`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`

`=uv-intv\ du`

`=x\ ln\ x-intx(dx)/x`

`=x\ ln\ x-intdx`

`=x\ ln\ x-x+K`