| (Oral Centrale) Soit {f(x)=\displaystyle\int_{0}^{+\infty}\!\!\dfrac{\text{e}^{-t^{2}x}}{1+t^{2}}\,\text{d}t\;}. On rappelle que : {\displaystyle\int_{0}^{+\infty}\!\!\!\text{e}^{-t^{2}}\,\text{d}t=\dfrac{\sqrt\pi}{2}}
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| (Oral Centrale) Soit {f(x)=\displaystyle\int_{0}^{+\infty}\!\!\dfrac{\text{e}^{-t^{2}x}}{1+t^{2}}\,\text{d}t\;}. On rappelle que : {\displaystyle\int_{0}^{+\infty}\!\!\!\text{e}^{-t^{2}}\,\text{d}t=\dfrac{\sqrt\pi}{2}}
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