To emphasize the act of combining:
* Co-integrate: To integrate together, usually two or more things.
* Inter-integrate: To integrate between different elements or systems.
* Re-integrate: To integrate again, after a period of separation or disruption.
To emphasize the result of integration:
* Dis-integrate: To break apart, the opposite of integrate.
* De-integrate: To separate or remove from a system, often used in the context of race or social groups.
Other relevant prefixes:
* Pre-integrate: To integrate beforehand, in preparation for something.
* Post-integrate: To integrate after an event or action.
The best prefix to use depends on the specific context and the meaning you want to convey.