Chapter 7 - Techniques of Integration - 7.4 Integration of Rational Functions by Partial Fractions - 7.4 Exercises - Page 541: 22

$\frac{x^3}{3}+\frac{1}{2}\ln|x^2+9|+\frac{2}{3}\tan^{-1}\left(\frac{x}{3}\right)+C$

$\int\frac{x^{4}+9x^{2}+x+2}{x^{2}+9}dx$ = $\int\left(x^{2}+\frac{x+2}{x^{2}+9}\right)dx$ = $\int\left(x^2+\frac{x}{x^{2}+9}+\frac{2}{x^{2}+9}\right)dx$ = $\frac{x^3}{3}+\frac{1}{2}\ln|x^2+9|+\frac{2}{3}\tan^{-1}\left(\frac{x}{3}\right)+C$