The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$ where C is a closed curve given by |z| = 1 is

Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction)

$$\int\limits_C {{{{z^3} - 6} \over {3z - i}}} dz$$ is where C is |z| = 1

Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around the unit circle C.

$$I\, = \,\oint\limits_C {\sec z\,dz} $$, z being a complex variable. The value of I will be