There is no way out of the box to do that. You'll have to install some
kind of a relay that will accept mail from your SharePoint servers and
then forward them on with authentication. SharePoint doesn't allow for
it itself.

The easiest way I've found to do is to activate the SMTP
service on one or more of the SharePoint Web Front End servers.

So how do you setup the SMTP relay to do that.

You'll need to install some third party somewhere to do it. Alternately
you might be able to talk to your email  server admins and have them
allow unauthenticated SMTP connections from the IP addresses of your
WFEs. I've seen that work a couple of times. They badmouth SharePoint,
"What? SharePoint can't authenticate SMTP traffic? Microsoft sucks!!"
but they do it just the same.

You can do this by configuring the delivery option of your smtp  server, where
you have option to choose authentication  mode and input user name and password.