aufgenommen
accepted
Describes the feeling or state of being integrated into and accepted by a group or community.
Vom ersten Tag an fühlte sie sich im neuen Team gut aufgenommen.
From the very first day, she felt well accepted in the new team.

accepted / recorded / absorbed
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accepted
Describes the feeling or state of being integrated into and accepted by a group or community.
Vom ersten Tag an fühlte sie sich im neuen Team gut aufgenommen.
From the very first day, she felt well accepted in the new team.

'Aufgenommen' is the past participle of the separable verb 'aufnehmen' (to take in / record). The different meanings as an adjective are directly derived from the meanings of the verb, e.g., to take someone into a group or to record a sound.
Der Verein hat zehn neue Mitglieder aufgenommen.
The club accepted ten new members.
The context shows which meaning is intended. If it is about feelings and groups, it means 'akzeptiert' (accepted). In connection with media such as film or music, it means 'aufgezeichnet' (recorded). In biological contexts, it means 'absorbiert' (absorbed).
Die aufgenommene Rede des Präsidenten wurde im Fernsehen gezeigt.
The recorded speech by the president was shown on television.
In the meaning 'akzeptiert sein' (to be accepted), 'aufgenommen' is very often combined with the verb 'sich fühlen' (to feel). An adverb such as 'gut' (well), 'herzlich' (warmly), or 'freundlich' (kindly) describes the nature of the reception.
Ich habe mich in der neuen Firma sofort herzlich aufgenommen gefühlt.
I immediately felt warmly accepted at the new company.
integrated
'integriert' and 'aufgenommen' can both describe that someone belongs to a group and is accepted. 'aufgenommen' emphasizes more the moment or feeling that a group accepts someone. 'integriert' describes the state afterward more strongly: the person is truly part of the group or society and is able to find their place there. Learners may confuse the words because both speak positively about belonging. In practical terms: a person is 'aufgenommen' into a group; over time, they are well 'integriert' there.

Im neuen Team wurde Ali freundlich aufgenommen und sofort zum Mittagessen eingeladen.
Ali was warmly accepted into the new team and immediately invited to lunch.
Nach einem Jahr im Verein fühlt sich Sofia gut integriert.
After a year in the club, Sofia feels well integrated.