One way to do it is to use regular expressions.
var str = "<img alt='' src='http://api.com/images/UID' /><br/>Some plain text<br/><a href='http://www.google.com'>http://www.google.com</a>";
var regex = /<img.*?src='(.*?)'/;
var src = regex.exec(str)[1];
console.log(src);