Use Residue Theorem to Integrate
Complex Analysis
Find the residues of f(z) = z+1/z(z^2+4)
We first of all find that the functions has simple poles at z=0 , 2i , -2i.
Then we can use the result of 2ipiS+ipiT
S is the sum of the residues in the upper half complex plane.
T is the sum of the residues on the real axis
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