Home
Class 12
MATHS
Evaluate: int(x-1)/((x+1)(x-2))\ dx...

Evaluate: `int(x-1)/((x+1)(x-2))\ dx`

Text Solution

Verified by Experts

`Let ((x-1))/((x+1)(x-2))=(A)/((x+1))+(B)/((x-2)).`
then`(x-1)-=A(x-2)+b(x+1).`
Putting `,x=-1` in (i), we get `A=(2)/(3).`
Putting `x=2 ` in (i) , we get `B=(1)/(3).`
`therefore ((x-1))/((x+1)(x-2))=(2)/(3(x+1))+(1)/(3(x-2))`
`implies int ((x-1))/((x+1)(x-2))dx=(2)/(3)int(dx)/((x+1))+(1)/(3)int(dx)/((x-2))`
`=(2)/(3)log |x+1|+(1)/(3)log |x-2|+C.`
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate: int(2x+1)/((x+1)(x-2))dx

Evaluate: int(1)/((x-1)(x+1)(x+2))dx

Evaluate : int(x^(2)-1)/((x+1)(x+2))dx

Evaluate: int(x+1)/((x-1)sqrt(x+2))dx

Evaluate: int(x+1)/((x-1)sqrt(x+2))dx

Evaluate: int(x^2)/((x-1)(x+1)^2)\ dx

Evaluate: int(x)/((x+1)(x^(2)+1))dx

Evaluate: int1/((x+1)^2(x^2+1))\ dx

Evaluate: int(x+3)/((x-1)(x^(2)+1))dx

Evaluate: int(x^2+x-1)/((x+1)^2(x+2))\ dx