public static void main(String[] args) {
     Connection conn = null;
     String driver = "com.microsoft.sqlserver.jdbc.SQLServerDriver";
     String url = "jdbc:sqlserver://localhost:1434;databasename=Test;";
     String userName = "sa";
     String password = "paquito";
     Statement stmt;
     try{
       Class.forName(driver);//.newInstance();
       conn = DriverManager.getConnection(url,userName,password);
       stmt = conn.createStatement();
       System.out.println("conectado = ");
       conn.close();
     } catch (Exception e) {
       e.printStackTrace();
     }
}

public static void main(String[] args) {
     Connection conn = null;
     String driver = "com.microsoft.sqlserver.jdbc.SQLServerDriver";
     String url = "jdbc:sqlserver://localhost:1434;databasename=Test;integratedSecurity=true";
     String userName = "paco";
     String password = "";
     Statement stmt;
     try{
       Class.forName(driver);//.newInstance();
       conn = DriverManager.getConnection(url,userName,password);
       stmt = conn.createStatement();
       System.out.println("conectado = ");
       conn.close();
     } catch (Exception e) {
       e.printStackTrace();
     }
}

com.microsoft.sqlserver.jdbc.SQLServerException: No se puede abrir la base de datos "Test" solicitada por el inicio de sesión. Error de inicio de sesión. ClientConnectionId:577da72f-f0d4-4ac6-abab-243f0f84d0e3
at com.microsoft.sqlserver.jdbc.SQLServerException.makeFromDatabaseError(SQLServerException.java:217)
at com.microsoft.sqlserver.jdbc.TDSTokenHandler.onEOF(tdsparser.java:279)
at com.microsoft.sqlserver.jdbc.TDSParser.parse(tdsparser.java:99)