Integrate

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

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

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

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

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

$E.$ None $of$ the given options