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Evaluate int((sinx+cosx)dx)/(sqrt(3+sin2...

Evaluate `int((sinx+cosx)dx)/(sqrt(3+sin2x)).`

Text Solution

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`int((sinx+cosx)dx)/(sqrt(3+sin2x))=int((sinx+cosx)dx)/sqrt(4-(sinx-cosx)^(2))`
`=int(dt)/(sqrt(4-t^(2))) " " ("Putting " sinx-cosx=t)`
`="sin"^(-1)(t)/(2)+c`
`="sin"^(-1)(sinx-cosx)/(2)+c`
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