Why only l=1 of spherical harmonics survives?

[mr.canadian]

Homework Statement

The question is about page 198 of Jackson's Classical Electrodynamics. The magnetic scalar potential is set to be:

Phi = ∫ (dΩ' cosθ'/ |x-x'|).

Using the spherical harmonics expansion of 1/|x-x'|, the book claims that only l=1 survives. I don't know why terms of l≠1 vanish

The Attempt at a Solution

I considered the addition theorem of 1/|x-x'| that contains on Y* (θ',ϕ'). I am trying to see whether the sin's and cos's inside Y* (θ',ϕ') are orthogonal to cosθ' for l≠1, but I had no success doing so. I could not think of other reasons why only l=1 terms survive.

Any ideas

 

[Simon Bridge]

Are sines and cosines not orthogonal?
Don't forget the range of the integration.