Calculate $\displaystyle \int_{|z|=3}\frac{e^{iz}}{z^2(z-2)(z+5i)}dz$ So the point Z= -5i is not enclosed by the contour.

So am i right that we only calculate the residues at z=0 and z=2 and sum them then multiply by 2i*pi to evaluate the integral?

Residue at z=0 = $\displaystyle \frac{-3}{25} +\frac{i}{20}$

Residue at z=2 = $\displaystyle \frac{e^{2i}}{58} - \frac{5ie^{2i}}{116}$

These just seem like strange answers, have i made a mistake somewhere?