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I have 

f[x_] := g[x]/g'[x] 
FullSimplify[Integrate[f[x], x]]

I'm trying to get F[x] in terms of g[x], but evaluating the above gives the random expression below as output 

1/4 (x^2 + 2 Log[x])

How would I get F[x] based on g[x] to be returned?

Improve this question
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  • $\begingroup$ What's the definition of g? $\endgroup$
    – John Doty
    Commented Aug 18, 2019 at 18:50
  • $\begingroup$ @JohnDoty Nothing, that's all I have input. I'm trying to make it generic so I didn't make g(x) anything I just want it to base it in terms of g(x). That's why I have no idea where it's getting the output from. $\endgroup$
    – Nick Arnold
    Commented Aug 18, 2019 at 19:16
  • $\begingroup$ It's possible you defined one of those functions earlier and forgot. To clear any such definitions, try quitting the kernel and re-evaluating that cell. You should get $\int \frac{g(x)}{g'(x)} \, dx$ (that's what I get). $\endgroup$
    – theorist
    Commented Aug 18, 2019 at 19:54
  • $\begingroup$ Is it possible that you are looking for Integrate[g'[x]/g[x], x] (*Log[g[x]]*)? $\endgroup$
    – Ulrich Neumann
    Commented Aug 18, 2019 at 19:58
  • 3
    $\begingroup$ The integral has no closed-form solution. $\endgroup$
    – AccidentalFourierTransform
    Commented Aug 18, 2019 at 20:42

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