Problems for Cauchy Integral Formula

[shirokuma]

Hello everyone!
I am currently stuck at the two type of questions below, because I am not really sure what method should be used to calculate these question...
Could you give me a hint how to do these questions? :(
View attachment 8449View attachment 8450

 

[Euge]

Welcome, Shirokuma!

Consider using partial fraction decomposition. You might need to use Cauchy's differentiation formula at some points.