Differential Equations

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