How do I know which method of integration to use?

In reality there's no way to know for certain and in fact some integrals can actually be proven to be impossible but they won't give you those in the exam. There's only really two main methods that you'll need to be able to use - use integration by parts when you have to integrate two things multiplied together (and hopefully one of them disappears when you differentiate it), and if that's not the case then for C4 your best bet is to try substitution (I'll show you how to know which bit to substitute). Occasionally you might have to use partial fractions or something else more interesting but there's really not much they're able to ask you for this exam.