换元法又称辅助元素法或变量代换法,是重要的数学方法之一,它涉及的题型较多,处理的方法灵活.其解题实质就是通过引入一些新的变量进行代换,并简化其结构,从而达到解决问题的目的.换元法可以化高次为低次、化分式为整式、化无理式为有理式、化超越式为代数式,因而在研究方程、不等式、函数、数列以及三角函数等问题中有着广泛的应用.换元的方法主要有局部换元、三角换元、均值换元等.下面笔者通过几个不同的例子介绍换元法的应用. The replacement method, also known as the auxiliary element method or the variable substitution method, is one of the important mathematical methods. It involves more types of questions and more flexible methods of processing. The essence of solving problems is to replace them by introducing some new variables. And to simplify its structure, so as to achieve the purpose of solving the problem. The method of changing the yuan can be high-order low-order, split-form is integral, rationalization is rational, and transcendence is algebraic, so the equations, inequalities, and functions are studied. There are a wide range of applications for problems such as series, trigonometric functions, and trigonometric functions. The methods of substitutions are local substitutions, trigonometric substitutions, mean value conversions, etc. The following authors introduce the application of the substitution method through several different examples.