Exercise · ZW-INDEFINITE-INTEGRAL-003 · ★☆☆ Basic
Compute \(\displaystyle\int \left(x^{4} + 2 x^{2} + 7\right)dx\).
Choose one option.
Show answer
- B. \(\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + 7 x + C\)
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 \(\frac{x^{5}}{5} + \frac{2 x^{3}}{3} + 7 x + C\).
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
- ZW-INDEFINITE-INTEGRAL-001 Compute ∫ (6 x^2 + 4 x - 5)dx.
- ZW-INDEFINITE-INTEGRAL-002 Compute ∫ (3 x^3 - 8 x)dx.
- ZW-INDEFINITE-INTEGRAL-004 Compute ∫ (4 √x + (1)/(x^2))dx.
- ZW-INDEFINITE-INTEGRAL-005 What is ∫ cos x dx?
- 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.