Cho hàm số f(x) liên tục trên R thỏa mãn f(x) = 2x.e^-x/1 + x^2

Chọn D.

Ta có $f\left(x\right)=\frac{2x.e^{-x}}{1+x^2}-f\text{'}\left(x\right),\forall x\in ℝ\iff f\left(x\right)+f\text{'}\left(x\right)=\frac{2x.e^{-x}}{1+x^2}\iff e^x.f\left(x\right)+e^x.f\text{'}\left(x\right)=\frac{2x}{1+x^2}.$

$\Rightarrow \left[e^x.f\left(x\right)\right]\text{'}=\frac{2x}{1+x^2}\Rightarrow \underset{0}{\overset{1}{\int }}\left[e^x.f\left(x\right)\right]\text{'}dx=\underset{0}{\overset{1}{\int }}\frac{2x}{1+x^2}dx=\ln 2.$