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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))` |
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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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