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The integral of sin^2(x) dx is (1/2)x - (1/4)sin(2x) + C.

To evaluate the integral of sin^2(x) dx, we can use the identity sin^2(x) = (1/2)(1 - cos(2x)). Therefore, we have:

∫sin^2(x) dx = ∫(1/2)(1 - cos(2x)) dx

= (1/2)∫(1 - cos(2x)) dx

= (1/2)(x - (1/2)sin(2x)) + C

= (1/2)x - (1/4)sin(2x) + C

Where C is the constant of integration. Therefore, the integral of sin^2(x) dx is (1/2)x - (1/4)sin(2x) + C.

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