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Is there a way to use only the symbol from the integral of the package euler without loading the whole package?

Thanks in advance!

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In the modern toolchain, with unicode-math, you can download the Neo Euler font and write:

\setmathfont[range = {\int, \oint}, Scale = MatchUppercase]{euler.otf}

With the legacy type 1 fonts, look up the symbol in appendix D of the amsfonts manual. The \int symbol is in the font euex, and we see that the display-style \int is in slot "5A and the text-style \int in slot "52. Therefore, we can load this font as a math alphabet and select the appropriate style using \mathchoice.

\documentclass[varwidth]{standalone}
\usepackage[T1]{fontenc}

\makeatletter
\DeclareSymbolFont{eulerex}{U}{euex}{m}{n}
\DeclareMathSymbol{\big@int}{\mathop}{eulerex}{"5A}
\DeclareMathSymbol{\little@int}{\mathop}{eulerex}{"52}
\DeclareRobustCommand{\int}[0]{\mathchoice%
{\big@int}%
{\little@int}%
{\little@int}%
{\little@int}}
\makeatother

\begin{document}
\( \displaystyle\int\ldots \) \\
\( \textstyle\int\ldots \) \\
\( \int_{\int_{\int}} \ldots \)
\end{document}

Euler integrals

And likewise for \oint if you need it.

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