Integrating the Inverse Exponential-Square Root Function

[physnoob]

Homework Statement

\int dx/(e^{x}\sqrt{1-e^{-2x}})

Homework Equations

The Attempt at a Solution

I have absolutely no idea of how to start the problem, any help is greatly appreciated!
thanks!

 

[rock.freak667]

Try a substitution of maybe u=e^-x. Then you should get it into a form where the anti-derivative should be easily found.

 

[Mark44]

Also, note that 1/e^x = e^-x.

 

[physnoob]

hmm, can i get a little more hint? if i do a u sub. of u = e^{-x}, how do i get rid of
e^{-2x}? I have tried do a u sub. of u = \sqrt{1-e^{-2x}}, but i ended up getting the \int du/e^{-x}, which i don't know how to proceed after this. What am i doing wrong?

 

[rock.freak667]

e^-2x=(e^-x)², so in terms of u it is?

 

[Mark44]

Doesn't e^-x*e^-x = e^-2x?

 

[physnoob]

o boy, that was embarrassing lol
just want to make sure, is the answer cos^{-1}(e^{-x}) + C?

 

[rock.freak667]

That should be correct.

I think -sin^-1(e^-x)+C should work as well.