\[ \int \frac {e^{\frac {2563093129+2096362816 x+688675888 x^2+115651112 x^3+10505414 x^4+513920 x^5+13600 x^6+184 x^7+x^8}{1+4 x+6 x^2+4 x^3+x^4}} \left (-8156009700-4911736672 x-1030398440 x^2-73629456 x^3+2569600 x^4+595520 x^5+28488 x^6+560 x^7+4 x^8\right )}{1+5 x+10 x^2+10 x^3+5 x^4+x^5} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\left (\left (\frac {225+45 x}{1+x}+x \right )^{2}+2\right )^{2}} \]
command
int((4*x^8+560*x^7+28488*x^6+595520*x^5+2569600*x^4-73629456*x^3-1030398440*x^2-4911736672*x-8156009700)*exp((x^8+184*x^7+13600*x^6+513920*x^5+10505414*x^4+115651112*x^3+688675888*x^2+2096362816*x+2563093129)/(x^4+4*x^3+6*x^2+4*x+1))/(x^5+5*x^4+10*x^3+10*x^2+5*x+1),x)
Maple 2022.1 output
\[{\mathrm e}^{\frac {x^{8}+184 x^{7}+13600 x^{6}+513920 x^{5}+10505414 x^{4}+115651112 x^{3}+688675888 x^{2}+2096362816 x +2563093129}{x^{4}+4 x^{3}+6 x^{2}+4 x +1}}\]
Maple 2021.1 output
hanged__________________________________________________________________________________