Continuous Random Variable X^n

Find the expected value of X^n, where n is an integer.

where fX(x) is 4x(1-x^2) (where 0 =< x =< 1)

So E(X^n) is the integral of x((4x(1-x^2))^n) between 1 and 0 I think...

Which I made out to be the integral of 4^n . x^n+1 . (1-x^2)^n

but I'm having trouble integrating...any help would be much appreciated.
Thanks.

No, E[X^n] is the integral of (x^n) fX(x)

So the expected value is

 1
 ∫ (x^n)(4x - 4x³) dx
0

=

 1
 ∫ [(4x^(n+1) - 4x^(n+3)] dx
0

  = 4/(n+2) - 4/(n+4)
  = 4((n+4) - (n+2)) / [(n+2)(n+4)]
  = 8 / [(n+2)(n+4)]