MHB Indefinite Integral: $\int \frac{1}{\sqrt{\sin 2x}}dx$

[juantheron]

$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$

 

[CaptainBlack]

$\displaystyle \int \frac{1}{\sqrt{\sin 2x}}dx$

How are you expecting this to be expressed? It is not elementary, but is an elliptic integral of the first kind.

CB