(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

\begin{equation} \int \frac{e^{x}+1}{e^{x}}\end{equation}

2. Relevant equations

3. The attempt at a solution

This problem comes out of the substitution section of my book, and the answer in the back of the book is [itex]x-e^{x}+C[/itex]

I started by changing the form to this:

\begin{equation}\int \frac{1}{e^{x}}e^{x}\end{equation}

I set u = [itex]e^{x}[/itex] and du is the same.

That left me with:

\begin{equation}\int \frac{1}{u} du\end{equation}

Integrating [itex]\frac{1}{u}[/itex] gives ln|u|

So plugging u back in gives [itex]ln|e^{x}|[/itex]

I plugged some test numbers into my answer and the book answer and they come out pretty close, so I thought both of them may be right, but I still can't figure out how to get [itex]x-e^{-x}[/itex].

Any ideas?

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# Homework Help: Substitutions with e

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