An embarrassing Multline error

Question

Here I am, trying to display an equation that takes way too long for one line, so I called multline.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\usepackage{amssymb,amsmath}
\usepackage{amsfonts}
\geometry{a4paper}  
\begin{document}
\begin{multline}
S_E=\int \mathrm{d}t \left[\frac{(f'\dot{\xi})^2}{2} \int \mathrm{d}x(\phi_0+1)^2+\frac{f^2}{2}\int \mathrm{d}x \phi'^2\\
+ \int \mathrm{d}x (\psi^2-1)^2(\psi^2-\delta_1)
+ \frac{1}{\gamma+\psi^2}\left[\left(f^2(\phi_0^2+1)-2f(\phi_0+1)\right)^2-\frac{\delta_2{4}(f(\phi_0+1)-3)(f(\phi_0+1))^2\right]\right] \\
\label{actionrescale}
\end{multline}
\end{document}

However, if I called \begin{equation} and \end{equation} instead of \begin{multline} and \end{multline} the equation would show up just fine (or at least as much of it that could fit on the resulting pdf file). What exactly is wrong with this document?

Answer 1

Here is a solution. I split it differently, and define a differential operator \d that has a correct spacing (it comes from one answer here, but I don't know where).

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\usepackage{amssymb,amsmath}
\usepackage{amsfonts}
\geometry{a4paper}

\renewcommand*{\d}{\mathop{}\mathopen{}\mathrm{d}}

\begin{document}

\begin{multline}
\label{actionrescale}
S_E=\int \d t \biggl[\frac{(f'\dot{\xi})^2}{2} \int (\phi_0+1)^2 \d x + \frac{f^2}{2}\int \phi'^2 \d x
+ \int (\psi^2-1)^2(\psi^2-\delta_1)\d x  \\ 
+ \frac{1}{\gamma+\psi^2}\Bigl[\left(f^2(\phi_0^2 + 1)-2f(\phi_0 + 1)\right)^2 -
 \frac{\delta_2}{4}\bigl(f(\phi_0 + 1)-3\bigr)\bigl(f(\phi_0 + 1)\bigr)^2\Bigr]\biggr]
\end{multline}

\end{document}