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

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SUMMARY

The discussion focuses on proving the integral ∫x/(1+x^n) dx = π/n/sin(2π/n) by calculating the residue of the function z/(1+z^n) at the point exp(iπ/n). The user seeks assistance in determining the residue, specifically res(z/(1+z^n), exp(iπ/n)). The conversation suggests examining specific cases for n=1, 2, and 3 to identify a pattern that aids in the proof.

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

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