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If In = ∫(sin nx/(1 + π^x)sin x) dx for x ∈ [-π,π], n = 0, 1, 2, ... then

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If In = ∫(sin nx/(1 + πx)sin x) dx for x ∈ [-π,π], n = 0, 1, 2, ... then 

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Best answer

Answer is

Let

Adding Eqs (i) and (ii), we get 

In+2 = In

Since In+2 = In, so 

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