Home
Class 12
MATHS
Evaluate: int1/(2x^2-x-1)dx...

Evaluate: `int1/(2x^2-x-1)dx`

Text Solution

Verified by Experts

`2 x^{2}-x-1=1 / 2(x^{2}-x / 2-1 / 2) `
`=1 / 2(x^{2}-x / 2+1 / 16-1 / 16-1 / 2) `
`=frac{1}{2}[(x-frac{1}{4})^{2}-frac{1}{16}-frac{1}{2}] `
`=frac{1}{2}[(x-frac{1}{4})^{2}-frac{9}{16}] `
`=frac{1}{2}[(x-frac{1}{4})^{2}-(frac{3}{4})^{2}]`
So integral becomes,
...
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: int1/(x^(2)-x-2)dx

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

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

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

Evaluate: int1/(3+2x-x^2)\ dx

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

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

Evaluate: int1/((x^2+1)(x^2+2))\ dx

Evaluate: int1/(sqrt(5x^2-2x))\ dx

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