What is int x / (x+3)^(1/2) dxx(x+3)12dx?

1 Answer
Mar 11, 2018

int x/(x+3)^(1/2) dx = 2/3(x+3)^(1/2)(x-6)+Cx(x+3)12dx=23(x+3)12(x6)+C

Explanation:

int x/(x+3)^(1/2) dx = int ((x+3)-3)/(x+3)^(1/2) dxx(x+3)12dx=(x+3)3(x+3)12dx

color(white)(int x/(x+3)^(1/2) dx) = int (x+3)^(1/2)-3(x+3)^(-1/2) dxx(x+3)12dx=(x+3)123(x+3)12dx

color(white)(int x/(x+3)^(1/2) dx) = 2/3(x+3)^(3/2)-6(x+3)^(1/2)+Cx(x+3)12dx=23(x+3)326(x+3)12+C

color(white)(int x/(x+3)^(1/2) dx) = 2/3(x+3)^(1/2)((x+3)-9)+Cx(x+3)12dx=23(x+3)12((x+3)9)+C

color(white)(int x/(x+3)^(1/2) dx) = 2/3(x+3)^(1/2)(x-6)+Cx(x+3)12dx=23(x+3)12(x6)+C