令 u = x^(-1/3) , 则 x = 1/u^3, 由 x→+∞ , 得 u→0+原极限 = lim ∫<0, u>[ t^2/√(1+t^2)]dt / u^3 （0/0）= lim [u^2/√(1+u^2)]/ (3u^2) = 1/3
