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

`int_(0)^((pi)/(2))(sin^(2)x-cos^(2)x)/(sin^(3)x+cos^(3)x)dx`

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

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int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx