1. Not finding help here? Sign up for a free 30min 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!

Integral of cos and ln

  1. Apr 8, 2007 #1
    Please, how can I solve this?

    ∫ cos x ln x dx

    I get this:

    ln x sin x - ∫sin x/x dx

    but how do I continue from here?

    Thanks in advance...
  2. jcsd
  3. Apr 8, 2007 #2
    The antiderivative of sin(x)/x isn't expressible in terms of elementary functions so perhaps it would be better to change the role of u and dv in your integration by parts.

    Edit: At least, I think that's the case. Couldn't hurt to try anyway.
  4. Apr 8, 2007 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    That won't change anything -- one cannot be expressed in terms of elementary functions iff the other cannot be expressed as well.
  5. Apr 8, 2007 #4
    look at it as an equation, and you need to integrate by parts at least twice
  6. Apr 9, 2007 #5


    User Avatar

    No, this won't help. Even Wolfram gives an answer with Si(x) in it - the integral of Sinx/x.
  7. Apr 9, 2007 #6
    So, can't sinx/x be integrated?
  8. Apr 9, 2007 #7


    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, of course it can- its integral is Si(x)! It cannot, however, be integrated in terms of elementary functions.
  9. Apr 9, 2007 #8
    It seems difficult to continue from ln x sin x - ∫sin x/x dx ...

    Thanks to averyone who posted. I'll tell you if something different appears.

    Thanks again.
  10. Apr 9, 2007 #9
    It is impossible to continue without introducing "special" functions or series expansions (from which you won't be able to obtain closed forms). So, play with it for a while, but don't spend too much time on it :smile:.
  11. Apr 10, 2007 #10

    Gib Z

    User Avatar
    Homework Helper

    If you really don't want Si(x), heres your only alternative:

    [tex]\frac{\sin x}{x} = \sum_{n=0}^{\infty} \frac{x^{2n}}{(2n+1)!}[/tex].

    Integrate that, and there you go.
  12. Apr 10, 2007 #11
    And don't forget this one:
    [tex] \frac{sin(x)}{x} = sinc(x)[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral of cos and ln
  1. Integration (ln) (Replies: 3)

  2. Integrate ln (Replies: 5)

  3. Integral of ln (Replies: 14)

  4. Deriving cos(x)^ln(x)? (Replies: 7)