 Hello and how are you all today? The question says integrate the following. Now here the function which is given to us is sin cube x into cos cube x. Now here we need to integrate the function sin cube x into cos cube x with respect to dx. So we can have, we can write sin cube x as sin square x into sin x, right? Further. Now sin square x can be written as 1 minus cos square x because sin square theta is equal to 1 minus cos square. Sin square x is equal to 1 minus cos square x. So we have further and multiplying cos cube x with 1 minus cos square x we have cos cube x minus cos 5 x into sin x into dx. Now let cos x be equal to t. That means we have minus sin x is equal to dt, right? So we can have minus t raise to the power 3 minus t raise to the power 5 into sin x dx is written as dt. Further. We have minus integral of sin, sorry dt plus integral of t raise to the power 5 into dt. That we have minus t raise to the power 4 divided by 4 plus t raise to the power 6 divided by 6 plus c. Now on substituting the value of cos x in place of t we have minus cos raise to the power 4 x divided by 4 plus cos raise to the power 6 x divided by 6 plus c. And this is the final answer to the session. So understood it well and have a nice day.