I have created the following "table" as part of a larger document:
\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[fleqn]{mathtools}
\usepackage{tikz}
\usetikzlibrary{positioning}
\newcommand*{\dd}[3][]{\tfrac{\mathrm{d}^{#1}#2}{\mathrm{d}#3^{#1}}}
\newcommand*{\D}[1]{\mathop{}\!\mathrm{d} #1}
\begin{document}
\begin{tikzpicture}[node distance=0.5ex and 1em]
\node (d0) {\(u\)};
\node[right=of d0] (i0) {\(\D{v}\)};
\node[below=of d0] (d1) {\(\dd{u}{x}\)};
\node[right=of d1] (i1) {\(\int \D{v} \D{x}\)};
\node[below=of d1] (d2) {\(\dd[2]{u}{x}\)};
\node[right=of d2] (i2) {\(\int\left(\int\D{v}\D{x}\right)\D{x}\)};
\node[below=of d2] (d3) {\(\cdots\)};
\node[right=of d3] (i3) {\(\int\left(\int\left(\int\D{v}\D{x}\right)\D{x}%
\right)\D{x}\)};
\node[below=of i3] (i4) {\(\cdots\)};
\draw (d0.east) -- (i1.west) (d1.east) -- (i2.west) (d2.east) -- (i3.west);
\end{tikzpicture}
\end{document}
Now this is okay (perhaps a little worse than that). How can I improve this design? I was thinking that to make the lines all straight making the first column right-aligned and the second column left-aligned would help, but I do not know how to do this. Any suggestions?

tikz. Use atabularenvironment for the table and usetikzmarkto mark the points where you want to draw the lines to/from. This example should get you started: Inserting an image properly in a table, but there are numerous other examples on this site. – Peter Grill Mar 11 '16 at 03:48