The correct option is C 1/2 cosec x+cot x+CI=∫(2 cos x+1)/(2+cos x)^2dx = ∫(2+cos x)cos x+sin^2 x/(2+cos x)^2dx =∫cos x/2+cos xdx ∫ sin^2 x/(2+cos x)^2dx = ...

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Byju's Answer

Standard XII

Mathematics

Strictly Increasing Functions

∫2+ x/1+2 x2 ...

Question

$\int \frac{(2 + s e c x)}{(1 + 2 s e c x)^{2}} d x =$

\frac{1}{2 c o s e c x + c o t x} + C

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2 c o s e c x + c o t x + C

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\frac{1}{2 c o s e c x - c o t x} + C

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2cosecx - cot x + C

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Solution

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

Suggest Corrections

∫(2+sec x)(1+2 sec x)2dx=

The correct option is A 12 cosec x+cot x+CI=∫(2 cos x+1)(2+cos x)2dx=∫(2+cos x)cos x+sin2x(2+cos x)2dx=∫cos x2+cos xdx−∫−sin2x(2+cos x)2dx=sin x2+cos x+c

$\int \frac{(2 + s e c x)}{(1 + 2 s e c x)^{2}} d x =$