`intxsqrt(x-1)dx=?`

Options

A. `(2)/(3)(x-1)^((3)/(2))+C`
B. `(2)/(5)(x-1)^((5)/(2))+C`
C. `(2)/(5)(x-1)^((5)/(2))+(3)/(2)(x-1)^((3)/(2))+C`
D. none of these

Answer

C

Explanation

`I=int{(x-1+1)sqrt(x-1)}dx=int{(x-1)^((3)/(2))+(x-1)^((1)/(2))}dx`.
`=(2)/(5)(x-1)^((5)/(2))+(3)/(2)(x-1)^((3)/(2))+C`.