The short answer to your question is no. I don't believe in taking back cheaters. People do make mistakes, but people who cheat once, tend to become repeat offenders. That's because these people have infidelity issues to begin with and it has nothing to do with you. Let's suppose for a second that you were a terrible girlfriend, even if this were true, that still wouldn't give your boyfriend a free pass to cheat. It's only decent that you end one relationship before you start another.
Let's say the same thing had happened to one of your girlfriends. Would you advice your friend to take back her boyfriend? I don't think so, I just know for a fact that you'll advice her to stay away from the cheating lair. So why would you try to convince yourself otherwise?
But then, let's set emotions aside and evaluate this situation properly. Do you think your boyfriend will stay faithful to you if you were to give him another chance? If your answer is no, then we can end the discussion here. But if you said yes, then you are lying to yourself because there is no way of knowing that he won't cheat on you again. It's not really about the uncertainty of the future, but it's rather the past that still leaves doubt. Cheaters tend to cheat again, and again.
To decide whether or not you would take him back, you would have to confront him and tell him how you feel about his action. Let him explain himself and decide for yourself if you are better off without him or with him. Whatever you do, do not let him pin this on you. There is not a single righteous reason to cheat on someone you love and you should really get a clue if he tries to sweet talk out of this mess he's created. Let him speak, give him your full attention, but do not let him manipulate you.
Ultimately, you'll have to decide whether or not you'd take him back. Whatever you do, accept the fact that the betrayal will hurt for a while and just ride out the tough time as well as you can. You will heal eventually, with him or without him. Let this be an experience that you come out learning something and not an experience that will leave your ability to love and trust all crippled. Trust in yourself and you will come out stronger and wiser at the end of this ordeal.
