Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 418: 1

$$\int\cos 2xdx=\frac{\sin 2x}{2}+C$$

$$A=\int\cos 2xdx$$ Let $u=2x$ Then $du=(2x)'dx=2dx$. So $dx=\frac{1}{2}du$. Substitute into $A$, we have $$A=\int\cos u\frac{1}{2}du$$ $$A=\frac{1}{2}\int\cos udu$$ $$A=\frac{1}{2}\sin u+C$$ $$A=\frac{\sin 2x}{2}+C$$