\[ \int \frac {e^{\frac {3+e^{10} \left (-x^2-x^3\right )}{-e^{10} x^2+e^{10} x^2 \log \left (\frac {x}{5 \log (x)}\right )}} \left (3+e^{10} \left (-x^2-x^3\right )+\left (3+e^{10} \left (x^2+2 x^3\right )\right ) \log (x)+\left (-6-e^{10} x^3\right ) \log (x) \log \left (\frac {x}{5 \log (x)}\right )\right )}{e^{10} x^3 \log (x)-2 e^{10} x^3 \log (x) \log \left (\frac {x}{5 \log (x)}\right )+e^{10} x^3 \log (x) \log ^2\left (\frac {x}{5 \log (x)}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\frac {3 \,{\mathrm e}^{-10}}{x^{2}}-x -1}{\ln \left (\frac {x}{5 \ln \left (x \right )}\right )-1}} \]
command
integrate(((-x**3*exp(5)**2-6)*ln(x)*ln(1/5*x/ln(x))+((2*x**3+x**2)*exp(5)**2+3)*ln(x)+(-x**3-x**2)*exp(5)**2+3)*exp(((-x**3-x**2)*exp(5)**2+3)/(x**2*exp(5)**2*ln(1/5*x/ln(x))-x**2*exp(5)**2))/(x**3*exp(5)**2*ln(x)*ln(1/5*x/ln(x))**2-2*x**3*exp(5)**2*ln(x)*ln(1/5*x/ln(x))+x**3*exp(5)**2*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
\[ e^{\frac {\left (- x^{3} - x^{2}\right ) e^{10} + 3}{x^{2} e^{10} \log {\left (\frac {x}{5 \log {\left (x \right )}} \right )} - x^{2} e^{10}}} \]