 Hello friends, and how are you all? Let us interpret the following function. Here the function which is given to us is sine cube x plus cos cube x divided by sine 2x cos 2x with respect to dx. Now we can write it as sine cube x divided by sine 2x cos 2x into dx plus cos cube x divided by sine square x cos square x into dx. Now on simplifying it we have left with sine x over cos square x into dx plus cos x over sine square x dx. Now we also know that 1 over cos square x can be written as sine x over cos x into cos x dx plus cos x over sine square x can be written as sine x into sine x. Now sine x over cos x can be written as tan x and 1 over cos x can be written as secant x. Similarly, here we have cos x into cot x into dx Further now the integral of secant x tan x into dx is equal to secant x plus integral of cos x into cot x dx is sorry, here we will have minus cos x plus c. So the required answer to the session is x minus cos x plus c. Wait, this completes my session. Hope you understood it and enjoyed it. Have a nice day.