I was a little stuck on this problem, so I took a look at the solution work and am confused as to how it works.
Given $\int{x^{2}e^{x^{3}}}dx$, find the indefinite integral.
Looking at the formula, I decided to have $u=x^{3}$ and $du=3x^{2}$
Multiplying and dividing by 3 on both sides, $\int{x^{2}e^{x^{3}}}dx= \frac{1}{3}\int{x^{2}e^{u}(3x^{2})}dx$
However, the book solution omits the $x^{2}$ in the second step, leaving just $\frac{1}{3}\int{e^{u}(3x^{2})}$dx
I have two questions:
1. why is the $x^{2}$ omitted in the book solution after multiplying and dividing by 3?
2. why does the solution not include simplifying $x^2e^{u}(3x^{2}) dx$ to result in $4x^{2}e^{u}dx$?