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I don't see a clear substitution to calculate that since when

$$u = 2x+x^2,\qquad dx = \frac{du}{2+x},$$

And so far as I've understand $dx$ shouldn't be in function of $x$ in order to calculate the integral.

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    No, $dx=du/(2+2x)$. Try that, and then do a little algebra before integrating.2011-09-27
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    Better yet, learn to work directly from $du=(2+2x)dx$. Notice that this is $du=2(x+1)dx$. Do you have the expression $(x+1)dx$ in your integral?2011-09-27
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    @BrianM.Scott you're right, my mistake; thanks.2011-09-27

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