If `int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x^2))^m+C`,for a suitable chosen integer m and a function A(x), where C is a constant of integration, then `(A(x))^m` equals

Answer

C

Explanation

`intsqrt(1-x^2)/x^4 dx =A(x) (sqrt(1-x^2))^m+C`
LHS `intsqrt(1/x^2-1)/x^3dx`
Let `1/x^2-1=t rArr -2/x^3 dx=dtrArr (dx)/x^3=-1/2dt`
`rArr -1/2intsqrt(t)dt=-1/3t^(3//2)+C=-1/3((1-x^2)/x^2)^(3//2)+c=-1/(3x^3)(sqrt(1-x^2))^3+C`
Comparing it with RHS `A(x)=-1/(3x^3)` and m =3 `therefore (A(x))^m =-1/(27x^9)`