 Hello and how are you all today? Let us integrate the following function which is given to us. Here the function is cos x minus sin x divided by 1 plus sin 2x with respect to dx. Now, we have cos x minus sin x divided by, we can write 1 as sin square x plus cos square x, isn't it? So we have sin square x plus cos square x plus sin 2x can be written as 2 sin x cos x to dx. Further, we have cos x minus sin x and here if you observe we have a square plus b square plus 2ab. So it can be written as sin x plus cos x the whole square into dx. Now let sin x plus cos x be equal to t. So cos x minus sin x into dx will be equal to what? It will be equal to dt. Further, we can write it as in the numerator we have dt and in the denominator we have t. So integrating the following function we have t minus 2 plus 1 divided by minus 2 plus 1 plus c. So we have t minus 1 divided by minus 1 plus c which can be written as minus 1 over t plus c. Now in place of t if we substitute the values so we have minus 1 over t was taken to be as cos x plus sin x. So we have minus 1 over cos x plus sin x plus c and this will be the required answer to the section. So this completes it. Hope you understand and have a nice day.