不定积分∫(x^2+1)^(1/2)/(x^4+1)^(1/2) dx积不出的证明

The proof about the indefinite integral ∫(x^2+1)^(1/2)/(x^4+1)^(1/2) dx is beyond element

初等函数在其定义域区间上的不定积分均存在,但是,初等函数的不定积分未必仍是初等函数,也即该不定积分不再由基本初等函数通过四则运算、复合运算来表示,这使得一些初等函数的不定积分积不出.利用函数不定积分积不出来的判别方法,证明不定积分∫(x^2+1)^(1/2)/(x^4+1)^(1/2) dx积不出来.

The indefinite integral of the elementary function exists on the interval of its definition.But not all the indefinite integral of the elementary function is still elementary function which can be expressed by thefour arithmetic operations,the composite operation of basic elementary functions.This makes some elementary functions be beyond element.Proved that the indefinite integral ∫√x^2＋1/√x^4＋1 dx is to be beyond element by the beyond element criterion.