exo7 824

Décomposer les fractions rationnelles suivantes ; en calculer les primitives.

1

1a2+x2\displaystyle{1 \over a^2+x^2}.

2

1(1+x2)2{1 \over{(1+x^2)}^2}.

3

x3x2−4\displaystyle{x^3 \over x^2-4}.

4

4x(x−2)2\displaystyle{4x \over{(x-2)}^2}.

5

1x2+x+1\displaystyle{1 \over x^2+x+1}.

6

1(t2+2t−1)2\displaystyle{1 \over{(t^2+2t-1)}^2}.

7

3t+1(t2−2t+10)2\displaystyle{3t+1 \over{(t^2-2t+10)}^2}.

8

3t+1t2−2t+10\displaystyle{3t+1 \over{t^2-2t+10}}.

9

1t3+1\displaystyle{ 1 \over{t^3+1}}.

10

x3+2(x+1)2\displaystyle{x^3+2 \over{(x+1)}^2}.

11

x+1x(x−2)2\displaystyle{x+1 \over{x{(x-2)}^2}}.

12

(x2−1)(x3+3)2x+2x2\displaystyle{(x^2-1)(x^3+3) \over2x+2x^2}.

13

x2(x2+3)3(x+1)\displaystyle{x^2 \over{{(x^2+3)}^3 (x+1)}}.

14

x7+x3−4x−1x(x2+1)2\displaystyle{x^7+x^3-4x-1 \over x{(x^2+1)}^2}.

15

3x4−9x3+12x2−11x+7(x−1)3(x2+1)\displaystyle{3x^4-9x^3+12x^2-11x+7\over(x-1)^3(x^2+1)}.

Exercice M9Ad

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