If 1-x^2 x^4 ~d x=A(x) ( 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

Step-by-step solution

1-x^2 x^4 ~d x=A(x) ( 1-x^2 )^m+C Let x= d x=- d aligned & 1- ^2 ^4 (- d )=- ^4 ^2 d & =- ^2 ^2 d & =- ^3 3 +C & =- 1 3 ( 1- ^2 )^3+C & =- 1 3 ( 1-x^2 x )^3+C & = -1 3 x^3 ( 1-x^2 )^3+C & A(x)=- 1 3 x^3 and m=3 aligned A(x) ^m= ( -1 3 x^3 )^3= -1 27 x^9