Is there a simple way to use Dependency Injection on my connections?

I use NInject to perform the Dependency Injection of my projects. I usually end with the configuration below:

Simple Factory Interface

public interface IDbConnectionFactory{    IDbConnection CreateConnection();}

Factory Implementation

public class SqlConnectionFactory : IDbConnectionFactory{    private readonly string _connectionString;    public SqlConnectionFactory(string connectionString)    {        _connectionString = connectionString;    }    public IDbConnection CreateConnection()    {        var conn = new SqlConnection(_connectionString);        conn.Open();        return conn;    }}

NInject Config:

Bind<IDbConnectionFactory>()    .To<SqlConnectionFactory>()    .WithConstructorArgument("connectionString",ConfigurationManager.ConnectionStrings["SqlConnection"].ConnectionString);

Example of a repository:

public class UserRepository : IUserRepository{    private readonly IDbConnectionFactory _dbConnectionFactory;    public UserRepository(IDbConnectionFactory dbConnectionFactory)    {        _dbConnectionFactory = dbConnectionFactory;    }    public IEnumerable<User> List()    {        using (var dbConnection = _dbConnectionFactory.CreateConnection())        {            ....        }    }}

Edit: I always let the ADO.NET take care of connection pooling. So I open and close the connection every single time that I need to perform a database operation.

This approach is working for me and is very simple as you mentioned in your question.