`intxsqrt(x^(2)-1)dx=?`

Options

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

Answer

B

Explanation

Put `(x^(2)-1)=t and2xdx=dt`.
`:." "I=(1)/(2)intsqrt(t)dt=(1)/(2)*(t^((3)/(2)))/(((3)/(2)))+C=(1)/(3)t^((3)/(2))+C=(1)/(3)(x^(2)-1)^((3)/(2))+C`.