Integration of x/sqrt(1-x^2)

Hi guys

I have problem integrating x/sqrt(1-x^2) dx since I choose apparently wrong subst. elements...can someone help me? thanks

use substitution u=1-x² ==>du=-2x.dx

==>xdx = -du/2 & √(1-x²) =√u

==>⌠x.dx/√1-x² =⌠(-du/2) /√u = -⌠(1/2√u)du

= - {√u } +C

= -√(1-x²) +C

Hi, what you should always do is simplify things in integration, then use u substitution if you think it is easier. Hopefully I did this right haha.
integral x(1-x^2)^(-1/2) dx
u = 1 - x^2
du = -2x
-2 integral u^(-1/2) du
-2(1/2 * u^1/2)
-u^1/2
(x^2 - 1)^1/2

......

∫ xdx/ sqrt (1-x^2)

use u substitution....

let u = 1-x^2
du = -2xdx

-1/2 du = xdx

-1/2 ∫ du / (u)^1/2

-1/2 ( (2) (u)^1/2)

- (1-x^2)^1/2 +C ANS....