Answer
$$
\int \sin(4\theta -7)d\theta=
=-\frac{1}{4}\cos (4\theta -7) +c
$$
Work Step by Step
Since $ u=4\theta -7$, then $ du=4d\theta $ and hence, $$
\int \sin(4\theta -7)d\theta=\frac{1}{4}\int \sin u d u= -\frac{1}{4}\cos u +c\\
=-\frac{1}{4}\cos (4\theta -7) +c
$$
