 Hello and welcome to the session. Let us discuss the following question. It says integrate the following function The given function is tan square 2x minus 3 To integrate this function, we need to know some formula formula is secant square x minus 1 is equal to tan square x and the integral of secant square x dx is tan x So this knowledge will work as key idea. Let us now move on to the solution and let I be the integral square 2x minus 3 dx Now x minus 3 can be written as secant square 2x minus 3 minus 1 by this formula into dx So this can be again written as secant square 2x minus 3 minus integral dx 1 into dx is dx. Now equal to 2x minus 3 Now dt is equal to 2 dx So this implies dx is equal to dt by 2 first integral say this as I1 and this as I2 so I integral secant square and dx is dt by 2. So it is dt by 2 minus the integral dx in this is equal to 1 by 2 into integral secant square minus dx. The integral of secant square x dx is tan x. Here we have the integral of secant square dt is tan t so it is 1 by 2 tan t minus integral dx is the constant of the integration. I put the value of minus 3 minus x plus c Hence the integral of the given function is 1 by 2 x minus 3 minus x plus c And this completes the question and the session. Life and outtake here. Have a good day