# Question:How do I integrate the following expression?

## Question:How do I integrate the following expression?

Maple

I would like to integrate the following expression that I call res

>res:= subs([S1 = C3-sqrt(C3^2+4*C1*s), S2 = C3+sqrt(C3^2+4*C1*s)], exp(s*t)*(S1*(sinh((1/2)*S1)-cosh((1/2)*S1))*(sinh((1/2)*S2*eta)-cosh((1/2)*S2*eta))-S2*(sinh((1/2)*S2)-cosh((1/2)*S2))*(sinh((1/2)*S1*eta)-cosh((1/2)*S1*eta)))*exp(C4)/((S2*(sinh((1/2)*S2)-cosh((1/2)*S2))-S1*(sinh((1/2)*S1)-cosh((1/2)*S1)))*C1*s^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.

> resdenom := denom(res):

>sol:=solve(resdenom,s)

But I then get the RootOf expression which I can't interpret. Are the poles/singularities of res somehow tractable from sol - the root of expression? If not how do I get the poles of res 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 res for s = -infinity..infinity.