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int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=...

`int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=`

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`
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Knowledge Check

  • If int(sin^(8)x-cos^(8)x)/(1-2sin^(2)xcos^(2)x)dx=A sin 2x+B, then A =

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    B
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    C
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    D
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    A
    `(1)/(2)cot^(-1)(sin^(2)x)+c`
    B
    `(1)/(2)cot^(-1)(sin^(2)x)+c`
    C
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    D
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