Question

calcule a função primitiva f(x)= 5x^3+x-2

Answer 1

$\int 5x^3+x-2 \ dx=5\int x^3+\int x -2 \int dx=\boxed{5\frac{x^4}{4}-\frac{x^2}{2}-2x+C }$

Se quiser calcule mmc e simplifique a expressão

Answer 2

✅ Após resolver os cálculos, concluímos que a primitiva da referida função é:

 $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \int(5x^{3} + x - 2)dx = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\:\:\:}}\end{gathered} }$

Seja a função:

               $\Large\displaystyle\begin{gathered}\tt f(x) = 5x^{3} + x - 2\end{gathered}$

Calculando a primitiva da referida função, temos:

$\Large\displaystyle\begin{gathered}\tt \int f(x)dx = \int(5x^{3} + x - 2)dx\end{gathered}$

                      $\Large\displaystyle\begin{gathered}\tt = \int 5x^{3}dx + \int xdx - \int 2dx \end{gathered}$

                       $\Large\displaystyle\begin{gathered}\tt = 5\cdot\int x^{3}dx + \int xdx - 2\cdot\int dx\end{gathered}$

                       $\Large\displaystyle\text{ \begin{gathered}\tt = 5\cdot\frac{x^{3 + 1}}{3 + 1} + \frac{x^{1 + 1}}{1 + 1} - 2x + c\end{gathered} }$

                       $\Large\displaystyle\begin{gathered}\tt = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\end{gathered}$

Portanto, a primitiva procurada é:

     $\Large\displaystyle\begin{gathered}\tt \int(5x^{3} + x - 2)dx = \frac{5}{4}x^{4} + \frac{1}{2}x^{2} - 2x + c\end{gathered}$

Saiba mais:

1. https://brainly.com.br/tarefa/46169101
2. https://brainly.com.br/tarefa/241726