Décomposer les fractions rationnelles suivantes ; en calculer les primitives.
1
\(\displaystyle{1 \over a^2+x^2}\).
2
\({1 \over{(1+x^2)}^2}\).
3
\(\displaystyle{x^3 \over x^2-4}\).
4
\(\displaystyle{4x \over{(x-2)}^2}\).
5
\(\displaystyle{1 \over x^2+x+1}\).
6
\(\displaystyle{1 \over{(t^2+2t-1)}^2}\).
7
\(\displaystyle{3t+1 \over{(t^2-2t+10)}^2}\).
8
\(\displaystyle{3t+1 \over{t^2-2t+10}}\).
9
\(\displaystyle{ 1 \over{t^3+1}}\).
10
\(\displaystyle{x^3+2 \over{(x+1)}^2}\).
11
\(\displaystyle{x+1 \over{x{(x-2)}^2}}\).
12
\(\displaystyle{(x^2-1)(x^3+3) \over2x+2x^2}\).
13
\(\displaystyle{x^2 \over{{(x^2+3)}^3 (x+1)}}\).
14
\(\displaystyle{x^7+x^3-4x-1 \over x{(x^2+1)}^2}\).
15
\(\displaystyle{3x^4-9x^3+12x^2-11x+7\over(x-1)^3(x^2+1)}\).