I have a problem to solve integral $$ I = \int^{\infty}_0 \frac{\mathrm{d}x}{(x-z)(1+x^2)^{\kappa+2}} $$
I can solve the same integral with borders $-\infty$ to $\infty$ using residue theorem but here I have a problem to define contour (if complex analysis if right way to do).
Could someone please help me?