- #1

kreil

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## Homework Statement

Calculate the following integral along three different circular contours,

[tex]\int_{C_j}\frac{dz}{z(3z-1)^2(z+2)}[/tex]

where

[tex]C_1:0<r_1<1/3[/tex]

[tex]C_2:1/3<r_2<2[/tex]

[tex]C_3: r_3>2[/tex]

## The Attempt at a Solution

The function has singularities at z=0, z=1/3 and z=-2. Thus all three contours enclose singularities and Cauchy's integral theorem doesn't hold (none of the integrals are immediately zero).

Along each circular contour,

[tex]z=re^{i \theta}\implies dz=ire^{i \theta}d \theta[/tex]

Am I going to need to use partial fractions for this? What is the best way to get started?

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