To me, integration at H2 syllabus can be divided into 4
different types
1) Basic integration, very direct type
2) f'(x) vs f(x) type
3) By Substitution
4) By Parts
For number (3), the substitution is usually given.
As a strategy, I would advise my students to go down the list of
1, 2 and 4 (for H2) since this is in order of ease of integrating.
If you cannot use 1, you move on to 2, and if still cannot, move on
to 4. But as you move on to (4), do try to take note if (2) still
applies.
Following this fixed strategy ensures your mind is geared
towards trying to identify which is the correct method to use
instead of getting bogged down by not even being able to apply what
is needed.
Finally, remember that in exams, to check for your answer for
this integration question, you do not need to redo it. Merely key
the definite integral in your calculator, and compare your
answer.
You do not need 100% to get A; you just need a high probability
of having little careless mistakes on questions you have trained
yourself to do.