How do I do this integration using u sub?

[shreddinglicks]

Homework Statement

∫x^2√(2+x)

using u sub

Homework Equations

∫x^2√(2+x)

The Attempt at a Solution

I can't seem to find anything to use for a u sub.

if I sub 2+x I just get 1, and if I sub x^2 I just get 2x

If I do √(2+x) I just get 1/2(1/√(2+x))

 

[HallsofIvy]

Frankly, I really don't know what you mean by
"if I sub 2+x I just get 1, and if I sub x^2 I just get 2x
If I do √(2+x) I just get 1/2(1/√(2+x)) "

You get 1 for what? The integral? Show your work! HOW did you get "1"?

 

[benorin]

Let $J:=\int x^2\sqrt{x+1}dx$. Put $u=x+1\Rightarrow du=dx$ to get $J=\int (u-1)^2\sqrt{u}du=\int \left( u^\frac{5}{2}-2u^\frac{3}{2}+u^\frac{1}{2}\right) du$

 

[shreddinglicks]

Frankly, I really don't know what you mean by
"if I sub 2+x I just get 1, and if I sub x^2 I just get 2x
If I do √(2+x) I just get 1/2(1/√(2+x)) "

You get 1 for what? The integral? Show your work! HOW did you get "1"?

The derivative of 2+x = 1

 

[shreddinglicks]

Let $J:=\int x^2\sqrt{x+1}dx$. Put $u=x+1\Rightarrow du=dx$ to get $J=\int (u-1)^2\sqrt{u}du=\int \left( u^\frac{5}{2}-2u^\frac{3}{2}+u^\frac{1}{2}\right)$

Thanks, so I use change of variable to get my answers, I should've seen that.