How Do You Solve This Challenging Integral Involving Trigonometric Substitution?

[Nikitin]

Homework Statement

integrate the following function: x*√(2x-x²)

Homework Equations

substitutions?

The Attempt at a Solution

I substituted x with x=2sin²u. From that I ended up with ∫x*√(2x-x²)= 16∫sin⁴u*cos²u

Now I'm supposed to use a formula from an integrals table.. but which?

 

[dextercioby]

You should complete the square under the sqrt. $\displaystyle{\sqrt{1-(1-x)^2}}$ and then make the natural substitution.

 

[Nikitin]

edit: nvm