Complex integration question? resizudes.?

Question

Hi all, really confused with complex integration, any help would be much appreciated.. I know I have to use residues, but I still don't understand how..

Problem: Find integral{ z^3 / (2z-1)^3 dz} over C, where C is positively oriented circle, |z|<2.

z's are complex numbers.

Thanks.

Answer 1

so using the theory your answer is 2π i Res f (1/2) and f (z) = [z^3 / 8] / (z-1/2)^3. The residue,since the pole order 3, is 1 / 2! {2nd derivative of z^3 / 8 evaluated at z = 1/2 } or [1/2] [6 / 16 ] = 3 / 16. Answer is 3 π i / 8