Find the following integral: $\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x$

Given integral: $\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x$
Multiply $x^{2}$ inside the parentheses:
$= \int \left(x^{2} \cdot 1 - x^{2} \cdot \frac{1}{x^{2}}\right) d x$
$= \int (x^{2} - 1) d x$
Apply the linearity property of integration:
$= \int x^{2} d x - \int 1 d x$
Using the power rule $\int x^{n} d x = \frac{x^{n+1}}{n+1} + C$:
$= \frac{x^{3}}{3} - x + C$
Where $C$ is an arbitrary constant of integration.