The answer on the book said (e^x)-(2e^-2x)+c but I not sure how you get to the final answer
See what I did - split it into two powers of e. Then integrate each one separately. You'll have to either do the inverse chain rule by inspection or use substitution.
It is e to the power of 3x + 4 divide by e to the power of 2x
So the bold print is the power. I guess I got it now. As the bear said, you should make two fractions of the term first: e^(3x) + 4/e^2x = (e^3x/^e^2x) + (4/e^2x).
So we got what TheMindGarage simplified: e^x + 4e^-2x. Now you can integrate separetedly as the bear said as well. For 4e^-2x, you have to substitute. For substitution, you can the ignore the factor 4. You multiply the integrated term of e^-2x with 4 as last step.