I read a post from a woman who wrote why she shouldn't forgive him. She was right, she ran after him when he left her and moved in with another woman. He LEFT her, begging him to come back was not the way to repair what was broke in their marriage.
The reason I am writing this is I believe you can forgive him, not for him, but for yourself to move on. My husband cheated and moved out of our home. I told him I wanted to try to work things out. That we needed to go to marriage counselling. I gave him a date to make up his mind so I would know when I could move on. Then I went out, didn't date, but I enjoyed myself. I didn't wait by the phone for him, I lived my life. He chose to come back, he chose to get counselling, he chose to ask me to renew our vows. It took some time, but I was able to trust him again, since I agreed to counselling, I was able to forgive him. But the trust wasn't as easy, but it can be happen.
It has now been 20 years and we are still together. And I wouldn't have it any other way.