Can any one suggest a solution or method for solving this integration with respect to x

Regards

James

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- Jun 2nd 2010, 05:02 AMJames4321Difficult integral.
Can any one suggest a solution or method for solving this integration with respect to x

Regards

James - Jun 2nd 2010, 05:28 AMCaptainBlack
Not elegant, but WolframAlpha gives:

integrate 1/(a-b cos(k x))^4 - Wolfram|Alpha

CB - Jun 2nd 2010, 09:21 AMJames4321
- Jun 2nd 2010, 10:18 PMsimplependulum
I'd like to make this more general , let the power to be

To handle such 'troublesome' integral , first thing to do is to reduce it to a simplier form :

Let the integral becomes

it looks better now and we wish to obtain a reduction formula .

Let

Use integration by parts ,

Thus

If , the reduction only consists of two variables but in general , it consists of three variables : , that means we have to find . By substituting we obtain :

I give you the case for , in the above expression , we asumme .

Sub.

If you know the sign of , you should be able to continue ... - Jun 3rd 2010, 01:05 AMJames4321
Thank you very much for this brilliant suggestion!

- Jun 3rd 2010, 03:20 AMHallsofIvy
- Jun 3rd 2010, 04:13 AMJames4321
Sorry about this! I would also like to thank Simplependulum for his elegant and complete solution.

James4321