Hi
I'm having a little trouble with this. Integrate using substitution, where $\displaystyle u=e^{x/2}$
$\displaystyle \int\frac{e^{x/2}}{1+e^x}dx$
Thanks
If $\displaystyle u=e^{\frac{x}{2}}$, then $\displaystyle \frac{\text{d}{u}}{\text{d}x} = \frac{1}{2}e^{\frac{x}{2}}$.
If $\displaystyle e^{x} =\left(e^{\frac{x}{2}}\right)^2$ and $\displaystyle \int\frac{e^{\frac{x}{2}}}{1+e^x}\;\text{d}x = 2\int\frac{e^{\frac{x}{2}}}{2(1+e^x)}\;\text{d}x$, can you finish it from here?
Well, given the information that you have, substitute $\displaystyle \frac{\text{d}u}{\text{d}x}$ and $\displaystyle e^x =\left(e^\frac{x}{2}\right)^2=u^2$ into the integral, and then "cancel" the $\displaystyle \text{d}x$.
Now you have something you know how to integrate.