How to integrate lnx by parts?

Integration by parts formula: ∫ udv/dx = uv - ∫ du/dxv dx

To solve this problem we need to use a trick by thinking of lnx as lnx1
So we can choose: u=lnx, dv/dx=1
The next step is to find du/dx and v.
du/dx=1/x                                          As we have differentiated each side with respect to x
v=x                                                         By integrating each side with respect to x
Now we have all the required parts to use the integration by parts formula.
∫ lnx = lnxx – ∫ 1/x*x dx
                       = xlnx – ∫ 1 dx
                       = xlnx – x + c