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U substitutuion help!

  1. Jan 29, 2009 #1
    I don't have a way of getting the equation to look nice but it's:

    integral of cos(pi/x^11) / x^12


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution

    I am having issues even finding what I could use as a U substitution. Any help would be great!
     
  2. jcsd
  3. Jan 29, 2009 #2
    Thing causing trouble is cos(pi/x^11) / x^12
     
  4. Jan 29, 2009 #3

    Dick

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    How about u=pi/x^11?
     
  5. Jan 29, 2009 #4
    problem with that is when you take the derivative, you don't have the dx int he problem.

    i'm almost certain the U has to equal x^12 as then du would then be 11x^11 and you can divide that by 11 and stick a 1/11 out front. I just don't know how to get du out of that stupid fraction. unless i'm going about it completely wrong and it's not a U substitution and it's a by parts question.
     
  6. Jan 29, 2009 #5

    Dick

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    If u=pi/x^11 then what do you think is du?
     
  7. Jan 29, 2009 #6
    (-11pi*x^10) / x^11

    if I used the quotient rule correctly
     
  8. Jan 29, 2009 #7

    Dick

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    You forgot to square the denominator.
     
  9. Jan 29, 2009 #8
    it looks like i did, i forgot the derivate of pi was zero, haha. dumb on my part.

    but that doesn't get me anywhere because no where in the original problem is the du. i have to get rid of that 1/x^12 somehow.
     
  10. Jan 29, 2009 #9

    Dick

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    Simplify (-11pi*x^10) / (x^11)^2.
     
  11. Jan 29, 2009 #10
    wow, can't believe i missed that. thanks for all your help, i'll post up my answer here in a couple minutes.
     
  12. Jan 29, 2009 #11
    -1/11pi * sin(pi/x^11) + C
     
  13. Jan 29, 2009 #12

    Dick

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    Looks ok to me.
     
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