Tabular integration by parts

Question

All I am trying to do is write an integration by parts table in LaTeX. I can't seem to find an .tex code examples anywhere though I have seen pictures of such tables in PDF form (like at http://cazelais.disted.camosun.bc.ca/187/parts.pdf for example). Hopefully someone can let me know real quick.

Answer 1

I assume you are asking about the tabular method of integration by parts, and one way would be to use tikzmark to note the location of the points and the after the table draw the arrows between the appropriate points:

Note:

• This does require two runs. First one to determine the locations, and the second to do the drawing.

• The \tikzmark is from Adding a large brace next to a body of text.

• You can globally alter the style of the arrows via Arrow Style.

Code

\documentclass{article} 

\usepackage{booktabs}
\usepackage{xparse}
\usepackage{tikz}
\usetikzlibrary{calc}

\tikzset{Arrow Style/.style={text=black, font=\boldmath}}

\newcommand{\tikzmark}[1]{%
    \tikz[overlay, remember picture, baseline] \node (#1) {};%
}

\newcommand*{\XShift}{0.5em}
\newcommand*{\YShift}{0.5ex}

\NewDocumentCommand{\DrawArrow}{s O{} m m m}{%
    \begin{tikzpicture}[overlay,remember picture]
        \draw[->, thick, Arrow Style, #2] 
                ($(#3.west)+(\XShift,\YShift)$) -- 
                ($(#4.east)+(-\XShift,\YShift)$)
        node [midway,above] {#5};
    \end{tikzpicture}%
}

\begin{document}
\[
    \renewcommand{\arraystretch}{1.5}
    \begin{array}{c @{\hspace*{1.0cm}} c}\toprule
       D & I \\\cmidrule{1-2}
      x^2\tikzmark{Left 1} & \tikzmark{Right 1}e^2x \\
      2x \tikzmark{Left 2} & \tikzmark{Right 2}\frac{1}{2} e^{2x} \\      
      2  \tikzmark{Left 3} & \tikzmark{Right 3}\frac{1}{4} e^{2x} \\      
      0  \tikzmark{Left 4} & \tikzmark{Right 4}\frac{1}{8} e^{2x} \\\bottomrule
    \end{array}
\]
%-----------------------------------------
\DrawArrow[draw=red]{Left 1}{Right 2}{$+$}%
\DrawArrow[draw=brown]{Left 2}{Right 3}{$-$}%
\DrawArrow[draw=blue]{Left 3}{Right 4}{$+$}%
\end{document}

Answer 2

Here's a start: There are various approaches to the arrows. I'll let someone else explain a tikz solution. But you can use pstricks and pst-nodes to accomplish it.

MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{pstricks,pst-node}
\pagestyle{empty}
\newcommand{\diff}[1]{\mathrm{d}#1}
\newcommand{\me}{\mathrm{e}}
\begin{document}

\noindent Use \verb=\boxed{...}= to enclose the contents of an equation in a frame.
\[
    \boxed{\int_0^\infty \me^{-x^2}\diff{x}}
\]
Use \verb=\quad= and \verb=\text{...}= to add space and add regular
text in an equation
\[
    u = x \quad \text{ and } \quad \diff v = \cos x \diff x
\]
Use the \verb=align= environment to align math equation upon a given
position in the equation indicated by \verb=&=
\begin{align*}
    \int x \cos x \diff{x} &= x \sin x - \int \sin x \diff x \\
    &= x \sin x + \cos x +C
\end{align*}

\noindent\verb=pstricks= provides \verb=pst-node= to allow you to label and
connect nodes.
\renewcommand{\arraystretch}{3}
\[\begin{array}{c@{\hspace*{6em}}c}
    D                   & I                                  \\\hline
    x^2\rnode[br]{A1}{} & \me^{2ex}                          \\
    2x\rnode[br]{B1}{}  & \rnode[l]{B2}{}\frac{1}{2}\me^{2x} \\
    2\rnode[br]{C1}{}   & \rnode[l]{C2}{}\frac{1}{4}\me^{2x}
\end{array}\]
%%
\ncline[nodesep=1em,arrows=->]{A1}{B2}
\lput{:U}{\rput[c]{U}(0,2ex){line label}}
%%
\ncline[nodesep=1em,arrows=->]{B1}{C2}
\lput{:U}{\rput[c]{U}(0,2ex){line label}}


\end{document}

If you would like to go the pdflatex route using pstricks try the following MWE:

\documentclass{article}
\usepackage{amsmath}
\usepackage{pstricks}
\usepackage{auto-pst-pdf}
\usepackage{pst-node}
\pagestyle{empty}
\newcommand{\diff}[1]{\mathrm{d}#1}
\newcommand{\me}{\mathrm{e}}
\begin{document}

\noindent Use \verb=\boxed{...}= to enclose the contents of an equation in a frame.
\[
    \boxed{\int_0^\infty \me^{-x^2}\diff{x}}
\]
Use \verb=\quad= and \verb=\text{...}= to add space and add regular
text in an equation
\[
    u = x \quad \text{ and } \quad \diff v = \cos x \diff x
\]
Use the \verb=align= environment to align math equation upon a given
position in the equation indicated by \verb=&=
\begin{align*}
    \int x \cos x \diff{x} &= x \sin x - \int \sin x \diff x \\
    &= x \sin x + \cos x +C
\end{align*}

\noindent%
\begin{postscript}
\verb=pstricks= provides \verb=pst-node= to allow you to label and
connect nodes.
\renewcommand{\arraystretch}{3}
\[\begin{array}{c@{\hspace*{6em}}c}
    D                   & I                                  \\\hline
    x^2\rnode[br]{A1}{} & \me^{2ex}                          \\
    2x\rnode[br]{B1}{}  & \rnode[l]{B2}{}\frac{1}{2}\me^{2x} \\
    2\rnode[br]{C1}{}   & \rnode[l]{C2}{}\frac{1}{4}\me^{2x}
\end{array}\]
%%
\ncline[nodesep=1em,arrows=->]{A1}{B2}
\lput{:U}{\rput[c]{U}(0,2ex){line label}}
%%
\ncline[nodesep=1em,arrows=->]{B1}{C2}
\lput{:U}{\rput[c]{U}(0,2ex){line label}}
\end{postscript}

\end{document}

This is following the instructions found in the answer to How to use PSTricks in pdfLaTeX?. Also, using the environment \begin{postscript}...\end{postscript} is per the instructions found at the pstricks webside

Answer 3

With {NiceArray} of nicematrix.

\documentclass{article} 
\usepackage{nicematrix}
\usepackage{booktabs}
\usepackage{tikz}

\begin{document}

\[
\renewcommand{\arraystretch}{1.5}
\begin{NiceArray}{c @{\hspace*{1.0cm}} c}[create-medium-nodes]
  \toprule
     D & I \\
  \cmidrule{1-2}
    x^2 & e^2x \\
    2x  & \frac{1}{2} e^{2x} \\      
    2   & \frac{1}{4} e^{2x} \\      
    0   & \frac{1}{8} e^{2x} \\
  \bottomrule
\CodeAfter
  \begin{tikzpicture} [->, name suffix = -medium]
  \draw [red] (2-1) -- node [above] {$+$} (3-2) ; 
  \draw [brown] (3-1) -- node [above] {$-$} (4-2) ; 
  \draw [blue] (4-1) -- node [above] {$+$} (5-2) ; 
  \end{tikzpicture}
\end{NiceArray}
\]

\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).