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

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

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Evaluate the following integrals: (1-35)pi/2int_(0)^( pi/2)(sin^(n)x)/(sin^(n)+cos^(n)x)dx

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For n gt 0 int_(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

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Prove that: int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx = pi^2