Feuille d'exercices sur les primitives.
Déterminer les primitives \(F\) sur \(I\) de chacune des fonctions \(f\) suivantes.
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\(f: x \mapsto 3x^3-2x+2 \quad I=\mathbb{R}\)
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\(f: x \mapsto x+2+\dfrac{1}{x^2} \quad I=]0,+\infty[\)
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\(f: x \mapsto \dfrac{3x^2+4x-2}{x^4} \quad I=]-\infty;0[\)
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\(f: x \mapsto \dfrac{3x}{(3x^2+2)^2} \quad I=\mathbb{R}\)
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\(f: x \mapsto (-2x+1)^5 \quad I=\mathbb{R}\)
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\(f: x \mapsto (x-1)(x^2-2x+7) \quad I=\mathbb{R}\)
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\(f: x \mapsto \dfrac{2x-1}{\sqrt{x^2-x}} \quad I=]1;+\infty[\)
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\(f: x \mapsto x^3(x^4-1)^3 \quad I=\mathbb{R}\)
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\(f: x \mapsto \dfrac{1}{\sqrt{-4x+3}} \quad I=\left]-\infty;\dfrac{3}{4}\right[\)
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\(f: x \mapsto \dfrac{\sin{x}}{(\cos{x}+1)^3} \quad I=]-\pi;\pi[\)
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\(f: x \mapsto \dfrac{\cos{\sqrt{x}}}{\sqrt{x}} \quad I=]0,+\infty[\)
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\(f: x \mapsto \dfrac{x^2+1}{(x^3+3x)^5} \quad I=]-\infty;-\sqrt{3}[\)
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\(f: x \mapsto \cos(3x-4) \quad I=\mathbb{R}\)
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\(f: x \mapsto \dfrac{6x-9}{(x^2-3x+2)^3} \quad I=]1;2[\)
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\(f: x \mapsto \cos^4(2x+1)\sin(2x+1) \quad I=\mathbb{R}\)
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\(f: x \mapsto \sin(x^3+1)\times x^2 \quad I=\mathbb{R}\)
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\(f: x \mapsto \tan^2 x \quad I=\left]-\dfrac{\pi}{2};\dfrac{\pi}{2}\right[\)