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

8308 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Evaluate f'(1) for the function f(x) = (x^2 + 2)^5


Find all the stationary points of the curve: y = (2/3)x^3 – (1/2)x^2 – 3x + 7/6 and determine their classifications.


Co-ordinate Geometry A-level: The equation of a circle is x^2+y^2+6x-2y-10=0, find the centre and radius of the circle, the co-ordinates of point(s) where y=2x-3 meets the circle and hence state what we can deduce about the relationship between them.


how do you differentiate y=x^2 from first principles?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences