$\int 2$ cos 2x In (tan⁡x )dx,is equal to

sin 2x In (tan x) – 2x + C

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sin 2xIn (tan x) + 2x + C

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sin xIn (tan x) – x + C

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none of these

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Solution

The correct option is A sin 2x In (tan x) – 2x + C
We have $I = I n (t a n x) \int 2$ cos 2xdx $- \int s i n 2 x . \frac{s e c^{2} x}{t a n x} d x$
= sin 2 x In(tan x) $- \int 2 d x$ = sin 2x In (tan x) - 2x + C

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