For $m,n \in \Bbb N$, find the antiderivative of $g:(0,1)\rightarrow\mathbb{R}$ defined by: $$g(x)=\frac{1}{(1-x^m)^n}$$
Mathematica gives a result with functions we didn't learn about yet. The question is correct, and it's over my head. Some ideas might help me find a possible alternative.
The reason Mathematica gives a result with Hypergeometric Functions is that you probably didn't specify $m,n$ had to be natural numbers. That being said, it would appear your integral can be written in the form (when $m$ is even):
$$\sum_{i=1}^{n-1} \frac{\alpha_i x}{(x^m - 1)^i} +\beta \log\left( \frac{x+1}{x-1}\right) + \gamma \tan^{-1} x $$ This can be achieved by expanding the denominator and writing it out as a sum of partial fractions.
