Answer
$\dfrac{\cos(\theta)}{2}-\dfrac{\cos(11\theta)}{22}+c$
Work Step by Step
Consider the integral $\int \sin 5 \theta \cos 6 \theta d\theta$
The given integral can be re-written as:
$ (\dfrac{1}{2})\int \sin (5 \theta-6 \theta)+\sin (5 \theta +6 \theta) d\theta=(\dfrac{1}{2}) \int \sin (-\theta) +\sin (11 \theta) d\theta$
We use the formula: $\int x^n dx=\int\dfrac{x^{n+1}}{n+1} dx$
This implies that $(\dfrac{1}{2})[\cos \theta -\dfrac{\cos(11 \theta)}{11}]+c=\dfrac{\cos(\theta)}{2}-\dfrac{\cos(11\theta)}{22}+c$
