256)/log( 
log(x))^2)+(2*x*exp(x)^2-1)*log(x)*exp(exp(x)^2)*log(log(x))^3)/(log(x)*lo 
g(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)^2+(-2*log(x)*exp(exp( 
x)^2)+2*x*log(x))*log(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)+( 
log(x)*exp(exp(x)^2)^2-2*x*log(x)*exp(exp(x)^2)+x^2*log(x))*log(log(x))^3) 
,x, algorithm="fricas")
 

Output:

x/(x + e^((x*log(log(x))^2 + 256)/log(log(x))^2) - e^(e^(2*x)))
 

Sympy [A] (verification not implemented)

Time = 2.87 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=- \frac {x}{- x - e^{\frac {x \log {\left (\log {\left (x \right )} \right )}^{2} + 256}{\log {\left (\log {\left (x \right )} \right )}^{2}}} + e^{e^{2 x}}} \] Input:

integrate((((1-x)*ln(x)*ln(ln(x))**3+512)*exp((x*ln(ln(x))**2+256)/ln(ln(x 
))**2)+(2*x*exp(x)**2-1)*ln(x)*exp(exp(x)**2)*ln(ln(x))**3)/(ln(x)*ln(ln(x 
))**3*exp((x*ln(ln(x))**2+256)/ln(ln(x))**2)**2+(-2*ln(x)*exp(exp(x)**2)+2 
*x*ln(x))*ln(ln(x))**3*exp((x*ln(ln(x))**2+256)/ln(ln(x))**2)+(ln(x)*exp(e 
xp(x)**2)**2-2*x*ln(x)*exp(exp(x)**2)+x**2*ln(x))*ln(ln(x))**3),x)
 

Output:

-x/(-x - exp((x*log(log(x))**2 + 256)/log(log(x))**2) + exp(exp(2*x)))
 

Maxima [A] (verification not implemented)

Time = 0.17 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\frac {x}{x + e^{\left (x + \frac {256}{\log \left (\log \left (x\right )\right )^{2}}\right )} - e^{\left (e^{\left (2 \, x\right )}\right )}} \] Input:

integrate((((1-x)*log(x)*log(log(x))^3+512)*exp((x*log(log(x))^2+256)/log( 
log(x))^2)+(2*x*exp(x)^2-1)*log(x)*exp(exp(x)^2)*log(log(x))^3)/(log(x)*lo 
g(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)^2+(-2*log(x)*exp(exp( 
x)^2)+2*x*log(x))*log(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)+( 
log(x)*exp(exp(x)^2)^2-2*x*log(x)*exp(exp(x)^2)+x^2*log(x))*log(log(x))^3) 
,x, algorithm="maxima")
 

Output:

x/(x + e^(x + 256/log(log(x))^2) - e^(e^(2*x)))
 

Giac [F]

\[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\int { \frac {{\left (2 \, x e^{\left (2 \, x\right )} - 1\right )} e^{\left (e^{\left (2 \, x\right )}\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{3} - {\left ({\left (x - 1\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{3} - 512\right )} e^{\left (\frac {x \log \left (\log \left (x\right )\right )^{2} + 256}{\log \left (\log \left (x\right )\right )^{2}}\right )}}{2 \, {\left (x \log \left (x\right ) - e^{\left (e^{\left (2 \, x\right )}\right )} \log \left (x\right )\right )} e^{\left (\frac {x \log \left (\log \left (x\right )\right )^{2} + 256}{\log \left (\log \left (x\right )\right )^{2}}\right )} \log \left (\log \left (x\right )\right )^{3} + e^{\left (\frac {2 \, {\left (x \log \left (\log \left (x\right )\right )^{2} + 256\right )}}{\log \left (\log \left (x\right )\right )^{2}}\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{3} + {\left (x^{2} \log \left (x\right ) - 2 \, x e^{\left (e^{\left (2 \, x\right )}\right )} \log \left (x\right ) + e^{\left (2 \, e^{\left (2 \, x\right )}\right )} \log \left (x\right )\right )} \log \left (\log \left (x\right )\right )^{3}} \,d x } \] Input:

integrate((((1-x)*log(x)*log(log(x))^3+512)*exp((x*log(log(x))^2+256)/log( 
log(x))^2)+(2*x*exp(x)^2-1)*log(x)*exp(exp(x)^2)*log(log(x))^3)/(log(x)*lo 
g(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)^2+(-2*log(x)*exp(exp( 
x)^2)+2*x*log(x))*log(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)+( 
log(x)*exp(exp(x)^2)^2-2*x*log(x)*exp(exp(x)^2)+x^2*log(x))*log(log(x))^3) 
,x, algorithm="giac")
 

Output:

undef
 

Mupad [B] (verification not implemented)

