Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 62

$$\sin (\sin t)+C $$

Given $$ \int \cos t \cos (\sin t) d t $$ Let $$u=\sin t \ \ \ \ \Rightarrow \ \ \ du =\cos tdt$$ \begin{aligned} \int \cos t \cos (\sin t) d t &=\int \cos u d u \\ &=\sin u+C \\ &=\sin (\sin t)+C \end{aligned}