Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Une intégrale de folie !

by mathman·
65
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Unreviewed. This problem has not been reviewed by trusted users yet.

∀n∈N∗\forall n\in\mathbb{N^{*}},

Montrez que :

∫0+∞(1+x2)nsin⁡(2narctan⁡(x))eπx+1dx=12(2n+1)\displaystyle\int_{0}^{+\infty}\frac{(1+x^{2})^{n}\sin(2n\arctan(x))}{\mathrm{e}^{\pi x}+1}\mathrm{d}x=\frac{1}{2(2n+1)}

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