If 8 x+1 2 x- 2 x ~d x= A 8 x+ c , where c is an arbitrary constant, then the value of A is

Step-by-step solution

aligned I & = 8 x+1 2 x- 2 x d x & = 2 ^2 ( 8 x 2 ) 2 x 2 x - 2 x 2 x d x aligned [ 1+ =2 ^2 2 ] aligned & = 2 ^2(4 x) 2 x 2 x ^2 2 x- ^2 2 x ~d x & = ^2(4 x) (4 x) (4 x) d x & [ array r 2 =2 and 2 = ^2 - ^2 array ] aligned aligned & = 1 2 2 (4 x) (4 x) d x & = 1 2 8 x ~d x & = - 8 x 2 8 +c & = - 8 x 16 +c aligned Comparing with ' A 8 x+ c ', we get A = -1 16