Let the solution curve y=f(x) of the differential equation (d y)/(d x)+(x y)/(x^2-1)=(x^4+2 x)/(√(1-x^2)), x ∈(-1,1) pass through the origin. Then…

Let the solution curve $\displaystyle y=f(x)$ of the differential equation $\displaystyle \frac{d y}{d x}+\frac{x y}{x^2-1}=\frac{x^4+2 x}{\sqrt{1-x^2}}, x \in(-1,1)$ pass through the origin. Then $$\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) d x \text { is } $$ equal to