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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?.. plz help me~

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?.. plz help me~

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