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  4. The value of ∫ ( sin 8 x- cos 8 x/1-2 sin 2 x cos 2 x) d x is :

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Q. The value of $\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x$ is :

Integrals

Solution:

$\int \frac{\sin ^8 x-\cos ^8 x}{\sin ^4 x+\cos ^4 x} d x=\int\left(\sin ^4 x-\cos ^4 x\right) d x=\int\left(\sin ^2 x-\cos ^2 x\right) d x=-\frac{1}{2} \sin 2 x+C$