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

DF
Answered by Daniel F. Maths tutor

14183 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I draw and sketch an equation?


A curve has parametric equations x=t(t-1), y=4t/(1-t). The point S on the curve has parameter t=-1. Show that the tangent to the curve at S has equation x+3y+4=0.


Let y be a function of x such that y=x^3 + (3/2)x^2-6x and y = f(x) . Find the coordinates of the stationary points .


How do you know if a function is odd or even?


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