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

1 Answer
Pablocito
Aug 11, 2017

#(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) #

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