`int ln\ x\ dx`
Our priorities list above tells us to choose the logarithm expression for `u`. (of course, there's no other choice here. :-)
So with `u=ln\ x`, we have `du=dx/x`.
Then `dv` will simply be `dv=dx` and integrating this gives `v=x`.
Subsituting these into the Integration by Parts formula gives:
`int ln\ x\ dx=int u\ dv`
`=x\ ln\ x-intx(dx)/x`
`=x\ ln\ x-intdx`
`=x\ ln\ x-x+K`