Integrate[x d/(x^2 + d^2)^(3/2), {x, 0, Infinity}, 
      Assumptions ->  d > 0]

q =1.60217653  10^(-19)

d  =  10^(-10)

(Subscript[ϵ, 0]) =  8.854187817 10^(-12)

w = q^2/(4 Pi (Subscript[ϵ, 0]) 4 d)