Home
Class 12
MATHS
The value of the integral overset(2)unde...

The value of the integral `overset(2)underset(0)int (log(x^(2)+2))/((x+2)^(2))`, dx is

A

`(sqrt2)/(3) tan ^(-1)sqrt2+ (5)/(12) log 2- 1/4 log 3`

B

`(sqrt2)/(3) tan ^(-1)sqrt2- (5)/(12) log 2- 1/4 log 3`

C

`(sqrt2)/(3) tan ^(-1)sqrt2+ (5)/(12) log 2+ 1/4 log 3`

D

`(sqrt2)/(3) tan ^(-1)sqrt2- (5)/(12) log 2+ 1/12 log 3`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|15 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos

  • HYPERBOLA

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-x))dx is equal to

The value of the integral overset(1)underset(1//3)int((x-x^(3))^(1//3))/(x^(4))dx is

The value of integral underset(2)overset(4)int(dx)/(x) is :-

The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in the integral

The value of the integral underset(0)overset(1)int cot^(-1) (1-x+x^(2))dx , is

The value of the integral int_(0)^(2)x[x]dx

The value of the integral underset(e^(-1))overset(e^(2))int |(log_(e)x)/(x)|dx is

The value of the integral int_(0)^(2) (log(x^(2)+2))/((x+2)^(2)) , dx is

The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equal to

VK JAISWAL ENGLISH-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The value of the integral overset(2)underset(0)int (log(x^(2)+2))/((x+...

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. int( (x^2+1)dx)/x

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. int( x^2+3)/(x^2+2)dx

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. int( x^3)/(x^2-3)dx

    Text Solution

    |

  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

    Text Solution

    |

  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

    Text Solution

    |

  16. int( x^3)/(x^2-2)dx

    Text Solution

    |

  17. If M be the maximum value of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  19. Find the vlaur of lim (n to oo) (1)/(sqrtn)(1+ (1)/(sqrt2) +(1)/(sqrt3...

    Text Solution

    |

  20. The maximum value of int (-pi/2) ^((3pi)/2) sin x. f (x) dx, subject t...

    Text Solution

    |

  21. Given a function g, continous everywhere such that g (1)=5 and int (0)...

    Text Solution

    |