<human>: Can you provide a brief rundown of the text in within 3 sentences?

My boyfriend and I have been living together for almost a year now- recently he was switched to a third shift so he's up late when I'm sleeping. 

Earlier this week I noticed that when I attempted to type reddit into my address bar, it autofilled with /r/r4r. I was a little taken aback, and I confronted him about perusing personals. Two arguments followed, him denying looking for a sexual or romantic connection. He was just lonely and looking for a platonic connection at 4 am because everyone was sleeping. So after being assured twice that he was doing no wrong, I attempted to let it go.

The day after, I opened my laptop and he was signed in on Skype. I figured it wasn't going too far if I checked out the recents and if nothing was out of the norm then to sign him out and close it. But he had an extensive conversation with someone that he met on the personals. After checking it out, I learned that he wasn't just trying to jerk off with someone else, but he was forming an oddly detailed pseudo relationship with this girl. 

Now, I don't want to go too much into detail in fear of this turning into a hateful rant- I just have one question:

I want to extend a second chance and mean it. But I've never had my trust violated this way (albeit not the most nightmarish thing that can happen to a relationship) and I don't know how to come back from him lying to me and being in MY home on my laptop when cheating. 

We've already talked and did the best to clear the air. But I don't know if this is going to habitual.

I don't know how to make myself open to a genuine attempt to repair the damage.

Are there any tips from anyone who's been there, done that and successfully moved past it while staying together?
<bot>: My boyfriend cheated on me on Skype and I need pointers to keep my cool and how to healthily try a second time.