Integrate x^2/Sqrt[1 - x^2] - Solve 0=0

[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 doesn't work properly
integration by parts results in 0=0 how do i do this?

 

[dextercioby]

You mean

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

How about the substitution [itex]x=\sin u [/tex] and then a nice trigonometrical identity involving a double angle...?<br /> <br /> Daniel.[/itex]

 

[dextercioby]

It can be done by parts,too.

Daniel.

 

[huan.conchito]

ok, i got it using x= sinU
can you give me a hint how to do it using integration by parts?

 

[Data]

Integration by parts uses

$$\int u \ dv = uv - \int v \ du$$

choose $u = x$ and

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

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

 

[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...?

 

[Data]

indeed, silly me ~