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-%%
-%% Ein Beispiel der DANTE-Edition
-%%
-%% 1. Auflage
-%%
-%% Beispiel 09-08-44 auf Seite 493.
-%%
-%% Copyright (C) 2011 Herbert Voss
-%%
-%% 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.
-%%
-%%
-%% ====
-% Show page(s) 1
-%%
-%%
-\documentclass[]{exaarticle}
-\pagestyle{empty}
-\setlength\textwidth{352.81416pt}
-\AtBeginDocument{\setlength\parindent{0pt}}
-\StartShownPreambleCommands
-\usepackage{mathtools} \newcommand*\diff{\mathop{}\!\mathrm{d}}
-\StopShownPreambleCommands
-\begin{document}
-\begin{align*}
-\MoveEqLeft[6]
- \frac{A}{x-x_1},\ \frac{A}{\left(x-x_1\right)^k},\ \frac{Ax+b}{x^2+px+q},\
- \frac{Ax+b}{\left(x^2+px+q\right)^k} \text{ mit } p^2<4q \text{ und } A\ne 0\\
- \int\frac{A}{x-x_1}\diff x &= A\ln\left|x-x_1\right|+C\\
- \int\frac{A}{\left(x-x_1\right)^k}\diff x&=-\frac{A}{(k-1)\left(x-x_1\right)^{k-1}}+C\\
- \int\frac{\diff x}{x^2+px+q}
- &= \frac{2}{\sqrt{4q-p^2}}\cdot\arctan\frac{2x+p}{\sqrt{4q-p^2}}+C\\
- \int\frac{Ax+B}{x^2+px+q}\diff x
- &= \frac{A}{2}\ln\left|x^2+px+q\right| +\frac{2B-Ap}{\sqrt{4q-p^2}}
- \cdot\arctan\frac{2x+p}{\sqrt{4q-p^2}}+C
-\end{align*}
-\end{document}