`intv(v^2+2)^2dv`

`=intv((v^2)^2+2v^2*2+2^2)dv`

`=intv(v^4+4v^2+4)dv`

`=int(v^5+4v^3+4v)dv`

apply the power rule,

`=v^6/6+4v^4/4+4v^2/2+C` , C is constant

`=v^6/6+v^4+2v^2+C`

`intv(v^2+2)^2dv`

`=intv((v^2)^2+2v^2*2+2^2)dv`

`=intv(v^4+4v^2+4)dv`

`=int(v^5+4v^3+4v)dv`

apply the power rule,

`=v^6/6+4v^4/4+4v^2/2+C` , C is constant

`=v^6/6+v^4+2v^2+C`