3 Equal Charges in Equilateral Triangle - Find KE @ Inf

[trixxstyle]

Homework Statement

Question is attached.

I know there's a few ways to solve this, but I'm wondering specifically why my integral of F ds isn't working.

Homework Equations

F = k * q^2 / r^2
U = ∫ F ds
cos 30 = √3/2
s= rcos30

The Attempt at a Solution

U = 2 * cos 30 * k * q^2 ∫ 1/r^2 ds
U = √3 * k * q^2 ∫ 1/r^2 * √3/2 dr - (a to inf)
U = 3/2 * k * q^2 * 1/a

 

[trixxstyle]

Any help would be appreciated. No one seems to be able to help me.

 

[haruspex]

I assume your model is to let all three move apart some small amount, symmetrically. dr will be the increase in distance between any pair, while ds is the distance each moves. If so, I get dr = ds √3, which does not seem to be what you have used.