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Show that underset(0)overset(pi//2)int (...

Show that `underset(0)overset(pi//2)int (x)/(sinx+cosx)dx=(pi)/(2sqrt(2))log (sqrt(2)+1)` .

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

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int_(0)^(pi//2)(x)/(sinx+cosx)dx .

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int_(0)^(pi//2) e^x(sinx+cosx) dx

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int_(0)^(pi//2)(sinx-cosx)log(sinx+cosx)dx=0