<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\chapter{数学公式与定理}

\section{公式示例}
\begin{equation}\label{eq:dewitt}
    \int  e^{ax} \tanh bx\ dx = 
    \begin{cases}
    \displaystyle{ \frac{ e^{(a+2b)x}}{(a+2b)} 
    {_2F_1}\left[ 1+\frac{a}{2b},1,2+\frac{a}{2b}, -e^{2bx}\right] }&amp; \\
    \displaystyle{
    \hspace{1cm}-\frac{1}{a}e^{ax}{_2F_1}\left[ 1, \frac{a}{2b},1+\frac{a}{2b}, -e^{2bx}\right]
    }
     &amp; a\ne b \\
    \displaystyle{\frac{e^{ax}-2\tan^{-1}[e^{ax}]}{a} } &amp; a = b
    \end{cases}
\end{equation}
    
你可以使用\lstinline|equation|环境插入公式，如\cref{eq:dewitt}，代码如下:
\begin{lstlisting}[language=TeX]
\begin{equation}\label{eq:dewitt}
    \int  e^{ax} \tanh bx\ dx = 
    \begin{cases}
    \displaystyle{ \frac{ e^{(a+2b)x}}{(a+2b)} 
    {_2F_1}\left[ 1+\frac{a}{2b},1,2+\frac{a}{2b}, -e^{2bx}\right] }&amp; \\
    \displaystyle{
    \hspace{1cm}-\frac{1}{a}e^{ax}{_2F_1}\left[ 1, \frac{a}{2b},1+\frac{a}{2b}, -e^{2bx}\right]
    }
        &amp; a\ne b \\
    \displaystyle{\frac{e^{ax}-2\tan^{-1}[e^{ax}]}{a} } &amp; a = b
    \end{cases}
\end{equation}
\end{lstlisting}

\section{定理环境}

\begin{proof}
    证明我是我
\end{proof}

\begin{definition}[他人]
    定义他人即地狱
\end{definition}</pre></body></html>