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# Integration watch

1. How would you integrate (e^3x +4)/e^2x ?
2. split it into two fractions & integrate them separately.
3. You can simplify the term by cancelling the fraction to e^x + 4, as e^3x/e^2x = e^x. The rest of it can be solved by substitution.
4. (Original post by Kallisto)
You can simplify the term by cancelling the fraction to e^x + 4, as e^3x/e^2x = e^x. The rest of it can be solved by substitution.
I don't think you can do that. (e^3x + 4) / e^2x = e^x + 4e^-2x.
5. (Original post by TheMindGarage)
I don't think you can do that. (e^3x + 4) / e^2x = e^x + 4e^-2x.
I guess I have misunderstand the fraction term. So the power is e^3x + 4 and not e^3x as I thought?
6. (Original post by CelaenSardothien)
How would you integrate (e^3x +4)/e^2x ?
The answer on the book said (e^x)-(2e^-2x)+c but I not sure how you get to the final answer
7. (Original post by Kallisto)
I guess I have misunderstand the fraction term. So the power is e^3x + 4 and not e^3x as I thought?
(e^(3x) +4)/e^2x

It is e to the power of 3x + 4 divide by e to the power of 2x
8. (Original post by CelaenSardothien)
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.
9. (Original post by CelaenSardothien)
(e^(3x) +4)/e^2x

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.

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