# How do you find the antiderivative of cos^4 x sin(2x) dx?

Jul 20, 2016

$= - \frac{1}{3} {\cos}^{6} x + C$

#### Explanation:

use $\sin 2 A = 2 \sin A \cos A$

it becomes $2 \int \setminus {\cos}^{5} x \sin x \setminus \mathrm{dx}$

$= 2 \int - \frac{1}{6} \setminus \frac{d}{\mathrm{dx}} \left({\cos}^{6} x\right) \setminus \mathrm{dx}$

$= - \frac{1}{3} {\cos}^{6} x + C$