How do I intregrate ln(x)?

To integrate ln(x) we will have to use integration by parts. 

The equation for integration by parts is: (then equation written on the whiteboard).

In the case of ln(x), let v=ln(x) and let du/dx=1.Then dv/dx=1/x and u=x.

Putting these values into the equation for integration by parts, integrating ln(x) gives (better with a whiteboard)  xln(x) - the integral of x/x = xln(x) - integral of 1 = xln(x) - x + c (don't forget the +c !!)

Hence the integral of ln(x) = xln(x) - x + c