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

Compute the integral: ∫ x^{2}/(x^{4}-4x^{2}+5)

2. Relevant equations

Uses Residue theorem.

3. The attempt at a solution

So I found the zeroes of x^{4}-4x^{2}+5 to be 2+i and 2-i, and therefore the one that is of relevance is 2+i since it is in the upper half-plane. Then I used residue theorem that said Res(P(z)/Q(z); 2+i) = P(2+i)/Q'(2+i) = (2+i)^{2}/(4(2+i)^{3}-8(2+i)) = (4i+3)/(36i-8) and then I multiplied by 2∏i which would leave me with a value in the complex plane. I think this is wrong because it should come out with a real valued number. Does it have something to do with the zero having a multiplicity of 2? And if so, how do I go about redoing it with that in mind, I don't remember learning how to do that...

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# Residue Theorem integral application

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