Integrate cos 2x/(cosx+sinx)^2.. ....????..................

Sir but the answer given at the back of the book is log|cos x + sin x | +C.. I have understood your concept but why answers are not matching.. Please help me sir

Hi there . In indefinite integration it is possible for a ques to have different answers both will be correct if method is correct. for your answer you can put cosx+Sinx =t and you can find its derivative in numerator ..hence answer is log|cosx+Sinx| +C