I have to find the anti derivative of x(x^2+2)^2

This is what I did:

f ' (x) = ( x^2 + 2)^2

= X (X^4 + 4x^2 + 4)

F(x) = (1/2x^2) (1/5x^5 + 4/3x^3 + C)

The book did not show any examples of problems like this and I was not sure if there was a product rule that I needed or if the Chain Rule came into play somehow.

Thanks.