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

Question Number 125050 by bramlexs22 last updated on 08/Dec/20

\underset{0}{\int^{π}} \frac{e^{\cos x}}{e^{\cos x} + e^{- \cos x}} d x = ?

Answered by liberty last updated on 08/Dec/20

r e p l a c e x b y π - x

I = \underset{0}{\int^{π}} \frac{e^{\cos x}}{e^{\cos x} + e^{- \cos x}} d x

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

I = \underset{0}{\int^{π}} \frac{e^{- \cos x}}{e^{- \cos x} + e^{\cos x}} d x

w e g e t 2 I = \underset{0}{\int^{π}} \frac{e^{\cos x} + e^{- \cos x}}{e^{\cos x} + e^{- \cos x}} d x

2 I = \underset{0}{\int^{π}} d x; I = \frac{π}{2}

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