If x-7 x-9 ~d x=A x^2-16 x+63 + |(x-8)+ x^2-16 x+63 |+c, (where c is a constant of integration) then A is

Step-by-step solution

Let I = x-7 x-9 ~d x aligned & = (x-7)(x-7) (x-9)(x-7) d x & = x-7 x^2-16 x+63 ~d x aligned Let (x-7)= A [ d d x (x^2-16 x+63 ) ]+ B aligned & x-7= A (2 x-16)+ B & x-7=2 ~A x-16 ~A + B & A = 1 2 , ~B =1 & I = 1 2 (2 x-16)+1 x^2-16 x+63 ~d x & = 1 2 2 x-16 x^2-16 x+63 ~d x+ 1 x^2-16 x+63 ~d x & = 1 2 2 x^2-16 x+63 + 1 (x-8)^2-(1)^2 ~d x & [ f ^ (x) f (x) d x=2 f (x) + c ] & I = x^2-16 x+63 + |x-8+ x^2-16 x+63 |+ c & aligned But, x-7 x-9 ~d x=A x^2-16 x+63 + |(x-8)+ x^2-16 x+63 |+ c Comparing, we get A=1