# What is the antiderivative of #1/(x^2+4)#?

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Calculate the indefinite integral:

by substituting:

so:

and undoing the substitution:

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The antiderivative of ( \frac{1}{x^2+4} ) is ( \frac{1}{2} \arctan \left( \frac{x}{2} \right) + 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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