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How to integrate lnx by parts?

Integration by parts formula: ∫ u*dv/dx = uv - ∫ du/dx*v dx

To solve this problem we need to use a trick by thinking of lnx as lnx*1
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 = lnx*x – ∫ 1/x*x dx
                       = xlnx – ∫ 1 dx
                       = xlnx – x + c

Ryan J. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

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