Update functions-app-settings.md

1) Add details for the system /user-assigned identity in conjunction with ApplicationInsights_AUTHENTICATION_STRING. 

2) Remove instead, as it might mislead the customer.

Author: Aghyad85

articles/azure-functions/functions-app-settings.md

@@ -58,11 +58,19 @@ Don't use both `APPINSIGHTS_INSTRUMENTATIONKEY` and `APPLICATIONINSIGHTS_CONNECT
 
 ## APPLICATIONINSIGHTS_AUTHENTICATION_STRING
 
-The connection string for Application Insights by using Microsoft Entra authentication. Use this setting when you must connect to your Application Insights workspace by using Microsoft Entra authentication. The string contains the client ID of either a system-assigned or a user-assigned managed identity that is authorized to publish telemetry to your Application Insights workspace. For more information, see [Microsoft Entra authentication for Application Insights](../azure-monitor/app/azure-ad-authentication.md).
+The connection string for Application Insights by using Microsoft Entra authentication. Use this setting when you must connect to your Application Insights workspace by using Microsoft Entra authentication. For more information, see [Microsoft Entra authentication for Application Insights](../azure-monitor/app/azure-ad-authentication.md).
 
-|Key|Sample value|
-|---|------------|
-|APPLICATIONINSIGHTS_AUTHENTICATION_STRING|`ClientId=<YOUR_CLIENT_ID>;Authorization=AAD`|
+  - For system-assigned identity:
+
+       | App setting    | Value    |
+       | -------------- |--------- |
+       | APPLICATIONINSIGHTS_AUTHENTICATION_STRING         | `Authorization=AAD`    |
+
+   - For user-assigned identity:
+
+       | App setting   | Value    |
+       | ------------- | -------- |
+       | APPLICATIONINSIGHTS_AUTHENTICATION_STRING         | `Authorization=AAD;ClientId={Client id of the User-Assigned Identity}`    |
 
 [!INCLUDE [functions-app-insights-disable-local-note](../../includes/functions-app-insights-disable-local-note.md)]
 
@@ -79,7 +87,7 @@ For more information, see [Connection strings](../azure-monitor/app/sdk-connecti
 |---|------------|
 |APPLICATIONINSIGHTS_CONNECTION_STRING|`InstrumentationKey=...`|
 
-To connect to Application Insights with Microsoft Entra authentication, you should instead use [`APPLICATIONINSIGHTS_AUTHENTICATION_STRING`](#applicationinsights_authentication_string).
+To connect to Application Insights with Microsoft Entra authentication, you should use [`APPLICATIONINSIGHTS_AUTHENTICATION_STRING`](#applicationinsights_authentication_string).
 
 ## AZURE_FUNCTION_PROXY_DISABLE_LOCAL_CALL