If `int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C` , then `a=` `-1//2` (b) `1//2` (c) `-1` (d) `1`

Explanation

Option a is correct

`int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C`


`=((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)
`
`=(sin^2x+cos^2x)(sin^2x−cos^2x)`

`=−int(cos2x)dx`

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