Need a little help starting this integral

[silverdiesel]

$$\int\frac{1}{e^x+1}dx$$

I have tried substitution, partial fraction decomposition, and integration by parts but I can't seem to figure it out. Any help is much appriciated.

 

[Physics Monkey]

Hint: multiply top and bottom by $$e^{-x}$$.

 

[silverdiesel]

okay, then I can use u sub, which nets...

$$-ln (1+e^{-x})$$

is that right?

 

[silverdiesel]

That does not seem right. What I have I done wrong?

$$\int\frac{e^{-x}}{1+e^{-x}}dx$$

$$u = 1+e^{-x}\\-du = e^{-x}$$

$$-\int\frac{1}{u}du$$

 

[d_leet]

That does not seem right. What I have I done wrong?

$$\int\frac{e^{-x}}{1+e^{-x}}dx$$

$$u = 1+e^{-x}\\-du = e^{-x}$$

$$-\int\frac{1}{u}du$$

It looks right to me, why do you think it's wrong?

 

[silverdiesel]

After further review, I don't think its wrong. I guess I am just working on building confidence in the integration process and I was hoping for some confirmation that is was done right. Thank you. These forums have been extremely helpful and I really appreciate all the quick and intelligent responces.