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Help with this integration!

  1. Sep 2, 2009 #1
    1. The problem statement, all variables and given/known data
    integral of cos(x)/(x^4)


    2. Relevant equations



    3. The attempt at a solution

    tried using integration by parts but lead to tons of work!. is there a simpler way?
     
  2. jcsd
  3. Sep 2, 2009 #2

    rock.freak667

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    Homework Helper

    Don't think there is a simpler way. u=cos(x); dv=1/x4 dx.
     
  4. Sep 2, 2009 #3
    You won't be able to find an integral in elementary functions, so I suggest you don't bother with it, unless you wrote the problem incorrectly.
     
  5. Sep 2, 2009 #4
    Cauchy Integral formula helps right? unless you are talking about Integral in complex plane.
     
  6. Sep 3, 2009 #5

    zcd

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    If it's an indefinite integral you could rewrite it as a taylor series.
     
  7. Sep 3, 2009 #6

    Hootenanny

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    Staff Emeritus
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    Gold Member

    As Bohrok suggests, the integral has no anti-derivative in terms of elementary functions. However, if it is a definite integral, it may be possible to write a solution in terms of non-elementary functions.
     
  8. Sep 3, 2009 #7
    Integrate by parts 3 times, then recognize the "sine integral" function
    [tex]-\frac{1}{3}\,{\frac {\cos \left( x \right) }{{x}^{3}}}+\frac{1}{6}\,{\frac {\sin
    \left( x \right) }{{x}^{2}}}+\frac{1}{6}\,{\frac {\cos \left( x \right) }{x}}
    +\frac{1}{6}\,{\rm Si} \left( x \right)
    [/tex]
     
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