Hmm after a while of thinking i've came up with something, however im not sure if its a correct method, i'm mostly worried about splitting the integrals up into parts such as which are divergent...
Now
Because of the symmetric property of we have:
where the is the set of natural numbers summed to infinity.
Now
Substituting this result back into our original equation yields:
Now
Substituting this back in leaves us with only:
Now let
Substituting these results back in yields:
But
Also
Therefore
The proof is complete.
so yeah, if anyone could confirm the validity of this, that'd be much appreciated!