Evaluate the contour integral of z^2/(4-z^2) around the circle |z+1|=2.
The question is attached in correct mathematical notation, along with the student's (incorrect) initial attempt. You will need to refer to this initial attempt when reading the solution.
Solution is attached.
OK, I've looked over what you've done and you're overcomplicating things a little. You would only need to use partial fractions if there was more than one singularity in the region of integration, which is not the case here.
I have written the last expression in that strange way for a ...
Cauchy's formula can be used to quickly evaluate contour integrals of complex valued functions. The solution comprises approximately one page written in Word with equations in Mathtype illustrating one example. The general procedure for these questions often involves decomposing into partial fractions, and students often make the "mistake" of doing this when in some cases, such as this one, it is unnecessary. The solution discusses this issue.