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

8441 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the difference between quotient rule, product rule and chain rule, and when to use them in differentiation?


Edexcel C3 June 2015 Q1: tan(x)=p, where p is a constant. Using standard trigonometric identities, find the following in terms of p. a) tan(2x). b) cos(x). c) cot(x-45).


How would I sketch the graph sin(x) + sin(2x - π/2) in my exam?


(C3 question). Find an expression for all stationary points on the curve y=sin(x)cos(x). How many such points are there and why?


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