I am going to evaluate the integral $$\int_{\mathbb{R}} \int^T_0 f(x,t) \dfrac{1}{\sqrt{t}}e^{-x^2/2t}dt$$
for some nice enough function $f$. The integrand has a very strong singularity at $t=0$. The function integral2 gives me warnings so often. Do we have some good function for an accurate answer?