Answer
$$\theta + \frac{1}{3}\sin 3\theta + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {1 + \cos 3\theta } \right)} d\theta \cr
& {\text{split the numerator}} \cr
& = \int {d\theta } + \int {\cos 3\theta } d\theta \cr
& {\text{integrate}}{\text{, use }}\int {\cos ax} dx = \frac{1}{a}\sin ax + C \cr
& letting{\text{ }}a = 3,{\text{ }}\theta = x \cr
& = \theta + \frac{1}{3}\left( {\sin 3\theta } \right) + C \cr
& = \theta + \frac{1}{3}\sin 3\theta + C \cr} $$
