This is a theorem from my complex analysis book, and one of the exercises is to prove it.
When n = 1, the result follows directly from Cauchys integral formula. When n is 0 or negative, the integral is just a regular polynomial. A regular polymoial is analytical everywhere, and an integral around a close curve around it is zero.
These two cases I get, but why is this integral 0 when n is a positive integer greater than or equal to 2?