Question

3x-13.(x-1) (x-2) (x-3)

Answer 1

The given integral is,

∫ 3x−1 ( x−1 )( x−2 )( x−3 ) dx

Let,

3x−1 ( x−1 )( x−2 )( x−3 ) = A ( x−1 ) + B ( x−2 ) + C ( x−3 ) 3x−1=A( x−2 )( x−3 )+B( x−3 )( x−1 )+C( x−2 )( x−1 ) (1)

Equate the coefficient of x and constant term.

A+B+C=0 −5A−4B−3C=3 6A+3B+2C=−1

Solve the above equations to obtain the values of Aand B.

A=1 B=−5 C=4

Substitute the values of A, Band C in equation (1).

3x−1 ( x−1 )( x−2 )( x−3 ) = 1 ( x−1 ) + −5 ( x−2 ) + 4 ( x−3 ) ∫ 3x−1 ( x−1 )( x−2 )( x−3 ) dx= ∫ 1 ( x−1 ) dx+ ∫ −5 ( x−2 ) dx + ∫ 4 ( x−3 ) dx =log| x−1 |−5log| x−2 |+4log| x−3 |+C