There are various 'connector' packages out there for the likes of SalesForce etc (https://www.google.co.uk/search?q=uccx+connector&aq=f&oq=uccx+connector&aqs=chrome.0.57j60j59j62l3.2057j0&sourceid=chrome&ie=UTF-8
) but in general the implementation of integration to the customer's CRM package is the job of the Cisco Partner or engineer. You wouldn't enter customer information into UCCX itself, but into a CRM app, and UCCX would 'trigger' the CRM app.
How that is done can take many forms:
Database/ODBC integration - e.g. looking up customer information during the 'script' phase of the call based on the customer CLI or account number that they enter
Web Service integration - SOAP/AXL or other such calls to web applications
Desktop Integration - e.g. keystroke macros, or calls to local applications or HTTP URLs to trigger or retrieve information
So the bottom line is that yes, you can do it, but what you can do depends on what CRM package the customer uses, and what APIs/methods of intregration are available. If you are 'lucky' they might use a package that there is an off-the-shelf integration for, but those would typically involve additional cost anyway...
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