How can I trust my partner again after his conversations with other women?

A little while back I discovered that my boyfriend anonymously likes to chat with women online in a very sexually explicit manner. We discussed this and he promised that it would stop. I however have felt insecure and hurt ever since. I know people make mistakes and deserve second chances but I have found many other things that point to the same thing, chatting to women online.

He doesn't think it's cheating as it's just chatting but I feel absolutely betrayed. I wanted to believe him and move on but I honestly have found myself doubting him on everything since. I feel like I don't trust him at all. I'm having trouble sleeping and feel sick every time I think of it. Am I being irrational? Please any advice would be brilliant. Thank you so much for your time.