integration by subsitution

use the subsitution u = 4 + x^2
integral of x^3 / (4 + x^2)^1/2 with 1 at the top and zero at the bottom = 1/3(16 - 7 root 5)

du/dx = 2x
x=(u-4)^1/2
x=1, u=5
x=0, u =4

dx = du/2(u-4)^1/2

so integral ( 5 at top and 4 at bottom) = (u-4)^3/2 / (u)^1/2 . du/2(u-4)^1/2

where do i go from here??

Look at the 1/2 and the 3/2 powers

so you get (u-4) / 2(u)^1/2with 5 at the top and 4 at bottom