As the betrayed person, I can say that your boyfriend's reaction certainly seems normal. None of us has a crystal ball, though, that will tell the future.
That, fortunately or unfortunately, is out of your control. All you can do is to work on why you cheated in the first place. If it's because you were under the influence, then maybe you should never drink again (or limit yourself to one). If you resented him in some way, then you need to learn to communicate better. If you needed attention from another man to make you feel attractive and wanted, then you need to work on your self esteem.
This work may not "win" your boyfriend back and restore his trust. What it may do, though, is make you a better partner for the next man you commit to. In the short term, you may lose someone extremely important to you, but in the long term, you have a brighter future.
Me? I'm forgiving because my WH was more or less faithful for 21 years. He earned another chance. If he were my BF or F, I'd be gone. That may not be what you want to hear, but it's true. I hope you and your BF are able to work through this and come out stronger than ever--whether it's together or not. Growing from our mistakes--building character--is what life's all about.