Integrate

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{-2x}cos(2x)dx$

A$.\frac{3}{4}{e}^{-2x}sin(2x)-\frac{1}{2}cos(2x)C$

B$.$ None of the given options

C$.e^{-2x}sin(2x)\frac{1}{4}{e}^{-2x}cos(2x)C$

D$.\frac{1}{4}{e}^{-2x}sin(2x)-\frac{1}{4}{e}^{-2x}cos(2x)C$

E$.\frac{1}{2}{e}^{-x}sin(x)-\frac{1}{4}{e}^{-2x}cos(x)C$