My girlfriend went to a party on our one year anniversary, and when she was there she got drunk and cheated on me. I know she was drunk and she wouldn't have done it otherwise.. me an her have been together for a year and we are so in love..
so is it normal that I want to forgive her and make things better between us?
so is it normal that I want to forgive her and make things better between us?

Furthermore, I find it highly disagreeable that a majority of women will frown upon promiscuous behavior, only to turn around, get plastered, and cheat on her bf. As a male, I revel in the fact that I've had sex with many women. Filthy nasty scary sex. As soon as you women quit treating your vaginas like they're the Holy Womb, maybe there won't be such a glaring double standard when it comes to sex. Think like a man and let's do this thing.
Lastly, dump the bitch. She put herself in that position, proceeded to get the pipe laid to her and violate you relationship. There is no forgivness for that behavior. Move on and find someone you can trust, and who can also give you the same amount of respect you give her.
Given that this is a long distance relationship..it's all about honesty and trust, of which she broke. Well not honesty unless you had to find it out from others...
I would say you are fairly normal to WANT to forgive her, but just ask yourself if its worth it and whether this relationship is going anywhere.
People have to stop blaming things on the alcohol! If you're wasted and wanna have sex, you're gonna have sex.. If you don't wanna have sex, then you won't.. It obviously wasn't an accident my dude.
Simple as that.
Anyway, she will do it again. If u forgive her now then she will do it again because she thinks you will let her off the hook again. Nobody is worth this. She can't be trusted and did something wrong. I don't care if she is drunk, you can still control yourself. What kind of person cheats in someone who they supposedly love?