Unfortunately, I cannot see your screenshots. By Fubini's theorem, you can integrate this with respect to any variable you choose first. The simplest integral is with respect to z, which returns the same integrand. The next simplest is integrating with respect to x. when we do this, remember that we treat y (and any other variables not dependent on x) as a constant. Thus, our integrand is just like where k is a constant. This should be a familiar derivative.
After this integral is done, then the last integral I would do would be y. This is in arbitrary order of simplicity however; since the limits are all constants, you are free to do the integral in whatever order you want without worrying about reparameterizing boundary curves.