<s>[INST] Surface Area by Integration $$2\pi\int_{3}^6\left(\frac{1}{3}x^\frac{3}{2}-x^\frac{1}{2}\right)\left(1+\left(\frac{1}{2}x^\frac{1}{2}-\frac{1}{2}x^\frac{-1}{2}\right)^2\right)^\frac{1}{2}dx$$
I've managed to simplify this down to the equation below (not sure if it'll help), but I still can't integrate it. 
Please help.
$$\frac{\pi}{3}\int_{3}^6(x^4-4x^3-2x^2+12x+9)^\frac{1}{2}dx$$
PS. The answer you should get is 9$\pi$.
 [/INST] HINT
I would say
$x^4-4x^3-2x^2+12x+9=(x^2-2x-3)^2$
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