Hello Sean, 

Thank you for contacting Infragistics. This is documented on MSDN

https://learn.microsoft.com/en-us/dotnet/desktop/wpf/advanced/walkthrough-hosting-a-wpf-composite-control-in-windows-forms?view=netframeworkdesktop-4.8

After you've added the assemblies for the XamSyntaxEditor, adding the component to a Windows Forms project is fairly straightforward. 

eg,

public partial class Form1 : Form
    {

        private ElementHost _ctrlHost;
        public XamSyntaxEditor syntaxEditor;
        public TextDocument document;
        public Form1()
        {
            InitializeComponent();
            _ctrlHost = new ElementHost();
            syntaxEditor = new XamSyntaxEditor();

            _ctrlHost.Child = this.syntaxEditor;
            document = new Infragistics.Documents.TextDocument();
            document.InitializeText("Hello, World!");
            syntaxEditor.Document = document;
            _ctrlHost.Width = 800;
            _ctrlHost.Height = 450;
            this.Controls.Add(_ctrlHost);
        }

Let me know if you have any questions.

Supported Languages - Infragistics WPF Help

syntaxEditor.Document.Language = TSqlLanguage.Instance;

But it tells me...

Cannot resolve symbol 'TSqlLanguage'

I'd also like to show line numbers.