2 x+5 7-6 x-x^2 ~d x= A 7-6 x-x^2 + B ⁻¹ ( x+3 4 )+ c (where c c is a constant of integration) then the value of A+B is

Step-by-step solution

aligned & Let I= 2 x+5 7-6 x-x^2 ~d x= 2 x+6-6+5 7-6 x-x^2 & =-1 -2 x-6 7-6 x-x^2 ~d x- 1 7+9- (9+6 x+x^2 ) d x & =-1 -2 x-6 7-6 x-x^2 ~d x- 1 (4)^2-(x+3)^2 ~d x aligned Let 7-6 x-x^2= t (-2 x-6) d x= dt aligned I & =- ( t )^ -1 2 dt - ⁻¹ ( x+3 4 )+ c & =-2 7-6 x-x^2 - ⁻¹ ( x+3 4 )+ c aligned array ll & A=-2 and B=-1 & A+B=-3 array