\[ \int \frac {e^{\frac {-36+36 e x-x^4-x^3 \log \left (e^e-x\right )}{-x^2+e x^3}} \left (72 x+72 e^2 x^3-x^4-2 x^5+e \left (-144 x^2+x^5+x^6\right )+e^e \left (-72-72 e^2 x^2+2 x^4+e \left (144 x-x^5\right )\right )+\left (e^e x^3-x^4\right ) \log \left (e^e-x\right )\right )}{-x^4+2 e x^5-e^2 x^6+e^e \left (x^3-2 e x^4+e^2 x^5\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {36}{x^{2}}-\frac {\left (x +\ln \left ({\mathrm e}^{{\mathrm e}}-x \right )\right ) x}{{\mathrm e} x -1}} \]
command
integrate(((x^3*exp(exp(1))-x^4)*log(exp(exp(1))-x)+(-72*x^2*exp(1)^2+(-x^5+144*x)*exp(1)+2*x^4-72)*exp(exp(1))+72*x^3*exp(1)^2+(x^6+x^5-144*x^2)*exp(1)-2*x^5-x^4+72*x)*exp((-x^3*log(exp(exp(1))-x)+36*x*exp(1)-x^4-36)/(x^3*exp(1)-x^2))/((x^5*exp(1)^2-2*x^4*exp(1)+x^3)*exp(exp(1))-x^6*exp(1)^2+2*x^5*exp(1)-x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (-\frac {x^{4}}{x^{3} e - x^{2}} - \frac {x^{3} \log \left (-x + e^{e}\right )}{x^{3} e - x^{2}} + \frac {36 \, x e}{x^{3} e - x^{2}} - \frac {36}{x^{3} e - x^{2}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {{\left (2 \, x^{5} + x^{4} - 72 \, x^{3} e^{2} - {\left (x^{6} + x^{5} - 144 \, x^{2}\right )} e - {\left (2 \, x^{4} - 72 \, x^{2} e^{2} - {\left (x^{5} - 144 \, x\right )} e - 72\right )} e^{e} + {\left (x^{4} - x^{3} e^{e}\right )} \log \left (-x + e^{e}\right ) - 72 \, x\right )} e^{\left (-\frac {x^{4} + x^{3} \log \left (-x + e^{e}\right ) - 36 \, x e + 36}{x^{3} e - x^{2}}\right )}}{x^{6} e^{2} - 2 \, x^{5} e + x^{4} - {\left (x^{5} e^{2} - 2 \, x^{4} e + x^{3}\right )} e^{e}}\,{d x} \]________________________________________________________________________________________