If you absolutely have to record it from youtube buy yourself a male-to-male cable. Plug one end into the speaker port, the other into the line-in port. Open up some sound editing software such as
Audacity. Select, "Line in" (In Audacity: from the drop-down menu located at the top-right of the application) as the recording source. Now turn up the system volume all the way, start the video, and start recording.