\[ \int \frac {\left (80-40 x-2 x^2+x^3\right ) \log (-2+x)+e^{3 e^x+x} \left (-60 x^2+30 x^3\right ) \log (-2+x)+\left (-40 x-10 e^{3 e^x} x^2-x^3\right ) \log \left (\frac {40+10 e^{3 e^x} x+x^2}{x}\right )}{e^{3 e^x} \left (-20 x^2+10 x^3\right ) \log ^2(-2+x)+\left (-80 x+40 x^2-2 x^3+x^4\right ) \log ^2(-2+x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (10 \,{\mathrm e}^{3 \,{\mathrm e}^{x}}+\frac {40}{x}+x \right )}{\ln \! \left (-2+x \right )}-5 \]
command
integrate(((-10*x**2*exp(3*exp(x))-x**3-40*x)*ln((10*x*exp(3*exp(x))+x**2+40)/x)+(30*x**3-60*x**2)*exp(x)*ln(-2+x)*exp(3*exp(x))+(x**3-2*x**2-40*x+80)*ln(-2+x))/((10*x**3-20*x**2)*ln(-2+x)**2*exp(3*exp(x))+(x**4-2*x**3+40*x**2-80*x)*ln(-2+x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\log {\left (\frac {x^{2} + 10 x e^{3 e^{x}} + 40}{x} \right )}}{\log {\left (x - 2 \right )}} \]