Integrate the following function. $sin x sin (cos x)$

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Solution

$\int sin x \cdot sin (cos x) d x$

Put $cos x = t \Rightarrow - sin x d x = d t$

$\Rightarrow \int sin x \cdot sin (cos x) d x = - \int sin t d t$

$= - [- cos t] + C$

$= cos t + C = cos (cos x) + C$

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