 Hello friends, and how are you all doing today? Let us integrate this function. We have the function as tan cube 2x into secant 2x into dx. Now, we can write tan cube 2x as tan square 2x into tan 2x, right? We will get multiplied by secant 2x into dx. Further, we know that tan square 2x can also be written as secant square 2x minus 1. So secant square 2x minus 1 will get multiplied by tan 2x and also secant 2x into sorry here it was dx into dx. Further, we have to let t be equal to secant 2x. So dt will be equal to the derivative, that will be 2 secant 2x into tan 2x dx. So here tan 2x and secant 2x into dx can be written as we need to take secant square 2x minus 1 sorry here since secant 2x is taken as t. So it will be t square minus 1 into dt divided by 2. Further, 1 by 2 into integral of t square into dt minus 1 by 2 into integral of 1 into dt. So we have the answer as 1 by 2 into t cube divided by 3 minus 1 by 2 into t plus c. Further can be written as 1 by 6 t cube minus 1 by 2 t plus c. Now here in place of t we can write secant 2x. So we have 1 by 6 secant cube 2x minus 1 by 2 secant 2x plus c and this is the required answer to the session This completes it. Hope you understood and enjoy it too. Have a nice day ahead