\[ \int \frac {5^{\frac {5}{\left (x+x^2 \log (5)\right ) \log (x)}} e^{-4+5^{\frac {5}{\left (x+x^2 \log (5)\right ) \log (x)}}} \left (-5 \log (5)-5 x \log ^2(5)+\left (-5 \log (5)-10 x \log ^2(5)\right ) \log (x)\right )}{\left (x^2+2 x^3 \log (5)+x^4 \log ^2(5)\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{-4+{\mathrm e}^{\frac {5}{\left (x^{2}+\frac {x}{\ln \left (5\right )}\right ) \ln \left (x \right )}}} \]
command
integrate(((-10*x*ln(5)**2-5*ln(5))*ln(x)-5*x*ln(5)**2-5*ln(5))*exp(5*ln(5)/(x**2*ln(5)+x)/ln(x))*exp(exp(5*ln(5)/(x**2*ln(5)+x)/ln(x))-4)/(x**4*ln(5)**2+2*x**3*ln(5)+x**2)/ln(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
\[ e^{e^{\frac {5 \log {\left (5 \right )}}{\left (x^{2} \log {\left (5 \right )} + x\right ) \log {\left (x \right )}}} - 4} \]