Compress integral symbol \int horizontally

Use \resizebox.

\documentclass{article}
\usepackage{graphicx}
\begin{document}
$\displaystyle\int$
\resizebox{.5\width}{\height}{$\displaystyle\int$}
$\displaystyle\int$
\end{document}

or use an upright integral symbol which is naturally narrower, e.g. from eulervm.

\documentclass{article}
\DeclareSymbolFont{eulargesymbols}{U}{zeuex}{m}{n}
\DeclareMathSymbol{\intop}{\mathop}{eulargesymbols}{"52}
\begin{document}
$\displaystyle\int$
\end{document}

Here I use scalerel package's \hstretch to compress the sign to 80, 60, and 40%, respectively. Unlike \resizebox, it automatically works across math styles. I have embodied it here as \varint[<scale>].

\documentclass{article}
\usepackage{scalerel}
\newcommand\varint[1][.8]{\mathrel{\hstretch{#1}{\int}}}
\begin{document}
\[
\int_0^x \varint_{\!\!\!0}^x \varint[.6]_{\!\!0}^x  \varint[.4]_{\!0}^x 
\]
\[
\scriptstyle \int \varint \varint[.6] \varint[.4]
\]
\end{document}

See this related question, Integral Sign $\int...$, for integral signs that are naturally more vertical and less slanted; in the Russian style, as it were.