I'm having lots of troubles while trying to find the second order derivatives of this integral... I don't think it admits a solution...
$$\int_{-\infty}^{\frac{x^2}{2}} e^{-(x^2+1)t^2} dt$$
Since I'm trying to compute its second order derivative w.r.t. $x$, after applying the rule for differentiation in the integral sign once, when I try to apply it for the second time, the argument of the integral goes to infinity... Can anyone help? Maybe there's some trivial substitution that I'm missing... Even if this differentiation doesn't seems trivial at all, at least for me...