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int(0)^((pi)/(2))(sin x-cos x)/(1+sin x ...

int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

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int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

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