Integration is a pretty important topic right across 2u, 3u, and 4u syllabi. However, the importance of having good integration technique is only fully realised when doing 4u mathematics.
Unfortunately, there aren’t that many variations in the types of questions in your textbooks, and so you may be forced to dip into your reserve of past papers a little earlier than you intended to. However, a long time ago, a man named Coroneous released his Maths textbook in to the world and in it had a challenge of completing 100 integrals. Finish them all and you should be incredibly proficient with integration.
As such here is arguably the best resource to practice integration for the NSW HSC 4 unit syllabus.
PDF : Find it here
PDF with solutions: Find it here
Video Solutions: Find it here
For those in the 2 unit and 3 unit courses, you may find some of the integrals doable, so definitely have a go at the first 10 or so!