How to register ILogger in Startup

I have a logging section in json settings:

{
    "logging": {
        "applicationInsights": {
            "samplingSettings": {
                "isEnabled": true,
                "excludedTypes": "Request"
            }
        }
    }
}

I need to register it in Startup so to be able to use in handlers.

So far I have tried various options but none of them work:

Option 1

    builder.Services.AddApplicationInsightsTelemetry(); // returns error: IServicesCollection does not contain a definition for AddApplicationInsightsTelemetry 

Option 1 Update

I added Microsoft.ApplicationInsights.AspNetCore to the project so AddApplicationInsightsTelemetry is now available but still ILogger gives null.

Option 2

    builder.Services.AddLogging(logging =>
    {
        logging.AddConfiguration(hostingContext.GetSection("logging"));
    }); // ILogger is null in handler

but can't find any information on my particular case

How to register ILogger in Startup that will keep using settings from my app json?

This is the handler I am using:

public class ExampleHandler : IRequestHandler<ExampleQuery, bool>
{
    private readonly ILogger _log;

    public ExampleHandler(ILogger log)
    {
        _log = log;
    }

    public async Task<bool> Handle(ExampleQuery request, CancellationToken cancellationToken)
    {
        // _log is null here;

        return true;
    }
}

1. Install Microsoft.ApplicationInsights.AspNetCore nuget package

2. Resolve typed logger:

public class ExampleHandler : IRequestHandler<ExampleQuery, bool>
{
    private readonly ILogger<ExampleHandler> _log;

    public ExampleHandler(ILogger<ExampleHandler> log)
    {
        _log = log;
    }
    ...
}