$\int x^{2} (1 - \frac{1}{x^{2}}) d x$ is equal to (where $C$ is constant of integration)

\frac{x^{3}}{3} - x + C

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\frac{x^{5}}{5} + x + C

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\frac{x^{4}}{4} + x + C

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\frac{x^{2}}{3} - x + C

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Solution

The correct option is A $\frac{x^{3}}{3} - x + C$
$\int x^{2} (1 - \frac{1}{x^{2}}) d x = \int (x^{2} - 1) d x = \int x^{2} d x - \int 1 d x = \frac{x^{3}}{3} - x + C$

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