Integrate x/√(1-x) using substitution

[noblerare]

Homework Statement

$$\int$$$$\frac{xdx}{\sqrt{1-x}}$$

Homework Equations

n/a

The Attempt at a Solution

I tried to multiple top and bottom by the conjugate:
$$\int$$$$\frac{x\sqrt{1+x}dx}{\sqrt{1-x^{2}}}$$

I tried trig substitution and u-substitution, but nothing seems to work.

I end up with -$$\int$$cos$$\theta$$$$\sqrt{1+cos\theta}$$

Can anyone help me out on this? And show steps, please? Thanks so much!

 

[nicksauce]

If you make a substitution u = 1-x (then x = 1-u), you now have the sum of two trivial integrals.

 

[noblerare]

thank you so much! oh, and sorry about the double post