Home
Class 12
MATHS
If int(tan^(9)x)dx=f(x)+log|cosx|, where...

If `int(tan^(9)x)dx=f(x)+log|cosx|,` where f(x) is a polynomial of degree n in tan x, then the value of n is

A

6

B

7

C

8

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I_(9)=int tan^(9)xdx=int tan^(7)x(sec^(2)x-1)dx`
`"i.e., "I_(9)=(tan^(8)x)/(8)-I_(7)`
`"Similarly, "I_(7)=(tan^(6)x)/(6)-I_(5)`
…………………………………..
………………………………..
……………………………….
`I_(3)=(tan^(2)x)/(2)-I_(1)=(tan^(2)x)/(2)-int tanxdx`
`=(tan^(2)x)/(2)+log|cos x|`
`therefore I_(9)=" (a polynomial of degree 8 in tan x)"+ log |cos x|+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 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

IF f(x)= log(tan(x/2)) , then the value of f'(x) is

Let f(x) be the polynomial of degree n, then Delta^(n-1) f(x) is a polynomial of degree.

If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​ is equals to

If f(x)=log(cosx), then the value of f''(x) is-

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If f(x)=log("tan"(x)/(2)) , then the value of f'(x) is -

int (tan x)/(log (cos x))dx

The value of int tan x dx is-

If int (dx)/(a^(2)-x^(2))=(1)/(2a) log |f(x)|+c then f(x) is-

If int e^x (tanx - log cos x) dx = f(x) log sec x then range of f(x) is

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
  1. If int x^(26).(x-1)^(17).(5x-3)dx=(x^(27).(x-1)^(18))/(k)+C where C is...

    Text Solution

    |

  2. If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-...

    Text Solution

    |

  3. If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degre...

    Text Solution

    |

  4. int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(e)(f(x))+g(x)+C where C is the...

    Text Solution

    |

  5. Evaluate:int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals

    Text Solution

    |

  6. int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0 is equal to

    Text Solution

    |

  7. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

    Text Solution

    |

  8. The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is

    Text Solution

    |

  9. Evaluate: int(dx)/(xsqrt(x^(6)-16))=

    Text Solution

    |

  10. int (dx)/(cos (2 x)cos (4x)) is equal to

    Text Solution

    |

  11. intx2^(ln(x^(2)+1))dx is equal to

    Text Solution

    |

  12. If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, ...

    Text Solution

    |

  13. Evaluate: int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals

    Text Solution

    |

  14. Evaluate: int((2x+1))/((x^(2)+4x+1)^(3//2))dx

    Text Solution

    |

  15. If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of th...

    Text Solution

    |

  16. The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals

    Text Solution

    |

  17. Evaluate :int(dx)/(xsqrt(x^(6)+1)) equals

    Text Solution

    |

  18. int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+...

    Text Solution

    |

  19. int(sin((pi)/(4)-x)dx)/(2+sin2x)=A tan^(-1)(f(x))+B, where A, B are co...

    Text Solution

    |

  20. If intsqrt(x+sqrt(x^(2)+2))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sq...

    Text Solution

    |