在使用Application Insights时，ILogger错误日志是默认情况下不会被Application Insights自动收集的。但是，我们可以通过自定义代码来实现将ILogger错误日志发送到Application Insights。

下面是一个示例代码，演示了如何将ILogger错误日志发送到Application Insights：

1. 首先，确保你的项目中已经添加了Microsoft.ApplicationInsights.AspNetCore包。

2. 在Startup.cs文件中，添加以下代码：

using Microsoft.ApplicationInsights;
using Microsoft.ApplicationInsights.Extensibility;
using Microsoft.ApplicationInsights.AspNetCore.Extensions;
using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Logging;

public class Startup
{
    public Startup(IConfiguration configuration)
    {
        Configuration = configuration;
    }

    public IConfiguration Configuration { get; }

    public void ConfigureServices(IServiceCollection services)
    {
        services.AddApplicationInsightsTelemetry(Configuration); // 添加Application Insights服务

        // 注册自定义ILogger提供程序
        services.AddSingleton();

        services.AddControllersWithViews();
    }

    public void Configure(IApplicationBuilder app, IWebHostEnvironment env)
    {
        // ...

        app.UseDeveloperExceptionPage();

        // ...
    }
}

3. 创建一个自定义的ILoggerProvider实现，用于将ILogger错误日志发送到Application Insights：

using Microsoft.ApplicationInsights;
using Microsoft.ApplicationInsights.DataContracts;
using Microsoft.ApplicationInsights.Extensibility;
using Microsoft.Extensions.Logging;

public class ApplicationInsightsLoggerProvider : ILoggerProvider
{
    private readonly TelemetryClient _telemetryClient;

    public ApplicationInsightsLoggerProvider(TelemetryConfiguration configuration)
    {
        _telemetryClient = new TelemetryClient(configuration);
    }

    public ILogger CreateLogger(string categoryName)
    {
        return new ApplicationInsightsLogger(_telemetryClient);
    }

    public void Dispose()
    {
        // 执行清理操作（如果需要的话）
    }
}

public class ApplicationInsightsLogger : ILogger
{
    private readonly TelemetryClient _telemetryClient;

    public ApplicationInsightsLogger(TelemetryClient telemetryClient)
    {
        _telemetryClient = telemetryClient;
    }

    public IDisposable BeginScope(TState state)
    {
        return null;
    }

    public bool IsEnabled(LogLevel logLevel)
    {
        return true; // 收集所有日志级别的日志
    }

    public void Log(LogLevel logLevel, EventId eventId, TState state, Exception exception, Func formatter)
    {
        if (exception != null)
        {
            var logEntry = new TraceTelemetry(formatter(state, exception), logLevel.ToSeverityLevel());
            _telemetryClient.TrackTrace(logEntry);
        }
        else
        {
            var logEntry = new TraceTelemetry(formatter(state, exception), logLevel.ToSeverityLevel());
            _telemetryClient.TrackTrace(logEntry);
        }
    }
}

public static class LogLevelExtensions
{
    public static SeverityLevel ToSeverityLevel(this LogLevel logLevel)
    {
        switch (logLevel)
        {
            case LogLevel.Trace:
                return SeverityLevel.Verbose;
            case LogLevel.Debug:
                return SeverityLevel.Verbose;
            case LogLevel.Information:
                return SeverityLevel.Information;
            case LogLevel.Warning:
                return SeverityLevel.Warning;
            case LogLevel.Error:
                return SeverityLevel.Error;
            case LogLevel.Critical:
                return SeverityLevel.Critical;
            default:
                return SeverityLevel.Information;
        }
    }
}

通过以上步骤，Application Insights将会收集并记录ILogger错误日志。在Application Insights的仪表板中，你将能够查看和分析这些错误日志。