一道高数题，谢谢各位!

∵ F(x) = ∫ƒ(x)dx
∴ ƒ(x) = dF/dx

∵ ƒ(x)F(x) = x
∴ [dF(x)/dx]F(x) = x
∴ F(x)dF(x) = xdx
½F²(x) = ½x²+C
F²(x) = x² + C

∵ F(0) = 1
∴ 1 = C
F²(x) = x² + 1

∵ F(x) > 0
∴ F(x) = √(x² + 1)

∵ F(x) = ∫ƒ(x)dx
∴ ∫ƒ(x)dx = √(x² + 1)

两边求导得：
ƒ(x) = x/√(x² + 1)

f(x)乘以F(X)=二分之一倍的[F^2(x)]'