If d x x( x-2)( x-3) =I+C , then I is equal to

Step-by-step solution

Let I₁= d x x( x-2)( x-3) Let t= x d t= d x x aligned I₁ & = d t (t-2)(t-3) & = [ 1 (t-3) - 1 (t-2) ] d t & = |(t-3)|- |(t-2)|+C & = | x-3 x-2 |+C I₁ & = d x x( x-2)( x-3) & = | x-3 x-2 |+C aligned But given, d x x( x-2)( x-3) =I+C On comparing, we get I= | x-3 x-1 |