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

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

Text Solution

Verified by Experts

`I=int frac{(x^{2}+1) d x}{(x-2)^{2}(x+3)} `
`text { Let } frac{x^{2}+1}{(x-2)^{2}(x+3)}=frac{A}{x-2}+frac{B}{(x-2)^{2}}+frac{C}{x+3} `
`Rightarrow frac{x^{2}+1}{(x-2)^{2}(x+3)}=frac{A(x-2)(x+3)+B(x+3)+C(x-2)^{2}}{(x-2)^{2}(x+3)} `
`Rightarrow x^{2}+1=A(x^{2}-2 x+3 x-6)+B(x+3)+C(x^{2}-4 x+4) `
`Rightarrow x^{2}+1=A(x^{2}+x-6)+B(x+3)+C(x^{2}-4 x+4)`
Equating coefficients of like terms
`A+C=1 ldots ldots ldots ldots ldots ldots(1)`
`A+B-4 C=0 ldots ldots ldots ldots ldots ldots . .(2)`
...
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+1)/((x+2)(x-3)^2)\ dx

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

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

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

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

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

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

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

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

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