\documentclass[a4paper]{report}
\usepackage{mathrsfs}
\usepackage{braket}
\begin{document}
\begin{equation}
\int_{\mathscr{B}, \mathscr{C}} db \, dc \, \ket{a', b, c} \bra{a', b, c} \rightarrow \ket{a'} \bra{a'},
\end{equation}
\end{document}
I want the db & dc to be 'normally' spaced with respect to the integral sign, so ignoring the subscript. I came across \llap and \rlap, but they are designed for text. I also briefly looked at this: https://www.math.lsu.edu/~aperlis/publications/mathclap/, but I wondered if there was a simpler solution by now.

