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

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    Integral Integrate
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Discussion Overview

The discussion revolves around the integration of the function f(x) = 1/(1 - A*cos(x))^3. Participants explore various methods and approaches to tackle this integral, which appears to be complex and potentially beyond introductory levels of calculus.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in starting the integration process and seeks help.
  • Another suggests simplifying the denominator with a substitution, implying a potential method to approach the integral.
  • A link to a solution from Wolfram Alpha is provided, but the poster admits to not understanding the solution.
  • Concerns are raised about the complexity of the integral, with one participant questioning whether it is appropriate for a freshman level.
  • A suggestion is made to use complex exponentials to express cosine, which might lead to a more manageable form of the integral.
  • Participants discuss the availability of step-by-step solutions on Wolfram Alpha, noting that it sometimes fails to provide detailed guidance for difficult integrals.

Areas of Agreement / Disagreement

There is no consensus on the best method to solve the integral, and participants express varying levels of understanding and comfort with the approaches suggested. The discussion remains unresolved regarding the most effective strategy for integration.

Contextual Notes

Participants note the integral's complexity and question its suitability for beginners. There are references to potential methods that may require advanced techniques, but no specific assumptions or limitations are fully explored.

Arash.
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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 anybody help me finding the integral?
f(x)=1/(1-A*cosx)^3

Thanks you ...
 
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Simplify the denominator with a substitution. Try the obvious substitution.
 
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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?
 
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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.
 
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MarcusAgrippa said:
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?
yes,i copied correctly. why??
 
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Emmanuel_Euler said:
yes,i copied correctly. why??
I believe the question was intended for the OP.
 
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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.
 
Arash. said:
wolframalpha also doesn't show step by step guide.
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.]
 
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