1.

\int \sqrt{1+\sin x} d x=\begin{array}{l}{-2 \sqrt{1-\sin x}+c} \\ {\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)} \\ {\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)} \\ {2 \sqrt{1-\sin x}+c}\end{array}

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