Let y=y(x) be the solution of the differential equation (d y)/(d x)+(2 x)/((1+x^2)^2) y=x e^(1/((1+x^2))); y(0)=0. Then the area enclosed by the…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $$\frac{d y}{d x}+\frac{2 x}{\left(1+x^2\right)^2} y=x e^{\frac{1}{\left(1+x^2\right)}} ; y(0)=0 . $$ Then the area enclosed by the curve $\displaystyle f(x)=y(x) \mathrm{e}^{-\frac{1}{\left(1+x^2\right)}}$ and the line $\displaystyle y-x=4$ is $\displaystyle \_\_\_\_$.