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Integrate the function
$\sin x \sin (\cos x)$
$\sin x \sin (\cos x)$
Solution:
1615 Upvotes
Verified Answer
Put $\cos x=t,-\sin x d x=d t$
$\begin{aligned}
&\int \sin x \sin (\cos x) d x=-\int \sin (\cos x)(-\sin x) d x \\
&=-\int \sin t d t=\cos t+c=\cos (\cos x)+c
\end{aligned}$
$\begin{aligned}
&\int \sin x \sin (\cos x) d x=-\int \sin (\cos x)(-\sin x) d x \\
&=-\int \sin t d t=\cos t+c=\cos (\cos x)+c
\end{aligned}$
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