Hi...would appreciate any suggestions re the following integral which has appeared in a celestial-mechanics calculation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]I = \int_0^{2\pi } {\frac{1}{{(1 + e\cos \theta )^3}}d\theta } [/tex]

where [tex]0 < e < 1[/tex].

Integration by parts seems a sensible approach but for some reason I can't get sensible results. I presume I'm making some idiotic mistake that I'm just not picking up when I check my calculations (frustrating as hell!). I'm pretty sure there is supposed to be a fairly neat result but MATLAB and Mathematica aren't giving me anything.

Any ideas? Thanks in advance.

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# Annoying trig integral

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