The correct integral of $\int \dfrac{\sin x}{\sqrt{1+\cos x}} d x$ (assuming integral constant as $c$ ) is $\_\_\_\_$ .
- $-2 \sqrt{2} \sin \dfrac{x}{2}+c$
- $-2 \sqrt{2} \cos \dfrac{x}{2}+c$
- $-\dfrac{1}{\sqrt{2}} \cos \dfrac{x}{2}+c$
- $-\dfrac{1}{\sqrt{2}} \sin \dfrac{x}{2}+c$