does Rational DOORS integrate with IBM X-Analysis, IBM IGC, and datawiki?

As far as I know, these integrations do not exist.

Expanding on Bas' answer ...

I'm not aware of pre-written integrations to these tools. However DOORS NG offers a number of APIs for integrations, and services teams can build them for you if you don't want to write the integration yourself.

Server-side:  OSLC APIs, reportable REST APIs, and Tracked Resource Set (TRS) APIs
Client-side (browser): Javascript APIs

And to expand in the ways to integrate with DNG:

• RRC Reportable API - creating custom reports to be run from DNG or RPE
  

• OSLC RM V2 API - the open standard way to programmatically integrate with DOORS Next Generation, there is an elaborate workshop to get you started here OSLC Workshop article. These programs can be from any language that support HTTP REST calls, e.g. Java, C# etc. Hence these are more flexible to run and can read and update DNG data, as part of a web server, or standalone, but have some limitations set by the current OSLC standard, for example module support.
  
• TRS (Tracked Resource Sets) is the REST API to hook into the stream of low level changes done to resources in the DNG application
  

• and additionally, there is the so called client extension capability, these are Javascript extension that generally added as widgets you can run from the dashboard, and can be used to view and edit DNG data. It's more tailored to DNG, so has better module support, but is limited to run in a browser/javascript environment.