Closed form for $\int \frac{1}{x^7 -1} dx$? I want to calculate:
$$\int \frac{1}{x^7 -1} dx$$
Since $\displaystyle \frac{1}{x^7 -1}  = - \sum_{i=0}^\infty x^{7i} $, we have $\displaystyle(-x)\sum_{i=0}^\infty \frac{x^{7i}}{7i +1} $. 
Is there another solution? That is, can this integral be written in terms of elementary functions?

Let u=x^2 and solve using u substitution.
=> 1/6 ln((x^6-1)/x^6)
