积分换元法的探讨

Discussion on the Method of Integration by Substitution

摘要: 换元法是求解不定积分、定积分的主要方法。本文指出不定积分和反常积分换元函数需要单调，而定积分则不需要单调，且换元函数的值域可以超出原来的积分区间。

Abstract: The substitution method is a primary approach for solving indefinite integrals and definite integrals. This article points out that the substitution function for indefinite integrals and improper integrals needs to be monotonic, while for definite integrals, it does not need to be monotonic, and the range of the substitution function can exceed the original integration interval.