- #1
LoA
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Homework Statement
The original problem is [itex] \int \, \frac {xe^{2x}}{(1+2x)^2} dx [/itex]. I utilized integration by parts to get:
[itex] -\frac {xe^{2x}}{2(1+2x)} \, + \, \frac {1}{4}e^{2x} \, + \, C [/itex]
which I know is correct. However, I am told by the book that this may also be expressed as:
[itex] \frac {e^{2x}}{4(2x+1)} + C [/itex]
It is a failing of my algebra skills that I am unable to make this translation. I have banged my head against this problem for close to an hour now. The truly frustrating thing is that it was very apparent to me yesterday (I was redoing the problem just to warm up for more i.b.p. problems), and I quickly wrote it down, but cannot seem to 'see' it today. Any help would be much appreciated.
Homework Equations
none
The Attempt at a Solution
I have tried expanding the denominator of the first term and factoring out the common [itex] \frac{1}{2} e^{2x} [/itex] but then I get stuck. In particular, I can't figure out how to deal with the x in the numerator and the negative sign. I think I'm pretty clearly forgetting/misapplying some algebraic rules, so the first thing in the way of suggestive assistance that might help would be just a reference to the relevant rules/ideas. I think that given such a push in the right direction I can figure this out on my own.
Additionally, if anyone could suggest some resources for practice with algebra of this level of difficulty I'd greatly appreciate it.