Here I go again...

All of theseline!integrals are on the circle |z|=2, with counterclockwise orientation.

1. int(z^104)dz

2. int(z*conjugate(z))d|z|

3. int(conjugate(z))dz

4. int(cos(z)/z^3)dz

5. int(sin(z)/(z^2-((pi)/2)^2)dz

Unfortunately I cannot use the residue theorem.

For numbers 4 and 5 I have been trying to write the integrands as power series, but I am having trouble relating those to line integrals.

For numbers 1, 2 and 3 I feel like I have to split them up into a real and imaginary parts and then do two integrals, but I am having trouble doing this.

And throughout I am always wondering why the line integral is evaluated at a circle of radius 2, instead of the usual 1. I think some of the functions have singularities in that region, but I'm not sure what that does.