How to Calculate the Inverse Mellin Transform of a Complex Residue Integral?

[zetafunction]

Homework Statement

i need to calculate the inverse Mellin transform $$\oint ds {x^{-s}}\frac{1}{\Gamma(s)cos(\pi s/2)}$$

Homework Equations

I can use Cauchy's integral theorem,

The Attempt at a Solution

i know that Gamma function has poles at -1,-2,-3, ... and that the cosine term has poles at every integer the question is how could i expand Gamma function and cosine term in order to obtain the complex integral.

 

[HallsofIvy]

What path is the integral taken over and, in particular, what integers are contained inside that path?