Integrate cos(3x) dx

Problem: Evaluate the indefinite integral $\int \cos(3x) \, dx$.

Steps

1. Apply $u$-substitution
   Let $u = 3x$, which means $du = 3 \, dx$ or $dx = \frac{1}{3} \, du$.
   $$\int \cos(u) \cdot \frac{1}{3} \, du$$
2. Factor out the constant
   $$\frac{1}{3} \int \cos(u) \, du$$
3. Integrate with respect to $u$
   $$\frac{1}{3} (\sin(u)) + C$$
4. Substitute back $u = 3x$
   $$\frac{1}{3} \sin(3x) + C$$