Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the integral of lnx?

  1. Aug 13, 2003 #1

    MathematicalPhysicist

    User Avatar
    Gold Member

    what is the integral of lnx?
     
    Last edited by a moderator: Feb 5, 2013
  2. jcsd
  3. Aug 13, 2003 #2
    Try writing it as 1*ln(x), then integrate by parts. (Should get x*ln(x)-x).
     
  4. Aug 13, 2003 #3

    MathematicalPhysicist

    User Avatar
    Gold Member

    could you show me the entire way?
     
  5. Aug 13, 2003 #4
    Sure

    ∫1*ln(x)dx

    du/dx = 1
    v = ln(x)

    u = x
    dv/dx = 1/x

    Now, integrating by parts:

    ∫1*ln(x)dx = u*v - ∫u*dv/dx
    = x*ln(x) - ∫dx
    = x*ln(x) - x (+ C to be pedantic)
     
  6. Aug 13, 2003 #5

    MathematicalPhysicist

    User Avatar
    Gold Member

    i got it, thanks.

    edit: just one problem should this ∫u*dv/dx=∫1
     
    Last edited: Aug 13, 2003
  7. Aug 25, 2003 #6

    MathematicalPhysicist

    User Avatar
    Gold Member

    lonewolf i think i am wrong but i need your verification on that.
     
  8. Aug 25, 2003 #7

    MathematicalPhysicist

    User Avatar
    Gold Member

    never mind i found my mistake.
     
  9. Aug 25, 2003 #8
    Oops, sorry LQG, I wasn't ignoring you intentionally. Glad you figured it out anyway :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook