Réponse:
Bonjour
exercice 1.
Derivons F de la forme Uⁿ
F'(x) = ½×2×(2x+3)(x²+3x)¹
F'(x) = (2x+3)(x²+3x)
F'(x) = f(x)
Donc F est une primitive de f.
exercice 2
1.
F(x) = x⁵/5 + sin(x)
2. f(x) = 4x-³
F(x) = 4×(-3)x-⁴
F(x) = -12/x⁴
3.
F(x) = 4×x³/3 + ⅓x²/2 + 5x
F(x) = 4/3 x³ + 1/6 x² + 5x
4.
F(x) = ⅓sin(3x-2)
5.
f(x) = (2x+1)(x²+x+7)²
on reconnait U'Uⁿ
F(x) = ⅓(x²+x+7)³
