 Hello and welcome to the session. Let us discuss the following question. It says integrate the following function The given function is cos x upon under the root 1 plus sin x. Let us now proceed on with the solution and let I Be the integral cos x upon under the root 1 plus sin x x dx Now we see that the derivative of 1 plus sin x is cos x. So put t equal to 1 plus sin x. So dt by dx is equal to cos x dx We don't need to write dx here Because derivative of sin x is cos x. So this implies dt is equal to cos x dx. So cos x dx is equal to dt now cos x dx and 1 plus sin x as t in the integral. So the integral becomes dt upon root t which can be further written as t to the power minus 1 by 2 dt Now the integral of t to the power minus 1 by 2 is t to the power minus 1 by 2 plus 1 upon minus 1 by 2 plus 1 plus c which is equal to t to the power 1 by 2 upon 1 by 2 plus c which is equal to 2 into t to the power 1 by 2 plus c. Now t is equal to 1 plus sin x So put t equal to 1 plus sin x. So this becomes 1 plus sin x to the power 1 by 2 plus c Hence answer to the given Question is or the integral of the given function is to under the root 1 plus sin x plus c and This completes the question. Hope you will be able to solve more of such problems. Bye and take care