integrate with respect to x the function f(x)= xln(x)

Use integration by parts

let u=ln(x)

let dv/dx=x

therefore du/dx=1/x and v=(1/2)x^2

therefore the integral of xln(x) is equal to the following:

(1/2)x^2ln(x) - (integral with respect to x of:((1/2)x^2)/x)

= (1/2)x^2ln(x) - (integral with respect to x of:((1/2)x))

=(1/4)x^2(2ln(x)-1) + c

(I will explain further how I reached this answer during the session with provision of the whiteboard to evaluate my integrals) 

Answered by Priya J. Maths tutor

2634 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equation y^3+2xy+x^2-5=0. Find dy/dx.


If given two parametric equations for a curve, how would you work out an equation for the gradient?


Find the derivative of f where f(x)=a^x.


You are given the equation of the line y=x^3+x^2-2x. Find the stationary points of the curve and determine the maximum and minimum points and find where it crosses the x-axis and thus sketch the graph


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