Use integration by parts to find the integral of ln x by taking ln x as the multiple of 1 and ln x

For integration by parts, the integral is uv - ∫ u' v dx. First we take u = ln x and v' = 1. While we could have u and v' be the opposite at this stage, it becomes apparent later on that we can't do this because we would still need to integrate ln x. Differentiating u gives u' = 1/x (this is a derivative that has to just be learnt) and integrating v' gives v = x. Therefore the integral is x ln x - ∫ x(1/x) dx = x ln x - ∫ dx. So the integral of ln x is x ln x - x.

JC
Answered by Jack C. Maths tutor

4521 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the derivative of x^x


Differentiate y=(3+sin(2x))/(2+cos(2x))


Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))


(i) Prove sin(θ)/cos(θ) + cos(θ)/sin(θ) = 2cosec(2θ) , (ii) draw draph of y = 2cosec(2θ) for 0<θ< 360°, (iii) solve to 1 d.p. : sin(θ)/cos(θ) + cos(θ)/sin(θ) = 3.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences