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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=pi^(2)

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