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.
Integration is smthng which has more of practical applicatons rather tha simply always try to have  a practical approach towards it...and most imp...approach any problem systematically...formula r used at the end...first try to simplify as much as u can...i hope u will develop these skills
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