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

  1. $-2 \sqrt{2} \sin \dfrac{x}{2}+c$
  2. $-2 \sqrt{2} \cos \dfrac{x}{2}+c$
  3. $-\dfrac{1}{\sqrt{2}} \cos \dfrac{x}{2}+c$
  4. $-\dfrac{1}{\sqrt{2}} \sin \dfrac{x}{2}+c$

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