 Hello and welcome to the session. Let us discuss the following question. Question says, find the following integrals. We have to find the integral of sec x multiplied by sec x plus tan x dx. First of all, let us understand that integral of fx plus gx dx is equal to integral of fx dx plus integral of gx dx and integral of sec square x dx is equal to tan x plus c, where c is the constant of integration. Also, integral of sec x tan x dx is equal to sec x plus c, where c is the constant of integration. We will use these three expressions as our key idea to solve the given question. Let us now start with the solution. Now we have to find the integral of sec x multiplied by sec x plus tan x dx. Now multiplying sec x by this bracket, we get integral of sec square x plus sec x multiplied by tan x dx. Now using expression 1 of the key idea, we can write this integral as integral of sec square x dx plus integral of sec x tan x dx. Now we know integral of sec square x dx is equal to tan x. We have already mentioned this in key idea and integral of sec x multiplied by tan x dx is equal to sec x and c is the constant of integration. So our required answer is, integral of sec x multiplied by sec x plus tan x dx is equal to tan x plus sec x plus c, where c is the constant of integration. This completes the session. Hope you understood the solution. Take care and keep smiling.