\documentclass{article}
\usepackage{prodint}
\def\d{\mathrm{d}}
\begin{document}
This is \verb+\prodi+ in action: $\prod_i\prodi\alpha_i(\d u)$. How does it look?
\bigskip
Now two equations to test \verb+\Prodi+
\[ 
\prod_{i=1}^n\Prodi_0^\tau \left(1-\d A_i(u)\right) 
\]

\[
\int_0^\infty \prod_{i=1}^n\Prodi_0^t\left(1-\lambda_i(u,z)\,\d u\right)\;\d F(z)\]

\bigskip
and one with \verb+\PRODI+
\[ \PRODI_0^t \left\{\int_0^u g(z)\,\d F(z)\right\}^2 \d u
\]

\end{document}