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Indefinite Integrals question

2024 · 29 Jan · Shift 2 · Q33

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JEE Main
Mathematics
Indefinite Integrals
2024 · 29 Jan · Shift 2 · Q33

Indefinite Integrals question

2024 · 29 Jan · Shift 2 · Q33

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

If

\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \cot x}+C

, where

C

is the integration constant, then

A B

is equal to

A
$2 \sec \theta$
B
$8 \operatorname{cosec}(2 \theta)$
C
$4 \operatorname{cosec}(2 \theta)$
D
$4 \sec \theta$

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