Would you stay in a relationship when trust is broken?

StarsInDarkPlaces
Would you stay with someone because you were in love, and invested time into a relationship where he has treated you better than any other man you've been with...
but... through a rough patch had downloaded a dating/hook up app? it never went further than the app, and he has apologized and tried super hard.. he even cried, begging me to stay, saying how much he really was in love with me..

but i struggle everyday with trust and self confidence and insecurity. I think about it... and I constantly worry... everyone says time will heal and to forgive... but he could do it so easily again...
Would you stay in a relationship when trust is broken?
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