Imaginar
"No puedes imaginar cuánto he deseado que llegara este momento."
"No te puedes imaginar lo mal que iba todo."
Inventar
This site doesn't provide much examples for this word but the page I found seems to imply that the meaning is identical with using both "inventar" and "inventarse" (according to this page: http://www.spanishdict.com/translate/inventar).
I just want to know the difference between the reflexive and regular verb forms, if there is any.