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$\int \frac{\sin^{8} x - \cos^{8} x}{1 - 2 \sin^{2} x \cos^{2} x} d x =$

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a

12sin⁡2x

b

−12sin⁡2x

c

−12sin⁡x

d

−sin2⁡x

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detailed solution

Correct option is B

∫sin8⁡x−cos8⁡x1−2sin2⁡xcos2⁡xdx∫sin4⁡x+cos4⁡xsin4⁡x-cos4⁡x1−2sin2⁡xcos2⁡xdx∫sin2⁡x+cos2⁡x2-2sin2xcos2xsin2⁡x+cos2⁡xsin2⁡x-cos2⁡x1−2sin2⁡xcos2⁡x=∫1−2sin2⁡xcos2⁡x-cos2x1−2sin2⁡xcos2⁡xdx=∫−cos⁡2xdx=−12sin⁡2x+C

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If $\int \frac{s i n^{2} x}{1 + s i n^{2} x} d x = x - K t a n^{- 1} (M t a n x) + C$ then

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