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%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
%%  3. Auflage
%%  Beispiel 10-05-2 auf Seite 221.
%%  Copyright (C) 2018 Herbert Voss
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%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%%  See http://www.latex-project.org/lppl.txt for details.
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\documentclass[10pt]{screxa}
\pagestyle{empty}
\setlength\textwidth{352.81416pt}
\AtBeginDocument{\setlength\parindent{0pt}}
%StartShownPreambleCommands
\usepackage{amsmath,esint,libertinust1math} \newcommand*\diff{\mathop{}\!\mathrm{d}}
%StopShownPreambleCommands
\begin{document}
\begin{align*}
\biggl(\int_{-\infty}^{\infty} e^{-x^2}\diff x\biggr)^2
  &= \int_{-\infty}^{\infty}\int_{-\infty}^\infty e^{-(x^2+y^2)}\diff x\diff y \\
  &= \int_0^{2\uppi}\int_0^{\infty} e^{-r^2}r\diff r\diff\theta                  \\
  &= \int_0^{2\uppi}\biggl(-{e^{-r^2}\over2}
        \bigg\vert_{r=0}^{r=\infty}\,\biggr)\diff\theta\\
  &= \uppi                                                         \tag*{q.e.d.}
\end{align*}
\end{document}