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

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

Text Solution

Verified by Experts

`int frac{2 x-3}{(x^{2}-1)(2 x+3)} d x`
`=int frac{(2 x-3)}{(x-1)(x+1)(2 x+3)} d x`
`text { Let } frac{2 x-3}{(x-1)(x+1)(2 x+3)}=frac{A}{x-1}+frac{B}{x+1}+frac{C}{2 x+3}`
`Rightarrow frac{2 x-3}{(x-1)(x+1)(2 x+3)}=frac{A(x+1)(2 x+3)+B(x+1)(2 x+3)+C(x^{2}-1)}{(x-1)(x+1)(2 x+3)}`
`Rightarrow 2 x-3=A(x+1)(2 x+3)+B(x-1)(2 x+3)+C(x+1)(x-1) ldots ldots ldots(1)`
`text { Putting } x+1=0 text { or } x=-1 text { in eq. (1) }`
`Rightarrow-2-3=B(-1-1)(-2+3)`
`Rightarrow-5=B(-2)(1)`
...
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(2x-3)/((x^2-1)(2x+3))dx

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

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

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

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

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

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

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

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

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