I have the following integrals to integrate where the contour is the positively oriented circle $|z| = 1$
$$ \int {e^z \over z^2(z-i)} dz$$ $$ \int {\sin z \over z(z^2+2)} dz$$ $$ \int {\cosh z \over z^3} dz$$
I have been working on contour integrals for quite a while now and am having a very hard time wrapping my head around them. I have tried to work out the first integral using the Cauchy Integral Theorem and the second using the Deformation Invariance Theorem but I am still having trouble working through them. Any hints or ideas would be very much appreciated!