Question:
$\frac{\cos x}{\sqrt{4-\sin ^{2} x}}$
Solution:
$\frac{\cos x}{\sqrt{4-\sin ^{2} x}}$
Let $\sin x=t \Rightarrow \cos x d x=d t$
$\Rightarrow \int \frac{\cos x}{\sqrt{4-\sin ^{2} x}} d x=\int \frac{d t}{\sqrt{(2)^{2}-(t)^{2}}}$
$=\sin ^{-1}\left(\frac{t}{2}\right)+\mathrm{C}$
$=\sin ^{-1}\left(\frac{\sin x}{2}\right)+\mathrm{C}$
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