anonymous
  • anonymous
Evaluate the Intergal
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{}^{}\frac{ 1 }{ \sqrt{e^x-1} }\]
anonymous
  • anonymous
I can't do u sub, trig sub partial fraction or Integration by parts :/ . How would I even approach this?
.Sam.
  • .Sam.
Try u-sub where \[u=e^x \\ \\ du=e^xdx \\ \\ \frac{du}{e^x}=dx\] \[\int\limits \frac{1}{\sqrt{u-1}}\frac{du}{e^x}\] \[\int\limits \frac{1}{\sqrt{u-1}(u)}du\]

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anonymous
  • anonymous
Umm okay.
.Sam.
  • .Sam.
You mean you're not allowed to use u-sub?
anonymous
  • anonymous
I am :P .
.Sam.
  • .Sam.
ok
anonymous
  • anonymous
Just thinking about afterwards.
anonymous
  • anonymous
I see a parts Integration but I don't think that's the best way.
anonymous
  • anonymous
Could I use Partial Fractions?
Zarkon
  • Zarkon
I would let \(u=\sqrt{e^x-1}\)
anonymous
  • anonymous
Why so? I was thinking abut that as well.
anonymous
  • anonymous
but I noticed that it's derivative isn't in the Intergal.
Zarkon
  • Zarkon
\[\Rightarrow e^x=u^2+1\]
anonymous
  • anonymous
Okay I see it. What about the DIfferential dx though?
Zarkon
  • Zarkon
\[du=\frac{1}{2\sqrt{e^x-1}}e^xdx\]
anonymous
  • anonymous
Ohh!
anonymous
  • anonymous
Nice one!
Zarkon
  • Zarkon
\[\frac{2u}{u^2+1}du=dx\]
anonymous
  • anonymous
How did you come up with that? :P .
Zarkon
  • Zarkon
I've done a lot of integrals
anonymous
  • anonymous
I plan on doing that as well :) .
anonymous
  • anonymous
Thanks!

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