In your request object there is a property called socket, which is a net.Socket object. The net.Socket object has a property remoteAddress, therefore you should be able to get the IP with this call:

request.socket.remoteAddress

(if your node version is below 13, use the deprecated now request.connection.remoteAddress)

EDIT

As @juand points out in the comments, the correct method to get the remote IP, if the server is behind a proxy, is request.headers['x-forwarded-for']