I'll take the question as simplified in the comments, "How to easily memorize a lot of similar formulas?"
The answer is, there is no easy way to memorize a lot of formulas. Worse than that: even if you manage to memorize a lot of formulas - even if you are allowed to have a sheet of paper in front of you with all the formulas you've ever seen - you will find that the real problem is deciding which formula(s) will be useful when you are faced with an integral that isn't on your list.
The good news is, there is a way to get to where you want to go; it just isn't easy. The way to get to where you want to go is to do a few dozen problems. A few hundred would be even better. The more problems you do, the more formulas you will find you have memorized, and the better you will become at judging which formula(s) to use on a given problem.
It's like that old joke:
Tourist: How do I get to Het Muziektheater?
Native: Practice, practice, practice.