Answer
$$\int \cos(5- 7\theta) d\theta= -\frac{1}{7}\sin (5- 7\theta)+c.$$
Work Step by Step
Let $ u=5- 7\theta $, then $ du=-7d\theta $ and hence
$$\int \cos(5- 7\theta) d\theta=-\frac{1}{7}\int \cos u du=-\frac{1}{7}\sin u +c= -\frac{1}{7}\sin (5- 7\theta)+c.$$