0-pi-e-cos-x-e-cos-x-e-cos-x-dx-

Question Number 151345 by peter frank last updated on 20/Aug/21

\int_{0}^{π} \frac{e^{\cos x}}{e^{\cos x} + e^{- \cos x}} dx

Answered by Olaf_Thorendsen last updated on 20/Aug/21

I = \int_{0}^{π} \frac{e^{\cos x}}{e^{\cos x} + e^{- \cos x}} d x (1)

Let u = π - x :

I = \int_{0}^{π} \frac{e^{- \cos u}}{e^{- \cos u} + e^{\cos u}} d u (2)

\frac{(1) + (2)}{2} : I = \frac{π}{2}