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Integrate the functions(sin^8x-cos^8x)/(...

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

Text Solution

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Given `(sin^8x-cos^8x)/(1-2sin^2xcos^2x)`
`=((sin^4x+cos^4x)(sin^4x-cos^4x))/((sin^2x+cos^2x)^2-2sin^2xcos^2x)`
`=((sin^4x+cos^4x)(sin^4x-cos^4x))/(sin^4x+cos^4x+2sin^2xcos^2x-2sin^2xcos^2x)`
`=((sin^4x+cos^4x)(sin^4x-cos^4x))/(sin^4x+cos^4x)`
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