%% %% An UIT Edition example %% %% Example 09-17-12 on page 193. %% %% Copyright (C) 2010 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{375.57637pt} \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{ with } p^2<4q \text{ and } 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}