TITLE: How to integrate $\int 1/(x^7 -x) dx$?
QUESTION [6 upvotes]: How should I proceed about this integral? 
$$\int {1/(x^7 -x)} dx$$
I've tried integration by parts or substitution but I can't seem to solve it. Can I have some hints on how should I get started?
These are some of the things I've tried:
IBP: $u = \frac {1}{x^6-1}$, $du = \frac {-5x^6}{x^6-1}$, $dv = \frac 1x dx$, $v = \ln|x|$
Tried substitution method, but not successful.

REPLY [3 votes]: Alternatively the fastest method is to simply observe the following 
$$\int \frac{1}{x^7-x}dx  = \int \frac{1}{x^7(1-x^{-6})}dx = \int \frac{x^{-7}}{1-x^{-6}}dx = \frac{1}{6}ln(1-x^{-6})$$