Home
Class 12
MATHS
The integral int (2x-3)/(x^2+x+1)^2 .dx ...

The integral `int (2x-3)/(x^2+x+1)^2 .dx` is equal to

A

a. `-16(2x+1)/((2x+1)^2+3)-(16)/(3sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))+C`

B

b.`-(1)/(x^(2)+x+1)-(4)/(3)tan^(-1)(4x+3)+C`

C

c.`(1)/(2(x^(2)+x+1))-((2x+1)^(2))/((x^(2)+x+1)^(2))+C`

D

d.`(1)/(4(x^(2)+x+1))+(2)/(3)tan^(-1)(2x+1)+C`

Text Solution

Verified by Experts

The correct Answer is:
a
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to : (Here C is a constant of integration)

Let f(x)=int _( x )^(2) (dy)/(sqrt(1+ y ^(3))). The value of the integral int _(0)^(2) xf (x ) dx is equal to:

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

The value of int((x-4))/(x^2sqrt(x-2)) dx is equal to (where , C is the constant of integration )

int(dx)/((x^3-1)^(2/3)x^2) is equal to

int_(0)^(1)x^(2)(1-x)^(3)dx is equal to

The integral int sec^(2//3)x cosec^(4//3)x dx is equal to : (Here C is a constant of integration)

The value of the integral int_(0)^(4)(x^(2))/(x^(2)-4x+8)dx is equal to

int(x^(3))/((1+x^(2))^(1//3))dx is equal to

Find the integral int(2x-3cosx+e^x)dx

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
  1. The integral int (2x-3)/(x^2+x+1)^2 .dx is equal to

    Text Solution

    |

  2. If int(xtan^(-1)x)/sqrt(1+x^(2))dx = sqrt(1+x^(2))f(x) + A " ln "sqrt(...

    Text Solution

    |

  3. "If " int xlog(1+1//x)dx=f(x)log(x+1)+g(x)x^(2)+Ax+C, then

    Text Solution

    |

  4. If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C, then

    Text Solution

    |

  5. The value of int (cos^3x+cos^5)/(sin^2x+sin^4x)dx

    Text Solution

    |

  6. If int(dx)/((x^(2)+1)(x^(2)+4))=k tan^(-1) x + l tan^(-1) . (x)/(2) +C...

    Text Solution

    |

  7. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

    Text Solution

    |

  8. If int(x^(5))/(sqrt(1+x^(3)))dx is equal to

    Text Solution

    |

  9. The value of : inte^(secx).sec^(3)x(sin^(2)x+cosx+sinx+sinxcosx)dx i...

    Text Solution

    |

  10. If int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=aln((x-1)/(x+1))+btan^(-1).(x)...

    Text Solution

    |

  11. Let f(x)=(x)/((1+x^(n))^(1//n)) for n ge 2 and g(x)=underset("n times"...

    Text Solution

    |

  12. The value of int ((ax^(2)-b)dx)/(xsqrt(c^(2)x^(2)-(ax^(2)+b)^(2))) is ...

    Text Solution

    |

  13. Evalaute: inte^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n))dx

    Text Solution

    |

  14. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

    Text Solution

    |

  15. int(x^(3))/((1+x^(2))^(1//3))dx is equal to

    Text Solution

    |

  16. int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C then find out (A ,B)

    Text Solution

    |

  17. What is int (x^(2) +1)/(x^(4) - x^(2) + 1) dx equal to ?

    Text Solution

    |

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

    Text Solution

    |

  19. int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to

    Text Solution

    |

  20. int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to

    Text Solution

    |