Not elegant, but WolframAlpha gives:
integrate 1/(a-b cos(k x))^4 - Wolfram|Alpha
CB
Not elegant, but WolframAlpha gives:
integrate 1/(a-b cos(k x))^4 - Wolfram|Alpha
CB
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 ...