Question

Calcule a integral indefinida ∫(3x³−2x²+x)dx e marque a opção correta.

Answer 1

Resposta:

Tenha em vista que $\int u^{n}\, du = \frac{u^{n+1}}{n+1} + C$, assim,

$\begin{aligned}\int (3x^{3}-2x^{2} + x)\, dx &= \int 3x^{2}\, dx - \int 2x^{2}\, dx + \int x\, dx \\ &= 3\cdot \frac{x^{4}}{4}+C_{1} - 2\cdot \frac{x^{3}}{3} +C_{2} + \frac{x^{2}}{2} +C_{3} \\ &= \frac{3}{4}x^{3} - \frac{2}{3} x^{3} + \frac{1}{2} x^{2} + C\end{aligned}$

onde, $C = C_1 + C_2 + C_3$.