I've been trying without success to do $$\int_0^\infty dx\; \exp(-x^2) \exp(-a\exp(bx^2)).$$

It's not in my integral tables. Wolfram online integrator won't do it. It doesn't seem to be amenable to a contour integral method, and the method of integrating $e^{-x^2}$ alone doesn't work either. I don't know if this is the kind of question asked here, but any help would be appreciated.

Thanks, Eric

hasa nice evaluation, and I'm much more likely to invest time into answering your question. $\endgroup$ – Theo Johnson-Freyd Sep 24 '11 at 0:15temporarilyas "too localized". At best, you will revise it, and my complaints will be moot, and you will get a useful answer, and the question will not be closed. Next best, if it is closed before you have time to make revisions, then after revising it you should "flag for moderator attention" and ask that the question be reopened. The point of closing it temporarily is to put some pressure on you to improve the question (I don't think we know each other, so it's hard for me to exert social pressure). $\endgroup$ – Theo Johnson-Freyd Sep 24 '11 at 0:17