For the basics of Integration and what you were supposed to know from Cambridge or NCEA 3.7, click here
Integration using trig identities
The following tutorials give different examples of integration using trig functions but use different identities and methods.
The following methods are not hard as such but the skill is spotting when to and what method to use.
Trig substitution/by inspection
Integration Using trig substitution
Integration by trig substitution, Further example and second
Demonstrations of all useful trig substitutions
Parametric functions
Integrating parametric functions - look at 2022 schol paper
Integrating trig functions with powers
Integrating complictaed looking trig functions with odd powers
Integrating complictaed looking trig functions with even powers
Integrating sec and tan functions with indices