This is precisely the content of exercise 14.9a. There are some hints given there as well. The point is that even with long range interaction, if you integrate a single unit cell, you are integrating the tails of the potential from atoms in neighboring unit cells, as well as the main parts of the potential from the atoms within that given unit cell. You can rearrange the integrals such that it is equal to the integral over the potential of a single atom over all of space.
Does that help at all?