$\int (\frac{c o s^{8} x - s i n^{8} x}{1 - 2 s i n^{2} x c o s^{2} x}) d x$ equals

- \frac{s i n 2 x}{2} + c

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\frac{s i n 2 x}{2} + c

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\frac{c o s 2 x}{2} + c

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- \frac{c o s 2 x}{2} + c

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Solution

The correct option is A $\frac{s i n 2 x}{2} + c$
$\int (\frac{c o s^{8} x - s i n^{8} x}{1 - 2 s i n^{2} x c o s^{2} x}) d x$
$= \int \frac{(c o s^{4} x + s i n^{4} x) (c o s^{4} x - s i n^{4} x)}{(1 - 2 s i n^{2} x c o s^{2} x)} d x$
$= \int (c o s^{2} x - s i n^{2} x) d x$ $= \int c o s 2 x d x$ $= \frac{s i n 2 x}{2} + C$

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