Chapter 8 - Techniques of Integration - 8.5 The Method of Partial Fractions - Exercises - Page 423: 13

$$x-3\tan^{-1}(x/3)+C$$

Given $$ \int \frac{x^{2} d x}{x^{2}+9}$$ Since \begin{align*} \int \frac{x^{2} d x}{x^{2}+9}&=\int\left( \frac{x^{2}+9-9}{x^{2}+9}\right)dx\\ &=\int\left(1- \frac{ 9}{x^{2}+9}\right)dx\\ &=x-3\tan^{-1}(x/3)+C \end{align*}