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

9149 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find integers A and B, such that (5x +4)/((2-x)(1+3x)) = A/(2-x) + B/(1+3x)


If f(x)= ( ((x^2) +4)(x-3))/2x find f'(x)


Solve for x, 5sin(x) - 3cos(x) = 2 , in the interval 0<x<2pi


express (3x + 5)/(x^2 + 2x - 15) - 2/(x - 3) as a single fraction its simplest form


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:

© 2026 by IXL Learning