How do you integrate ln(x) with respect to x?

This integral must be done using integration by parts. Therefore, we set u=ln(x) and dv=dx, which gives du=1/x and v=x.
Then, using the integration by parts formula the integral now equals x*ln(x)-int[dx]. This is then easily solved to give x[ln(x)-1], and we can't forget the constant of integration so to the end of this we add "+ c", giving a final answer of x[ln(x)-1] + c.