When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.
Doron ZeilbergerNo Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.
Doron ZeilbergerLet me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.
Doron Zeilberger