Most of the integration problems are bounded with integration rules. The formulas are only methods to do a integration problem. But trigonometry chapters like multiple angles or sub multiple angle are very impotent to simplify the integration as well. If you find a integration problem which is hard just try to think totally different way every big and complex integration are short in between 4-5 steps. And if its taking long then check again.
Mind it In complex integration we often use substitution methods.