Should I take back my ex boyfriend? HELP

Okay so I've been with this guy for 3 yrs on and off mostly and in this time our biggest struggle in our relationship is everyone always telling me he's cheating. Let me give y'all some examples his ex girlfriend has wrote me a couple time telling me they're still sleeping together but he just says she's crazy they both never showed me proof of who was the one lying so I ended up believing him over her. And about a year ago there was a rumor he tried to take a waiter home she told ppl at her job and my close friend works there and told me what she had been saying so I confronted him about it and he said he was there but she was going after him and he kept denying her and she got embarrassed and made it all up I made him confront the girl over Facebook but of course she never replied.. And about six months ago I was hearing he slept with this girl which I confronted him about it and he denied denied denied it ever happened but I already knew they did and finally when I was crying in front of him asking for him to tell the truth he finally did tell me they slept together but when we were broken up. I broke up with him for lying to me but we've been kinda off and on since like we'd try being friends and end up hooking up again. Well anyways 3 weeks ago I went on a date with his friend which I had no idea they were friends at all but long story short I found out they new each other and when I told the guy he was my ex he was confused about when I even dated him I told him we dated on and off for 3 years and he started saying no way you were his secret girlfriend he'd always cheat on and he started going into details about times he cheated on me and stuff (yes awkward first date). My ex says it was because he was trying to get in my pants that he was saying that and he wanted to come off as a good guy. Keep in mind he never once posted pictures of us together or showed me off at all on social media. So now he's begging for me back and saying he never cheated and telling me things will change he'll show me off more and I'm not sure what to do. Like I want to be with him because I love him but I don't trust him or believe him. When we were together he was the best guy ever he'd open doors for me buy me things randomly take me on dates but things like this would always happen and ruin it. He also used to be a big drinker and a party boy but he's calmed down a lot and is saying he's ready to settle down and stop going out so much he even offered for me to move in with him so he can prove hes ready. I don't really have anyone to talk to about this all my friends are so over this situation and don't want me with him I'm just not sure what to do I need some advise from someone who's been in my situation.