 Hello friends and how are you all today? Let us integrate this function. Here the function given to us is cos x divided by 1 plus cos x into dx. Now we know that 1 plus cos x is equal to 2 cos square x y 2. Right, so on using it we have equal to adding 1 and subtracting 1 from the numerator we have 1 plus cos x minus 1 divided by 1 plus cos x into dx. Further we can write it as integral of 1 minus sorry integral of 1 into dx minus integral of 1 divided by 1 plus cos x into dx. That is equal to integral of 1 into dx is x minus here 1 plus cos x can be written as 2 cos square x y 2 into dx. Further we have x minus 1 by 2. Now 1 upon cos square x y 2 can be written as secant square x y 2 into dx right and the integral of secant square x is equal to what? It is equal to tan x y 2 divided by the derivative of the theta that is 1 by 2 plus c. So we have the answer as x minus here 1 by 2 will get cancelled. We are left with tan x by 2 plus c and this is the required answer to the question. So take care of your simplifications and have a nice day.