如何用垂直线连接等式符号？

Question

我想创建一个如下所示的布局，但更加自动化，这样我就不必在每种情况下手动调整间距（如下所示）。

谁知道该怎么做？

\documentclass{minimal}
\usepackage{amsmath}
\begin{document}
\begin{align}
    I(a,b) &= \int_0^{\pi/2}\frac{d\Phi}{\sqrt{a^2\cos^2(\Phi)+b^2\sin^2(\Phi)}}\nonumber\\[-4ex]
    &\hspace*{1mm}\left|\begin{aligned}&~\\[3ex]
    \hline\\[-2ex]
    ~~&\text{Substitution } \boxed{t = b\cdot \tan \Phi}:\qquad 0 < t < \infty\\
    &\frac{dt}{d\Phi} = b\cdot(1+\tan^2\Phi)=b+\frac{t^2}{b}=\frac{t^2+b^2}{b}\quad\Longrightarrow\quad\frac{d\Phi}{dt} = \frac{b}{t^2+b^2}\\
    &1+\tan^2\Phi = \frac{1}{\cos^2\Phi} \quad\Longrightarrow\quad \cos^2\Phi = \frac{b^2}{b^2+b^2\tan^2\Phi}=\frac{b^2}{b^2+t^2}\\
    &\sin^2\Phi = 1- \cos^2\Phi = \frac{b^2+t^2-b^2}{b^2+t^2} = \frac{t^2}{b^2+t^2}\\[2ex]
    \hline\\[2ex]
    \end{aligned}\right.\nonumber\\[-2ex]
    &= \int_0^{\infty} \frac{1}{\sqrt{a^2\cdot\frac{b^2}{b^2+t^2} + b^2\cdot\frac{t^2}{b^2+t^2}}}\cdot\frac{b}{t^2+b^2} dt\nonumber
\end{align}
\end{document}

Answer 1

这会自动完成但是你真的喜欢这个布局吗？

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{tikzmark}
\begin{document}
\begin{align}
    I(a,b) &\tikzmarknode{eq1}{=} 
    \int\limits_0^{\pi/2}\frac{\mathrm{d}\Phi}{\sqrt{a^2\cos^2(\Phi)+b^2\sin^2(\Phi)}}
    \notag\\
    &\quad\begin{array}{>{\displaystyle}l}
    \hline
    \text{Substitution } \boxed{t = b\cdot \tan \Phi}:\qquad 0 < t < \infty\\
    \frac{\mathrm{d}t}{\mathrm{d}\Phi} = b\cdot(1+\tan^2\Phi)=b+\frac{t^2}{b}=\frac{t^2+b^2}{b}
    \quad\Longrightarrow\quad\frac{\mathrm{d}\Phi}{\mathrm{d}t} = \frac{b}{t^2+b^2}\\
    1+\tan^2\Phi = \frac{1}{\cos^2\Phi} \quad\Longrightarrow\quad \cos^2\Phi = \frac{b^2}{b^2+b^2\tan^2\Phi}=\frac{b^2}{b^2+t^2}\\
    \sin^2\Phi = 1- \cos^2\Phi = \frac{b^2+t^2-b^2}{b^2+t^2} = \frac{t^2}{b^2+t^2}
    \\ \hline
    \end{array}\notag\\
    &\tikzmarknode{eq2}{=}  \int\limits_0^{\infty} \frac{1}{\sqrt{a^2\cdot\frac{b^2}{b^2+t^2} + b^2\cdot\frac{t^2}{b^2+t^2}}}\cdot\frac{b}{t^2+b^2} 
    \,\mathrm{d}t
\end{align}\tikz[overlay,remember picture]{\draw[shorten >=1pt,shorten <=1pt] (eq1) -- (eq2);}
\end{document}