Calculus: Early Transcendentals (2nd Edition)

You would expand $\int(x^4+2)^2 dx$ so that the integral becomes $\int(x^8+4x^4+4) dx$
Integrating $\int(x^4+2)^2 dx$ is a lot harder than integrating $\int(x^8+4x^4+4) dx$. $\int(x^4+2)^2 dx = \int(x^4+2)(x^4+2) dx$ = $\int(x^8+4x^4+4) dx$.