 Hello friends and how are you all today? My name is Priyanka and I shall be helping you with the following question. Please integrate the following. Here the function which is given to us is sin raised to the power 4x. Here we need to integrate this function with respect to dx. Now we can write it as sin square x whole raised to the power 2 into dx and sin square x can be written as 1 minus 2 by 2 whole raised to the power into dx. Now we have now on expanding we have integral of 1 minus 2 cos 2x plus cos square 2x whole divided by 4 into dx. Taking out 1 by 4 common we have 1 by 4 into integral of 1 into dx minus 2 by 4 integral of cos 2x dx plus 1 by 4 integral of cos square 2x dx. Now we have x by 4 minus 1 by 2 integral of cos 2x is sin 2x by 2 plus 1 by 4 here cos square 2x can be written as 1 plus cos 4x by 2 into dx plus c1. So we have x by 4 minus sin 2x by 4 plus 1 by 8 integral of 1 into dx plus 1 by 8 into integral of cos 4x dx plus c1. Now further we have again x by 4 minus sin 2x by 4 plus x by 8 plus sin 4x divided by 8 was already there into 4 plus c1 plus c2. Further we have on adding these two terms 3x by 8 minus 1 by 4 sin 2x plus 1 by 32 that is 8 into 4 sin 4x and c1 plus c2 can be combined and written as c. So the final answer to the session is 3x by 8 minus 1 by 4 sin 2x plus 1 by 32 sin 4x plus c. So this completes the session hope you understood it well and enjoyed it too.