The following complex integration question has me stuck...
$$\int_{C(0,1)}(2z-3)\cos5zdz$$
So I wondered is there a way of applying a theorem to quickly solve this or should I look at integration by parts?
Perhaps $\cos(5z)$ being an entire function could be applied somewhere.
Or should I look at the root of $(2z-3)$ which is $z=\frac{3}{2}$
But $\frac{3}{2}$ is not $\in D(0,1+\epsilon)$ which means the integral is $0$
All help is appreciated
A holomorphic\analytic function's integral on a closed circut is 0. (one of Cauchy's theorem I believe) Since your function is analytic as a product of two analytic functions, the integral is 0.