Zhang zhiyang's blog
不过是些许风霜罢了

math

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我听别人说这世界上有一种鸟是没有脚的,它只能够一直的飞呀飞呀,飞累了就在风里面睡觉,这种鸟一辈子只能下地一次,那一次就是它死亡的时候。

hugo博客搭建

hugo博客搭建

Sunday, Oct 11, 2020

@ Zhang zhiyang

0x00 环境搭建 installation 下载得到hugo.exe链接名称 # macos brew install hugo # linux sudo apt/yum install hugo 配置环境变量 安装成功 λ hugo -h hugo is the main command, used to build your Hugo site. Hugo is a Fast and Flexible Static Site Generator built with love by spf13 and friends in Go. Complete documentation is available at http://gohugo.io/. Usage: hugo [flags] hugo [command] Available Commands: config Print the site configuration convert Convert your content to different formats deploy Deploy your site to a Cloud provider.
Math

Math

Tuesday, Aug 13, 2019

@ Zhang zhiyang

不定积分 $\int \tan xdx=\ln|\sec x|+C$ $\int \cot xdx=\ln|\csc x|+C$ 换源积分法 去根号 $ \sqrt[n]{ax+b}=t$ 三角变换 $\sqrt[n]{a^2-x^2},令x=a\sin t,则\sqrt[n]{a^2-x^2}=acost$ $\sqrt[n]{a^2+x^2},令x=a\tan t,则\sqrt[n]{a^2+x^2}=a\sec t$ $\sqrt[n]{x^2-a^2},令x=a\sec t,则\sqrt[n]{x^2-a^2}=a\tan t$ 分部积分法 $$\int f(x)dg(x)=f(x)g(x)-\int g(x)df(x)$$ $\int f(x)[指数函数]dx->\int f(x)d[指数函数]$ $\int f(x)[三角函数]dx->\int f(x)d[三角函数]$ $\int f(x)[对数函数]dx->\int [对数函数]df(x)$ $\int f(x)[反三角函数]dx-\int [对数函数]df(x)$ 令反三角函数为t $\int x^2arctanxdx$ 令$arctanx =t$ 则$x=\tan t$ 原式$=\int \tan^2t*td(\tan t)$ $=\int (\sec^2t-1)tdt$ $=\int \sec^2t*tdt-\int tdt$ $=\int td(\tan t)-t^2/2$ $=t*\tan t-\int tantdt-\frac{t^2}{2}$ $=t*\tan t-\ln |\sec t|-\frac{t^2}{2}+C$

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