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int(0)^( pi/2)(x+sin x)/(1+cos x)dx=...

int_(0)^( pi/2)(x+sin x)/(1+cos x)dx=

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Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)