AX 2012 Error: An attempt has been made to use a data extension 'AXREPORTDATAPROVIDER'

If you get the following error message from SSRS:

"An attempt has been made to use a data extension 'AXREPORTDATAPROVIDER' that is either not registered for this report server or is not supported in this edition of Reporting Services. (rsDataExtensionNotFound)"

Then the solution would be to:

1. Try reinstalling AX report extensions.
2. If that doesn't work, try uninstalling report extensions, uninstalling SSRS, installing SSRS and finally installing report extensions again.
3. If it still doesn't work, then you seemingly have to reinstall the entire SQL database.

Sometimes step 1 is enough, but I've seen a case where we couldn't get it to work until we completed step 3.

Let me know if you know a simpler solution. 

NB: the configuration files for SSRS were correct and didn't change after completing any of the above steps, so the source of the error is someplace else.