i had a question on how substitution works exactly.

 

i know that the dervitive of the sub. needs to be infront.

but what if its not?

 

lets take an example.

x^2 sqrt(x^3 +1)

here you would make x^3 + 1 = u

and du would be 3x^2

but you have only x^2 infront would'nt dividing by 3 change it?

 

what if for example you only had x infront?

 

maybe im just confused *sighs*

It all depends on why you actually want to substitute something. The example you gave looks like you want to substitute to integrate the function. Well, some functions are simply not easily integrable (or not at all) analytically. Substitution is not a method that guarantees you an easy solution. Sometimes, you´re simply screwed.