Cauchy’s integral theorem and residue theorem, what’s the difference

[GGGGc]

TL;DR Summary

when to use residue theorem and when to use Cauchy’s integral theorem?

May I ask when we should use Cauchy’s integral theorem and when to use residue theorem? It seems for integral 1/z, we can use both of them. What are the conditions for each of them?
Thanks in advance!

 

[fresh_42]

The residue theorem covers more than one pole. Furthermore, it is a question which is easier to calculate. There are a lot of formulas that help to calculate residues, e.g.
https://www.physicsforums.com/insights/an-overview-of-complex-differentiation-and-integration/