<s>[INST] Integrate $\frac{3}{\sqrt{-5x^2-4\sqrt{5}x+2}}$ 
Integrate $\frac{3}{\sqrt{-5x^2-4\sqrt{5}x+2}}$

For this question I first factored out the 3, seeing as its a constant
$$3\int\frac{1}{\sqrt{-5x^2-4\sqrt{5}x+2}}dx$$
I then noticed that this integral has a similar form to the integral of $\arcsin(x)$
$$\int\frac{1}{\sqrt{a^2-x^2}}dx=\arcsin(\frac{x}{a})+C,   \vert x \vert \lt a$$
The similarities between these two integrals is clear, but I dont know how to get from $$-5x^2-4\sqrt{5}x+2$$ to $$a^2-x^2$$
Any help or ideas would be highly appreciated!
 [/INST] Hint: Write 
$$-5x^2-4\sqrt{5}x+2=6-(\sqrt{5}x+2)^2$$
and let substitution $\sqrt{5}x+2=\sqrt{6}\sin\theta$.
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