Finding Residue of z/(1+z^n) for Homework

Thread starter Dassinia
Start date Mar 17, 2014
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Residue

Mar 17, 2014

Dassinia

Hello,
I can't find the result to

Homework Statement

Have to prove that ∫x/(1+x^n) dx = π/n/sin(2π/n)
so I'm trying to prove that by starting to find :
2πi*res(z/(1+z^n), exp(iπ/n))

but don't know what is res(z/(1+z^n), exp(iπ/n))

Thanks

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Mar 17, 2014

vela

Staff Emeritus

Science Advisor

Homework Helper

Try considering the cases where n=1, 2, and 3 and look for a pattern.

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