Home
Class 12
MATHS
Evaluate I=int (x^2+x+1)/((x+1)^2(x+2))d...

Evaluate `I=int (x^2+x+1)/((x+1)^2(x+2))dx`

Text Solution

Verified by Experts

Given `int (x^2+x+1)/((x+1)^2(x+2))dx`
Let `(x^2+x+1)/((x+1)^2(x+2))=A/(x+2)+(Bx+C)/(x^2+1)`
`=>x^2+x+1=A(x^2+1)+(Bx+C)(x+2)`...........(1)
By solving we get `A=3/5 , B=2/5, C=1/5`
`:. I= int((3/5)/(x+2)+((2x)/5+1/5)/(x^2+1))dx`
`=3/5 int 1/(x+2)dx+1/5 int (2x)/(x^2+1)dx+1/5 int1/(x^2+1)dx`
`=3/5 log|x+2|+1/5 log|x^2+1|+1/5 tan^(-1)x+C`
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate I= int (x+1/x)^2dx

Evaluate I=int(dx)/(2x(1-x)) .

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

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

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

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

Evaluate: int_(1)^(2)(1)/((x+1)(x+2))dx( ii) int_(1)^(2)(1)/(x(1+x^(2)))dx

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

Evaluate : I= "int(x^2)/((x^(3)-1))dx

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