# Thread: Integration of e^x (with fraction)

1. ## Integration of e^x (with fraction)

This is my first post, hopefully it works. I missed a day of school and I have a test tomorrow; I've been working on some review but just forgot how to do this type of problem so hopefully someone can help:

take the integral:

(e^4x - e^2x + 1) / (e^x)

Thanks for the help and sorry I don't know how to use the codes to make it without carrots etc...

2. Originally Posted by rootbeer
This is my first post, hopefully it works. I missed a day of school and I have a test tomorrow; I've been working on some review but just forgot how to do this type of problem so hopefully someone can help:

take the integral:

(e^4x - e^2x + 1) / (e^x)

Thanks for the help and sorry I don't know how to use the codes to make it without carrots etc...
$\frac{e^{4x}-e^{2x}+1}{e^{x}}=e^{3x}-e^{x}+e^{-x}$

I hope this helps

3. Thanks, but can you do the steps/ explain more in depth how to get to the answer?

4. Originally Posted by rootbeer
Thanks, but can you do the steps/ explain more in depth how to get to the answer?
It's just simple algebra. He split up the fraction, and then reduced using this property of exponents:

$\frac{a^m}{a^n}=a^{m-n}.$

5. Originally Posted by Reckoner
It's just simple algebra. He split up the fraction, and then reduced using this property of exponents:

$\frac{a^m}{a^n}=a^{m-n}.$
But isn't that just simplifying it and not integration?
(Sorry if I'm wrong, we only learned it this week so I haven't had much practice)

6. Originally Posted by rootbeer
But isn't that just simplifying it and not integration?
(Sorry if I'm wrong, we only learned it this week so I haven't had much practice)
Yes, but the point is that the expression should be really easy to integrate in that simplified form. Remember that you can split up integrals between sums and differences.

7. Ok, wow I feel kinda dumb for not realizing that. Thanks!
But if there's addition in the numerator and the denominator you can't split it up right? Then you have to use u and du and that stuff?

8. Originally Posted by rootbeer
Ok, wow I feel kinda dumb for not realizing that. Thanks!
But if there's addition in the numerator and the denominator you can't split it up right? Then you have to use u and du and that stuff?
You can split up fractions by the terms in the numerator (that is what TheEmptySet did). You cannot do the same with the denominator, but you may still be able to rewrite such a fraction using polynomial long division or partial fraction decomposition (which your course might not have covered yet).

9. Originally Posted by Reckoner
You can split up fractions by the terms in the numerator (that is what TheEmptySet did). You cannot do the same with the denominator, but you may still be able to rewrite such a fraction using polynomial long division or partial fraction decomposition (which your course might not have covered yet).
Thanks so much for the help. I figured out my other problem too. We haven't done partial fraction decomposition but we've done a little long division- but I'm only in AB calc. But thanks again for the help and hopefully I'll do ok on my quiz.