Find the integral of log|x| by integration by parts

The question says to use integration by parts on this question, but at the minute we only have one variable.

Therefore, we introduce a 1, so that log|x|= 1*log|x|, here we have not altered the value of the function, but have intoduced a variable so that integration by parts can be used.

The derivative of Log|x| is simply 1/x, so it will be the 1 that we will integrate, which is x.

We then sub these into the by parts formula of uv-∫u'v

This is therefore equal to xlog|x|-∫x/x.dx

=xlog|x|-∫1dx

=xlog|x|-x.

LP
Answered by Laura P. Maths tutor

5190 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

dx/dt = -5x/2, t>=0. Given that x=60 when t=0, solve the differential equation, giving x in terms of t.


Find the tangent to the curve y = x^3 - 2x at the point (2, 4). Give your answer in the form ax + by + c = 0, where a, b and c are integers.


Explain the chain rule of differentiation


Find dy/dx when y = (3x-1)^10


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:

© 2025 by IXL Learning