1. ## Integration by substitution

Hi

I'm having a little trouble with this. Integrate using substitution, where $u=e^{x/2}$

$\int\frac{e^{x/2}}{1+e^x}dx$

Thanks

2. If $u=e^{\frac{x}{2}}$, then $\frac{\text{d}{u}}{\text{d}x} = \frac{1}{2}e^{\frac{x}{2}}$.

If $e^{x} =\left(e^{\frac{x}{2}}\right)^2$ and $\int\frac{e^{\frac{x}{2}}}{1+e^x}\;\text{d}x = 2\int\frac{e^{\frac{x}{2}}}{2(1+e^x)}\;\text{d}x$, can you finish it from here?

3. I get to there but not sure where to go.

Thanks

4. Well, given the information that you have, substitute $\frac{\text{d}u}{\text{d}x}$ and $e^x =\left(e^\frac{x}{2}\right)^2=u^2$ into the integral, and then "cancel" the $\text{d}x$.

Now you have something you know how to integrate.