Tìm nguyên hàm (F(x)) của hàm số (fleft( x ight) = x.{e^{2x}}.)

A. \(F\left( x \right) = \frac{1}{2}{e^{2x}}\left( {x - \frac{1}{2}} \right) + C\)

B. \(F\left( x \right) = \frac{1}{2}{e^{2x}}\left( {x - 2} \right) + C\)

C. \(F\left( x \right) = 2{e^{2x}}\left( {x - \frac{1}{2}} \right) + C\)

D. \(F\left( x \right) = 2{e^{2x}}\left( {x - 2} \right) + C\)