How do you integrate ln(x) with respect to x?

Rewrite ln(x) as 1ln(x) then integrate by parts.  The formula for integration by parts is  uv' = uv -  vu', here use u = ln(x) and v' = 1.  By differentiating u we get u' = 1/x, and by integrating v' we get v = x.  Putting these numbers into this formula gives  1ln(x) = xln(x) -  x/x dx = xln(x) -  1 dx.  The integral of 1 is x, so the final answer is x*ln(x) - x + c, for a constant c.

AG
Answered by Anthony G. Maths tutor

2829 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Simplify: 4log2 (3) + 2log2(5)


Given that y = 16x + x^(-1), find the two values of x for which dy/dx = 0


Find, using calculus, the x coordinate of the turning point of the curve with equation y=e^3x cos 4


Solve for x, between 0 and 360 degrees, 4cos2 (x) + 7sin (x) – 2 = 0


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