\documentclass{ctexart}
\usepackage{amsthm}
\usepackage{amsmath}

\usepackage[skins]{tcolorbox}
\newtheorem{Example}{例}
\newtheorem*{MySolution}{解}
\tcolorboxenvironment{MySolution}{
    colframe = blue!50!black, % 边框颜色
    colback = blue!10, % 背景颜色
    fonttitle = \bfseries, % 标题字体加粗
    before upper = {\itshape}, % 内容字体为斜体
    title = 解,
    boxrule = 1pt % 边框宽度
}
\begin{document}
    \begin{Example}
        证明
        \begin{equation*}
            \int_{0}^{1} \frac{1}{x} \mathrm{d}x = \ln 2.
        \end{equation*}
    \end{Example}
    \begin{MySolution}
        \begin{equation*}
            \int_{0}^{1} \frac{1}{x} \mathrm{d}x = \int_{0}^{1} \frac{1}{x} \cdot \frac{1}{1    \mathrm{d}x} = \int_{0}^{1} \frac{1}{1} \cdot \frac{1}{x} \mathrm{d}x = \int_{0}^{1} \frac{1}{x} \mathrm{d}x.
        \end{equation*}
        因此
        \begin{equation*}
            \int_{0}^{1} \frac{1}{x} \mathrm{d}x = \ln 2.
        \end{equation*}
    \end{MySolution}
\end{document}