I'm trying to integrate this here fella:
$\int_0^{2\pi} \frac{d\theta}{1+\cos^2\theta}$
from examples in Ablowitz I know that for $|A|^2>|B|^2$ and $A>0$, $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$ has solution $\frac{2*\pi}{\sqrt{A^2+B^2}}$
Since that is the only similar example I can find, the only approach would be to substitute A and B accordingly, but in my case I cannot substitute A=1 and B=$cos\theta$ since for $\theta=0$ or $\theta=2\pi*n$, A=B so the inequality $|A|>|B|$ is not strict.
Does this mean that the integral diverges? An answer here claims so: How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$? But I wanted to see if anyone has any other approaches to this problem.
Many thanks