This is the exercise $25$, Section $14.3$ (Cauchy's Integral Theorem) from Advanced Engineering Mathematics. It was translated to Portuguese and I do not have the book in English. So I will try to translate the exercise to English.
I want to evaluate the following integral $\oint_{C}\dfrac{\cos z}{z} dz$, where $C$ is the curve consisting of $|z|=1$ (anticlockwise) and $|z|=3$ (clockwise). Why $C$ is a curve?
I would appreciate your help.