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

14087 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y = (sin(x))^2 (find dy/dx)


What is the equation of the tangent at the point (2,1) of the curve with equation x^2 + 3x + 4.


A curve C has equation y = x^2 − 2x − 24x^(1/2) x > 0 find dy/dx


Show that the curve with equation y=x^2-6x+9 and the line with equation y=-x do not intersect.


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