Can anyone help me show that the following equations are equivalent? 

$$x-\ln|1+e^x| = -\ln|e^{-x}+1|$$

I'm having a little trouble. It should be an easy solution, where I take one equation, start with it, and show that it can turn into the opposing one. I know it involves the properties of logs, but I am just stuck on it. 

I got both the equations when solving for the anti-derivative of $1/(1+e^x)$, and am under the impression they are the same, but I do not understand how. I can show my work for this if it would help, just ask. Thank you. 

Little help? Would appreciate any insight.