It’s really up to you. 

If you don’t tell her, then she doesn’t get closure on it and it could hurt her. I personally would be in this camp, as anyone who cheated on me is dead to me. There’s also a zero percent chance she changes (or near zero, at least)

If you do tell her, she might change, she might not. Regardless, she’ll get closure and (might) move on from the relationship 

I’ll tell you what though, if you decide to tell her then make sure you’ve 100% decided on whatever you do. She’ll either try to break down and start crying to persuade you, or take the adult route and break up amicably. I’ve seen more of 1 than 2, so take that as you will.