\[ \int \frac {e^{\frac {3}{50 x-25 x^3+e^x \left (-10+5 x^2\right )}} \left (-90+135 x^2+e^x \left (18-18 x-9 x^2\right )\right )}{500 x^2-500 x^4+125 x^6+e^{2 x} \left (20-20 x^2+5 x^4\right )+e^x \left (-200 x+200 x^3-50 x^5\right )} \, dx \]
Optimal antiderivative \[ 3 \,{\mathrm e}^{\frac {3}{\left (5 x -{\mathrm e}^{x}\right ) \left (-5 x^{2}+10\right )}}-4 \]
command
integrate(((-9*x^2-18*x+18)*exp(x)+135*x^2-90)*exp(3/((5*x^2-10)*exp(x)-25*x^3+50*x))/((5*x^4-20*x^2+20)*exp(x)^2+(-50*x^5+200*x^3-200*x)*exp(x)+125*x^6-500*x^4+500*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 3 \, e^{\left (-\frac {3}{5 \, {\left (5 \, x^{3} - x^{2} e^{x} - 10 \, x + 2 \, e^{x}\right )}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: RuntimeError} \]________________________________________________________________________________________