I need help with this antiderivative calculus problem:?

Question

find the antiderivative of: x^2e^(x^3-1)dx
(pretend there is an integral symbol in front of that derivative)
so, the answer in my book is 1/3e^(x^3-1)+C
however, i do not understand why i have to multiply by the 1/3, or where the heck that comes from! any help is greatly appreciated! thank youuu!

Answer 1

Put x^3-1=z
so 3x^2dx =dz and the yntegral becomes
1/3Inte^z dz = 1/3 e^z +C =1/3 e^(x^3-1)+C

Answer 2

Without going through all the gory details, it looks like finding the derivative of x^3-1 which gives you 3x^2. The 1/3 is needed since the 3 is not already there.