\documentclass{article}
\newcommand{\iint}{\int\!\!\!\int}
\newcommand{\iiint}{\int\!\!\!\int\!\!\!\int}
\newcommand{\idotsint}{\int\cdots\int}
\begin{document}\noindent
Multiple integral symbols in text formulas: $\iint$, $\iiint$, $\idotsint$

\noindent Multiple integral symbols in displayed formulas:
\[ \iint\quad\iiint\quad\idotsint \]
\end{document}
