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**Pranas** Hi.

So I am asked to analyze

$\displaystyle \displaystyle \[\int\limits_0^{2\pi } {\frac{{dx}}{{1 + \varepsilon \cdot \cos x}}} \]$

However I believe substitution $\displaystyle \displaystyle \[u = \tan \frac{x}{2}\]$ might be very wrong in this situation because of discontinuity.

Also I guess this may diverge when $\displaystyle \displaystyle \[\left| \varepsilon \right| \geqslant 1\]$

Unfortunately at this very moment I am not aware of a nice proper solution, maybe you have an idea?