\[ \int \frac {e^{\frac {-2-x}{\left (-x+2 x^3\right ) \log (x)}} \left (-2-x+4 x^2+2 x^3+\left (-2+12 x^2+4 x^3\right ) \log (x)\right )}{\left (x^2-4 x^4+4 x^6\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {2+x}{\ln \left (x \right ) \left (-2 x^{3}+x \right )}} \]
command
integrate(((4*x**3+12*x**2-2)*ln(x)+2*x**3+4*x**2-x-2)*exp((-2-x)/(2*x**3-x)/ln(x))/(4*x**6-4*x**4+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
\[ e^{\frac {- x - 2}{\left (2 x^{3} - x\right ) \log {\left (x \right )}}} \]