Given an Annulus with $A(0,r,R)$ show by considering Cauchy's Theorem for primitives that there is no holomorphic function with $f'(z)=\dfrac{1}{z}$.
I am struggling to picture this since but it seems like there are issues because $f(z)=\log z$ isn't well defined in the same range as $\dfrac{1}{z}$.
Am I looking to show that $\int_Ag(z)dz = 0$ where $g(z) = \dfrac{1}{z}$?