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`int(cos2x)/((sinx+cosx)^(2))dx` बराबर है :A. `(-1)/(sinx+cosx)+C`B. `log|sinx+cosx|+C`C. `log|sinx-cosx|+C`D. `(1)/((sinx-cosx)^(2))`

Answer» Correct Answer - B
माना `I=int(cos2x)/((sinx+cosx)^(2))dx`
`" "=int(cos^(2)x-sin^(2)x)/((sinx+cosx)^(2))dx`
`" "=int((cosx-sinx)(cosx+sinx))/((sinx+cosx)(sinx+cosx))dx`
`" "=int(cosx-sinx)/(sinx+cosx)dx`
माना `" "sinx+cosx=t " "rArr" "(cosx-sinx)dx=dt`
`therefore" "I=int(1)/(t)dt=log|t|+C`
`" "=log|sinx+cosx|+C`


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