Simple integral with $e^x$ - how to decompose it? How to calculate this integral?
$$\int \frac{e^{2x}+2}{e^x+1}dx$$
I have tried various substitions such as: $t = e^x, t = e^x + 1, t = e^x +2, t = e^{2x}$
and none seem to work. 
According to wolframalpha I can simplify this expression into:
$$\frac{e^{2x}+2}{e^x +1} = e^x + \frac{3}{e^x+1} - 1$$
And then it'd be rather simple. But still no idea how to decompose it like that.
Any tips?

For the last integral you can substitute$$\int\frac{1}{e^x+1}dx$$ $$t=e^x+1$$ and $$dt=e^xdx=(t-1)dx$$ or $$dx=\frac{1}{t-1}dt$$
