When I work at this I get it as being 4[(x+2)^3/4 ] / 3 + C Is this correct?
Note that x + 2 - 2 = x. It is done to facilitate breaking the integral up into two more obvious integrals. As an alternative, you could make the substitution u = x + 2 and go from there.
By the way, you can check an answer to an integal by differentiating it and seeing whether the result is equal to the integrand.