Elementary Integration of Superelliptic Integrals

Thierry Combot

Consider a superelliptic integral $I=\int P/(Q{S}^{1/k})dx$ with $\mathbb{K}=\mathbb{Q}(\xi )$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in \mathbb{K}[x]$ and $S$ has simple roots a…