- 2 cos 2 x In tan x dx- is equal toA- sin 2 x Intan x-2 x-CB- sin 2 x Intan x-2 x-CC- sin x Intan x-x-CD- none of these

The correct option is A sin 2x In (tan x) – 2x + CWe have I = In (tan x) ∫ 2 cos 2xdx ∫ sin 2x . sec^2x/tan xdx = sin 2 x In(tan x) ∫ 2dx = sin 2x In (tan ...

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Byju's Answer

Standard XII

Mathematics

Integration by Parts

∫ 2 cos 2 x I...

Question

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

The correct option is A sin 2x In (tan x) – 2x + CWe have I=In(tanx)∫2 cos 2xdx −∫sin2x.sec2xtanxdx = sin 2 x In(tan x) −∫2dx = sin 2x In (tan x) - 2x + C

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

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