一、不定積分的概念
原函數(shù)
<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" />
不定積分定義
- 所有原函數(shù)就是不定積分
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-5.png" width="500" />
- 求不定積分就是求所有原函數(shù)
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-6.png" width="500" />
- 微分和積分互為逆運(yùn)算, 對(duì)于一個(gè)函數(shù)f(x)先求積分再求積分等于本身f(x)， 先求微分再求積分等于f(x)+C (C是常數(shù)，注意：不定積分必須有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，不定積分的計(jì)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" />
不定積分的性質(zhì)
<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" />
- 直接積分法( 就是找規(guī)律，向不定積分性質(zhì)靠攏)
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-13.png" width="500" />
第一類換元法
- 直接湊（湊微分法）
<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" />
- 間接法（先湊微分，在湊公式）
<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" />
第二換元法?。ê?jiǎn)單理解）
- 根式換元
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-20.png" width="500" />
- 三角換元 ( 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" />
分部積分法
- 分部積分法則
<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" />
- 分部積分u,v‘的確認(rèn)?。ㄗ⒁猓哼@是分部積分的重點(diǎn)也是難點(diǎn)）
<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" />
簡(jiǎn)單有理函數(shù)求微分
- 簡(jiǎn)單有理函數(shù)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" />
- 簡(jiǎn)單有理函數(shù)求微分的方法：先分項(xiàng)，后微分
<img src="https://raw.githubusercontent.com/liangxifeng833/my_program/master/images/math/math-jifen-31.png" width="500" />
