# How do you find the antiderivative of #(x-6)^2#?

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To find the antiderivative of (x-6)^2, you can use the power rule for integration, which states that ∫x^n dx = (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.

Applying this rule to (x-6)^2, first expand the expression to (x-6)(x-6). Then integrate each term separately using the power rule:

∫(x-6)^2 dx = ∫(x^2 - 12x + 36) dx

= (1/3) * x^3 - (1/2) * 12x^2 + 36x + C

= (1/3) * x^3 - 6x^2 + 36x + C

Therefore, the antiderivative of (x-6)^2 is (1/3) * x^3 - 6x^2 + 36x + C.

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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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