If 1-x² x⁴ d x=A( x ) ( 1-x² )^ 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

A(x) ( 1-x² )^ m +C= 1-x² x⁴ d x= 1 x² -1 x³ d x Let 1 x² -1=u² - 2 x³ = 2 u d u d x d x x³ =-u d uA(x) ( 1-x² )^ m +C= (-u² ) d u=- u³ 3 +C array l =- 1 3 ( 1 x² -1 )^ 3 2 +C =- 1 3 1 x³ (1-x² )^ 3 2 +C = -1 3 x³ ( 1-x² )³+C array Compare both sides, array l A(x)=- 1 3 x³ and m=3 (A(x))³= -1 27 x⁹ array