
mühsam
arduous
Involving great effort, exertion, or patience; difficult or time-consuming.
Der Aufstieg auf den Berg war mühsam, aber die Aussicht hat sich gelohnt.
The climb up the mountain was arduous, but the view was worth it.
arduous / tedious
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arduous
Involving great effort, exertion, or patience; difficult or time-consuming.
Der Aufstieg auf den Berg war mühsam, aber die Aussicht hat sich gelohnt.
The climb up the mountain was arduous, but the view was worth it.

tedious
Colloquial for a person or situation that is exhausting, complicated, or annoying.
Die Diskussion mit ihm ist immer so mühsam, weil er nie nachgibt.
The discussion with him is always so tedious because he never gives in.
The adjective 'mühsam' (arduous / tedious) is derived from the noun 'die Mühe' (effort). The ending '-sam' means something like 'full of'. So 'mühsam' literally means 'full of effort'.
Das war eine mühsame Aufgabe, aber jetzt ist sie fertig.
That was a tedious task, but now it's finished.
In its main meaning, 'mühsam' often describes physical or mental efforts. Typical nouns are 'Arbeit' (work), 'Aufgabe' (task), 'Weg' (path/way), or 'Suche' (search).
Die Suche nach der verlorenen Brieftasche war lang und mühsam.
The search for the lost wallet was long and arduous.
As an adverb, 'mühsam' describes how an action is carried out: slowly and with a lot of effort. It then stands directly with the verb.
Der alte Mann bewegte sich mühsam die Treppe hinauf.
The old man moved laboriously up the stairs.
Colloquially, 'mühsam' can also describe a person or situation that you find annoying or complicated. This use is informal and slightly negative.
Ein Gespräch mit ihm zu führen ist mühsam, er hört einfach nicht zu.
Having a conversation with him is tedious; he simply doesn't listen.
heavy / difficult
Schwer and mühsam can both describe a task that is not easy to complete. Schwer generally emphasizes the high level of difficulty. Mühsam, on the other hand, highlights the great effort, patience, or length of time involved in carrying it out.

Die Aufgabe ist mühsam, weil jeder Wert einzeln geprüft werden muss.
The task is arduous because each value has to be checked individually.
Die Aufgabe ist schwer, weil sie komplizierte Berechnungen verlangt.
The task is difficult because it requires complicated calculations.