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Evaluate: int(sinx)/(sin(x-a))\ dx...

Evaluate: `int(sinx)/(sin(x-a))\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`(x-a)cosa+sin a log|sin(x-a)|+C`
`int(sinx)/(sin(x-a))dx=int(sin(x-a+a))/(sin(x-a)) dx`
`=int(sin(x-a)cosa+cos(x-a)sina)/(sin(x-a))dx`
`=cos a int dx+sin a int(cos(x-a))/(sin(x-a))dx`
`=(cosa)x+sina|log sin(x-a)|+C`
`=xcosa+sin a log|sin(x-a)|+C`
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