Compress cases environment horizontally

Question

I currently have the following cases environment:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{lipsum}

\begin{document}

\lipsum[66]
\[
G(x,u) = \begin{cases}
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi + x - u)}{4\sinh \pi} & \text{for \(0 \le x \le u \le \pi\)}\vspace{0.25em}\\
-\dfrac{\cosh (\pi - x - u) + \cosh(\pi + x + u) - 2\cosh (\pi - x + u)}{4\sinh \pi} & \text{\phantom{for} \(0 \le u \le x \le \pi\).}
\end{cases}
\]

\end{document}

but it produces a result that sticks out into the margin:

I think the natural way to fix this would be to intersperse the expressions and conditions in the following way (apologies for bad image editing, but hopefully it's clear what I mean):

Is there a straightforward way of achieving this with cases or similar?

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This is similar to the desired output in this question, which used a hack to produce something along the right lines. But the answers in that case focused on splitting the expressions, which doesn't work well for me.

Answer 1

You can move the condition to a new line:

\documentclass{article}
\usepackage{mathtools}
\usepackage{lipsum}

\begin{document}

\lipsum[66]
\begin{equation}
G(x,u) = \begin{cases}
-\dfrac{\cosh(\pi-x-u)+\cosh(\pi+x+u)-2\cosh(\pi+x-u)}{4\sinh\pi} & \\
                     & \makebox[0pt][r]{for $0 \le x \le u \le\pi$} \\[2ex]
-\dfrac{\cosh(\pi-x-u)+\cosh(\pi+x+u)-2\cosh(\pi-x+u)}{4\sinh\pi} & \\
                     & \makebox[0pt][r]{$0\le u\le x\le\pi$}
\end{cases}
\end{equation}

\end{document}