Bonjour ;
1)
[tex]f(x) = \dfrac{5}{3} x^4-\dfrac{4}{5}x^3 +\dfrac{1}{2} \Rightarrow F(x) = \dfrac{5}{3} \dfrac{x^5}{5} - \dfrac{4}{5}\dfrac{x^4}{4}+\dfrac{x}{2} +C : C \in \mathbb R \\\\ \Rightarrow F(x) = \dfrac{x^5}{3} - \dfrac{x^4}{5} + \dfrac{x}{2} + C : C \in \mathbb R .[/tex]
2)
[tex]f(x) = \dfrac{3,14}{\pi x} = \dfrac{3,14}{\pi} \dfrac{1}{x} \Rightarrow F(x) = \dfrac{3,14}{\pi} Ln(x) + C : C \in \mathbb R .[/tex]
3)
[tex]f(x) = x^2 + x + \dfrac{1}{x} + \dfrac{1}{x^2} \Rightarrow F(x) = \dfrac{x^3}{3} + \dfrac{x^2}{2} + Ln(x) - \dfrac{1}{x} + C : C \in \mathbb R . [/tex]
4)
[tex]f(x) = - sin(\pi + 6x) \Rightarrow F(x) = \dfrac{1}{6} cos(\pi + 6x) + C : C \in \mathbb R .[/tex]
5)
[tex]f(x) = cos(\dfrac{\pi}{2} - 4x) \Rightarrow F(x) = - \dfrac{1}{4} sin(\dfrac{\pi}{2} - 4x) + C : C \in \mathbb R .[/tex]
