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int(0)^( pi/4)((x)/(x sin x+cos x))^(2)d...

`int_(0)^( pi/4)((x)/(x sin x+cos x))^(2)dx=`

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int_(0)^((pi)/(2))(x sin x*cos x)dx

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