Complex integral

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complex integral....

let be the integral [tex]\int_{-i\infty}^{i\infty}\frac{1}{exp(s)-1}ds [/tex] then their poles are [tex] 2n\pi [/tex] my question is How would we calculate this integral? i think that the contribution from the poles is [tex] -{\pi}Res(z_0) [/tex] the main problem i find is when i make the change of variables s=iu so we have the improper integral [tex]\int_{-\infty}^{\infty}\frac{1}{exp(iu)-1}ds [/tex] but it has singularities at 2npi so i don,t think if the first integral will be convergent or not...could someone help?..thanks
 

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fresh_42
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You have to find an integration path around the poles.
 
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This looks divergent.

##\int_{-\infty}^\infty \frac{1}{e^{ix}-1}dx = -x-i\cdot log \left( 1- e^{ix}\right)\bigg|_{-\infty} ^\infty##
 

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