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int0^(pi/2) sin^(5/2x)/(sin^(5/2)x+cos^(...

`int_0^(pi/2) sin^(5/2x)/(sin^(5/2)x+cos^(5/2)x)dx` is equal to :

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int_0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

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By using the properties of definite integrals, evaluate the integral: int_0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx