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 = lnx
x – ∫ 1/x*x dx
                       = xlnx – ∫ 1 dx
                       = xlnx – x + c

RJ
Answered by Ryan J. Maths tutor

8864 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates of the points where this line intersects the axes


Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms


Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))


How do I do definite integrals?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning