一、不定积分的概念
原函数
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-1.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-2.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-3.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-4.png" width="500" />
不定积分定义
- 所有原函数就是不定积分
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-5.png" width="500" />
- 求不定积分就是求所有原函数
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-6.png" width="500" />
- 微分和积分互为逆运算, 对于一个函数f(x)先求积分再求积分等于本身f(x)， 先求微分再求积分等于f(x)+C (C是常数，注意：不定积分必须有C)
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-7.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-8.png" width="500" />
三，不定积分的计算
基本公式
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-9.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-10.png" width="500" />
不定积分的性质
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-11.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-12.png" width="500" />
- 直接积分法( 就是找规律，向不定积分性质靠拢)
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-13.png" width="500" />
第一类换元法
- 直接凑（凑微分法）
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-14.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-15.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-16.png" width="500" />
- 间接法（先凑微分，在凑公式）
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-17.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-18.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-19.png" width="500" />
第二换元法 （简单理解）
- 根式换元
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-20.png" width="500" />
- 三角换元 ( 了解就可以了 )
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-21.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-22.png" width="500" />
分部积分法
- 分部积分法则
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-23.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-24.png" width="500" />
- 分部积分u,v‘的确认 （注意：这是分部积分的重点也是难点）
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-25.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-26.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-27.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-28.png" width="500" />
简单有理函数求微分
- 简单有理函数概念
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-29.png" width="500" />
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-30.png" width="500" />
- 简单有理函数求微分的方法：先分项，后微分
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-31.png" width="500" />
