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

3475 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the gradient of the tangent and the normal to the curve f(x)= 4x^3 - 7x - 10 at the point (2, 8)


A curve has equation y = x^3 - 3x^2 -24x + 5, find the x co-ordinates of the two stationary points of the curve and hence determine whether they are maximum or minimum points.


For rectangles of area 100 m^2 what is the perimeter of the rectangle with the smallest perimeter?


Find the equation of the tangent to the unit circle when x=sqrt(3)/2 (in the first quadrant)


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