\[ \int \frac {e^{-\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (e^{\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (x^2 \log (x)+2 x \log ^2(x)+\log ^3(x)\right )+e^{e^{-\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}} \left (-2 e^{\frac {-5 x+e^5 x+\left (-5+e^5\right ) \log (x)+\log \left (\frac {x}{\log (x)}\right )}{x+\log (x)}}+x\right )} \left (x+\left (1-x+x^2\right ) \log (x)+(-1+2 x) \log ^2(x)+\log ^3(x)+(1+x) \log (x) \log \left (\frac {x}{\log (x)}\right )\right )\right )}{x^2 \log (x)+2 x \log ^2(x)+\log ^3(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{-2+x \,{\mathrm e}^{-\frac {\ln \left (\frac {x}{\ln \left (x \right )}\right )}{x +\ln \left (x \right )}-{\mathrm e}^{5}+5}}+x \]
command
integrate((((1+x)*ln(x)*ln(x/ln(x))+ln(x)**3+(-1+2*x)*ln(x)**2+(x**2-x+1)*ln(x)+x)*exp((-2*exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x)))+x)/exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x))))+(ln(x)**3+2*x*ln(x)**2+x**2*ln(x))*exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x))))/(ln(x)**3+2*x*ln(x)**2+x**2*ln(x))/exp((ln(x/ln(x))+(exp(5)-5)*ln(x)+x*exp(5)-5*x)/(x+ln(x))),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ x + e^{\left (x - 2 e^{\frac {- 5 x + x e^{5} + \left (-5 + e^{5}\right ) \log {\left (x \right )} + \log {\left (\frac {x}{\log {\left (x \right )}} \right )}}{x + \log {\left (x \right )}}}\right ) e^{- \frac {- 5 x + x e^{5} + \left (-5 + e^{5}\right ) \log {\left (x \right )} + \log {\left (\frac {x}{\log {\left (x \right )}} \right )}}{x + \log {\left (x \right )}}}} \]