# How do you find the indefinite integral of #int x(cos(8x))^2dx#?

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To find the indefinite integral of ∫x(cos(8x))^2dx, you can use trigonometric identities and integration techniques. First, use the identity cos^2(x) = (1 + cos(2x))/2. Then, substitute u = 8x and du = 8dx. After integrating, you'll get the result in terms of u, then substitute back in terms of x. The final result is:

(1/16) * x^2 + (1/128) * sin(16x) + 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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