My weakest point in calculus has always been solving actual integrals. Of course I understand how everything works, and can apply things. The problem keeps that I waste a lot of time on, as discovered later, dead ends...
I have a lot of trouble deciding if I see a random function how I would start. Should I try to use the integration by parts rule? The substitution rule (good substition)? Convert the function first to a different function? Especially when things become non trivial and a combination is required I more often than not first try the wrong method.
Is this problem just a lack of experience and something that can only be solved by exercising more problems. Or are there tricks/standard approaches (ie: first try substitution then ... ) I can follow?
An very simple example of a solution I simply couldn't see is (though this is just an example):