<s>[INST] Integral determination I am trying to figure out this integral:
$\int \frac{x}{(x^2+4)^6}dx$
Substitution:
$t = x^2+4$
$dt = 2xdx => dx=\frac{dt}{2x}$
Then:
$\int \frac{x}{(x^2+4)^6}dx = \int \frac{x}{t^6}\frac{dt}{2x} = \frac{1}{2} \frac{1}{t^6} + C = $ but how to continue now?
 [/INST] $$\int \frac{xdx}{(x^2+4)^6}=\frac12 \int \frac{dt}{t^6}=\int t^{-6}dt=\frac{1}{2}\cdot \frac{t^{-5}}{-5}+c=\frac{-1}{10(x^2+4)^5}+c$$
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