`int(sin^(-1)x)/(sqrt(1-x^(2)))dx` is equal to
Where, C is an arbitrary constant.

Options

A. `log(sqrt(1-x^2))+C`
B. `(1)/(2)(sin^(-1)x)^2+C`
C. `log(sqrt(1-x^2))+C`
D. `sin(cos^(-1x))+C`

Answer

B

Explanation

Let `l=int (sin^(-1)x)/(sqrt(1-x^2))dx`
Put `sin^(-1)x=t`
`rArr (1)/(sqrt(1-x^2))dx=dt`
`therefore l=int t dt=(t^2)/(2)+C`
`=((sin^(-1)x)^2)/(2)+C`