$\int \frac{2 - s i n 2 x}{1 - c o s 2 x} e^{x} d x$ is equal to

- e^{x} c o t x + c

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e^{x} c o t x + c

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2 e^{x} c o t x + c

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- 2 e^{2} c o t x + c

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Solution

The correct option is A $- e^{x} c o t x + c$
Let $I = \frac{2 - s i n 2 x}{1 - c o s 2 x} e^{x} d x$

$= \frac{2 - s i n x c o s x}{2 s i n^{2} x} e^{x} d x$

$= c o s e c^{2} x e^{2} d x - c o t x e^{x} d x$

$- c o t x e^{x} - c o t x e^{x} d x - c o t x e^{x} + c$

$= - c o t x e^{x} + c$

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