How Does Integral Rewriting Transform Two Integrals into One?

[aaaa202]

On the attached picture the double integral in the first line is rewritten in the second line by introducting the variable τ=τ1-τ2
But how exactly does this happen? I simply can't see how two integrals can turn into one.

 

[dirk_mec1]

The first integral is just beta. It eventually cancels out.

 

[aaaa202]

I don't understand why it is just beta. There is a Green's function in the integrand. Do you say this because there is no beta in the second line? Because for all I know this could be a typo.

 

[Office_Shredder]

Can you do the full substitution where you introduce new variables, say
$$\tau = \tau_1 - \tau_2 \text{ and } \mu = \tau_1 + \tau_2$$
to turn a two dimensional integral into a two dimensional integral? You will see the integration over $\mu$ become trivial.

 

[aaaa202]

hmm I'd would say it would give something like the attached, but I don't see any trivial integral. What did I do wrong?