Stuck with this, dunno what to do $\int\ln\left(p^{f(s)}\right)\,ds$

Question

For up upcoming paper of mine: I need to pick some brains about rewriting $$\int\ln\left(p^{f(s)}\right)ds$$ where $f(s)$ is some polynomial in $s$. Twist: I do not know much about $p$. I can provide some more information if needed. Question: How would you solve/rewrite this integral

1. if $p$ is NOT a function of $s$
2. how about if $p$ is some function of $s$ instead???