Here's a guide. He kinda makes it out to be that you can use the same capacitor...
http://myoriginalxbox.weebly.com/capacitor-removal.html
It's way easier/different for a PlayStation. Here's a list for purchasing capacitors
https://www.google.com/search?q=xbox+capacitor+location&client=safari&sa=X&hl=en-us&biw=375&bih=559&tbs=vw:l,ss:44&tbm=shop&prmd=sivn&srpd=12093525339579367855&prds=num:1,of:1,epd:12093525339579367855&ved=0ahUKEwiFrYXB44bRAhXqwVQKHVvDAssQgjYIiwQ
It does say it will operate without the capacitor, though the clock won't