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Question
Integrate the function:
`sinx/(sin (x - a))`
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Solution
Let `I = int(sin x)/(sin (x - a))`dx
`= int (sin [(x - a) + a])/(sin (x - a)) dx`
`= int (sin (x - a)cos a + cos (x - a)sin a)/(sin (x - a)) dx`
`= int (sin (x - a) cos a)/(sin (x - a)) dx + int (cos (x - a) sin a)/(sin (x - a)) dx`
= cos a ∫ 1 · dx + sin a ∫ cot (x - a) dx
= cos a · x + sin a log |sin (x - a)| + C
= sin a · log |sin (x - a)| + x cos a + C
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