Integrate ln(x) with respect to x.

Here we can use integration by parts. Notice that ln(x) can be written as ln(x)1, so we can integrate 1 and differentiate ln(x).
Then using the formula int(uv') dx = uv - int(u'v) dx, we find that the integral of ln(x) is xln(x) - int(1/x * x) dx = xln(x) - int(1) dx = xln(x) - x + c, where c is a constant of integration.