# Integration Y= (1/(e^x + 1))

1. Dec 23, 2005

### hypermonkey2

I seem to be having trouble with this antiderivative can i please see a solution? Y= (1/(e^x + 1))

I tried substituting e^x + 1 as u, but that left me with the quest to find an antiderivative of 1/(u^2 - u). i feel like im missing something silly here. thanks

2. Dec 23, 2005

### benorin

You have it, keep going use partial fractions: $\frac{1}{u(u-1)}= -\frac{1}{u}+\frac{1}{u-1}$

3. Dec 23, 2005

### d_leet

Try multiplying top and bottom by e^(-x)

4. Jan 4, 2006

### benorin

Here it is (the integral)

For

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

put $u=e^x +1\Rightarrow x=\log (u-1) \mbox{ so that }dx=\frac{du}{u-1}$

to get

$$\int\frac{dx}{e^x +1} = \int\frac{du}{u(u-1)} = \int\left( -\frac{1}{u}+\frac{1}{u-1}\right) du = -\log |u| + \log |u-1| + C$$
$$= -\log \left| e^x +1\right| + \log \left| e^x\right| + C = -\log \left| e^x +1\right| + x + C$$

5. Jan 4, 2006

### VietDao29

???
Why on Earth are there still some people just post a complete solution (which is definitely, certainly, obviously, seriously, blah blah blah... against the forum's rules), without giving the OP an opportunity to solve the problem on his own???
Isn't your #2 post of this thread enough? Can't you wait for the OP to tell you if he can solve it or he still needs a little bit more help?
Am I really missing something???