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!