The initial problem is to calculate
The Attempt at a Solution
I have, by transformation and use of the symmetry of both integrals come to
which is easily solveable using Mathematica.
Alas the solution provided by mathematica is absolutely non-obvious to me.
Any good idea for a substitution and/or other ways?
I've tried splitting the fraction into smaller parts, but got an integral with i in it, which is not allowed as this is real calculus.
Thanks in advance