# How do you find the integral of #cos^3 2x dx#?

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see below

Another approach

integrating by inspection

which can be shown by trig identities to be equivalent to the previous solution. This is left for the reader to verify

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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)). Apply this identity to cos^3(2x), integrate, and then substitute back for 2x. The result will be:

∫cos^3(2x) dx = (1/8)sin(2x) + (3/32)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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