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

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

Text Solution

Verified by Experts

I=`int(2x^2-x-1)dx`
I=`1/2int(x^2 - x/2 +1/16 -1/16 -1/2)dx`
=`1/2[(x-1/4)^2-9/16]`
=`1/2[(x-1/4)^2-(3/4)^2]`
Thus,`int 1/2dx/[(x-1/4)^2-(3/4)^2]`
=`1/2(2/3)log((x-1/4-3/4)/(x-1/4+3/4))+c`
=`1/2log((2x-2)/(2x+1))+c`
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: 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

Evaluate: int1/((x+2)(x+3))dx