Contour integral using branchcut

[qlsn4123]

I want to compute kind of following problems.

int(from 0 to infinity) e^(-x) / (x-1) dx= I

using contour integrals, then

2 pi i I = -pi i / (2) Res[e^(-x) ln(x) /(x-1) , x = 1] - pi i / (2) Res[e^(-x) /(x-1) (ln(x) + 2 pi i) , x = 1]

I = e^(-1) / (2) pi i

I know there is some error... so, what is the problem, I mean that how could I solve this problem?.. please help me~

 

[Hyperbolful]

What kind of contour are you using?

 

[qlsn4123]

I use the branch cut~, real positive axis.

I know that the integrant is kind of exponential integrals.

Actually I try to solve following integral.

I(V, H) = int(from 0 to infinity) { 1 / (k sinh kH - cosh kH) - 2 e^(-kH) / (k - 1) } * (k + 1) * cosh(kV) * e^(-kH) dk

ps. How could I use "Latex code" in this forums? It is not work.. $$\int [\tex]..<br /> <br /> thank you.$$