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Thread: need clarifiction of this integral

  1. #1
    Oct 2008

    need clarifiction of this integral

    hi i'm working through a past exam problem and i dont have any solutions i was wandering if some one could tell me if im doing this correctly

    we have the real integral from negative infinity to possitive infinty of

    1/(x^4 +1)

    so to work this out i work in terms of z instead of x.

    factorise z^4 +1 into its linear factors. which are:

    e^(pi/4), -e^(pi/4), e^(-pi/4), -e^(-pi/4)

    then looking at where the singularites occur we notice that two are in the upper half of the complex plane and two are in the lower half.

    therefore the integrand = 2 the integral from 0 to positive infinity

    we then find the residues of the two singularities and and then apply the residue theorem

    so im pretty good up here, but then finding the residues i got a bit lost with all the exponentials and positives and negatives.

    so if anyone could just help me out it should be all good.

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  2. #2
    Nov 2007
    Take a look at this tutorial
    Theorem 22 there can make the residue computation easier. It also has the same problem you're working on. This tutorial helps me a lot. It will help you too.
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