Just solve a lot and let your intuition guide you. Probably, you can remember or memorize stuff(if you have a talent of that sort). But mostly, JEE Advanced tests you on stuff that can be done by simple substitutions and basic knowledge about integration(both definite and indefinite.)

Solving past year papers may give you edge about what to substitute in a problem to get the answer in the specific format of the options of the question.

Shortcut tricks are really derieved from fundamentals. So your fundamentals must be strong.However, in some special cases of integration, you need to use your imagination.

All the very best and good luck.

Hi pradnya

There's nothing like shortcuts for calculus.

But you should clear your concept, learn formula, practice as much as you can.