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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  sin⁡  xsin⁡ (x  −  α)  dx\int \,\,\frac{{\sin \,\,x}}{{\sin \,(x\,\, - \,\,\alpha )}}\,\,dx is
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Correct option: D
x  cos⁡  α  +  sin⁡  α  log⁡  sin⁡  (x−α)  +  cx\,\,\cos \,\,\alpha \,\, + \,\,\sin \,\,\alpha \,\,\log \,\,\sin \,\,\left( {x - \alpha } \right)\,\, + \,\,c
Option D (xcos⁡α+sin⁡αlog⁡sin⁡(x−α)+cx\cos \alpha + \sin \alpha \log \sin (x - \alpha ) + c) is correct because it is the result of integrating the given expression using trigonometric identities and substitution.

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