I have the following problem:
$$\int_{\alpha}^{\beta} (ax^4 + bx^3 + cx^2 + dx + e)\exp{(fx^4 + gx^3 + hx^2 + ix + j)}\ dx$$
$b,c,d,e,g,h,i,j\in\mathbb{R}$. One can assume the final value of the integral is finite even if $\alpha\rightarrow-\infty$ and $\beta\rightarrow\infty$ (the polynomial coefficient $a,f<0$ ).
Does it has a closed form solution ? Is there any special numerical method to evaluate this ?