\[ \int \frac {e^{\frac {4-4 x-3 x^2+2 x^3+x^4}{x-2 e^{e^8 x} x+e^{2 e^8 x} x}} \left (4+3 x^2-4 x^3-3 x^4+e^{e^8 x} \left (-4-3 x^2+4 x^3+3 x^4+e^8 \left (-8 x+8 x^2+6 x^3-4 x^4-2 x^5\right )\right )\right )}{-x^2+3 e^{e^8 x} x^2-3 e^{2 e^8 x} x^2+e^{3 e^8 x} x^2} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\left (x^{2}+x -2\right )^{2}}{x \left (1-{\mathrm e}^{x \,{\mathrm e}^{8}}\right )^{2}}} \]
command
integrate((((-2*x^5-4*x^4+6*x^3+8*x^2-8*x)*exp(4)^2+3*x^4+4*x^3-3*x^2-4)*exp(x*exp(4)^2)-3*x^4-4*x^3+3*x^2+4)*exp((x^4+2*x^3-3*x^2-4*x+4)/(x*exp(x*exp(4)^2)^2-2*x*exp(x*exp(4)^2)+x))/(x^2*exp(x*exp(4)^2)^3-3*x^2*exp(x*exp(4)^2)^2+3*x^2*exp(x*exp(4)^2)-x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Exception raised: TypeError} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (\frac {x^{4}}{x e^{\left (2 \, x e^{8}\right )} - 2 \, x e^{\left (x e^{8}\right )} + x} + \frac {2 \, x^{3}}{x e^{\left (2 \, x e^{8}\right )} - 2 \, x e^{\left (x e^{8}\right )} + x} - \frac {3 \, x^{2}}{x e^{\left (2 \, x e^{8}\right )} - 2 \, x e^{\left (x e^{8}\right )} + x} - \frac {4 \, x}{x e^{\left (2 \, x e^{8}\right )} - 2 \, x e^{\left (x e^{8}\right )} + x} + \frac {4}{x e^{\left (2 \, x e^{8}\right )} - 2 \, x e^{\left (x e^{8}\right )} + x}\right )} \]