# Chapter 8 - Techniques of Integration - 8.5 The Method of Partial Fractions - Exercises - Page 423: 22

$$x-\frac{1}{\sqrt{3}}\tan^{-1}\left(\frac{x}{\sqrt{3}}\right)+C$$

#### Work Step by Step

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

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