email update
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continuous-integration/drone/push Build is passing
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parent
d2c1a18e98
commit
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@ -98,7 +98,7 @@ uglyURLs = false
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# 名字
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# 名字
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name = "InkSoul"
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name = "InkSoul"
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# 邮箱
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# 邮箱
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email = "qingci30@163.com"
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email = "blog@inksoul.top"
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# 座右铭或简介
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# 座右铭或简介
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motto = ""
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motto = ""
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# 头像
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# 头像
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@ -53,6 +53,8 @@ date: 2022-12-24T13:05:40+08:00
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- [倒代换](#倒代换)
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- [倒代换](#倒代换)
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- [指数代换](#指数代换)
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- [指数代换](#指数代换)
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- [万能代换](#万能代换)
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- [万能代换](#万能代换)
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- [除法积分](#除法积分)
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- [部分相消法](#部分相消法)
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- [组合积分法](#组合积分法)
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- [组合积分法](#组合积分法)
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- [值得记忆的定积分公式](#值得记忆的定积分公式)
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- [值得记忆的定积分公式](#值得记忆的定积分公式)
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- [线性代数](#线性代数)
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- [线性代数](#线性代数)
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@ -399,6 +401,27 @@ $$
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原积分转化为$\int R(\frac{1-t^2}{1+t^2},\frac{2t}{1+t^2})\frac{2}{1+t^2}dt$
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原积分转化为$\int R(\frac{1-t^2}{1+t^2},\frac{2t}{1+t^2})\frac{2}{1+t^2}dt$
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##### 除法积分
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$$
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\int \frac{u}{v}dx = \int \frac{u^{'}}{v^{'}}dx - \int (\frac{u}{v})^{'} \cdot \frac{u}{v^{'}} dx
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$$
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例如计算$\int \frac{x+\sin x}{1 + \cos x}dx$
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$原式 = \int \frac{1+\cos x}{- \sin x}dx + \int (\frac{x+\sin x}{1+ \cos x})^{'} \cdot \frac{1+\cos x}{\sin x}dx \\\\= \int \frac{1+\cos x}{-\sin x} + \int \frac{1+\cos x}{\sin x}d(\frac{x+\sin x}{1+\cos x}) \\\\ =\frac{1+\cos x}{\sin x} \cdot \frac{x+\sin x}{1 + \cos x} - \int \frac{x+\sin x}{1+ \cos x} \cdot \frac{-\sin^2 x -(1+\cos x) - x}{\sin^2 x}dx \\\\= \frac{x+\sin x}{\sin x}$
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##### 部分相消法
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对于一个可视为两个函数相乘的积分,可进行拆分后相消
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$原式 \rightarrow \\\\ \int f_1(x)dx + \int u(x)dv(x) \rightarrow \\\\ \int f_1(x)dx + u(x)v(x) - \int v(x)du(x) = \\\\ u(x)v(x)+C$
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例如计算$\int e^{2x}(\tan x + 1)^2dx$
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$原式 = \int e^{2x}(\tan^2 x + 2\tan x +1)dx \\\\= \int e^{2x}(\sec^2 x + 2\tan x)dx \\\\= \int e^{2x}\sec^2 x dx + 2\int e^{2x}\tan x dx \\\\= \int e^{2x} d\tan x + 2\int e^{2x} \tan x dx \\\\= \tan x \cdot e^{2x} -2\int \tan x e^{2x} dx + 2\int e^{2x} \tan x dx \\\\ = \tan x \cdot e^{2x} + C
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$
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##### 组合积分法
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##### 组合积分法
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对于
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对于
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