Q: Integral from -infinity to infinity, sinx/(x^2 + 6x + 10)

I am supposed to use residue theorem, so I tried Integral from -infinity to infinity, e^iz/(z^2 + 6z + 10)

but I get stuck after separating e^ix to cosx and i(sinx) Not sure what to do to elimiate cosx. Because of 6x, I can't say any of them are odd/even function.

Any help would be appreciated...