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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???
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    $\begingroup$ If $p$ is not a function of $s$ then this is just $\ln(p)\times \int f(s)\,ds$. $\endgroup$
    – lulu
    Apr 14 '18 at 17:49
  • $\begingroup$ ah, of course. How about when $p=g(s)$ then. Can someone think of a way to do this $\endgroup$
    – frencho
    Apr 14 '18 at 19:25
  • $\begingroup$ It's too broad. All you get is $\int f(x)\ln p(s)\, ds$. But that's not any better than a general product of functions. $\endgroup$
    – lulu
    Apr 14 '18 at 19:34

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