高等数学不定积分的换元与分布 好学高数七

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Today, the editor brings you

the studious high number (seven): The concept of indefinite integral and the method of integration by substitution.

一、不定积分的的概念与性质

1、求不定积分就是求导函数的原函数，但是必须记得在求出原函数后加上常数C。

一定要记得加常数C！！！

2、不定积分的几何含义：一组平行的曲线族

3、一般会求导就会求不定积分

特例：

（注意自变量的取值范围）

4、不定积分公式

（1）

（2）

1. Finding indefinite integral is to find the original function of derivative function, but you must remember to add constant C after finding the original function. Remember to add the constant C!!!

2. Geometric meaning of indefinite integral: a group of parallel curve families

3. Generally, indefinite integral can be obtained if derivative can be obtained.

(Note the value range of the independent variable)

4. Indefinite integral formula

二、积分换元法

1、第一类换元法

（总体来说比较简单，但需要多练题提高熟练度）

需要记的公式：

2、第二类换元法

（相比第一类换元法来说更加麻烦，一般需要令新的字母换元，有时候还需要借助三角函数，特别需要注意自变量的范围）

下面给出一道例题，还需要大家自行品味：

1. Formulas to remember for the first type of substitution method (generally simple, but requires more exercises to improve proficiency):

2. The second type of substitution method (more troublesome than the first type of substitution method, which generally requires the substitution of new letters, and sometimes requires the use of trigonometric functions, especially the range of independent variables). Here is an example to be tasted by everyone:

END

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翻译：谷歌翻译参考：《高等数学》第七版上册 同济大学数学系声明：本文由LearningYard新学苑原创，若有侵权请联系删除！

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