Can you record music with a keyboard with headphones on
 

I'm getting ready to buy a keyboard. My biggest concern is that I want to be able to play music with headphones on so that I don't wake up my roommates. I think all keyboards have that. But I also want to record my music without using an external microphone but by the keyboard directly recording the inputs into its computer. That way I can avoid making noise that will wake up my roommates as well as record at the same time. Is this possible?

Yes, it is possible.

Is it easy? Or do I have to buy some extra equipment.

You don't need any extra equipment.

How do you know this?

I make music.
This is also an incredibly basic question that anyone with a bit of everyday technical knowledge or even just a bit of logical thinking could answer easily.