\[ \int \frac {e^{\frac {1}{-400 x^5+\left (2000 x^4+400 x^5\right ) \log (x)}} (-5+4 x+(-20-5 x) \log (x))}{200 x^7+\left (-2000 x^6-400 x^7\right ) \log (x)+\left (5000 x^5+2000 x^6+200 x^7\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{-\frac {1}{400 x^{4} \left (x +\left (-x -5\right ) \ln \left (x \right )\right )}} \]
command
integrate(((-5*x-20)*ln(x)+4*x-5)/((200*x**7+2000*x**6+5000*x**5)*ln(x)**2+(-400*x**7-2000*x**6)*ln(x)+200*x**7)/exp(-1/((400*x**5+2000*x**4)*ln(x)-400*x**5)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ 2 e^{\frac {1}{- 400 x^{5} + \left (400 x^{5} + 2000 x^{4}\right ) \log {\left (x \right )}}} \]