Complex analysis formula for an integral

[nugget]

Homework Statement

Find a formula for:

$\int$[itex]1/(z-a)^m(z-b)ⁿ[/itex]dz

around a ball of radius R, centred at z₀

where |a| < R < |b| and m,n$\in$N.

Homework Equations

Not sure which equations to use, a cauchy integral formula maybe...?

The Attempt at a Solution

I've attempted to split the fraction up into partial fractions, so that the integral is now:

$\int$[itex]1/(z-a)^m(b-a)ⁿ[/itex]+[itex]1/(z-b)ⁿ(b-a)^m[/itex]dz

but I don't think this has made it any easier to solve...

any suggestions?

 

[lanedance]

so do you mean
$$\int \frac{1}{(z-a)^m(z-b)^n} dz$$

how about considering poles & residues?