$\int_\gamma\frac{f'(z)}{z-z_0}\,dz=\int_\gamma\frac{f(z)}{(z-z_0)^2}\,dz$

Let f be analytic on a domain D and let \(\gamma\) be a closed curve in \(D .\) . For any \(z _ { 0 }\) in \(D\) not on \(\gamma ,\) show that

\[ \int _ { \gamma } \frac { f ^ { \prime } ( z ) } { ( z - z _ { 0 } ) } d z = \int _ { \gamma } \frac { f ( z ) } { ( z - z _ { 0 } ) ^ { 2 } } d z \]

Give a generalization of this result.