Question

shortcut method for learn integration formulas

Answer 1

wolfram.....

Answer 2

you should really learn the proofs first and be familiar then when you are comfortable just use an integration table or calculator to make it easier.

Answer 3

^exactly
The best way to learn integration formulas is to derive them.
That way you will remember them, they actually make sense, and you can see how many are connected (or even the same formula in a different guise).