Question

calcule a primitiva de fx=5x^2+7x+2

Answer 1

Boa noite

f(x) = 5x² + 7x + 2

primitiva

F(x) = 5x³/3 + 7x²/2 + 2x + C 

Answer 2

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

$\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \int (5x^{2} + 7x + 2)dx = \frac{5}{3}x^{3} + \frac{7}{2}x^{2} + 2x + c\:\:\:}}\end{gathered} }$    

Seja a função:

                   $\Large\displaystyle\begin{gathered} f(x) = 5x^{2} + 7x + 2\end{gathered}$

Calculando a primitiva da referida função temos:

 $\Large\displaystyle\begin{gathered} \int f(x)dx = \int (5x^{2} + 7x + 2)dx\end{gathered}$

                        $\Large\displaystyle\begin{gathered} = \int 5x^{2}dx + \int 7xdx + \int 2dx\end{gathered}$

                        $\Large\displaystyle\begin{gathered} = 5\cdot\int x^{2}dx + 7\cdot\int xdx + 2\cdot\int dx\end{gathered}$

                         $\Large\displaystyle\text{ \begin{gathered} = 5\cdot\frac{x^{2 + 1}}{2 + 1} + 7\cdot\frac{x^{1 + 1}}{1 + 1} + 2x + c\end{gathered} }$

                         $\Large\displaystyle\begin{gathered} = \frac{5}{3}x^{3} + \frac{7}{2}x^{2} + 2x + c\end{gathered}$

✅ Portanto, a primitiva da função é:

  $\Large\displaystyle\begin{gathered} \int (5x^{2} + 7x + 2)dx = \frac{5}{3}x^{3} + \frac{7}{2}x^{2} + 2x + c\end{gathered}$

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