How do I integrate ln(x), using integration by parts?

This is a common question among A-Level Maths students, as integration by parts requires 2 things: 1. Something to integrate ; 2. Something to differentiate. In ln(x), we can immediately see that ln(x) is the 'something' that we differentiate. But what about the 'something' to integrate? Here, we have to put our creative mathematical hats on, and imagine a constant '1' behind the ln(x), so imagine it written as 1 x ln(X). Aha! Now we have the 'something' to integrate, which is the constant '1'. After clarifying this issue, the rest of the solution just requires the implementation of the integration by parts technique, which I'll happily demonstrate in the live session!

MK
Answered by Mustafa K. Maths tutor

3825 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C


Q4 on 2017 Edexcel C4 paper, concerns differentiation of multiple variables.


Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.


Integrate 1/(1 - 3*x) with respect to x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning