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Integrate the following functions: (cosx...

Integrate the following functions: `(cosx-sinx)/(1+sin(2x)`

Text Solution

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`(cosx-sinx)/(1+sin2x) = (cosx-sinx)/(cosx+sinx)^2`
`int(cosx-sinx)/(1+sin2x) dx`
= `int (cosx-sinx)/9cosx+sinx)^2 dx`
Let t = cosx+sinx.
Then `dt = (-sinx+cosx)dx`
therefore` int(cosx-sinx)/(1+sin2x) dx`
=`int dt/t^2 = -1/t+c`
= `-1/(cosx+sinx)+c`
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