How do I integrate ln(x)

This is an integral many people struggle with, but, with a simple trick it becomes a little more straight forward. We will approach this integral using integration by parts.

But what are the parts?

Well, we can write ln(x) as 1ln(x).

We choose u=ln(x) and dv=1, so du=1/x and v=x

So the integral ln(x) becomes:

 xln(x) – integral(x/x)

Which is:

 x*ln(x)- x + c

Which is our final answer.

TM
Answered by Tom M. Maths tutor

4573 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How to integrate and differentiate ((3/x^2)+4x^5+3)


Express asin(x) + bcos(x) in the form Rsin(x+c), where c is a non-zero constant.


Let z=x+yi such that 16=5z - 3z*, What is z?


Differentiate y=sin(x)/5x^3 with respect to 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