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int(cos 2x)/((sin x + cos x)^(2)) dx " i...

`int(cos 2x)/((sin x + cos x)^(2)) dx " is equal to : "`

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The correct Answer is:
b
`" Let I "= int(cos2x)/((sin x + cos x)^(2))dx`
`=int(cos^(2) x-sin^(2)x)/((sin x+cos x)^(2))dx`
` =int((cos x-sin x)(cos x+ sin x))/((sin x+cos x)(sin x+cos x))dx`
`=int( cos x- sinx)/(sin x+cos x)dx`
`" Let " sin x cos x=t rArr (cos x-sin x) dx=dt`

`:. I= int (1)/(t) dt= log|t|+C`
`=log |sin x+cos x| +C`
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