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Integrate the function
$\int \frac{\cos x}{\sqrt{4-\sin ^2 x}} d x=I(s a y)$
$\int \frac{\cos x}{\sqrt{4-\sin ^2 x}} d x=I(s a y)$
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Verified Answer
Put $\sin x=2 t$ so that $\cos x d x=2 d t$
$I=\int \frac{d t}{\sqrt{1-t^2}}=\sin ^{-1} t+c=\sin ^{-1}\left(\frac{\sin x}{2}\right)+c$
$I=\int \frac{d t}{\sqrt{1-t^2}}=\sin ^{-1} t+c=\sin ^{-1}\left(\frac{\sin x}{2}\right)+c$
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