anonymous
  • anonymous
Integrate (e^2x)/(e^x-3) times dx
Calculus1
katieb
  • katieb
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anonymous
  • anonymous
|dw:1363307046027:dw|
anonymous
  • anonymous
let us consider e^x = t => st = e^x dx
anonymous
  • anonymous
|dw:1363307129744:dw|

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anonymous
  • anonymous
|dw:1363307205619:dw|
anonymous
  • anonymous
|dw:1363307271643:dw|
anonymous
  • anonymous
It's a simple \(u=e^x-3,\, du=e^xdx\) substitution.\[ \int \frac{e^{2x}}{e^x-3}dx = \int\frac{u+3}{u}du = \int 1 + \frac{3}{u}du \]
tkhunny
  • tkhunny
Note: It's not "times" dx. There is no multiplication, there.
anonymous
  • anonymous
Oh that's true. So which one of the answers is the correct way to solve then? Integration is a real struggle for me
tkhunny
  • tkhunny
Well, you are supposed to be learning. A bit of difficulty should not be construed as a bad sign. Put in the time and thought. Looks like wio and DHASHNI already did most of the work for you. You do the rest.

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