Time = 7.43 (sec) , antiderivative size = 215, normalized size of antiderivative = 8.27 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=\frac {{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\left (x^3\,{\ln \left (\ln \left (x\right )\right )}^6\,{\ln \left (x\right )}^2-512\,x^2\,{\ln \left (\ln \left (x\right )\right )}^3\,\ln \left (x\right )\right )+x^3\,{\ln \left (\ln \left (x\right )\right )}^6\,{\ln \left (x\right )}^2-x^4\,{\ln \left (\ln \left (x\right )\right )}^6\,{\ln \left (x\right )}^2+512\,x^3\,{\ln \left (\ln \left (x\right )\right )}^3\,\ln \left (x\right )-2\,x^3\,{\ln \left (\ln \left (x\right )\right )}^6\,{\mathrm {e}}^{2\,x+{\mathrm {e}}^{2\,x}}\,{\ln \left (x\right )}^2}{\left (x+{\mathrm {e}}^{x+\frac {256}{{\ln \left (\ln \left (x\right )\right )}^2}}-{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\right )\,\left (x^2\,{\ln \left (\ln \left (x\right )\right )}^6\,{\ln \left (x\right )}^2-x^3\,{\ln \left (\ln \left (x\right )\right )}^6\,{\ln \left (x\right )}^2+512\,x^2\,{\ln \left (\ln \left (x\right )\right )}^3\,\ln \left (x\right )-2\,x^2\,{\ln \left (\ln \left (x\right )\right )}^6\,{\mathrm {e}}^{2\,x+{\mathrm {e}}^{2\,x}}\,{\ln \left (x\right )}^2-512\,x\,{\ln \left (\ln \left (x\right )\right )}^3\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,\ln \left (x\right )+x^2\,{\ln \left (\ln \left (x\right )\right )}^6\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,{\ln \left (x\right )}^2\right )} \] Input:

int(-(exp((x*log(log(x))^2 + 256)/log(log(x))^2)*(log(log(x))^3*log(x)*(x 
- 1) - 512) - log(log(x))^3*exp(exp(2*x))*log(x)*(2*x*exp(2*x) - 1))/(log( 
log(x))^3*(x^2*log(x) + exp(2*exp(2*x))*log(x) - 2*x*exp(exp(2*x))*log(x)) 
 + log(log(x))^3*exp((2*(x*log(log(x))^2 + 256))/log(log(x))^2)*log(x) + l 
og(log(x))^3*exp((x*log(log(x))^2 + 256)/log(log(x))^2)*(2*x*log(x) - 2*ex 
p(exp(2*x))*log(x))),x)
 

Output:

(exp(exp(2*x))*(x^3*log(log(x))^6*log(x)^2 - 512*x^2*log(log(x))^3*log(x)) 
 + x^3*log(log(x))^6*log(x)^2 - x^4*log(log(x))^6*log(x)^2 + 512*x^3*log(l 
og(x))^3*log(x) - 2*x^3*log(log(x))^6*exp(2*x + exp(2*x))*log(x)^2)/((x + 
exp(x + 256/log(log(x))^2) - exp(exp(2*x)))*(x^2*log(log(x))^6*log(x)^2 - 
x^3*log(log(x))^6*log(x)^2 + 512*x^2*log(log(x))^3*log(x) - 2*x^2*log(log( 
x))^6*exp(2*x + exp(2*x))*log(x)^2 - 512*x*log(log(x))^3*exp(exp(2*x))*log 
(x) + x^2*log(log(x))^6*exp(exp(2*x))*log(x)^2))
 

Reduce [B] (verification not implemented)

Time = 0.17 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {e^{e^{2 x}} \left (-1+2 e^{2 x} x\right ) \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (512+(1-x) \log (x) \log ^3(\log (x))\right )}{e^{\frac {2 \left (256+x \log ^2(\log (x))\right )}{\log ^2(\log (x))}} \log (x) \log ^3(\log (x))+e^{\frac {256+x \log ^2(\log (x))}{\log ^2(\log (x))}} \left (-2 e^{e^{2 x}} \log (x)+2 x \log (x)\right ) \log ^3(\log (x))+\left (e^{2 e^{2 x}} \log (x)-2 e^{e^{2 x}} x \log (x)+x^2 \log (x)\right ) \log ^3(\log (x))} \, dx=-\frac {x}{e^{e^{2 x}}-e^{\frac {\mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2} x +256}{\mathrm {log}\left (\mathrm {log}\left (x \right )\right )^{2}}}-x} \] Input:

int((((1-x)*log(x)*log(log(x))^3+512)*exp((x*log(log(x))^2+256)/log(log(x) 
)^2)+(2*x*exp(x)^2-1)*log(x)*exp(exp(x)^2)*log(log(x))^3)/(log(x)*log(log( 
x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)^2+(-2*log(x)*exp(exp(x)^2)+ 
2*x*log(x))*log(log(x))^3*exp((x*log(log(x))^2+256)/log(log(x))^2)+(log(x) 
*exp(exp(x)^2)^2-2*x*log(x)*exp(exp(x)^2)+x^2*log(x))*log(log(x))^3),x)
 

Output:

( - x)/(e**(e**(2*x)) - e**((log(log(x))**2*x + 256)/log(log(x))**2) - x)