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

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

Text Solution

Verified by Experts

The correct Answer is:
` -(1)/(sqrt(5))log_(e)|(2x+1-sqrt(5))/(2x+1+sqrt(5))|+C`
`I= -int(dx)/(x^(2)+x-1)= -int(dx)/((x+(1)/(2))^(2)-(5)/(4))`
`=-(1)/(2*(sqrt(5))/(2))"log"_(e)|((x+(1)/(2))-(sqrt(5))/(2))/((x+(1)/(2))+(sqrt(5))/(2))|+C`
`= -(1)/(sqrt(5))log_(e)|(2x+1-sqrt(5))/(2x+1+sqrt(5))|+C`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.6|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.7|10 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.4|20 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Evaluate int(dx)/((1-x^(2))sqrt(1-x^(2))).

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

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

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

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

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

Evaluate int(dx)/(1+sqrt(x^(2)+2x+2)) .

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

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

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

Home
Profile