∫ cos2x / (cos²x * sin²x) dx
= ∫ cos2x / (cosx*sinx)² dx
= ∫ cos2x / (1/2 * 2sinx*cosx)² dx
= ∫ cos2x / [(1/2)² * (sin2x)²] dx
= ∫ cos2x / [(1/4) * sin²2x] dx
= 4∫ cos2x / sin²2x dx
= (4/2)∫ cos2x / sin²2x d(2x)
= 2∫ d(sin2x) / (sin2x)²
= -2/sin2x + C
= -2csc2x + C
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