9

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:

enter image description here

14

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.

enter image description here

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