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How to integrate 1/(1-A*cosx)^3?

  1. Apr 27, 2015 #1
    Hello every body.
    I'm searching for a solution to integrate the function below but i couldn't find anything suitable yet.I don't know even how to start it !

    can any body help me finding the integral?

    Thanks you ...
  2. jcsd
  3. Apr 27, 2015 #2


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    Simplify the denominator with a substitution. Try the obvious substitution.
  4. Apr 27, 2015 #3
  5. Apr 27, 2015 #4


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    Ok. Judging from Emmanuel_Euler's Mathematica solution, evaluating the integral you wrote out above is certainly not a freshman exercise. Are you sure that you have copied out your integral correctly? Or is this something that arose in more advanced work?
  6. Apr 27, 2015 #5


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    Is this homework? If so, then see https://www.physicsforums.com/help/homeworkhelp/ .

    One way to approach this would be to express the cosine using complex exponentials, then use the obvious substitution to get the integral into the form [itex]\int du/P(u)[/itex], where P is a polynomial. This might then be doable using partial fractions.
  7. Apr 28, 2015 #6
    yes,i copied correctly. why??
  8. Apr 28, 2015 #7
    I believe the question was intended for the OP.
  9. Apr 29, 2015 #8
    Thanks you every body ,
    But yet i couldn't find the right way , and the integral i wrote is correct.
    wolframalpha also doesn't show step by step guide.
  10. Apr 29, 2015 #9
    It does usually, but with this one it seems to take forever to load.
    Anyway, you saw the answer, are you comfortable with that sort of an answer ?
    [EDIT:- Ah, I see what you mean, after loading it said the solution was not avaliable, this can happen sometimes with hard integrals like the one you provided.]
    Last edited: Apr 29, 2015
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