How to integrate ln(x)?

You need to use a clever trick for this! Write ln(x) as 1ln(x), and use integration by parts:u=ln(x) v'=1u'=1/x v=xThen applying the formula we obtain∫ln(x)dx = xln(x) - ∫[(1/x)x] dx = = xln(x) - ∫1 dx = = xln(x) - x + C = x(ln(x) - 1) + CAnd if we have some data we can work out the constant of integration C.

KW
Answered by Krzysztof W. Further Mathematics tutor

2362 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

For f(x) = (3x+4)^(-2), find f'(x) and f''(x) and hence write down the Maclaurin series up to and including the term in x^2.


Find the volume of revolution formed by rotating the curve y = sinx 2pie around the x- axis


How to calculate the integral of sec(x)?


How do you find the square roots of a complex number?


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