How do you integrate ln(x)?

Use the method of integration by parts. uv-integral(v.du/dx). Make u equal to ln(x) and dv/dx equal to 1. Therefore v=x and du/dx=1/x. Hence uv=xln(x). And v.du/dx=x/x=1. Substituting these into the 'by parts' formula gives xln(x)-integral(1 dx)= xln(x)-x+C (where C is the constant of integration)