Home
Class 12
MATHS
int (dx)/(cos (2 x)cos (4x)) is equal to...

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

A

`(1)/(2sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

B

`(1)/(2sqrt2)log|(1-sqrt2sin2x)/(1+sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

C

`(1)/(sqrt2)log|(1+sqrt2sin2x)/(1-sqrt2sin2x)|-(1)/(2)(log|sec2x-tan2x|)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sin(4x-2x)dx)/(sin(2x)cos(2x)cos(4x))`
`=int(sin(4x)dx)/(sin(2x)cos(4x))-int sec2xdx`
`=2int(cos2xdx)/(cos4x)-(1)/(2)(log|sec 2x-tan 2x|)`
`=2int(cos2xdx)/(1-2sin^(2)2x)-(1)/(2)(log|sec2x-tan2x|)`
`=int(dt)/(1-2t^(2))-(1)/(2)(log|sec 2x-tan2x|)`
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

The value of int(dx)/(sin x cos x) is equal to -

int (dx)/(sin^(4)x+cos^(4)x)

int dx/(cos3x-cos x)

int dx/(5 + 4 cos x)

int (cos x dx)/(cos3x)

int (dx)/(3 sin x-4cos x)

int (cos x dx)/(8+cos^(2)x)

int e^(x) cos^(2)x dx

The value of int e^(x)((2+sin2x)/(1+cos2x))dx is equal to -

int e^(3x)cos4x dx

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
  1. The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. int(dx)/(x^(2)sqrt(16-x^(2))) has the value equal to

    Text Solution

    |

  16. Evaluate int(tan(pi/4 -x))/(cos^(2)x sqrt(tan^(3)x+tan^(2) x+ tan x))d...

    Text Solution

    |

  17. int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

    Text Solution

    |

  18. int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=

    Text Solution

    |

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

    Text Solution

    |

  20. If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0), and f...

    Text Solution

    |