1.
Let the solution curve y=f(x)y = f(x) of the DE dydx+xyx2−1=x4+2x1−x2\frac{dy}{dx} + \frac{xy}{x^2-1} = \frac{x^4 + 2x}{\sqrt{1-x^2}}, x∈(−1,1)x\in(-1,1) pass through the origin. Then ∫−3/23/2f(x) dx\int_{-\sqrt{3}/2}^{\sqrt{3}/2} f(x)\,dx is equal to