u^2=2+x, so 2udu=dx, and integral(xsqrt(2+x)dx)=integral((u^2-2)u*2udu)=integral(2u^4-4u^2)du). This integrates to 2u^5/5-4u^3/3=2u^3(u^2/5-2/3). Substitute u=sqrt(2+x): (2(2+x)^(5/2))/5-(4(2+x)^(3/2))/3 or 2(2+x)^(3/2)[(2+x)/5-2/3]=2(3x-4)(2+x)^(3/2)/15.