How to analytically compute $\iiint \frac{1}{\sqrt{a+b \sin c}}\,da\,db\,dc$

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I'm wondering whether the following integral can be analytically computed:

$$\iiint\frac{1}{\sqrt{a+b \sin c}}\,da\,db\,dc$$

(Octave didn't yield any closed form associated with that.)

Edit: $c$ may vary between $0$ to $2\pi$ (unit circle), but $a$ and $b$ may vary in $R^{\ge 0}$.