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