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On se propose de calculer 2 2+ 2 -2 dx . 23 + 3x2 -9x -27 (i) On commence par factoriser le denominateur de la

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On se propose de calculer 2 2+ 2 -2 dx . 23 + 3x2 -9x -27 (i) On commence par factoriser le denominateur de la fraction rationnelle. On trouve x3+ 3x2- 9x - 27= (2 -a) (2-6)2 avec a # b . Quels sont a et b ? a = Number b = Number (ii) Ensuite on ecrit la fraction sous la forme x2+ 2 A B C + 23 + 3x2 -9x-27 x - a (x - 6)2 Donnez les valeurs exactes de A , B et C. A = B = DO. C= (iii) On utilise enfin cette decomposition pour calculer l'integrale. Donnez sa valeur approximative a 3 decimales pres. 52 2 2 2 + 2 da ~ Number 23 +3x2-9x-27

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