\[ \int \frac {e^{\frac {3 x^2+5 x^3+2 x^4}{(4+8 x) \log \left (x^2\right )}} \left (-6 x^2-22 x^3-24 x^4-8 x^5+\left (6 x^2+21 x^3+28 x^4+12 x^5\right ) \log \left (x^2\right )+\left (-8-32 x-32 x^2\right ) \log ^2\left (x^2\right )\right )}{\left (4 x^3+16 x^4+16 x^5\right ) \log ^2\left (x^2\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{\frac {x \left (\frac {x}{1+2 x}+x^{2}+2 x \right )}{4 \ln \left (x^{2}\right )}}}{x^{2}} \]
command
integrate(((-32*x**2-32*x-8)*ln(x**2)**2+(12*x**5+28*x**4+21*x**3+6*x**2)*ln(x**2)-8*x**5-24*x**4-22*x**3-6*x**2)*exp((2*x**4+5*x**3+3*x**2)/(8*x+4)/ln(x**2))/(16*x**5+16*x**4+4*x**3)/ln(x**2)**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
\[ \frac {e^{\frac {2 x^{4} + 5 x^{3} + 3 x^{2}}{\left (8 x + 4\right ) \log {\left (x^{2} \right )}}}}{x^{2}} \]