 Hello friends, let's work out the following problem. It says integrate the following function. It is sin x into sin cos x. To integrate this function, we first need to know the formula for the integral of sin y dy. It is equal to minus cos y plus c, where c is the constant of integral. This will be the key idea. Let us now proceed on with the solution. We have to integrate sin x into sin cos x dx. Now here we see that the derivative of cos x is sin x. So we put y equal to cos x. Now we differentiate this with respect to x. So dy by dx is equal to minus sin x. So this implies dy is equal to minus sin x dx and this implies sin x dx is equal to minus dy. So sin x into dx is equal to minus dy and cos x is equal to y. So we substitute all these values in the integral. So the integral becomes sin y minus dy, which is equal to minus integral sin y dy. Now the integral of sin y dy is minus cos y plus c. So this becomes minus cos y plus c, which is equal to cos y plus c. Now we substitute the value of y in this. y is cos x. So this becomes cos cos x plus c. Hence the integral of the given function is cos cos x plus c. And this completes the question. Why for now take care. Have a good day.