Home
Class 12
MATHS
Integrate the functions (sin^(8)x-cos^...

Integrate the functions
`(sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)`

A

`(1)/(2)sin2x+C`

B

`-(1)/(2)sin2x+C`

C

`-(1)/(2)sinx+C`

D

`-sin^(2)x+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)dx=int((sin^(2)x-cos^(2)x)(sin^(4)x+cos^(4)x))/(1-2sin^(2)xcos^(2)x)`
`=int-cos2xdx=-(1)/(2)sin2x+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.9|15 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Find the imtegrals of the functions (sin^(3)x+cos^(3)x)/(sin^(2)xcos^(2)x)

Integrate the function (sin^(-1)x)^(2)

Integrate the functions sqrt(sin2x)cos2x

int (sin^(8) x - cos ^(8) x)/( 1 - 2 sin^(2) x cos^(2) x) dx is

int(sin^(6)x + cos^(6)x)/(sin^(2)xcos^(2)x)dx

Integrate the function xcos^(-1)x

Integrate the functions (sin^3x+cos^3x)/(sin^2xcos^2x)

CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
  1. Integrate the functions (sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)

    Text Solution

    |

  2. "If " int(cos 4x+1)/(cotx-tanx)dx=Acos4x+B, " then "

    Text Solution

    |

  3. int(sqrt((a+x)/(a-x))+sqrt((a-x)/(a+x)))dx " is equal to "

    Text Solution

    |

  4. int sqrt(1-sinx)dx " is equal to "

    Text Solution

    |

  5. Evaluate: int((3sinx-2)cosx)/(5-cos^2x-4sinx)\ dx

    Text Solution

    |

  6. If intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l co...

    Text Solution

    |

  7. int(sqrt(x-1))/(x sqrt(x+1))dx " is equal to "

    Text Solution

    |

  8. IfI=int(dx)/(secx+cos e cx),t h e nIe q u a l s 1/2(cosx+sinx-1/(sqr...

    Text Solution

    |

  9. int("sin"(5x)/(3))/("sin"(x)/(2))dx is equal to (where, C is a constan...

    Text Solution

    |

  10. int (cos 5x + cos 4x)/(1-2cos3x) dx

    Text Solution

    |

  11. IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q u a l sqrt(x+2)sqrt(5+x)+3si...

    Text Solution

    |

  12. int(sin2x)/(sin5xsin3x)dx is equal to

    Text Solution

    |

  13. int(dx)/(x(x+1)) is

    Text Solution

    |

  14. Evaluate: int1/(sqrt(sin^3xsin(x+alpha)))\ dx ,\ alpha!=npi,\ \ n in ...

    Text Solution

    |

  15. int (px^(p+2q-1)-qx^(q-1))/(x^(2p+2q)+2x^(p+q)+1) dx is equal to (1...

    Text Solution

    |

  16. If y=int1/(1+x^2)^(3/2)dx and y=0 when x=0 , then value of y when x=1 ...

    Text Solution

    |

  17. int sqrt(x)(1+x^(1//3))^(4)dx " is equal to "

    Text Solution

    |

  18. int(In(tanx))/(sinx cosx)dx " is equal to "

    Text Solution

    |

  19. If m is a non-zero number and int (x^(5m-1)+2x^(4m-1))/(x^(2m)+x^m+1)^...

    Text Solution

    |

  20. If l^(prime)(x) means logloglog x , the log being repeated r times, th...

    Text Solution

    |