If 3 x+1 (x-1)(x-2)(x-3) d x A |x-1| B |x-2|+C |x-3|+C , then the values of A, B and C are respectively

Step-by-step solution

We have, 3 x+1 (x-1)(x-2)(x-3) d x Let 3 x+1 (x-1)(x-2)(x-3) = A x-1 + B x-2 + C x-3 (3 x+1)=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2) Put x-1=0 x=1 Then, 3 1+1=A(-1)(-2) 4=2 A A=2 Put x-2=0 x=2 Then, 7=B(2-1)(2-3) 7=B(1)(-1) B=-7 And put x-3=0 x=3 Then, 10=C(3-1)(3-2) 10=C(2)(1) C=5 3 x+1 (x-1)(x-2)(x-3) = 2 x-1 - 7 x-2 + 5 x-3 3 x+1 (x-1)(x-2)(x-3) d x = 2 x-1 d x- 7 x-2 d x+ 5 x-3 d x 3 x+1 (x-1)(x-2)(x-3) d x=2 |x-1|-7 |x-2|+5 |x-3|+C=A |x-1|+B |x-2|+C |x-3|+C( Given ) A=2, B=-7, C=5