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

[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

 

[vela]

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