Consider it as 1*ln(x) and use parts.
If you don't feel like doing it, you can always use:
It gives the answer:
-x + x \ln x
Is [x] greatest integer function??
Hmm, didn't consider that. I'm not sure there'd be a closed form expression for [itex]\int ln[x] dx [/itex]
where [itex][x][/itex] is the next greatest integer function. It'd be easy enough to get a numerical answer if the interval was specified though.
You could break the integral into a summation. [x] is constant between intervals of integers, so you end up with a sum of trivial integrals.
I think this is what Lonewolf is proposing (please excuse my ignorance!)
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