integral
Essential, fundamental, or indispensable to a whole; a firmly belonging part of it.
Vertrauen ist ein integraler Bestandteil einer funktionierenden Partnerschaft.
Trust is an integral part of a functioning partnership.

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Essential, fundamental, or indispensable to a whole; a firmly belonging part of it.
Vertrauen ist ein integraler Bestandteil einer funktionierenden Partnerschaft.
Trust is an integral part of a functioning partnership.

You can tell from the context whether the general or the mathematical meaning is intended. Words like 'Bestandteil' (component) or 'Teil' (part) point to the general meaning, while terms like 'Funktion' (function) or 'Rechnung' (calculation) refer to mathematics.
Kreativität ist ein integraler Teil des Designs.
Creativity is an integral part of design.
The adjective 'integral' is very often used in the fixed phrase 'integraler Bestandteil' (integral part/component). It emphasizes that something is an essential and inseparable part of a whole.
Die Einhaltung der Menschenrechte ist ein integraler Bestandteil einer Demokratie.
Respect for human rights is an integral part of a democracy.
In its general meaning, 'integral' belongs to elevated written language or formal contexts. It is rarely used in everyday conversation.
Die ethische Reflexion ist ein integraler Aspekt des Forschungsprojekts.
Ethical reflection is an integral aspect of the research project.
essential / significantly
'wesentlich' and 'integral' can both mean that something firmly and importantly belongs to a whole. 'wesentlich' is the more general word and sounds more natural in everyday language. 'integral' sounds more formal and especially emphasizes that something is a fixed part of a system, plan, or whole. If you simply want to say that something is very important, 'wesentlich' almost always fits. If you want to show that something is not only important but a necessary part of the whole, 'integral' can be more precise.

Regelmäßige Gespräche sind ein integraler Teil unseres Projekts.
Regular conversations are an integral part of our project.
Ein ruhiger Ort ist für konzentriertes Lernen wesentlich.
A quiet place is essential for focused learning.