(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int \frac{e^{2x}}{e^{2x}+3e^{x}+2}dx[/tex]

I don't understand what I am doing wrong here. I missed this one question on a quiz but it looks right to me, I have went over it a dozen times.

2. Relevant equations

3. The attempt at a solution

[tex]\int \frac{e^{2x}}{e^{2x}+3e^{x}+2}dx[/tex]

Fraction part:

[tex]\frac{e^{2x}}{(e^{x}+1)(e^{x}+2)} = \frac{Ae^{x}}{e^{x}+1} + \frac{Be^{x}}{e^{x}+2}[/tex]

[tex]e^{2x} = e^{2x}(A+B)+e^{x}(2A+B)[/tex]

[itex]A + B = 1[/itex]

[itex]2A + B = 0[/itex]

[itex]A=-1[/itex] and [itex]B=2[/itex]

Integral stuff:

[tex]\int -\frac{e^{x}}{e^{x}+1} + \frac{2e^{x}}{e^{x}+2}dx[/tex]

My solution:

[tex]-ln(|e^{x}+1|) + 2ln(|e^{x}+2|) + C[/tex]

??

Edit: Additionally:

If one of the factors were (e^(2x)+1), does that count as a non-reducible polynomial and get A(e^x)+B as it's numerator instead of just plain A?

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# Integral kicking my butt

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