 Hi and welcome to the session. Let us discuss the following question. The question says, integrate the following functions, given function is 2 plus sine 2x phi but plus cos 2x into e to the power x. Let's now begin with the solution. This question we have to integrate the function 2 plus sine 2x phi 1 plus cos 2x into e to the power x with respect to x. Now this is equal to integral 2 plus sine 2 theta is equal to 2 sine theta cos theta. So sine 2x is equal to 2 sine x cos x phi. We know that 1 plus cos 2 theta is equal to 2 cos square theta. So 1 plus cos 2x is equal to 2 cos square x into e to the power x dx. This is equal to integral secant square x plus tan x into e to the power x dx. Now consider as tan x. Now f dash x is equal to secant square x. So we can see that this integral is of the form e to the power x into ff dash x. We know that integral of e to the power x into ff dash x with respect to x is e to the power x into fx plus. So using this, this integral is equal to e to the power x tan e to the power x into tan x plus c. So this completes this session. Bye.