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Evaluate: int(cosx-sinx)/(sqrt(8-sin2x))...

Evaluate: `int(cosx-sinx)/(sqrt(8-sin2x))\ dx`

Text Solution

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Given,
I=`int(cosx-sinx)/(sqrt(8-sin2x))\ dx`
Putting `cosx+sinx=t` in the integral
`⟹(cosx−sinx)dx=dt`
`(cosx+sinx)^2=t^2`
`⟹cos^2x+sin^2x+2sinxcosx=t^2`
`⟹1+sin2x=t^2`
`I=∫(​dx​)/(sqrt(9−(1+sin2x))`
...
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