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\begin{document}
\newcommandx\VolInt[2][usedefault, addprefix=\global, 1=]{\int_{\mathsf{V}#1}#2\,\mathrm{d}\mathsf{V}}


Example 1 (without optional argument):$\VolInt{\frac{\partial\phi}{\partial t}}$

Example 2 (with optional argument): $\VolInt[(t)]{\frac{\partial\phi}{\partial t}}$
\end{document}
