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" ate "int(0)^( pi/2)(x sin x cos x)/(si...

" ate "int_(0)^( pi/2)(x sin x cos x)/(sin^(4)x+cos^(4)x)dx

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Prove that : int_(0)^(pi//2) (x sin x cos x)/(sin^(4) x+ cos^(4)x)dx =(pi)/(16)

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

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