$\int \frac{s e c x}{\sqrt{s e c x + t a n x}} d x$

\frac{- 2}{\sqrt{s e c x + t a n x}} + c

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\frac{2}{\sqrt{s e c x + t a n x}} + c

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2 \sqrt{s e c x + t a n x} + c

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None

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Solution

The correct option is A $\frac{- 2}{\sqrt{s e c x + t a n x}} + c$
$\int \frac{s e c x}{\sqrt{s e c x + t a n x}} d x = \int \frac{s e c x (s e c x + t a n x)}{(s e c x + t a n x)^{3 / 2}} d x (P u t s e c x + t a n x = t, s e c x (s e c x + t a n x) d x = d t = \frac{- 2}{\sqrt{s e c x + t a n x}} + c$

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