Question
Integrate the functions in Exercises:
$\sin\text{x}\sin(\cos\text{x)}$
$\sin\text{x}\sin(\cos\text{x)}$
✓
Answer
Putting $\cos \text{x}=\text{t}\ \ \ \ \ \Rightarrow \ \ \ \ \ -\sin\text{x}=\frac{\text{dt}}{\text{dx}}\ \ \ \ \ \Rightarrow\ \ \ \ -\sin\text{x}\text{ dx = dt}$ $\therefore\ \ \ \ \ \int\sin\text{x}\sin(\cos\text{x})\text{ dx}$ $=-\int\sin(\cos\text{x})(-\sin\text{x dx})$ $=-\int\sin\text{t dt}=-(-\cos\text{t})+\text{c}$ $=\cos\text{t}+\text{c}=\cos(\cos\text{x})+\text{c} $
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