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Integrate the following functions: cos(2...

Integrate the following functions: `cos(2x)/(cosx+sinx)^2`

Text Solution

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`(cos2x)/(cosx+sinx)^2 = (cos^2x-sin^2x)/(cosx+sinx)^2`
`=(cosx-sinx)/(cosx+sinx)`
Put cosx+sinx = t
Then dt = (-sinx+cosx) dx
therefore` int(cos2x)/(cosx+sinx)^2 dx`
=`int dt/t = log|t|+c`
=`log|cos+sinx|+c`
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