<s>[INST] Evaluate the integral $\int \frac{x}{(x^2 + 4)^5} \mathrm{d}x$ 
Evaluate the integral $$\int \frac{x}{(x^2 + 4)^5} \mathrm{d}x.$$

If I transfer $(x^2 + 4)^5$ to the numerator, how do I integrate? 
 [/INST] with $u = x^2 + 4$:
$$  \int  (x^2 + 4)^{-5 }  {x dx}  
=   \frac 12 \int u^{-5} {du}
=  - \frac 1{8} u^{-4} 
=  - \frac 1{8} (x^2 + 4)^{-4} 
$$
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