Question: evaluate the indefinite integral by using substitution

$\displaystyle \int \frac{e^x+1}{e^x}$

The answer key has $\displaystyle x-e^{-x}+C$

I tried the substitutions

- $\displaystyle u=e^x\Rightarrow du=e^x dx$
- $\displaystyle u=e^x+1\Rightarrow du=e^x dx$

1. doesn't really work so I think 2. is a better bet. I think I need to somehow get $\displaystyle du=\frac{dx}{e^x}$ but I don't know how.