Home
Class 12
MATHS
int(cos e c^2x-2005)/(cos^(2005)x)dx is ...

`int(cos e c^2x-2005)/(cos^(2005)x)dx` is equal to (a) `-(cotx)/((cosx)^(2005))+c` (b) `(tanx)/((cosx)^(2005))+c` (c) `-(tanx)/((cosx)^(2005)+c` (d) none of these

A

`(cotx)/((cosx)^(2005))+c`

B

`(tan x)/((cosx)^(2005))+c`

C

`(-(tan x))/((cosx)^(2005))+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`int("cosec"^(2)x-2005)/(cos^(2005)x)dx`
`=int(cotx)^(-2005)"cosec"^(2)xdx-2005 int (dx)/(cos^(2005)x)`
`=(cosx)^(-2005)(-cot x)-int (-2005)(cosx)^(-2006)(-sinx)(-cotx)dx-2005int(dx)/(cos^(2005)x)`
`= -(cotx)/((cosx)^(2005))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Exercises (Multiple Correct Answers Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Exercises (Linked Comprehension Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.9|15 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

I=int(e^x(1+sinx))/(1+cosx)dx is equal to

int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c (b) ((2cosx)/(3sinx+2))+c (c) ((2cosx)/(3cosx+2))+c (d) ((2sinx)/(3sinx+2))+c

int cosx/(cos2x)dx

int(In(1+cosx)-xtan(x/2))dx is equal to

I=int(cos4x+1)/(cotx-tanx)dx is equal to ?

IfI=int(sin2x)/((3+4cosx)^3)dx ,t h e nIe q u a l s (a) (3cosx+8)/((3+4cosx)^2)+C (b) (3+8cosx)/(16(3+4cosx)^2)+C (c) (3cosx)/((3+4cosx)^2)+C (d) (3-8cosx)/(16(3+4cosx)^2)+C

int (dx)/(cosx(5+3 cos x))

int(ln(tanx)/(sinxcosx)dx is equal to (a) 1/2ln(tanx)+c (b) 1/2ln(tan^2x)+c (c) 1/2(ln(tanx))^2+c (d) none of these

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

    Text Solution

    |

  2. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

    Text Solution

    |

  3. Find the value of " int x sec^(2)x dx

    Text Solution

    |

  4. int x sinx sec^(3)x dx is equal to

    Text Solution

    |

  5. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

    Text Solution

    |

  6. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

    Text Solution

    |

  7. int e^(x^4) (x^3) dx is equal to

    Text Solution

    |

  8. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

    Text Solution

    |

  9. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

    Text Solution

    |

  10. int((x+2)/(x+4))^2 e^xdx is equal to

    Text Solution

    |

  11. inte^(tanx)(secx-sinx)dxi se q u a lto e^(tanx)cosx+C e^(tanx)sinx...

    Text Solution

    |

  12. int(cos e c^2x-2005)/(cos^(2005)x)dx is equal to (a) -(cotx)/((cosx)^...

    Text Solution

    |

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

    Text Solution

    |

  14. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

    Text Solution

    |

  15. If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x)...

    Text Solution

    |

  16. The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-...

    Text Solution

    |

  17. int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

    Text Solution

    |

  18. int(2sinx)/(3+sin2x)dx is equal to

    Text Solution

    |

  19. 4int(sqrt(a^6+x^8))/x dx is equal to (a)sqrt(a^6+x^8)+(a^3)/2ln|...

    Text Solution

    |

  20. IfI(m , n)=intcos^m xsinn xdx ,t h e n7I(4,3)-4I(3,2)i se q u a lto c...

    Text Solution

    |