Make Underbrace ignore Brackets

\documentclass{article}


\begin{document}
\begin{equation}
    h_n\biggl[f_X(0)\underbrace{\int_0^{+\infty}K(z)^2dz}_{\equiv\beta} +o_p(1)\biggr]
\end{equation}
\end{document}

I am not advocating this solution, but onw way to solve this issue and still allow for "automatic" resizing is to use \smash and an appopriate \vphantom:

Code:

\documentclass{article}

\begin{document}
\begin{equation}     
   h_n\left[f_X(0)\vphantom{\int}\smash{\underbrace{\int_0^{+\infty}K(z)^2dz}}_{\equiv\beta} +o_p(1)\right]
\end{equation}
\end{document}