Integrate the function: sin x sin(cos x) - Vidyadip

Question

Integrate the function: sin x sin(cos x)

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Answer

Putting cos x = t
$\Rightarrow - \sin x = \frac{{dt}}{{dx}}$
$\Rightarrow - \sin xdx = dt$
$\therefore \int {\sin x\sin \left( {\cos x} \right)dx} $
$= \int {\sin \left( {\cos x} \right)\left( { - \sin xdx} \right)} $
$= - \int {\sin t} dt$
= - (-cos t) + c
= cos t + c = cos (cos x) + c

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