
fluchen
to swear
To use swear words or expletives to express anger, pain, or frustration.
Er fluchte laut, als er mit dem Hammer seinen Daumen traf.
He swore loudly when he hit his thumb with the hammer.
to curse / swear
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to swear
To use swear words or expletives to express anger, pain, or frustration.
Er fluchte laut, als er mit dem Hammer seinen Daumen traf.
He swore loudly when he hit his thumb with the hammer.

to curse
To wish evil on someone or something and express this with strong, negative words (curses).
Sie fluchte auf den Regen, der ihre Pläne für das Picknick zunichtemachte.
She cursed the rain that ruined her plans for the picnic.
The verb 'fluchen' (to curse/swear) is closely related to the noun 'der Fluch' (curse). While 'fluchen' describes the act of swearing, 'der Fluch' is a curse meant to bring misfortune to someone.
Auf dem alten Schloss soll ein schrecklicher Fluch liegen.
A terrible curse is said to lie on the old castle.
You can simply 'fluchen' (swear/curse) in general, without naming a target. But if you want to express what or whom you are angry about, you use the preposition 'auf' with the accusative.
Er fluchte leise, als er den Schlüssel nicht finden konnte.
He swore quietly when he could not find the key.
To describe the way someone is swearing, the verb is often combined with adverbs like 'laut' (loudly), 'leise' (quietly), 'wütend' (angrily), or 'vor sich hin' (to oneself).
Als er sich den Kopf stieß, fluchte er laut.
When he bumped his head, he swore loudly.
to insult
Beschimpfen and fluchen can both involve strongly negative words. Beschimpfen requires a clear target who is being personally insulted, while fluchen can simply express anger, pain, or frustration without attacking anyone. Choose beschimpfen for an attack on someone and fluchen for mere frustration.

Die Frau fluchte, als das Gerät schon wieder kaputtging.
The woman swore when the device broke again.
Die Frau beschimpfte den Verkäufer, weil das Gerät schon wieder kaputt war.
The woman insulted the salesperson because the device had broken again.