I was able to get integrated authentication to work (after installing initially to a temp database using mixed-mode).
Note: Make sure you stop JIRA before doing this.
First I changed my dbconfig.xml (in JIRA home directory) to have the following:
<url>jdbc:sqlserver://SERVER;databaseName=JIRADATABASE;integratedSecurity=true</url>
<driver-class>com.microsoft.sqlserver.jdbc.SQLServerDriver</driver-class>
I then downloaded the Microsoft SQL Server JDBC Driver 2.0 from here: http://www.microsoft.com/en-us/download/details.aspx?id=2505
Once you extract the files from that, copy sqljdbc4.jar into the "lib" folder in the JIRA install (not home) directory.
Then, you'll want to find the appropriate dll file from the "auth" folder (within the files extracted above) called "sqljdbc_auth.dll". Copy that into c:\windows\system32. Make sure you choose the right file for your system (i.e. x86 = 32-bit).
That's it. I restarted JIRA and it worked.
Sorry, didn't realize I was in a Crowd bug. The above was for JIRA, but may be helpful here too.