<s>[INST] Give me a hint to solve this integral $$\int_0^1 \frac{1}{(x^2+x+1)^2} dx$$
I don't have any clue as to where to even start. I am struggling on this one. 
Please shed some light by giving me a Hint
 [/INST] $$\dfrac{d\left[\dfrac{ax^2+bx+c}{x^2+x+1}\right]}{dx}$$
$$=\dfrac{(x^2+x+1)(2ax+b)-(ax^2+bx+c)(2x+1)}{(x^2+x+1)^2}$$
We need $1=(x^2+x+1)(2ax+b)-(ax^2+bx+c)(2x+1)=(a-b)x^2+(a-2c)x+b-c$
$\implies a-b=0,a-2c=0,b-c=1\implies \cdots$
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