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Evaluate: int(sqrt(tanx)-sqrt(cotx))dx...

Evaluate: `int(sqrt(tanx)-sqrt(cotx))dx`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(2)sin^(-1)(sinx-cosx)+C`
`int(sqrt(tanx)+sqrt(cotx))dx=int(sinx+cosx)/(sqrt(sinxcosx))dx`
`=sqrt(2)int(sinx+cosx)/(sqrt(sin2x))dx`
`=sqrt(2)int(sinx+cosx)/(sqrt(1-(sinx-cosx)^(2)))dx`
`=sqrt(2)int(dt)/(sqrt(1-t^(2)))`
`=sqrt(2)sin^(-1)t+C`
`=sqrt(2)sin^(-1)(sinx-cosx)+C`
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