# How do you find the integral of #int [cos^3 (2x)] dx #?

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To find the integral of ∫cos^3(2x) dx, you can use the trigonometric identity cos^3(x) = (1/4)(3cos(x) + cos(3x)). So, the integral becomes ∫(1/4)(3cos(2x) + cos(6x)) dx. You can then integrate each term separately. The integral of 3cos(2x) dx is (3/2)sin(2x), and the integral of cos(6x) dx is (1/6)sin(6x). Therefore, the final result is (3/2)sin(2x) + (1/6)sin(6x) + C, where C is the constant of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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