我想以书的形式写出数学问题和答案，供学生阅读。有人能帮我创建问题、解决方案和提示环境，以便我每次都能添加方程式吗？另外我不明白为什么我的方程式很混乱。
我附上了一张关于解决方案的图片
\documentclass[12pt]{article}
%i have used few packages
\usepackage[margin= 1cm]{geometry}
\usepackage{amsmath}
\usepackage{tcolorbox}
\usepackage{multicol}
\usepackage{xcolor}
%document begins here
\begin{document}
%section heading
\section{Questions on Basic integration}
%question with bold and box
\begin{tcolorbox}
subsection begins here, the word question should be in bold
\subsection*{Question 1} Solve the following integral. $$\int \sec x(\sec x+\tan x) d x $$
\end{tcolorbox}
%solution word in bold
\subsubsection*{Solution}
this is a quick tip, to be highlighted
\textcolor{blue}{$$
\begin{array}{l}
\int \sec ^{2} x d x=\tan x \\
\int \sec x \tan x=\sec x
\end{array}
$$}
%the solution
$$
\begin{aligned}
\int \sec x(&\sec x+\tan x) d x \\
&=\int\left(\sec ^{2} x+\sec x \tan x\right) d x \\
&=\int \sec ^{2} x d x+\int \sec x \tan x d x \\
&=\tan x+\sec x+C
\end{aligned}
$$
%second question
\begin{tcolorbox}
%question 2 begins here
\subsection*{Question 2} Solve the following integral. $$\int \frac{1}{x+x\log x} dx$$
\end{tcolorbox}
%solution in bold
\subsubsection*{Solution}
\textcolor{blue}{$$
\begin{array}{l}
\text { Put } 1+x \log x=t \\
\text { then, } \frac{1}{x}\; d x=d t
\end{array}
$$}
% solution begins
\begin{center}$\displaystyle{
\begin{array}{l}
\int \frac{1}{x+x \log x} d x \\
\text { Simce, } \frac{1}{x} d x=d t \text { and }(1+\log x)=t \\
=\int \frac{d t}{t} \\
=\log (t)+C \\
=\int \log (1+\log x)+C
\end{array}
}$ \end{center}
\end{document}
答案1
像这样？请注意，虽然我提供了名为 的宏的代码\tip，但我没有定义单独的问题和答案环境，因为我认为这样做不会解决混乱问题。（实际上，这些环境可能会加剧混乱问题。）我只能建议您更熟悉该amsmath包的多行数学环境。
\documentclass[12pt]{article}
\usepackage[margin=2.5cm,a4paper]{geometry}
\usepackage{amsmath,tcolorbox}
\newcommand\tip[1]{\smash{\boxed{\color{blue}\array{r} #1 \endarray}}}
\begin{document}
\section{Questions on basic integration}
\begin{tcolorbox}
\subsection*{Question 1} Solve the following integral.
\quad$\displaystyle \int \sec x(\sec x+\tan x)\, dx $
\end{tcolorbox}
\paragraph{Solution}
\begin{align*}
&\int \sec x(\sec x+\tan x)\, dx
\hspace{3cm} \tip{ \int \sec ^{2} x\, dx=\tan x \\[1ex]
\int \sec x \tan x \,dx=\sec x} \\
&\quad=\int\bigl(\sec ^{2} x+\sec x \tan x\bigr)\, dx \\
&\quad=\int \sec ^{2} x\, dx+\int \sec x \tan x\, dx \\
&\quad=\tan x+\sec x+C
\end{align*}
\begin{tcolorbox}
\subsection*{Question 2} Solve the following integral.
