Home
Class 12
MATHS
The value of int(1+logx)/(sqrt((x^(x))^...

The value of ` int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is " `

A

`sec^(-1)(x^(x))+C`

B

`log|x^(x)+sqrt(x^(2x)-1)|+C`

C

`log|x^(x)-sqrt(x^(2x)-1)|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
We have , `I=int(1+logx)/(sqrt(x^(2x)-1))dx`
`=int(1)/(x^(x)sqrt((x^(x))^(2)-1^(2)))d(x^(x))=sec^(-1)(x^(x))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Solved Example|92 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|3 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 value of int(1)/(x+sqrt(x-1))dx , is

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

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

The value of int_(1)^(7sqrt(2)) (1)/(x(2x^(7)+1)dx is

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

The value of int(1)/((2x-1)sqrt(x^(2)-x))dx is equal to (where c is the constant of integration)

The value of int_(0)^(oo)(logx)/(a^(2)+x^(2))dx is

int_(1)^(2) (x)/(sqrt(1+2x^(2)))dx

The value of int (dx)/((1+sqrtx)(sqrt(x-x^2))) is equal to

The value of int(sqrt(1+x))/(x)dx , is

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
  1. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |