If ^ 3 5 x ^3 x ~d x= -1 ~m ^ m x+ 1 n ^ n x+ c , (where c is the constant of integration), then ( m , n )=

Step-by-step solution

Let aligned I & = ^ 3 5 x ^3 x ~d x & = ^ 3 5 x (1- ^2 x ) x ~d x & = ^ 3 5 x x ~d x- ^ 13 5 x x ~d x aligned Let x= t - x ~d x= dt aligned I & =- t^ 3 5 d t+ t^ 13 5 d t & = -1 ( 8 5 ) t^ 8 5 + 1 ( 18 5 ) t^ 13 5 +c & = -1 ( 8 5 ) ^ 8 5 x+ 1 ( 18 5 ) ^ 13 5 x+ c aligned Comparing with -1 ~m ^ m x+ 1 n ^ n x+ c , we get m = 8 5 , n = 18 5