A function f(x)f(x)f(x) satisfies ∫0xf(t)dt=xe2x−∫0xe2tdt\int_{0}^{x} f(t) dt = x e^{2x} - \int_{0}^{x} e^{2t} dt∫0xf(t)dt=xe2x−∫0xe2tdt. Determine the expression for f(x)f(x)f(x).
f(x)=e2xf(x) = e^{2x}f(x)=e2x
f(x)=2xe2xf(x) = 2x e^{2x}f(x)=2xe2x
f(x)=1+2xe2xf(x) = 1 + 2x e^{2x}f(x)=1+2xe2x
f(x)=e2x+2xe2xf(x) = e^{2x} + 2x e^{2x}f(x)=e2x+2xe2x