\[ \int \frac {e^{\frac {e^{9+2 x} \left (10+2 x^2\right )+e^{9+x} \left (100 x+20 x^3\right )+e^9 \left (250 x^2+50 x^4\right )}{x^2}} \left (100 e^9 x^4+e^{9+2 x} \left (-20+20 x+4 x^3\right )+e^{9+x} \left (-100 x+100 x^2+20 x^3+20 x^4\right )\right )}{x^3} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {10 \left (x^{2}+5\right ) {\mathrm e}^{9} \left (x +\frac {{\mathrm e}^{x}}{5}\right ) \left (5 x +{\mathrm e}^{x}\right )}{x^{2}}} \]
command
integrate(((4*x^3+20*x-20)*exp(9)*exp(x)^2+(20*x^4+20*x^3+100*x^2-100*x)*exp(9)*exp(x)+100*x^4*exp(9))*exp(((2*x^2+10)*exp(9)*exp(x)^2+(20*x^3+100*x)*exp(9)*exp(x)+(50*x^4+250*x^2)*exp(9))/x^2)/x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (50 \, x^{2} e^{9} + 20 \, x e^{\left (x + 9\right )} + \frac {100 \, e^{\left (x + 9\right )}}{x} + \frac {10 \, e^{\left (2 \, x + 9\right )}}{x^{2}} + 250 \, e^{9} + 2 \, e^{\left (2 \, x + 9\right )}\right )} \]