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I need to find the residue of exp[i.kx] / [ 1 - k^2 ], where k is my complex variable, and x is positive.

I have poles at 1 and -1 in my integral. Now everywhere I look, a pole of order n is when one has say, in my case, ( 1 - k^2)^n.....the n being outside the bracket. In what I have above, 1 - k^2, is this still of order 2???

Ive tried computing the residue but I cant get the correct answer, sin(x). My method is as follows:

multiply the above by (k - 1)^2, and then evaluate at k = 1, -1.....what am I doing wrong here?