Two ways that I know of ...
1)
SELECT ServerProperty('IsIntegratedSecurityOnly')
1 = Integrated Security
0 = SQL & Integrated Security
2)
EXEC master.dbo.xp_instance_regread N'HKEY_LOCAL_MACHINE', N'Software\Microsoft\MSSQLServer\MSSQLServer', N'LoginMode'
1 = Integrated Security
2 = SQL & Integrated Security