Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 26

$$\sin (\sin x) +c$$

Given $$\int \cos x \cos (\sin x) d x$$ Let $$ u= \sin x\ \ \ \Rightarrow \ \ \ du=\cos xdx$$ Then \begin{align*} \int \cos x \cos (\sin x) d x&= \int \cos \left(u\right)du\\ &= \sin u +c\\ &= \sin (\sin x) +c \end{align*}