✅ Após resolver os cálculos, concluímos que a primitiva da referida função é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf \int(5x^{3} + x - 2)dx = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\:\:\:}}\end{gathered}$}[/tex]
Seja a função:
[tex]\Large\displaystyle\text{$\begin{gathered}\tt f(x) = 5x^{3} + x - 2\end{gathered}$}[/tex]
Calculando a primitiva da referida função, temos:
[tex]\Large\displaystyle\text{$\begin{gathered}\tt \int f(x)dx = \int(5x^{3} + x - 2)dx\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\tt = \int 5x^{3}dx + \int xdx - \int 2dx \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\tt = 5\cdot\int x^{3}dx + \int xdx - 2\cdot\int dx\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\tt = 5\cdot\frac{x^{3 + 1}}{3 + 1} + \frac{x^{1 + 1}}{1 + 1} - 2x + c\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered}\tt = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\end{gathered}$}[/tex]
Portanto, a primitiva procurada é:
[tex]\Large\displaystyle\text{$\begin{gathered}\tt \int(5x^{3} + x - 2)dx = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\end{gathered}$}[/tex]
Saiba mais:
- https://brainly.com.br/tarefa/46169101
- https://brainly.com.br/tarefa/241726
