sich Mühe geben
A fun look at the meaning of the umlaut-monster die Mühe and the effort you have to make to say making an effort in German. Also: a really dumb pun with cows.
die Mühe, mühelos, sich Mühe geben, sich bemühen
This root is not 100% certain and it is only mentioned in German sources, but not in English ones.
The core idea of the root (if it existed) was something along the lines of:
being string willed, striving towards
It is thought to be the origin of the Latin mōs, which was a strong custom or will, and which is the origin of moral.
The other likely English relative is mood.