integrate $ \frac {(x^3 + 36)} {(x^2 + 36)}$ I know I have to use long division first, but I don't really know how to do it in this case
$$\int \frac{x^3 + 36}{x^2 + 36}dx$$

Using http://en.wikipedia.org/wiki/Partial_fraction_decomposition#Procedure
$$ \frac{x^3+36}{x^2+36} = \frac{x(x^2+36)- 36x +36 }{x^2+ 36} $$
$$ \frac{x^3+36}{x^2+36} = \frac{x(x^2+36)}{x^2+36} - \frac {36x}{x^2+36} + \frac{36}{x^2+36} $$
$$ \int \frac{x^3+36}{x^2+36}dx  = \int \frac{x(x^2+36)}{x^2+36} dx -\int \frac {36x}{x^2+36}dx + \int\frac{36}{x^2+36}dx $$
$$ \int \frac{x^3+36}{x^2+36}dx = \int x*dx - 18\int\frac{2x}{x^2+36}dx + \int\frac{36}{x^2+36}dx $$
I hope now you can proceed.
