Ivan Shishkin, Rye (1878)

Problems/Real analysis

ohhh !!! la belle primitive que voilà !

by mathman·
50
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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ReviewedReviewed by FiniteField
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Français
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λ\lambda est un paramètre réel, xx est une variable réelle.

Montrez que :

∫0xdtcosh⁡(λ)+cos⁡(t)sinh⁡(λ)=x−2arctan⁡(sinh⁡(λ2)sin⁡(x)cosh⁡(λ2)+cos⁡(x)sinh⁡(λ2))\displaystyle\int_{0}^{x}\frac{\mathrm{d}t}{\cosh(\lambda)+\cos(t)\sinh(\lambda)}=x-2\arctan\left(\frac{\sinh(\frac{\lambda}{2})\sin(x)}{\cosh(\frac{\lambda}{2})+\cos(x)\sinh(\frac{\lambda}{2})}\right)

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