# How do I do this integration using u sub?

1. Jun 9, 2014

### shreddinglicks

1. The problem statement, all variables and given/known data
∫x^2√(2+x)

using u sub

2. Relevant equations
∫x^2√(2+x)

3. 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))

2. Jun 9, 2014

### HallsofIvy

Staff Emeritus
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"?

3. Jun 9, 2014

### benorin

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

4. Jun 9, 2014

### shreddinglicks

The derivative of 2+x = 1

5. Jun 9, 2014

### shreddinglicks

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