Home
Class 12
MATHS
If f(n)(x) = log log…..log x(log is repe...

If `f_(n)(x) = log log…..log x(log` is repeated n-times), then `int (xf_(1)(x)f_(2)(x)…..f_(n)(x))^(-1)` dx is equal to,

A

`f_(n+1)(x)+c`

B

`(f_(a+1)(x))/(n+1)+c`

C

`nf_(n)(x)+c`

D

`(f_(n)(x))/n+c`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLIC FUNCTIONS

    SIA PUBLICATION|Exercise Problems|16 Videos

  • LIMITS AND CONTINUITY

    SIA PUBLICATION|Exercise Problems|46 Videos

Similar Questions

Explore conceptually related problems

int (f'(x))/(f(x)log f(x))dx=

log ( x )^(n) = n .log x is true for n .

int (log (1+(1)/(x)))/(x(1+x))dx=

The function F(x)=int_(0)^(pi)log((1-x)/(1+x))dx is

f(x) = log((1+x)/(1-x)) satisfies the equation: f(x_(1)) +f(x_(2))

int (1)/(log x)-(1)/((log x)^(2))dx=

I_(m, n)= int_(0)^(1) x^(m) (ln x)^(n) dx=

SIA PUBLICATION-INDEFINITE INTEGRATION -PROBLEMS
  1. int (1+cos4x)/(cotx-tanx)dx=

    Text Solution

    |

  2. int (7x^(8)+8x^(7))/((1+x+x^(8))^(2))dx=f(x)+c rArr f(x)=

    Text Solution

    |

  3. If f(n)(x) = log log…..log x(log is repeated n-times), then int (xf(1)...

    Text Solution

    |

  4. int (1-cosx)"cosec"^(2)x dx=f(x)+c rArr f(x)=

    Text Solution

    |

  5. int (dx)/((x+1)sqrt(4x+3))=

    Text Solution

    |

  6. int(2-sin 2x)/(1-cos2x)e^(x) dx is equal to

    Text Solution

    |

  7. If I(n) = int(sin^(n))dx, then nI(n)-(n-1)I(n-1) equals to

    Text Solution

    |

  8. If int(e^(x))(1-sinx)/(1-cosx)dx=f(x) constant, then f(x) is equal to

    Text Solution

    |

  9. If I(n)= intx^(n) e^(cx) dx for n ge 1, then c, I(n) + nI(n-1) is equa...

    Text Solution

    |

  10. If inte^(x)(1+x) sec^(2)(xe^(x))dx = f(x) + constant, then f(x) is equ...

    Text Solution

    |

  11. If int(e^(x)-1)/(e^(x)+1)dx = f(x)+c, then f(x) is equal to

    Text Solution

    |

  12. int tan^(-1) (sqrt((1-x)/(1+x)))dx is equal to

    Text Solution

    |

  13. int(sinx + 8 cosx)/(4 sinx + 6 cosx)dx is equal to

    Text Solution

    |

  14. Assertion (A) (x^(2)-1)/(x^(2))e^(x^(2)+1)/x dx = e^(x^(2)+1)/x + c ...

    Text Solution

    |

  15. If intsqrt(x/(a^(3)-x^(3)))dx = g(x)+c, then g(x) is equal to

    Text Solution

    |

  16. If int(dx)/(x^(2) + 2x+2) =f(x) +c, then f(x) is equal to

    Text Solution

    |

  17. If int(sinx)/(cosx(1+cosx))dx = f(x)+c, then f(x) is equal to

    Text Solution

    |

  18. If int(x^(49)tan^(-1)(x^(50))/(1+x^(100)))dx = k(tan^(-1)(x^(50))^(2)+...

    Text Solution

    |

  19. If int sin^(-1)(2x)/(1+x^(2))dx = f(x) - log(1+x^(2))+c, then f(x) is ...

    Text Solution

    |

  20. int (dx)/((x+100)sqrt(x+99))=f(x)+c rArr f(x)=

    Text Solution

    |