%%
%% The LaTeX Companion, 3ed
%%
%% Example 11-2-28 on page II-147 in "breqn --- Automatic line breaking in math displays".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3examargin}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{330.59894pt}

  % Shorten the vertical size of the example ...
  \AtBeginDocument{%
    \setlength\abovedisplayskip{.2\abovedisplayskip}%
    \setlength\belowdisplayskip{.2\belowdisplayskip}%
  }

%StartShownPreambleCommands
\usepackage{breqn}
\newcommand\ve{\varepsilon}  \newcommand\tve{t_{\varepsilon}}
\newcommand\vf{\varphi}      \newcommand\yvf{y_{\varphi}}
\newcommand\bfE{\mathbf{E}}
%StopShownPreambleCommands

\begin{document}
  \begin{dmath}
    f_{h, \ve}(x, y)
    = \ve \bfE_{x, y} \int_0^{\tve} L_{x, \yvf(\ve u)} \vf(x) \,du
    = h \int L_{x, z} \vf(x) \rho_x(dz) + h
    \biggl[ \frac{1}{\tve}
      \biggl( \bfE_{y} \int_0^{\tve}  L_{x, y^x(s)} \vf(x) \,ds
      - \tve \int L_{x, z} \vf(x) \rho_x(dz)      \biggr)
      + \frac{1}{\tve}
      \biggl( \bfE_{y} \int_0^{\tve}  L_{x, y^x(s)} \vf(x) \,ds
      - \bfE_{x, y} \int_0^{\tve} L_{x, \yvf(\ve s)}
      \vf(x) \,ds    \biggr) \biggr]
  \end{dmath}
\end{document}