Is it possible to customize an "int" symbol with three index notation?

Question

like this

I need an extra index notation for the integral symbol .

I know the /displaylimits could modify the position of index notation, but I wonder how to add three index notation to an integral symbol?

Answer 1

The macro \inttriple, defined below, may do the job.

\documentclass{article} % or some other suitable document class
\usepackage{mathtools} % for '\mathclap' macro
\newlength\mylen 
\settowidth\mylen{$\displaystyle\int$}

%% define a new macro:
\newcommand\inttriple[3]{\mathop{{\int\limits_{\mathclap{#1}}}
                                 \kern-\mylen 
                                 {\int_{#2}^{#3}}}}
           
\begin{document}
\begin{align*}
x &= \int_{0}^{\infty} \\
  &= \inttriple{\gamma}{0}{\infty} \\
  &= \inttriple{\text{hello}}{0}{\infty}
\end{align*}
\end{document}