- #1
QuarkCharmer
- 1,051
- 3
Homework Statement
[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.
Homework Equations
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?
Last edited: