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

$$\underset{0}{\stackrel{\pi }{\int }}\frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}}dx=?$$

Answered by liberty last updated on 08/Dec/20

$$replacexby\pi -x$$$$I=\underset{0}{\stackrel{\pi }{\int }}\frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}}dx$$$$I=\underset{\pi }{\stackrel{0}{\int }}\frac{e^{-\cos x}}{e^{-\cos x}+e^{\cos x}}(-dx)$$$$I=\underset{0}{\stackrel{\pi }{\int }}\frac{e^{-\cos x}}{e^{-\cos x}+e^{\cos x}}dx$$$$weget2I=\underset{0}{\stackrel{\pi }{\int }}\frac{e^{\cos x}+e^{-\cos x}}{e^{\cos x}+e^{-\cos x}}dx$$$$2I=\underset{0}{\stackrel{\pi }{\int }}dx;I=\frac{\pi }{2}$$

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