# Integration (e)

1. Mar 7, 2010

### physnoob

1. The problem statement, all variables and given/known data
$$\int dx/(e^{x}\sqrt{1-e^{-2x}})$$

2. Relevant equations

3. The attempt at a solution
I have absolutely no idea of how to start the problem, any help is greatly appreciated!
thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 7, 2010

### 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.

3. Mar 8, 2010

### Staff: Mentor

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

4. Mar 8, 2010

### 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 dont know how to proceed after this. What am i doing wrong?

5. Mar 8, 2010

### rock.freak667

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

6. Mar 8, 2010

### Staff: Mentor

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

7. Mar 8, 2010

### physnoob

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

8. Mar 8, 2010

### rock.freak667

That should be correct.

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