$\cfrac{{\cos x}}{{\sqrt {4 - {{\sin }^2}x} }}$
$\cfrac{{\cos x}}{{\sqrt {4 - {{\sin }^2}x} }}$
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NCERT & Exemplar
Let $I = \int {\cfrac{{\cos x}}{{\sqrt {4 - {{\sin }^2}x} }}} dx$
Let $\sin x = t$ $\Rightarrow$ $\cos xdx = dt$
$\therefore$ $I = \int {\cfrac{{dt}}{{\sqrt {4 - {t^2}} }} = {{\sin }^{ - 1}}\left( {\cfrac{t}{2}} \right)} + C = {\sin ^{ - 1}}\left( {\cfrac{{\sin x}}{2}} \right) + C$
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