If ^ 3/2 x + ^ 3/2 x ^3x ^3x (x- ) dx = A x - + B - x + C, where C is the integration constant, then AB is equal to

JEE Main 2024 Mathematics question

If , where C is the integration constant, then AB is equal to

Answer: (D)

Split into I₁ + I₂ with I₁ = ∫sec²x dx/√(tan x cosθ − sinθ) and I₂ = ∫cosec²x dx/√(cosθ − cot x sinθ). Putting tan x cosθ − sin θ = t² gives

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Question ID VK-016822