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

Answered by Ryan J. Maths tutor

8231 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Question 3 on the OCR MEI C1 June 2015 paper. Evaluate the following. (i) 200^0 (ii) (9/25)^(-1/2)


Integrate 1/u(u-1)^2 between 4 and 2


Differentiation basics: What is it?


How do you take the derivative of a^x ?


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