Suppose that f is analitic in an opened region $G$, which has $0$. Suppose $C$ is a closed curve in $G$, which encloses $0$, also it is positive and it begins and ends in $z_0$. Show that
$\oint_C (Ln (z))f'(z) dz= 2πi(f(z_0)-f(0))$
I try with integration by parts, but I'm not sure how to do it, because it appears an evaluation in $C$.