Exercise · ZW-INDEFINITE-INTEGRAL-001 · ★☆☆ Basic
Compute \(\displaystyle\int \left(6 x^{2} + 4 x - 5\right)dx\).
Choose one option.
Show answer
- D. \(2 x^{3} + 2 x^{2} - 5 x + C\)
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 \(2 x^{3} + 2 x^{2} - 5 x + C\).
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-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.