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

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1. Apr 27, 2015

### Arash.

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?
f(x)=1/(1-A*cosx)^3

Thanks you ...

2. Apr 27, 2015

### MarcusAgrippa

Simplify the denominator with a substitution. Try the obvious substitution.

3. Apr 27, 2015

### Emmanuel_Euler

4. Apr 27, 2015

### MarcusAgrippa

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?

5. Apr 27, 2015

### bcrowell

Staff Emeritus
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 $\int du/P(u)$, where P is a polynomial. This might then be doable using partial fractions.

6. Apr 28, 2015

### Emmanuel_Euler

yes,i copied correctly. why??

7. Apr 28, 2015

### certainly

I believe the question was intended for the OP.

8. Apr 29, 2015

### Arash.

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.

9. Apr 29, 2015

### certainly

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