\[ \int \frac {e^{\frac {5}{-4 x^2+x^2 \log (\log (x))}} (-5+40 \log (x)-10 \log (x) \log (\log (x)))}{16 x^3 \log (x)-8 x^3 \log (x) \log (\log (x))+x^3 \log (x) \log ^2(\log (x))} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {5}{x^{2} \left (\ln \left (\ln \left (x \right )\right )-4\right )}} \]
command
integrate((-10*ln(x)*ln(ln(x))+40*ln(x)-5)*exp(5/(x**2*ln(ln(x))-4*x**2))/(x**3*ln(x)*ln(ln(x))**2-8*x**3*ln(x)*ln(ln(x))+16*x**3*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
\[ e^{\frac {5}{x^{2} \log {\left (\log {\left (x \right )} \right )} - 4 x^{2}}} \]