I'm being asked to integrate $f(z) = \frac{e^z}{z^2 + 2z + 1}$ around a $5 \times 5$ square, centered at $i$, in the counter clockwise direction. It seems to me that applying Cauchy's integral formula for the first derivative directly yields an answer, but I am concerned the approach is incorrect due to a double pole at $z =-1$. Is there any special case that I am missing?
Proper application of Cauchy integral formula
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complex-analysis
contour-integration
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0This is just a guess, but I think the exercise is supposed to let you calculate the integral in order to demonstrate to which Cauchy's integral formula applies. And yes, the pole at $-1$ should make you suspicious. – 2011-12-12
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0This exercise was preceded with the same question for f(z) = z-1/z+1. That was a much easier case in which I could double-check Cauchy by integrating directly. Lectures haven't mentioned anything regarding two poles at a single location, hence my hesitation with calling my question done by applying Cauchy again. – 2011-12-12