# How do you find the antiderivative of # [(e^(2x)) +4]^2 dx#?

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To find the antiderivative of (\left(e^{2x} + 4\right)^2) with respect to (x), you can use the substitution method. Let (u = e^{2x} + 4). Then, (du/dx = 2e^{2x}) or (du = 2e^{2x} dx). Solving for (dx) gives (dx = du/(2e^{2x})). Substituting these into the integral, it becomes ((1/2) \int u^2 du). Integrating this gives ((1/2) \cdot (u^3/3) + C), where (C) is the constant of integration. Substituting back for (u), the antiderivative is ((1/6)(e^{2x} + 4)^3 + 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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