\(\displaystyle 11.\int(x+1)\sqrt{2x+x^2}dx\)

\(\displaystyle u=x+1\)

\(\displaystyle du=1dx\)

\(\displaystyle 2x+x^2=u^2-1\)

\(\displaystyle u\sqrt{u^2-1}du\)

\(\displaystyle u(u^2-1)^1/2du\)

\(\displaystyle 1/2u^2*2/3(u^2-1)^3/2\)

\(\displaystyle 1/3u^2(u^2-1)^3/2\)

\(\displaystyle 1/3(2x+x^2+1)(2x+x^2)^3/2\)

but the answer is simply \(\displaystyle 1/3(2x+x^2)^3/2\)

what did i do wrong