Theorem connecting the inverse of a holomorphic function to a contour integral

[IDontKnow1]

I tried posting this at stack exchange but it never got the question answered. I want to prove this:

If f:U→C is holomorphic in U and invertible, P∈U and if D(P,r) is a sufficently small disc about P, then


f^{-1}(w) = \frac{1}{2\pi i} \oint_{\partial D(P,r)}{\frac{sf'(s)}{f(s)-w}}ds

 

[lurflurf]

That is just Cauchy's formula.

f^{-1}(w)=\frac{1}{2\pi\imath}\oint_{\partial D(P,r)} \frac{s}{f(s)-w}d(f(s))