How do I integrate log(x) or ln(x)?

The integral of log(x) is not necessarily straight-forward. Though we can use the fact that d/dx(log(x)) = 1/x to help us.

Rather than simply trying to integrate log(x), we can use integration by parts on 1 x log(x) (as in 'one times' log(x)).

So we can differentiate the log(x) part and integrate the 1 part to give:

xlog(x) - ∫ 1 dx = xlog(x) - x

Note: if the middle step isn't clear, we can write it more explicitly as

u = log(x)  v' = 1

u' = 1/x     v = x

Where the rule for integration by parts is written as:

uv' = uv - ∫ u'v    ,  where u and v are functions of x

Answered by Daniel F. Maths tutor

14154 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

When is an arrangement a combination, and when a permutation?


Find the derivative of x^x


A curve has equations: x=2sin(t) and y=1-cos(2t). Find dy/dx at the point where t=pi/6


What is a stationary point and how do I find where they occur and distinguish between them?


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