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

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

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Show that int_(0)^(pi//2) (x)/(sinx+cosx)dx=(pi)/(2sqrt(2))log (sqrt(2)+1) .

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