`int1/(sqrt(x+3)-sqrt(x+2))\ dx`

Options

A. `(2)/(3)(x+3)^((3)/(2))-(2)/(3)(x+2)^((3)/(2))+C`
B. `(2)/(3)(x+3)^((3)/(2))+(2)/(3)(x+2)^((3)/(2))+C`
C. `(3)/(2)(x+3)^((3)/(2))-(3)/(2)(x+2)^((3)/(2))+C`
D. none of these

Answer

B

Explanation

`I=int(1)/({sqrt(x+3)-sqrt(x+2)})xx({sqrt(x+3)+sqrt(x+2)})/({sqrt(x+3)+sqrt(x+2)})dx`.
`=int{(sqrt(x+3)+sqrt(x+2))/((x+3)-(x+2))}dx=intsqrt(x+3)dx+intsqrt(x+2)dx`
`=((x+3)^((3)/(2)))/(((3)/(2)))+((x+2)^((3)/(2)))/(((3)/(2)))+C=(2)/(3)(x+3)^((3)/(2))+(2)/(3)(x+2)^((3)/(2))+C`.