I have solved the problem of integration $$\int_0^\infty \frac{1}{x^n+1}dz$$
using the contour as an arc of a circle. But I don't know how to approach this problem: $$I=\int_0^\infty\frac{1}{x^{n-1}+x^{n-2}+\cdots +x+1}dz$$ Please Help me with this problem
Edit:
With the help of geometric series (suggested in comment), I can reduce the integral to the evaluation of $$\int_0^\infty\frac{1-x}{1-x^n}dx$$
Now it's $1-x$ that's causing the problem if I choose the contour to be arc with angle $2\pi /n$. I still need little help.