Question

Integral of [x/(3-x)^1/2]?

Answer 1

`(2/3)(3-x)^(3/2) - 6(3-x)^(1/2)`

Explanation:

U Substitution
Let u = 3 - x => x = 3 - u
du = - dx => dx = - du

`int x / (3-x)^(1/2) dx => int - (3-u)/u^(1/2) du`

`int (u-3)/u^(1/2) du => int u^(1/2) du - int 3u^(-1/2) du`

`(2/3) u^(3/2) - 6 u^(1/2)`

`(2/3) (3-x)^(3/2) - 6 (3-x)^(1/2)`