How can a make a product of nested exponentials look nicer?

Question

Ideally, I would like to squeeze all of the exponentials under this integral together so that everything doesn't look so spaced out. My latex is

$$
\int_0^1 
e^{e^{e^{e^{e^{e^{e^{e^{e^{e^x}}}}}}}}}e^{e^{e^{e^{e^{e^{e^{e^{e^x}}}}}}}} 
e^{e^{e^{e^{e^{e^{e^{e^x}}}}}}} e^{e^{e^{e^{e^{e^{e^x}}}}}} 
e^{e^{e^{e^{e^{e^x}}}}} e^{e^{e^{e^{e^x}}}} e^{e^{e^{e^x}}} e^{e^{e^x}} 
e^{e^x} e^x \exd x
$$

which results in this:

You could introduce some negative \kern but I somehow don't think one can make this look good. — Skillmon, Aug 17 '18 at 19:17
Why don't you just define $\tau(0,x) = x, \tau(n,x) = e^{\tau(n-1,x)}$ and then write $\int\limits_0^1!\mathrm{d}x\ \sum_{n=1}^10\tau(n,x)$? — leftaroundabout, Aug 17 '18 at 22:21
Yeah I could do that, but I am still curious about how to format this. — SFSH, Aug 17 '18 at 23:46
the extra whitespace on the right when nesting superscript is a peculiarity of core TeX, see https://tex.stackexchange.com/a/144611/4686 for an approach to get bounding box tight even with many many nested superscripts... — , Sep 06 '18 at 13:18

score 14 · Accepted Answer · answered Aug 17 '18 at 20:05

Maybe this one:

\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\epowersx}{m}
 {
  \mathmakebox[1.5em][l]
   {
    e\prg_replicate:nn { #1 - 1 } { ^\c_group_begin_token \scriptstyle e }
    ^{ \scriptstyle x }
    \prg_replicate:nn { #1 - 1 } { \c_group_end_token }
   }
 }
\ExplSyntaxOff

\begin{document}

\[
\int_{0}^{1}
\epowersx{10}
\epowersx{9}
\epowersx{8}
\epowersx{7}
\epowersx{6}
\epowersx{5}
\epowersx{4}
\epowersx{3}
\epowersx{2}
e^x
\,
dx
\]

\end{document}

but I'd use different notation.

How can a make a product of nested exponentials look nicer?

1 Answers1