 Hello and welcome to the session. Let us discuss the following question. It says integrate the following function. The given function is sin A x plus b into cos A x plus b. Now before integrating this function, we write the formula for the integral of sin y. The integral of sin y dy is minus cos y plus c and this will be the key idea. Let us now move on to the solution. Let i be the integral sin A x plus b into cos A x plus b. Now we know that the formula of sin 2 theta is 2 sin theta cos theta. So to make that formula we need to multiply and divide this integral by 2. So this integral becomes 1 by 2 into 2 sin A x plus b into cos A x plus b. Now this is equal to 1 by 2 into integral of sin 2 into A x plus b by the formula sin 2 theta is equal to 2 sin theta cos theta. Now theta is equal to 2 sin theta is A x plus b. So this integral becomes 1 by 2 into the integral sin 2 A x plus 2 b dx. Now put y is equal to 2 A x plus 2 b. So dy by dx is equal to 2 A x plus 2 A dx and this implies dy is equal to 2 A dx because derivative of y with respect to x is 2 A only. Then we cross multiply. So dy is equal to 2 A dx and this implies dx is equal to dy by 2 A. So dx is equal to dy by 2 A. So the integral becomes 1 by 2 into the integral sin y dy by 2 A. So again this is equal to 1 by 4 A integral sin y dy. Now the integral of sin y dy is minus cos y plus c. So this is equal to 1 by 4 A into cos y plus c. Let us now substitute the value of y here. So this becomes 1 upon 4 A into cos A x plus 2 b plus c and we have a minus sign because the integral of sin y dy is minus cos y plus c. Hence the derivative of the given function is minus 1 upon 4 A into cos A x plus 2 b plus c and this completes the question. Let me now take care. Have a good day.