Prove
Question:

$\frac{\cos x}{\sqrt{1+\sin x}}$

Solution:

Let $1+\sin x=t$

$\therefore \cos x d x=d t$

$\Rightarrow \int \frac{\cos x}{\sqrt{1+\sin x}} d x=\int \frac{d t}{\sqrt{t}}$

$=\frac{t^{\frac{1}{2}}}{\frac{1}{2}}+\mathrm{C}$

$=2 \sqrt{t}+\mathrm{C}$

$=2 \sqrt{1+\sin x}+\mathrm{C}$

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