In this Artin-Schreier extension of $k(x)$, when is the differential $x^iy^jdx$ holomorphic at the point ramified over infinity?

Question

Assume that $k$ is algebraically closed of characteristic $p$. Let $E/k(x)$ be defined by the equation $y^p-y=f(x)$ where $f\in k[x]$. For what non-negative values of $i,j$ is the differential $x^iy^jdx$ holomorphic at the point ramified over infinity? I tried converting this differential to the form (something) $du$ where $u$ is the uniformizer at the place ramified over infinity, but I could not get a way to write it out explicitly.