Problems for Cauchy Integral Formula

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The discussion centers on the application of the Cauchy Integral Formula in solving complex analysis problems. Participants suggest using partial fraction decomposition as a method for tackling specific questions related to the formula. Additionally, Cauchy's differentiation formula is recommended for certain calculations. These techniques are essential for effectively addressing the posed mathematical challenges.

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shirokuma
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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? :(
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Welcome, Shirokuma!

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

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