Home
Class 12
MATHS
The value of the integral int0^oo(xlogx)...

The value of the integral `int_0^oo(xlogx)/((1+x^2)^2)dx ,is` (a)0 (b) log 7 (c) 5 log 13 (d) none of these

A

`0`

B

`log7`

C

`5 log 13`

D

none of these

Text Solution

AI Generated Solution

To solve the integral \[ I = \int_0^\infty \frac{x \log x}{(1+x^2)^2} \, dx, \] we will use the substitution \( x = \frac{1}{t} \). ...
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_0^oo(xlogx)/((1+x^2)^2)dx (a) 0 (b) log 7 (c) 5 log 13 (d) none of these

The value of integral int_(0)^(1)(log(1+x))/(1+x^(2))dx , is

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

The value of the integral int_(-1)^(1)log(x+sqrt(x^(2)+1))dx is

The value of the integral int_0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx

The value of the integral int_(0)^(pi//2)log |tan x cot x |dx is

The value of the integral int_(-1//2)^(1//2) cos x log((1+x)/(1-x))dx , is

The value of integral int_(1)^(e) (log x)^(3)dx , is

The volue of the ddefinite integral int _(0)^(oo) (ln x )/(x ^(2) +4)dx is:

Evaluate the following integral: int_0^1("log"(1+x))/(1+x^2)dx

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. The value of int0^((3pi)/2)(|tan^(-1)tanx|-|sin^(-1)sinx|)/(|tan^(-1)t...

    Text Solution

    |

  2. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

    Text Solution

    |

  3. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

    Text Solution

    |

  4. int0^pi(xtanx)/(secx+cosx)dxi s (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2...

    Text Solution

    |

  5. Ifint(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" 4 (b) ...

    Text Solution

    |

  6. The solution for x of the equation int(sqrt(2))^x(dt)/(tsqrt(t^2-1))=p...

    Text Solution

    |

  7. Which of the following is incorrect? int(a+ c)^(b+c)f(x)dx=inta^bf(x...

    Text Solution

    |

  8. The value f the integral int(-pi)^pisinm xsinn xdx , for m!=n(m , n in...

    Text Solution

    |

  9. int((e^x(2-x^2))/((1-x)sqrt(1-x^2))\ dx) is equal to

    Text Solution

    |

  10. int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logx dx is equal to (a) -pi/2logpi (...

    Text Solution

    |

  11. If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf''(x)...

    Text Solution

    |

  12. The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2...

    Text Solution

    |

  13. The value of int1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b)...

    Text Solution

    |

  14. If f(pi) = 2 int0^pi (f(x)+f^(x)) sinx dx=5, then f(0) is equal to (it...

    Text Solution

    |

  15. If int1^2e^(x^2)dx=a ,t h e ninte^(e^4)sqrt(1n x)dx is equal to (a)...

    Text Solution

    |

  16. int(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e...

    Text Solution

    |

  17. The value of the expression (int0^a x^4(sqrt(a^2-x^2)))/(int0^a x^2(sq...

    Text Solution

    |

  18. IfA=int0^pi(cosx)/((x+2)^2)dx ,t h e nint0^(pi/2)(sin2x)/(x+1)dx is eq...

    Text Solution

    |

  19. int0^4((y^2-4y+5)sin(y-2)dy)/([2y^2-8y+11]) is equal to (a) 0 (b) 2 ...

    Text Solution

    |

  20. The values of a for which the integral int0^2|x-a|dxgeq1 is satisfie...

    Text Solution

    |