What is int x / (x+3)^(1/2) dx∫x(x+3)12dx?
1 Answer
Mar 11, 2018
Explanation:
int x/(x+3)^(1/2) dx = int ((x+3)-3)/(x+3)^(1/2) dx∫x(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) dx∫x(x+3)12dx=∫(x+3)12−3(x+3)−12dx
color(white)(int x/(x+3)^(1/2) dx) = 2/3(x+3)^(3/2)-6(x+3)^(1/2)+C∫x(x+3)12dx=23(x+3)32−6(x+3)12+C
color(white)(int x/(x+3)^(1/2) dx) = 2/3(x+3)^(1/2)((x+3)-9)+C∫x(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)+C∫x(x+3)12dx=23(x+3)12(x−6)+C