, , is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

∫1sin⁡3x sin⁡(x+α) dx\int \frac{1}{\sqrt{\sin^3 x\,\sin(x + \alpha)}}\,dx, α≠nπ,n∈Z\alpha \neq n\pi, n \in \mathbb{Z}, is equal to (a) −2cosec⁡α(cos⁡α−tan⁡xsin⁡α)1/2+C-2\operatorname{cosec}\alpha (\cos \alpha - \tan x\sin \alpha)^{1/2} + C (b) −2(cos⁡α+cot⁡xsin⁡α)1/2+C-2(\cos \alpha + \cot x\sin \alpha)^{1/2} + C (c) −2cosec⁡α(cos⁡α+cot⁡xsin⁡α)1/2+C-2\operatorname{cosec}\alpha (\cos \alpha + \cot x\sin \alpha)^{1/2} + C (d) −2cosec⁡α(sin⁡α+cot⁡xcos⁡α)1/2+C-2\operatorname{cosec}\alpha (\sin \alpha + \cot x\cos \alpha)^{1/2} + C

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