If x 3+4 ^2 x ~d x= A ⁻¹( ~B x)+ C , (where c is a constant of integration), then the value of A + B is

Step-by-step solution

Let I = x 3+4 ^2 x ~d x Put x= t - x ~d x= dt x ~d x=- dt aligned I & = - dt 3+4 t ^2 & =-1 1 4 t ^2+3 aligned =-1 1 (2 t)^2+( 3 )^2 =-1 1 2 3 ⁻¹ ( 2 t 3 )+ c I = -1 2 3 ⁻¹ ( 2 x 3 )+ c But x 3+4 ^2 x ~d x= A ⁻¹( ~B x)+ c Comparing above equations, we get aligned A & = -1 2 3 , ~B = 2 3 A & + B = -1 2 3 + 2 3 = 3 2 3 = 3 2 aligned