`int (dx)/(sqrt(1 - x^2)sin^(-1)(x))` Evaluate the indefinite integral.

You need to evaluate the indefinite integral, using the following substitution, such that:

`sin^(-1) x = t => dx/(sqrt(1 - x^2)) = dt`

Replacing t for x yields:

`int dx/((sin^(-1) x)sqrt(1 - x^2)) = int (dt)/t`

`int (dt)/t = ln|t| + c`

Replacing back` sin^(-1) x ` for t yields:

`int dx/((sin^(-1) x)sqrt(1 - x^2)) = ln|sin^(-1) x| + c`

Hence, evaluating the indefinite integral, using the substitution `sin^(-1) x = t` , yields `int dx/((sin^(-1) x)sqrt(1 - x^2)) = ln|sin^(-1) x| + c.`