Exercise · ZW-INDEFINITE-INTEGRAL-008 · ★★☆ Intermediate
Compute \(\int \frac{x^{2}+1}{x}\,dx\) for \(x>0\).
Choose one option.
Show answer
- A. \(\frac{x^{2}}{2}+\ln x+C\)
Explanation
Split it into \(x+\frac{1}{x}\) and integrate each term: \(\int x\,dx=\frac{x^{2}}{2}\) and \(\int\frac{1}{x}\,dx=\ln x\).
Review the concept: Indefinite integral
The indefinite integral of \(f\) is the family of all its antiderivatives, written with a constant of integration \(C\).
\[\int x^{n}\,dx=\frac{x^{n+1}}{n+1}+C\quad(n\neq-1)\]
More practice problems: indefinite integral
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