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We can split the integral into two parts:∫ (cos x / sin² x) dx - ∫ (2e^(2x)) dxFor the first part, cos x / sin² x can be rewritten as (cos x / sin x) * (1 / sin x) = cot x * csc x. The integral of csc x cot x is -csc x. So, ∫ (cos x / sin² x) dx = -csc x + C1.For the second part, ∫ (2e^(2x)) dx, let u = 2x, then du = 2 dx. The integral becomes ∫ e^u du = e^u + C2 = e^(2x) + C2.Combining both parts: -csc x - e^(2x) + C.