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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`
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