1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integral of a Natural Log

  1. Feb 5, 2004 #1

    It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate.

    double integral 1/(x+y) dA


    R = [1,2] X [0,1]

    So what I did first was integrate with respect to y first. I ended up with


    with an upper limit of 1 and a lower limit of 0. Once simplified I get

    ln(x+1) - ln x or ln( (x+1)/x )

    Now I have to integrate with respect to x. But I can't remember how to take the integral of a natural log function. How do I proceed from here?

    I can't remember if I can do the following:

    Let G(x) = integral of ln( (x+1)/x ) dx


    e^G(x) = integral of e^ln( (x+1)/x ) dx

    which would simplify to

    integral of (x+1)/x dx.

    After I get a solution to the above equation I would then take the log of

    ln e^G(x) = ln (answer)

    to get

    G(x) = ln (answer).

    Can I do that? I can't remember. If not, how do I proceed from here?

    Any help is appreciated. Thankyou.
  2. jcsd
  3. Feb 5, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    You can't move the exponential into the integral like that.

    That said, IIRC:

    [tex]\int ln(x) dx= x ln(x)-x[/tex]
    (You can derive this by using parts)
  4. Feb 5, 2004 #3

    I should have known I could have done it by parts. I see that now. Thanks NateTG.
  5. Feb 6, 2004 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    And it's a lot easier to integrate [itex]\ln(x+1) - \ln x[/itex] than it is to integrate [itex]\ln (x+1)/x[/itex]. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook