(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\oint _{|z+i|=1} \frac{e^z}{1+z^2} dz =?[/tex]

3. The attempt at a solution

I substituted z+i=z' and [itex]z'=e^{i\theta}[/tex] to arrive at

[tex]e^{-i} \int _0 ^{2 \pi} \frac{e^{e^{i \theta}}}{-ie^{i \theta}-2} d \theta[/tex]

I have no clue how to solve such an integral, any ideas??

(I also did a similar excercise to arrive at the same integral but now [itex]sin(\pi/4 + exp(i \theta))[/tex] in the numerator. Are these kind of integrals analytically solvable??)

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# Complex integral

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