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int(0)^(2 pi)(X sin^(2n)X)/(sin^(2n)X+co...

int_(0)^(2 pi)(X sin^(2n)X)/(sin^(2n)X+cos^(2n)X)dX

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

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