\[ \int \sqrt{1+\sin x} d x= \] \( \mathrm{P} \) (A) \( \frac{1}{2}...

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\[
\int \sqrt{1+\sin x} d x=
\]
\( \mathrm{P} \)
(A) \( \frac{1}{2}\left(\sin \frac{x}{2}+\cos \frac{x}{2}\right)+c \)
\( \mathrm{W} \)
\[
\theta
\]
(B) \( \frac{1}{2}\left(\sin \frac{x}{2}-\cos \frac{x}{2}\right)+c \)
(C) \( 2 \sqrt{1+\sin x}+c \)
(D) \( -2 \sqrt{1-\sin x}+c \)
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