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Question
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
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Solution
\[\int\left( \frac{x^3 - 1}{x^2} \right) dx\]
\[ = \int\left( \frac{x^3}{x^2} - \frac{1}{x^2} \right)dx\]
\[ = \int\left( x - x^{- 2} \right)dx\]
\[ = \frac{x^2}{2} - \frac{x^{- 2 + 1}}{- 2 + 1} + C\]
\[ = \frac{x^2}{2} + \frac{1}{x} + C\]
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