
sich integrieren
to integrate
To become part of a group or society and adapt to its social and cultural circumstances.
Es fiel ihm leicht, sich in das neue Team zu integrieren.
It was easy for him to integrate into the new team.
to integrate
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to integrate
To become part of a group or society and adapt to its social and cultural circumstances.
Es fiel ihm leicht, sich in das neue Team zu integrieren.
It was easy for him to integrate into the new team.

to integrate
To insert or include something in a larger whole; to combine different parts into one unit.
Wir müssen die neuen Funktionen nahtlos in die bestehende Software integrieren.
We need to integrate the new features seamlessly into the existing software.

to integrate
In mathematics, to apply integral calculus to a function in order to find its antiderivative or a definite integral.
Der Lehrer erklärte, wie man die Funktion f(x) = 2x von 0 bis 1 integriert.
The teacher explained how to integrate the function f(x) = 2x from 0 to 1.
Pay attention to the difference: 'sich integrieren' (to integrate oneself / to integrate) is reflexive and means that a person becomes part of a group. 'Etwas integrieren' (to integrate something) is transitive and means that you insert a part into a whole.
Die neuen Mitarbeiter haben sich schnell ins Team integriert.
The new employees integrated into the team quickly.
The verb 'integrieren' (to integrate) is almost always used with the preposition 'in' followed by the accusative. This expresses what someone or something is integrated into.
Sie hat sich gut in die neue Schulklasse integriert.
She integrated well into the new school class.
You can clearly recognize the mathematical meaning of 'integrieren' (to integrate) from the context. It is used only in mathematics, often together with words like 'Funktion' (function), 'Kurve' (curve), or 'von ... bis' (from ... to).
Können Sie uns zeigen, wie man diese Funktion integriert?
Can you show us how to integrate this function?
to install / incorporate
Integrieren and einbauen can both mean taking something into a larger context. Integrieren emphasizes more strongly that it forms a coherent whole with the other parts. Einbauen focuses more on inserting it at a specific place.

Wir integrieren die neue Szene so in das Stück, dass sie gut zur Handlung passt.
We are integrating the new scene into the play so that it fits well with the plot.
Wir bauen die neue Szene direkt vor dem letzten Gespräch in das Stück ein.
We are inserting the new scene into the play directly before the final conversation.