\[ \int \frac {e^{\frac {-e+\log (3)}{-20-x+x \log (x)}} (e-\log (3)) \log (x)}{400+40 x+x^2+\left (-40 x-2 x^2\right ) \log (x)+x^2 \log ^2(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {-\ln \left (3\right )+{\mathrm e}}{20+x -x \ln \left (x \right )}} \]
command
integrate((-ln(3)+exp(1))*ln(x)*exp((ln(3)-exp(1))/(x*ln(x)-x-20))/(x**2*ln(x)**2+(-2*x**2-40*x)*ln(x)+x**2+40*x+400),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ e^{\frac {- e + \log {\left (3 \right )}}{x \log {\left (x \right )} - x - 20}} \]