<s>[INST] Integral of a rational expression involving quadratics. I want to solve this integral but I have some problems...

$$\int_2^3 \frac{(x^2-2x+1)}{(x^2+2x+1)}$$

I transformed both in $(x-1)^2$ and $(x+1)^2$ respectively but didn't find any answer. I tried as well to transform the rational expression into $1 -\frac{4x}{(x^2+2x+1)}$, but I wasn't capable of finding any antiderivative.
Thanks for responding!
 [/INST] \begin{gather*}
I=\int ^{3}_{2}\frac{x^{2} -2x+1}{x^{2} +2x+1} dx\\
\text{Decompose $x^{2} -2x+1$ into partial fractions of $( x+1)$}\\
I=\int ^{3}_{2} 1-\frac{4x+4-4}{x^{2} +2x+1}\\
I=\int ^{3}_{2} 1-\frac{4}{x+1} +\frac{4}{x^{2} +2x+1}\\
I=\int ^{3}_{2} 1-\frac{4}{x+1} +\frac{4}{( x+1)^{2}} dx\\
\end{gather*}Can you take it from here?
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