Do you know how to do this integral please?

[blueyellow]

What is the value of

closed integral (C) of [cosh z/(z^2 -z)] dz

if C is
a) the circle |z|=2
b)the circle |z-i|=1/2
c)the circle |z-1|=1/2

i've tried reading up on cauchy's integral formulae in textbooks and my notes but i couldn't find an example which was similar. what do i do? do i hav to first turn the cosh z into a formula involving e's?

 

[cupid.callin]

is the whole z thing in cos ?

if that is so then take z common cancel it
you'll be left with 1/(Z-1)