Number 361 in my List of Fiendish Integrals:
Prove that:
I tried the Weierstrass substitution but that got very complicated:
... and I can't get Integration by Parts to work. I fleetingly looked at manipulating it into the form:
... but that doesn't look hopeful either.
It's probably all about the substitution, as usual, but I haven't found one that works.
Any takers?