Complete the indefinite integral : ∫x lnx dx

Use the formula: ∫uv' dx = uv - ∫u'v dx (use I = the integral we're looking for)Note we cant integrate ln x easily but we can differentiate into 1/x so we use:u = ln x and v' = x we have u' = 1/x and v = x2/2 subbing these values into the above formula we get:I = x2/2 lnx - ∫1/x x2/2 dx = x2/2 lnx - ∫x/2 dx= x2/2 lnx - x2/4 + C

Answered by Katy D. Maths tutor

5613 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve: x^2-7x+6=0


Find the max/min value of the function: f(x) = 5x^2 - 20x + 15


Find the stationary points of the curve f(x) =x^3 - 6x^2 + 9x + 1


The curve C has equation: 2x^2y + 2x + 4y – cos (piy) = 17. Use implicit differentiation to find dy/dx in terms of x and y.


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