# Complex analysis fun!

## Homework Statement

Show that $$\frac{z}{(z-1)(z-2)(z+1)}$$ has an analytic antiderivative in $\{z \in \bold{C}:|z|>2\}$. Does the same function with z^2 replacing z (EDIT: I mean replacing the z in the numerator, not everywhere) have an analytic antiderivative in that region?

## Homework Equations

Um lots of things I imagine.

## The Attempt at a Solution

Well, I'm pretty sure that I can do a partial fraction decomposition in both cases, then the appropriate logarithms would give me a function that's analytic on the region minus whatever line I do the branch cut on. But unless there's some huge typo in the problem, I don't think that's what's being sought. I'm not really sure what else to do in this situation though. I have some other thoughts on the problem that may or may not work, but they're kind of long winded, and I'd rather not go into them unless I really have to. So, any suggestions?

Last edited: