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
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.