Chapter 7.2, Problem 60E

Stan and Ollie work on the integral

${\displaystyle \int 2x\left(x^2+2\right)dx}$.

Stan lets $u=x^2+2$ and proceeds to get

${\displaystyle \int 2x\left(x^2+2\right)dx}=\frac{u^2}{2}+C=\frac{{\left(x^2+2\right)}^2}{2}+C$

Ollie multiplies out the function under the integral and gets

${\displaystyle \int \left(2x^3+4x\right)dx}=\frac{x^4}{2}+2x^2=e^{x^3}+C$

How can they both be right.?