Should i forgive my boyfriends cyber cheating? plz help!!?

ok so a little back story....bf n i have been together for 4 months been friends for 5 years or more we know majority about each others pasts like a month or so into our relationship he goes thru my phone which was locked and saw my ex sending me inappropriate messages and although i didn't initiate or feed into his convo i didn't immediately shoot him down or dead the conversation......now a few days ago while i was at his house he was acting really shady on aim and skype all while receiving texts and i noticed that while hes on skype hes opening it really fast responding just as fast and making sure to close it quickly so im like hmmmm really suspect behavior but im like i know in the past i messed up too n he gave me so much crap about it he wouldn't turn around n do the exact same thing n he loves me he wouldn't do that later that night i ask him are u doing anything shady he looks me in my face n says no ok so i sleep on it i wake up n i still feel like something isn't right so he left his computer open with his last activity being his gmail so i say hmm i take a look....long story short hes exchanging messages with this islamic chick from who knows where shes sending him videos going into detail bout her day n hes telling her he doesn't have a girlfriend and to top it off he sent her a video of him playing with his privates!!! all around the time of my birthday :( we aren't a perfect couple the fact that we know so much about each other causes us to not fully trust each other which is y we argue a lot he says he did it thinking that right after shooting the video he was going to break up with me because we were going thru yet another argument but then realized he loves me too much n decided to not break up with me n regretted it n felt bad after the video was sent to the girl.....now my question is if u were me n u love this guy a lot n understand that i nay not be the easiest to be with n i may push ppl away sometime but do u stay when ur bf does something like that to u when u haven't done anything of the sort but tried to be a good girlfriend?? thanks in advance (and sorry about the long read)