\quad$\displaystyle\int \frac{1}{x+x\log x}\,dx$
\end{tcolorbox}
\paragraph{Solution}
\begin{align*}
&\int \frac{1}{x+x \log x}\, dx \\
&\quad= \int \frac{1}{x(1+\log x)}\, dx
\hspace{3cm}\tip{\text{\textbf{Tip:} Put } 1+\log x = t \\[1ex]
\text{then } \frac{1}{x}\, dx = dt} \\
&\quad=\int \frac{dt}{t} \\
&\quad=\log (t)+C \\
&\quad=\int \log (1+\log x)+C
\end{align*}
\end{document}
附录回答 OP 的后续问题之一。可以定义一个\question 宏如下（序言部分）：
\newcommand\question[2]{%
\tcolorbox
\subsection*{Question #1}
Solve the following integral.\quad$\displaystyle #2$
\endtcolorbox}
然后\question{1}{\int \sec x(\sec x+\tan x)\, dx}在文档正文中写入。
答案2
这就是你想要的吗？
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage[dvipsnames]{xcolor}
\usepackage{mdframed}
\mdfsetup{
leftmargin=-5,
rightmargin=-5,
innerleftmargin=5,% Distance from content to frame. To align the content with
innerrightmargin=5,% the surrouding text, the sum of leftmargin and innerleftmargin must be zero.
linecolor=white,% The frame consists of inner-, middle-, and outerline. linecolor changes all three.
innertopmargin=0\topskip,
}
\mdtheorem[backgroundcolor=PineGreen!15!white]{tip}{Tip}%[section] % Uncomment if you want to include section number.
\mdtheorem{quest}{Question}%[section] % Uncomment if you want to include section number.
\mdtheorem{sol}{Solution}%[section] % Uncomment if you want to include section number.
\newcommand{\dd}[0]{\,\mathrm{d}} % puts a thin space and an upright 'd'.
\begin{document}
\section{Questions on Basic integration}
\begin{quest}
Solve the following integral:
\begin{equation*}
\int \sec x(\sec x+\tan x) \dd x.
\end{equation*}
\end{quest}%
%
\begin{sol*}
\begin{tip*}
\begin{align*}
\int \sec^{2} x \dd x &= \tan x + C\\
\int \sec x \tan x \dd x &= \sec x + C
\end{align*}
\end{tip*}%
%
\begin{align*}
\int \frac{1}{x+x \log x} \dd x &= \int\frac{1}{x(1+\log(x))} \dd x\\
&= \int \frac{\dd t}{t} \\
&= \log (t)+C \\
&= \log (1+\log x)+C
\end{align*}
\end{sol*}
\end{document}
编辑：正如您在评论中要求的“问题 1”后没有换行符，这里是一个更新版本。
\documentclass[12pt]{article}
\usepackage{amsmath,amsthm}
\usepackage[dvipsnames]{xcolor}
\usepackage{mdframed}
\mdfsetup{
leftmargin=-5,
rightmargin=-5,
innerleftmargin=5,% Distance from content to frame. To align the content with
innerrightmargin=5,% the surrouding text, the sum of leftmargin and innerleftmargin must be zero.
linecolor=white,% The frame consists of inner-, middle-, and outerline. linecolor changes all three.
innertopmargin=0\topskip,
}
\newtheorem{quest}{Question} % for numbered questions
\newtheorem*{quest*}{Question} % for unnumbered questions
\newtheorem{tip}{Tip} % for numbered tips
\newtheorem*{tip*}{Tip} % for unnumbered tips
\surroundwithmdframed[backgroundcolor=PineGreen!15!white]{tip} % get the shiny box around (numbered) tips.
\surroundwithmdframed[backgroundcolor=PineGreen!15!white]{tip*} % get the shiny box around (unnumbered) tips.
\newtheorem{sol}{Solution} % for numbered solutions
\newtheorem*{sol*}{Solution} % for unnumbered solutions
\newcommand{\dd}[0]{\,\mathrm{d}} % puts a thin space and an upright 'd'.
\begin{document}
\section{Questions on Basic integration}
\begin{quest}
Solve the following integral:
\begin{equation*}
\int \sec x(\sec x+\tan x) \dd x.
\end{equation*}
\end{quest}%
%
\begin{sol*}
~ % For some reason the tip-environment covers the word 'solution' when there is nothing between them.
\begin{tip*} Here can be some text.
\begin{align*}
\int \sec^{2} x \dd x &= \tan x + C\\
\int \sec x \tan x \dd x &= \sec x + C
\end{align*}
\end{tip*}%
%
\begin{align*}
\int \frac{1}{x+x \log x} \dd x &= \int\frac{1}{x(1+\log(x))} \dd x\\
&= \int \frac{\dd t}{t} \\
&= \log (t)+C \\
&= \log (1+\log x)+C
\end{align*}
\end{sol*}
\end{document}