> I would like to integrate the following expression that I call s2
> s2 := (1/2/Pi+2*Q*u/(1+u^2))^2/((1+beta^2*(1/2/Pi+2*Q*u/(1+u^2))^2)*(1+u^2));
using the residue theorem. To do this I first want to find the roots (poles) of the expression. I do this by solving for the denominator equal to zero as below.
> s4:= solve(s3=0,u);
but I then get the RootOf expression which I can't interpret. Are the poles/singularities of s2 somehow tractable from s4 - the root of expression? If not how do I get the poles of s2 or otherwise calculate the residues? I am really interested in getting the residues but only if this can't be done then I would appreciate any advice as to alternative ways of evaluating the integral of s2 for u = -infinity..infinity.
Please help me in anyway you can as I am completely stuck.