# Indefinite Integration

1. Apr 6, 2005

### huan.conchito

$$\!$$∫x^2/Sqrt[1 - x^2] \[DifferentialD]x$$$$

I need to find the integral of
(x^2)/ Sqrt(1-(x^2))
if the above doesnt work properly
integration by parts results in 0=0 how do i do this?

2. Apr 6, 2005

### dextercioby

You mean

$$\int \frac{x^{2}}{\sqrt{1-x^{2}}} \ dx$$

How about the substitution $x=\sin u [/tex] and then a nice trigonometrical identity involving a double angle...? Daniel. 3. Apr 6, 2005 ### dextercioby It can be done by parts,too. Daniel. 4. Apr 6, 2005 ### huan.conchito ok, i got it using x= sinU can you give me a hint how to do it using integration by parts? 5. Apr 6, 2005 ### Data Integration by parts uses $$\int u \ dv = uv - \int v \ du$$ choose [itex] u = x$ and

$$v = \frac{x}{\sqrt{1-x^2}}$$

Edit: That should be $dv = (x / \sqrt{1-x^2}) \ dx$!

Last edited: Apr 6, 2005
6. Apr 6, 2005

### dextercioby

Not really,Data.U needn't specify "u" & "v",but the factors in the LHS,"u" & "dv"...

So

$$u=x \ \mbox{and} \ dv=\frac{x}{\sqrt{1-x^{2}}} \ dx$$

Daniel.

P.S.Data,u see the difference,right...?:uhh:

7. Apr 6, 2005

### Data

indeed, silly me :tongue2:~

Last edited: Apr 6, 2005