Home
Class 12
MATHS
int(cot^(-1)(e^x))/e^xdx is equal to...

`int(cot^(-1)(e^x))/e^xdx` is equal to

A

`(1)/(2)ln(e^(2x)+1)-(cot^(-1)(e^(x)))/(e^(x))+x+C`

B

`(1)/(2)ln(e^(2x)+1)+(cot^(-1)(e^(x)))/(e^(x))+x+C`

C

`(1)/(2)ln(e^(2x)+1)-(cot^(-1)(e^(x)))/(e^(x))-x+C`

D

`(1)/(2)ln(e^(x)+1)-(cot^(-1)(e^(x)))/(e^(x))-x+C`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE|Exercise Objective Type Questions (More than one answer)|29 Videos
  • INTEGRALS

    AAKASH INSTITUTE|Exercise Linked Comprehension Type Questions|7 Videos
  • INTEGRALS

    AAKASH INSTITUTE|Exercise Competition level Questions|76 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

int(cot^(-1)(e^(x)))/(e^(x))dx is equal to

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

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

int cot^(-1)xdx

int sqrt((e^(x)-1)/(e^(x)+1))dx is equal to

int(e^x)/(e^(x)+1)dx" is equal to "

int (e^x-1)e^xdx

int(dx)/(e^(x)+e^(-x)) is equal to

int(x^(e-1)+e^(x-1))/(x^(e)+e^(x)) dx is equal to

AAKASH INSTITUTE-INTEGRALS-Objective Type Questions (Only one answer)
  1. int\ 7^(7^(7^x)) * 7^(7^x) * 7^x \ dx

    Text Solution

    |

  2. If intf(x)dx=f(x), then int{f(x)}^2dx is equal to

    Text Solution

    |

  3. int(cot^(-1)(e^x))/e^xdx is equal to

    Text Solution

    |

  4. value of e^(tantheta)(sectheta-sintheta)d(theta) is equal to

    Text Solution

    |

  5. The value of int(1-x^7)/(x(1+x^7))dx is equal to

    Text Solution

    |

  6. (x^4+1)/(x(x^2+1)^2)dx=Aln|x|+B/(1+x^2)+C ,

    Text Solution

    |

  7. If int e^(3x)cos4xdx=e^(3x)(Asin4x+Bcos4x)+C, then:

    Text Solution

    |

  8. int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=alog((x+1)/(x-1))+b"tan"^(-1)(x)/...

    Text Solution

    |

  9. intsinx d (cosx) is equal to

    Text Solution

    |

  10. int(dx)/(x*(lnx)(ln(lnx)).......(lnlnln...lnx)(20\ "times") is equal t...

    Text Solution

    |

  11. If int(dx)/(3sqrt(sin^(11)x*cosx))=-(a(b+ctan^(2)x))/(d tan^(2)x(tanx)...

    Text Solution

    |

  12. If int (sqrtx)^5/((sqrtx)^7+x^6) dx= alog(x^k/(1+x^k))+c then a and k ...

    Text Solution

    |

  13. int{1+tanx*tan(x+A)}dx=cotA*ln|f(x)|+C then f(x) equal to

    Text Solution

    |

  14. The value if int(x^(2)-1)/((x^(2)+1)(sqrt(x^(4)+1)))dx equal to (1)/(s...

    Text Solution

    |

  15. If intf(x)cos x dx = 1/2 f^(2)(x)+C, then f(x) can be

    Text Solution

    |

  16. int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=

    Text Solution

    |

  17. If the value of lim(n->oo){1/(n+1)+1/(n+2)+.......+1/(6n)} is 'K' th...

    Text Solution

    |

  18. If [] and { } represents greatest integar function and fractional func...

    Text Solution

    |

  19. Value of int(1)^(9)(x-2)(x-4)(x-6)(x-8)(x-5)dx is

    Text Solution

    |

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

    Text Solution

    |