# Math Help - Substitution, again...

1. ## Substitution, again...

Please show steps. I'm trying to learn how to do these. I have the answers in the back of the book I just need to know how to get there. Thanks.

2. ## Re: Substitution, again...

Originally Posted by njdurkin

Please show steps. I'm trying to learn how to do these. I have the answers in the back of the book I just need to know how to get there. Thanks.
1. Let $u = 2+e^x~\implies~\frac{du}{dx} = e^x~\implies~\boxed{du=e^x \cdot dx}$

2. Re-write the integral:

$\int\left(\frac{e^x}{2+e^x}\right) dx = \int\left(\frac1{2+e^x}\right) e^x \cdot dx$

3. Now replace $2+e^x$ by u and $e^x \cdot dx$ by du. Your integral becomes now:

$\int\left(\frac1u \right) du$

4. Afterwards re-substitute to get a function wrt x.