Solve the integral:
Well, no one answered. It's a simple enough problem to do by integration by parts but I like the solution I found as it doesn't have to do with parts.
Let giving dx = - dz.
After some work with the addition of angles formulas:
x and z are "dummy" variables so change the z on the RHS to x and move the last term on the right to the LHS:
The integral on the RHS is elementary and gives: