summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx')
-rw-r--r--Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx43
1 files changed, 43 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx b/Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx
new file mode 100644
index 00000000000..f7104d10ab9
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/einfuehrung2/09-08-44.ltx
@@ -0,0 +1,43 @@
+%%
+%% Ein Beispiel der DANTE-Edition
+%%
+%% 2. Auflage
+%%
+%% Beispiel 09-08-44 auf Seite 469.
+%%
+%% Copyright (C) 2016 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}