2 Samuel 1

This is another chapter that I am struggling to gain any insight or learning from.  I find it interesting that when David learns of Saul's death he seems truly stricken with grief and writes a heart felt eulogy to a loss of someone he seems to have loved.  The man that has been trying to hunt him down and kill him has died yet he seems sad.  I can understand the sorrow for losing Jonathon, but not Saul.  Is there a lesson in there, I'm not getting it?