I am not a mathematician and always wondered this as integration problems come far too often where a creative genius can solve what others can't: what is the co

I am not a mathematician and always wondered this as integration problems come far too often where a creative genius can solve what others can't: what is the computational complexity of symbolic integration like? how come general purpose algorithms can't seem to solve some whereas humans can? from what I see in online discussions, it sounds like hard problems require the type of "human creativity" where bruteforce or algorithmic machinery won't trivially suffice which is quite interesting to me.