作差：
(x^3+1)-(x^2+x)
=(x+1)(x^2-x+1)-x(x+1)
=(x+1)(x^2-2x+1)
=(x+1)(x-1)^2
∴当x＞－1且不等于1时,(x+1)(x-1)^2＞0,即有：x^3+1＞x^2+x
当x＜－1时,(x+1)(x-1)^2＜0,即有：x^3+1＜x^2+x
当x＝－1或1时,(x+1)(x-1)^2＝0,即有：x^3+1＝x^2+x