Exercise · ZW-INDEFINITE-INTEGRAL-004 · ★★☆ Intermediate
Compute \(\displaystyle\int \left(4 \sqrt{x} + \frac{1}{x^{2}}\right)dx\).
Choose one option.
Show answer
- A. \(\frac{8 x^{\frac{3}{2}}}{3} - \frac{1}{x} + C\)
Explanation
Integrate term by term with \(\int c\,x^{n}\,dx=\dfrac{c\,x^{n+1}}{n+1}\) and add the constant C. The result is \(\frac{8 x^{\frac{3}{2}}}{3} - \frac{1}{x} + C\).
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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- ZW-INDEFINITE-INTEGRAL-006 Compute ∫ cos (2x) dx.
- ZW-INDEFINITE-INTEGRAL-007 Compute ∫ e^2x dx.
- ZW-INDEFINITE-INTEGRAL-008 Compute ∫ (x^2+1)/(x) dx for x>0.
- ZW-INDEFINITE-INTEGRAL-009 Compute ∫ 2x e^x^2 dx.