 Hello students, let's solve the following problem on integration, it says integrate the following function. The given function is sin x upon 1 plus cos x whole squared. Let us now proceed on with the solution and let I be the integral sin x upon 1 plus cos x whole squared dx. Here we see that the derivative of 1 plus cos x is minus sin x. So put t equal to 1 plus cos x. So dt by dx is equal to minus sin x and this implies dt is equal to minus sin x dx and this implies sin x dx is equal to minus dt. So sin x into dx is minus dt and t is equal to 1 plus cos x. Substituting all these values in the integral, integral i becomes 1 upon t square minus dt which can be further written as minus integral t to the power minus 2 dt. Its integral is equal to minus t t to the power minus 2 plus 1 upon minus 2 plus 1 plus sin. As we know that the integral of x to the power n dx is given by x to the power n plus 1 upon n plus 1 plus c. Now here n is minus 2. So this is equal to minus t to the power minus 1 upon minus 1 plus c. This is again equal to 1 upon t plus c. Now t is 1 plus cos x substituted. Hence the integral of the given function is 1 upon 1 plus cos x plus c. And this completes the question and the session. Hope you will be able to solve more of such problems. I for now take care. Have a good day.