The function $y=f\left(x\right)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ in $\left(-1,1\right)$ satisfying $f\left(0\right)=0.$ Then ${\int }_{\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}f\left(x\right)dx$ is

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