 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says, find an anti-derivative or integral of the following by the method of inspection. We have sin 2x minus 4 into e raised to part 3x. So let us start with the solution to this question. Now what we do here is, we find the anti-derivative of sin 2x, then we find the anti-derivative of 4 into e raised to part 3x, then we subtract them. First of all we see that, we consider d by dx of cos 2x that will be equal to minus 2 sin 2x because derivative of cos 2x is minus sin 2x multiplied the derivative of 2x that is 2. So we can say that cos 2x or we can say sin 2x will be equal to the d by dx of minus 1 by 2 cos 2x. Now we consider d by dx of 4 into e raised to part 3x is 4 into 3 into e raised to part 3x because 4 being a constant remains as it is derivative with respect to x of e raised to part 3x is e raised to part 3x multiplied by the derivative of 3x that is 3. So we can say that 4 into e raised to part 3x is equal to 1 by 3 into d by dx of 4 into e raised to part 3x or we can write it as d by dx of 4 by 3 into e raised to part 3x. Hence an antiderivative of sin 2x minus 4 into e raised to part 3x is minus 1 by 2 cos 2x minus 4 by 3 into e raised to part 3x. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.