Home
Class 12
MATHS
Evaluate: int(x+1)/(x^2+x+3)dx...

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

Text Solution

Verified by Experts

`(x+1)/(x^2+x+3)=A/(x-2)+B/(x-3)=frac{A(x-3)+B(x-2)}{(x-2)(x-3)}`
`x-1=x(A+B)-(3A+2B)`
`A+B=1 ---(1)`
`3A+2B=1 ---(2)`
Solving 1 and 2, we get, `A=-1` and `B=2`
`int(x+1)/(x^2+x+3)dx=2 int frac{dx}{x-3}-int frac{dx}{x-2}`
`=2 ln abs(x-3)-ln abs(x-2)+C`
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(x-1)/(3x^2-4x+3)\ dx

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

evaluate int(3x-1)/(x^(2)-1)dx

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

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

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

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

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

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

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