<s>[INST] Evaluating $\int \frac{1}{x^{7} - x} ~ d{x} $. How do I evaluate the following indefinite integral?
$$
\int \frac{1}{x^{7} - x} ~ d{x}.
$$
Could someone give me some advice as to what method I should use or the steps that I should take?

Note: The OP originally requested for help in evaluating $ \displaystyle \int \left( \frac{1}{x^{7}} - x \right) ~ d{x} $, which may not have been his/her actual intention.
 [/INST] $\displaystyle \int\frac{1}{x^7-x}dx = \int\frac{1}{x^7.\left(1-\frac{1}{x^6}\right)}dx$
Put $\displaystyle \left(1-\frac{1}{x^6}\right) = t$ and $\displaystyle \frac{6}{x^7}dx = dt$
$\displaystyle = \frac{1}{6}\int\frac{1}{t}dt = \frac{1}{6}\ln \mid t \mid+C$
$\displaystyle = \frac{1}{6}\ln \left|\frac{x^6-1}{x^6}\right|+C$
</s>