Most screen recording apps need rooted phones.
I usually use Ashot (capture and cast phone screen from PC, http://www.mightypocket.com/2010/08/android-screenshots-screen-capture-screen-cast/). This one does not require root. Of course, the frame rate is not so good. You may check a sample video we created for S Note (https://www.allaboutgalaxynote.com/s-note-tutorial-how-to-use-productivity-tools/)
