The question is:
Compute $\lim_{p\rightarrow0^{+}}\int_{C_p}\frac{e^{3iz}}{z^{2}-1}dz$
Where $C_p: z = 1 + pe^{i\theta}$
My initial thought was to use residues, yet the poles are -1 and 1, so they're on the real line (thus the Residue Theorem does not apply). My next thought was to find some way to make the integral work with the Cauchy Integral Formula, but I can't find a way to do that since a partial fraction decomposition won't work in this case. So, I am stuck.