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Déterminer \(\displaystyle \int_{-\infty}^\infty e^{ix}\;\frac{x-i}{x+i}\;\frac1{x^2+1}\,dx\) et \(\displaystyle \int_{-\infty}^\infty e^{-ix}\;\frac{x-i}{x+i}\;\frac1{x^2+1}\,dx\).
Déterminer \(\displaystyle \int_{-\infty}^\infty e^{ix}\;\frac{x-i}{x+i}\;\frac1{x^2+1}\,dx\) et \(\displaystyle \int_{-\infty}^\infty e^{-ix}\;\frac{x-i}{x+i}\;\frac1{x^2+1}\,dx\).