-3-2 c-0-2d x is equal toA- sin x-2-3 cos x-CB- 2 cos x-2-3 sin x-cC- 2 cos x-2-3 cos x-cD- 2 sin x-2-3 sin x-c

The correct option is A ( sin x/2+3cos x )+cDivide above and below by sin^2x, then ∫3cosec^2x+2cosec x cot x/(2cosec x+3cot x)^2.dx Put 2cosecx + 3cotx = t ( ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios for Sum of Two Angles

∫3+2 c/√0+2d ...

Question

$\int \frac{3 + 2 c o s x}{(2 + 3 c o s x)^{2}} d x$ is equal to

(\frac{s i n x}{2 + 3 c o s x}) + c

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(\frac{2 c o s x}{2 + 3 s i n x}) + c

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(\frac{2 c o s x}{2 + 3 c o s x}) + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{2 s i n x}{2 + 3 s i n x}) + c

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Solution

The correct option is A $(\frac{s i n x}{2 + 3 c o s x}) + c$
Divide above and below by $s i n^{2} x$ , then
$\int \frac{3 c o s e c^{2} x + 2 c o s e c x c o t x}{(2 c o s e c x + 3 c o t x)^{2}} . d x$
Put 2cosecx + 3cotx = t
$(- 2 c o s e c x c o t x - 3 c o s e c^{2} x) d x = d t$
$= \int - \frac{d t}{t^{2}} = \frac{1}{t} + c = \frac{1}{2 c o s e c x + 3 c o t x} + c = \frac{s i n x}{2 + 3 c o s x} + c$

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∫3+2cos x(2+3cos x)2dx is equal to

The correct option is A (sin x2+3cos x)+cDivide above and below by sin2x, then ∫3cosec2x+2cosec x cot x(2cosec x+3cot x)2.dx Put 2cosecx + 3cotx = t (−2cosec x cot x−3 cosec2x)dx=dt =∫−dtt2=1t+c=12cosecx+3cot x+c=sin x2+3cos x+c

$\int \frac{3 + 2 c o s x}{(2 + 3 c o s x)^{2}} d x$ is equal to