I've been reading several blog posts about application insights and Sitecore logs, and I've not been able to get the proper configuration working. This is using Sitecore 9 ARM templates on Azure app service.
We've got a QA instance that has one AI instance, and a CM/CD instance set that has another AI instance. Doing some reading, I saw that I needed to edit the ApplicationInsights.config file in the web root to include the InstrumentationKey value from the AI properties. I did this for the appropriate environment instance, using the App Service Editor (since the keys are different per environment, I didn't want to include the config file in my project root).
I did a restart of my QA app service as a test, then logged into Sitecore and bounced around. I then went to the Azure portal and to the AI instance for my QA, and clicked the Search option to check for the last 24 hours. I didn't get any results, and I'd expect to at least get the "audit" message when I logged in as admin, if not all the startup messages I'm used to seeing in the Sitecore log files.
I'm not sure if there's a time point at which log results write over, if I'm looking in the wrong place, or if there's additional configuration required. I haven't seen a good definitive "this is how you do it" blog on the matter (though I intend to write one once I have this figured out).