If d x ^3 x 2 2 x =( x)^A+C( x)^B+ k where k is a constant of integration, then A + B + C equals

Step-by-step solution

Let I aligned & = d x ^3 x 2 2 x & = d x ^3 x 2(2 x x) & = 1 2 ^3 x x x ~d x & = 1 2 ^4 x x ~d x aligned Put x= t ^2 x ~d x= dt aligned I & = 1 2 1+t^2 t d t & = 1 2 t^ - 1 2 d t+ 1 2 t^ 3 2 d t aligned aligned & = 1 2 ( t ^ 1 2 1 2 )+ 1 2 ( t ^ 5 2 5 2 )+ k & =( x)^ 1 2 + 1 5 ( x)^ 5 2 + k A & = 1 2 , B= 5 2 , C= 1 5 & A+B+C= 16 5 aligned