Home
Class 12
MATHS
Evaluate: int(x^2+6x-8)/(x^3-4x)dx...

Evaluate: `int(x^2+6x-8)/(x^3-4x)dx`

Text Solution

Verified by Experts

`I=int(frac{x^{2}+6 x-8}{x^{3}-4 x}) d x`
`=int frac{(x^{2}+6 x-8)}{x(x^{2}-4)} d x`
`=int frac{(x^{2}+6 x-8)}{x(x-2)(x+2)} d x`
Let `frac{x^{2}+6 x-8}{x(x-2)(x+2)}=frac{A}{x}+frac{B}{x-2}+frac{C}{x+2}`
`Rightarrow frac{x^{2}+6 x-8}{x(x-2)(x+2)}=frac{A(x-2)(x+2)+B(x)(x+2)+C(x)(x-2)}{x(x-2)(x+2)}`
`Rightarrow x^{2}+6 x-8=A(x^{2}-4)+B(x^{2}+2 x)+C(x^{2}-2 x)`
Putting `x-2=0`
`Rightarrow x=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(3x^(2)-x+4)/(x^(3)+4x)dx

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

int(6x-8)/(3x^(2)-8x+5)dx

Evaluate int 1/(x^2+4x+8) dx

Evaluate: int(2x-3)/(x^2+6x+13)\ dx

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

Evaluate: int(x^(2)+4x)/(x^(3)+6x^(2)+5)dx

Evaluate int((x^(2)+8)^(2))/(x^(4))dx

Evaluate int (3x^2+4x-5)/((x^2-1)(x+2))dx

Evaluate int (3x^2+4x^3)dx