<s>[INST] How to solve $\int \frac{1}{x^2+4x+7} dx$? How to solve $\int \frac{1}{x^2+4x+7} dx$?
I think the first step is to write it in the following form: $$\int \frac{1}{(x+2)^2+3} dx$$
 [/INST] A second step could be the change of variable
$$
x+2=\sqrt{3}u, \implies (x+2)^2+3=3u^2+3=3(u^2+1)
$$ giving
$$
\int \frac{1}{(x+2)^2+3} dx=\frac1{\sqrt{3}}\int \frac{1}{u^2+1} du
$$ which is now a standard integral.
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