Question

Evaluate the Intergal

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ \sqrt{e^x-1} }\]

Answer 2

I can't do u sub, trig sub partial fraction or Integration by parts :/ . How would I even approach this?

Answer 3

Try u-sub where
\[u=e^x \\ \\ du=e^xdx \\ \\ \frac{du}{e^x}=dx\]
\[\int\limits \frac{1}{\sqrt{u-1}}\frac{du}{e^x}\]
\[\int\limits \frac{1}{\sqrt{u-1}(u)}du\]

Answer 4

Umm okay.

Answer 5

You mean you're not allowed to use u-sub?

Answer 6

I am :P .

Answer 7

ok

Answer 8

Just thinking about afterwards.

Answer 9

I see a parts Integration but I don't think that's the best way.

Answer 10

Could I use Partial Fractions?

Answer 11

I would let \(u=\sqrt{e^x-1}\)

Answer 12

Why so? I was thinking abut that as well.

Answer 13

but I noticed that it's derivative isn't in the Intergal.

Answer 14

\[\Rightarrow e^x=u^2+1\]

Answer 15

Okay I see it. What about the DIfferential dx though?

Answer 16

\[du=\frac{1}{2\sqrt{e^x-1}}e^xdx\]

Answer 17

Ohh!

Answer 18

Nice one!

Answer 19

\[\frac{2u}{u^2+1}du=dx\]

Answer 20

How did you come up with that? :P .

Answer 21

I've done a lot of integrals

Answer 22

I plan on doing that as well :) .

Answer 23

Thanks!