integrate by parts ln(x)/x^3

The question states to use integration by parts. So first we recall the integration by parts formula is integrate(u(x)v'(x)  dx)=     (v(x)u(x))    -    integrate(u'(x)v(x)   dx)+c (note these integrals are with respect to x.. u(x) v(x) are functions of x and u'(x)=du/dx). To integrate ln(x)/x^3 notice that ln(x)/x^3 can be written as ln(x)*1/x^3. Then we let u(x)=ln(x) as we can differentiate ln(x) to 1/x but cannot easily integrate ln(x). So v(x)=1/x^3 Putting this into the formula we get integrate(ln(x)/x^3  dx)=  -0.5x^(-2) *ln(x)-integrate(-0.5x^(-2)*x^(-1)  dx)+c=  -0.5ln(x)/x^2+1/(4x^2)+c

Answered by Prit S. Maths tutor

3153 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Consider f(x)=a/(x-1)^2-1. For which a>1 is the triangle formed by (0,0) and the intersections of f(x) with the positive x- and y-axis isosceles?


A ball is released from rest at a height of 4m. At what speed does it hit the ground?


Prove by contradiction that there is an infinite number of prime numbers.


Differentiate y = 3x4-8x3-3


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