I understand that its the integration version of the chain-rule... but say I have

the integral of

(√x²+1) (square root for the entire thing)

I don't actual need to do U-sub because theres only one function, correct? So I just integrate "normally"?

I also don't understand what the point is of putting parenthesis around a function like 2x-1 and then asking for the integral (as opposed to just asking for the integral of 2x-1)... is there any real purpose?

Also, I get that you could solve the integral of 1/√x by moving x up and making it x to the -1/2 and integrating from there, but could you also just make it ln|√x| since the integral of 1/x is ln|x|?

Thanks and sorry this was kind of long but these are all pretty basic questions.