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Integrate:

$$\int{\cfrac{x^2+2}{x^2+9}dx}$$

$\cfrac{\frac{1}{3}x^3+2x}{\frac{1}{3}x^3+9x}+C$

$(\cfrac{1}{3}x^3+2x)(\cfrac{1}{3}arctan(\cfrac{x}{3}))+C$

$x-\cfrac{7}{3}arctan(\cfrac{x}{3})+C$

$x-\cfrac{7}{9}arctan(\cfrac{x}{9})+C$